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Again, this is done using trigonometry, because the angle and the vertical component of the force are known. Practice Exercises Exercise While moving out of her dorm room, Bridget carries a kg box to her car, holding it in both arms.

Forces 41 Exercise A flower pot of mass 4. What is the tension in each rope supporting the flower pot? Answer: Exercise The ACE towing company tows a disabled kg automobile off the road at a constant speed. If the tow line makes an angle of The feeder creates a tension of N in each side of the the rope. Exercise After pulling his car off to the side of the road during a rainstrom, Travis is dismayed to find that the car has become stuck in the mud.

Travis ties one end of a rope to the front of the car and the other end to a tree Forces 43 Pressure Vocabulary Pressure: The force per unit area. It is very easy to confuse pressure with force. While force is a push or a pull, pressure is a push or pull on a certain area.

For a given force, the pressure due to that force is inversely proportional to the area on which the force is exerted. Therefore, if the area of contact is small, the amount of pressure between two surfaces is much greater than if the force were exerted over a larger area.

For example, place a pencil between the palms of your hands with the pointed end pushing against one palm and the eraser end against the other. As you squeeze your hands together, you will feel a much more unpleasant sensation at the pencil tip than at the eraser! The eraser has a larger area, so the force is spread out more evenly over the nerve endings of your hand.

Solved Examples Example Brooke comes home from school and puts her books down on the kitchen table while she goes to grab a snack. The books have a combined weight of 25 N and the area of contact is 0.

What pressure do the books apply on the table? Solution: First, find the area of the surface that is pressing down on 60 White Oak Road Wellesley Ma Kr the table. The full mug applies more pressure because a larger force is spread over the given area.

The force exerted by the full mug is its weight. To find the radius, use the equation for the area of a circle. Forces 45 Exercise Miss Culp, a high school English teacher, marches next to Miss Vance, a physics teacher, in the graduation procession across the football field. Each woman has a mass of Would you calculate that Morgan is standing, sitting, or lying on the bed? Answer: Exercise Caleb is filling up water balloons for the Physics Olympics balloon toss competition.

Caleb sets a 0. While on the moon, Buzz Aldrin carried on his back a support system that would weigh over N on Earth. A A common malady in runners who run on too hard a surface is shin splints. A In the district soccer championship finals, Elizabeth kicks a 0. How much does she accelerate the soccer ball from rest in the process?

What amount of force moves the bottle down the ramp? A Sarah, whose mass is What force of friction will eventually bring Sarah to a stop? A In her physics lab, Molly puts a 1. She pulls the combination across another wooden board with a constant speed to determine the coefficient of sliding friction between the two surfaces.

If Molly must pull with a force of 6. A A kg slippery hippo slides down a mud-covered hill inclined at an angle of A Erma receives a 5. If Erma lifts the box by the string in the center so that each piece of string makes an angle of Forces 47 A To make extra money during the summer, Mr.

Garber, a What is the tension in each of the two cables? A While camping in Denali National Park in Alaska, a wise camper hangs his pack of food from a rope tied between two trees, to keep the food away from the bears. If the 5. A In the figure, a kg wrecking ball is pulled back with a horizontal force of N before being swung against the side of a building. A What force must you exert on a ball point pen in order to apply a pressure of 0.

A Asad cuts his knee in a fall while chasing a soccer ball. A The amazing Gambini walks across a If the coefficient of friction of the slide is 0. Solution: Start by constructing a triangle showing all the forces acting on the lifeguard.

Then find the normal force acting on Linc when he is inclined at an angle to the horizontal. Because the normal force always acts perpendicular to the surface on which the object sits, find this force with the use of trigonometry.

B Noah is loading the ark and the last animal on board is a stubborn kg elephant who refuses to budge. What is the coefficient of sliding friction between the elephant and the loading platform? B Blythe lies in a hospital bed with her foot in traction, as shown.

How much tension will the traction device exert on her foot? B Madison, whose mass is If the coefficient of sliding friction is 0. Ignore the initial effects of starting friction. B A chunk of rock of mass If the rock accelerates at a rate of 3. If Cheryl has a mass of B Gooluk, the Inuit, is pulling a On the back of the sled is his The coefficient of sliding friction between the sled and the snow is 0. What force does Gooluk need to exert to keep the sled moving with a constant speed while the sack is pulled back across it?

Momentum is a vector quantity. Vocabulary Impulse: The product of the force exerted on an object and the time interval during which it acts. The impulse given to an object is equal to the change in momentum of the object. In other words, impulse is the thing that you do, while change in momentum is the thing that you see. The units for impulse and momentum are equivalent. What impulse does he impart to the ball?

With what force did Wayne hit the puck? It leaves her racket with a speed of Solution: In this exercise, the tennis ball is coming toward Venus with a speed of Therefore, you must think about velocity vectors and call one direction positive and the opposite direction negative.

The 1. What average force does the pumpkin exert to stop the pellet? Remember, in order to find the time, you must use the average velocity, vav. Actually, the impact was a glancing blow. Momentum 53 Exercise 2: Auto companies frequently test the safety of automobiles by putting them through crash tests to observe the integrity of the passenger compartment.

If a Answer: Exercise 3: Rhonda, who has a mass of She is wearing her seatbelt, which brings her body to a stop in 0. Exercise 4: If million people in the United States jumped up in the air simultaneously, pushing off Earth with an average force of N each for a time of 0. Show a calculation that justifies your answer. He notices that the cue ball is lined up for a perfect head-on collision, as shown.

Each of the balls has a mass of 0. Suppose Maurice hits the cue ball by exerting a force of N for 5. Calculate the resulting velocity of the 8 ball. Answer: Exercise 6: During an autumn storm, a 0. What average force did the car exert to stop the damaging hail stone? Answer: Conservation of Momentum According to the law of conservation of momentum, the total momentum in a system remains the same if no external forces act on the system.

Consider the two types of collisions that can occur. Vocabulary Elastic collision: A collision in which objects collide and bounce apart with no energy loss. In an elastic collision, because momentum is conserved, the mv before a collision for each of the two objects must equal the mv after the collision for each of the two objects. Momentum 55 Vocabulary Inelastic collision: A collision in which objects collide and some mechanical energy is transformed into heat energy.

A common kind of inelastic collision is one in which the colliding objects stick together, or start out stuck together and then separate. However, in an inelastic collision the objects need not remain stuck together but may instead deform in some way. Because momentum is also conserved in an inelastic collision, the mv before the collision for each of the two objects must equal the mv after the collision for each of the two objects.

Solved Examples Example 5: Tubby and his twin brother Chubby have a combined mass of Melinda has a mass of After the elastic collision, the twins continue ahead with a speed of 4. Solution: Notice that you must add the mass of the bumper car to the mass of the riders.

If an Solution: Since the two vehicles lock bumpers, both objects have the same final velocity. How fast does Charlotte move backwards when the spear is shot? Solution: To start, Charlotte and the spear are together and both are at rest. Therefore, Charlotte would travel with a speed of 0. Momentum 57 Practice Exercises Exercise 7: Jamal is at the state fair playing some of the games.

At one booth he throws a 0. Exercise 8: Jeanne rolls a 7. One pin is still standing, and Jeanne hits it head-on with a velocity of 9. The 2. What is the new velocity of the bowling ball? Upon collision, Biff continues to travel forward at 1. How fast is Bruce knocked backwards? While Exercise To test the strength of a retainment wall designed to protect a nuclear reactor, a rocket-propelled F-4 Phantom jet aircraft was crashed head-on into a concrete barrier at high speed in Sandia, New Mexico on April 19, The wall sat on a cushion of air that allowed it to move during impact.

If the wall and F-4 moved together at 8. Answer: Momentum 59 Exercise Valentina, the Russian Cosmonaut, goes outside her ship for a spacewalk, but when she is floating 15 m from the ship, her tether catches on a sharp piece of metal and is severed. Valentina tosses her 2. Exercise A The engineer sees the moose but is unable to stop the train in time and the moose rides down the track sitting on the cowcatcher. What is the new combined velocity of the locomotive and the moose?

Answer: Exercise Lee is rolling along on her 4. This causes the skateboard to go flying forward with a speed of Ethel returns the ball to the child by hitting it with her 2. If the impact lasts for 0. A When Reggie stepped up to the plate and hit a 0. If the impact lasted for 0. A The U. On a jump, a kg Knight lands on the beach with a speed of 4. With what average force did the parachuter hit the sand?

A The late news reports the story of a shooting in the city. Investigators think that they have recovered the weapon and they run ballistics tests on the pistol at the firing range. A About 50 years ago, in an area located outside Flagstaff, Arizona, a giant 4.

To undock from the space station Pilot Melroy released hooks holding the two spacecraft together and the 68 kg shuttle pushed away from the space station with the aid of four large springs. A Tyrrell throws his 0. After the collision, the football bounces straight back with a speed of 3.

A A Isaac, whose mass is What is the velocity of the boat after Isaac jumps? A Miguel, the The What is the new velocity of Miguel and the bull as they move across the arena? A A space shuttle astronaut is sent to repair a defective relay in a What is the combined velocity when the astronaut grabs hold of the satellite?

Constitution, the oldest fully commissioned war ship in the world, is docked in Boston, Massachusetts. Mounted on bearings that allow them to recoil at a speed of 1. If a carronade fires a Challenge Exercises for Further Study B On a hot sumer afternoon, Keith and Nate are out fishing in their rowboat when they decide to jump into the water and go for a swim.

Keith, whose mass is If the B Lilly, whose mass is How long will it take before Lilly coasts to a stop? B In a train yard, train cars are rolled down a long hill in order to link them up with other cars as shown.

A car of mass The coefficient of rolling friction between the train and the track is 0. What velocity would the car have if it linked up with 3 identical cars sitting on flat ground at the bottom of the track?

Hint: The equation for rolling friction is just like the one for sliding friction. For maximum work to be done, the object must move in the direction of the force. If the object is moving at an angle to the force, determine the component of the force in the direction of motion. Remember, if the object does not move, or moves perpendicular to the direction of the force, no work has been done.

Vocabulary Power: The rate at which work is done. One person is more powerful than another if he or she can do more work in a given amount of time, or can do the same amount of work in less time.

Solved Examples Example 1: Bud, a very large man of mass kg, stands on a pogo stick. How much work is done as Bud compresses the spring of the pogo stick 0. There are many ways to tell them apart, the most important of which is to understand how they are used in the context of the exercise. Also, the units used for each are quite different: weight is measured in newtons, and work is measured in joules.

Last of all, weight is a vector and work is a scalar. Example 2: After finishing her physics homework, Sherita pulls her How much work does Sherita do in ascending the stairs? Her muscles exert a force to carry her weight up the stairs. It is important to note that when you are solving for the work done, you need know only the displacement of the body moved.

The number of stairs climbed or their steepness is irrelevant. All that is important is the change in position. The next evening, in a rush to catch her favorite TV show, she runs up the stairs in 3.

Practice Exercises Exercise 1: On his way off to college, Russell drags his suitcase Exercise 2: Katie, a How much work does Katie do in order to reach the cat? How much force must Marrisa exert on the window shade? Answer: Exercise 4: Atlas and Hercules, two carnival sideshow strong men, each lift Atlas lifts his barbells in 1.

There are many different types of energy. This chapter will focus on only mechanical energy, or the energy related to position potential energy and motion kinetic energy. Vocabulary Potential Energy: Energy of position, or stored energy.

An object gains gravitational potential energy when it is lifted from one level to a higher level. In addition to gravitational potential energy, there are other forms of stored energy. For example, when a bow is pulled back and before it is released, the energy in the bow is equal to the work done to deform it.

Springs possess elastic potential energy when they are displaced from the equilibrium position. The equation for elastic potential energy will not be used in this chapter.

Vocabulary Kinetic Energy: Energy of motion. The kinetic energy of an object varies with the square of the speed. Notice that this is the same unit used for work.

When work is done on an object, energy is transformed from one form to another. The sum of the changes in potential, kinetic, and heat energy is equal to the work done on the object. Mechanical energy is transformed into heat energy when work is done to overcome friction.

Conservation of Energy According to the law of conservation of energy, energy cannot be created or destroyed. The total amount of mechanical energy in a system remains constant if no work is done by any force other than gravity.

Solution: For a given object, the change in PE depends only upon the change in position. The apple does not need to fall all the way to the ground to experience an energy change. What is the KE of a How fast was the ball moving when it left the pool table? Use the law of conservation of energy. Therefore, it cancels out and does not need to be included in the calculation.

When an earthquake strikes, his kg hot-dog cart rolls down Nob Hill and reaches point A at a speed of 8. How fast is the hot-dog cart going at point B when Frank finally wakes up and starts to run after it? Solution: Because mass is contained in each of these equations, it cancels out and does not need to be included in the calculation.

Also, the inclination of the hill makes no difference. All that matters is the change in height. If Galileo had dropped a 5. Answer: Exercise 6: The Belmont Stakes winner, Commendable, ran the horse race at an average speed of If Commendable and jockey Pat Day had a combined mass of Answer: Exercise 7: Brittany is changing the tire of her car on a steep hill She trips and drops the What is the speed of the tire at the top of the next hill, which is 5.

Ignore the effects of rotation KE and friction. Exercise 9: A The hill is The pig slips and begins to slide down the hill. If Neil Armstrong jumped up on the moon with an initial speed of 1. Three common machines are the lever, pulley, and incline. The actual mechanical advantage, or AMA, of the machine is a ratio of the magnitude of the force out resistance to the magnitude of the force in effort. The more efficient the machine, the greater work output you will get for your work input.

Solved Examples Example 8: A crate of bananas weighing N is shipped from South America to New York, where it is unloaded by a dock worker who lifts the crate by pulling with a force of N on the rope of a pulley system. What is the actual mechanical advantage of the pulley system? N The pulley exerts Notice that mechanical advantage has no units. Example 9: Two clowns, of mass The smaller clown stands on the lower end of the seesaw while the larger clown jumps from the trampoline onto the raised side of the seesaw, propelling his friend into the air.

N on the seesaw as he jumps, how much force is exerted on the smaller clown? The seesaw acts as a lever with the fulcrum 0. The ideal mechanical advantage is found by comparing the two distances. N2 The car rises 2. What is the ideal mechanical advantage of the jack? At the well, Jill used a force of The force on the bucket of water is Fout and the force exerted by Jill is Fin.

N on a rope wrapped around a pulley system. Answer: Energy and Machines 75 Exercise A windmill uses sails blown by the wind to turn an axle that allows a grindstone to grind corn into meal with a force of The windmill has sails of radius 6. Exercise Winnie, a waitress, holds in one hand a 5. The length of her arm from her hand to her elbow is How much force must her biceps exert to allow her to hold the tray?

Answer: Exercise When building the pyramids, the ancient Egyptians were able to raise large stones to very great heights by using inclines. If an incline has an ideal mechanical advantage of 4. How much work is done by gravity on Bob as he goes down the hill? A A pile driver is a device used to drive stakes into the ground. While building a fence, Adam drops a pile driver of mass The pile driver is opposed by a resisting force of 5.

How far is the stake driven into the ground on the first stroke? The train of cars has a mass of kg. A A flea gains 1. What is the mass of the flea? Energy and Machines 77 A At target practice, Diana holds her bow and pulls the arrow back a distance of 0.

What is the potential energy stored in the bow the moment before the arrow is released? A The coyote, whose mass is What force does the ground exert on the coyote as he makes a coyote-shaped dent 0. A A 0. A Blackie, a cat whose mass is 5. Blackie has a KE of How tall is the refrigerator?

A Calories measure energy we get from food, and one dietary Calorie is equal to J. The average food energy intake for human beings is Assume you have a mass of How high a mountain would you have to climb to do so? Note: This calculation ignores the large amount of energy the body continually loses to heat.

A From a height of 2. If his regulation-size basketball has a mass of 0. A Mr. Macintosh, a computer technician, uses a screwdriver with a handle of radius 1.

The screw moves out 0. What is the ideal mechanical advantage of the screwdriver? A A nutcracker 16 cm long is used to crack open a Brazil nut that is placed 12 cm from where your hand is squeezing the nutcracker. What is the ideal mechanical advantage of the nutcracker? This portion of the stream rises at an angle of B A kg shopping cart full of groceries sitting at the top of a 2. Upon impact, a 0.

How deep a dent is made in the car? B Using her snowmobile, Midge pulls a The snowmobile exerts a force of N parallel to the hill. If the coefficient of friction between the skis and the snow is 0. Ignore the effects of the static friction that must be overcome to initially start him in motion. B Jose, whose mass is The sand provides a force of friction of 6.

B Eben lifts an engine out of his Volkswagen with the help of a winch that allows him to raise the engine 0. Eben expends J of energy to lift the Vocabulary Frequency: The number of rotations or revolutions per unit time.

Period and frequency are reciprocals of each other. The time it takes 6 Oak Knoll Road Mendham Nj Ge for one revolution is the period, T. Although the velocity is constant in magnitude speed , it is always changing direction. This acceleration, which is always directed in toward the center of the circle, is called centripetal acceleration.

This force, called the centripetal force, is always directed inward toward the center of the circle. Solved Examples Example 1: After closing a deal with a client, Kent leans back in his swivel chair and spins around with a frequency of 0. What is the linear speed of the scratch as it turns?

Solution: The record makes 45 revolutions every The ride takes 2. Solution: The ride takes 2. If Captain Chip flies his plane in a circle whose radius is Solution: First, convert km to m and min to s.

If it spins with a frequency of revolutions per minute, what is the period of spin of the compact disc? Answer: Exercise 2: Hamlet, a hamster, runs on his exercise wheel, which turns around once every 0.

What is the frequency of the wheel? Answer: Exercise 3: A sock stuck to the inside of the clothes dryer spins around the drum once every 2.

Exercise 4: What is the radius of an automobile tire that turns with a frequency of 11 Hz and has a linear speed of Answer: 84 Circular Motion Exercise 5: Luigi twirls a round piece of pizza dough overhead with a frequency of 60 revolutions per minute. Explain the reason for your answer. Exercise 6: Earth turns on its axis approximately once every 24 hours. The radius of Earth is 6. Compare your linear speed at the equator to your linear speed while standing near one of the poles.

Exercise 7: Jessica is riding on a merry-go-round on an outer horse that sits at a distance of 8. The merry-go-round turns around once every Circular Motion 85 Exercise 8: A cement mixer of radius 2. What is the centripetal acceleration of a small piece of dried cement stuck to the inside wall of the mixer? If Mr. One such test involves spinning the astronauts in a device called a centrifuge that subjects them to accelerations far greater than gravity.

Hint: The speed of light is 3. A tiny, 0. What is the radius of the blender at this location? Answer: Torque Vocabulary Torque: A measurement of the tendency of a force to produce a rotation about an axis. The longer the lever arm, the larger the torque.

This is why it is easier to loosen a tight screw with a long wrench than with your hand or a short pair of tweezers. If a torque causes a counterclockwise rotation of an object around the fulcrum, it is positive.

If the torque causes a clockwise rotation of an object around the Circular Motion 87 fulcrum, it is negative. This convention works even if the object remains balanced and the torques just attempt to cause a rotation.

However, unlike work, which is measured in the same unit, torque is not a form of energy and is not equivalent to a joule. In most of the exercises in this book, all the torques are balanced. For example, if two people are sitting on either side of a seesaw and they want to remain level, they can position themselves so that all the torques on one side of the seesaw equal all the torques on the other side.

Keep in mind that when an object is balanced, all the torques must also balance. Vocabulary Center of Gravity: The point on any object that acts like the place at which all the weight is concentrated.

The weight of an object, which acts as if it is concentrated at the center of gravity, is one of the forces that can cause it to rotate. The weight produces a torque if the object is not supported at its center of gravity.

Solved Examples Example 5: Ned tightens a bolt in his car engine by exerting 12 N of force on his wrench at a distance of 0. How much torque must Ned produce to turn the bolt? Mabel weighs N and she sits 2. Where should Solution: It helps to draw a diagram of the situation to allow yourself to visualize what is happening.

N Practice Exercises Exercise A water faucet is turned on when a force of 2. How much torque must be produced to turn the handle? Answer: Exercise Nancy, whose mass is If Nancy sits on the very end of a 3. Answer: Circular Motion 89 Exercise Barry carries his tray of food to his favorite cafeteria table for lunch.

The 0. Barry holds the tray by the left edge with one hand, using his thumb as the fulcrum, and pushes up 0. How much upward force must his finger tips exert to keep the tray level? She hangs a 0. If the lever arm itself has negligible mass, where must the support string be placed so that the arm balances?

Answer: Exercise Orin and Anita, two paramedics, rush a The stretcher is 2. How much force must Orin and Anita each exert to keep the man horizontal? The equation for the moment of inertia varies depending upon the shape of the rotating object.

Other moments of inertia can be found in your textbook, and are summarized as follows. Similarly, an object that is rotating tends to continue spinning at a constant rate unless an unbalanced force acts to alter that rotation. This is called the rotational inertia. Vocabulary Angular Momentum: The measure of how difficult it is to stop a rotating object. Think of angular momentum as being the rotational equivalent of linear momentum.

Just as linear momentum is the product of the mass and the velocity, angular momentum is the product of the mass and the velocity for an object rotating at a distance r from the axis. Circular Motion 91 Momentum is conserved when no outside forces are acting.

Similarly, angular momentum is conserved when no outside torques are acting. A spinning ice skater has angular momentum. When the skater pulls her arms in decreasing her radius of spin , she spins faster increasing her velocity.

Doing so conserves her angular momentum. What is the moment of inertia of this disk-shaped wheel? Solution: A disk is a thin cylinder, so the moment of inertia of a disk is the same as that of a cylinder. What is the moment of inertia of the baton as it spins about its center of gravity?

In their caps and gowns, seniors roll wooden hoops in a race in which the winner is said to be the first in the class to marry. Hilary rolls her 0. The moment of inertia of the hoop is 0. What is the radius of the hoop? What is the moment of inertia of the wheel? What is the moment of inertia of Earth as it turns on its axis? Assume her mass is evenly distributed all along her body. What is the moment of inertia of the ring?

What was the angular momentum of the mouse on each of the three hands? Answer: Answer: Answer: Exercise In a physics experiment, Ingrid, the ice skater, spins around in the rink at 1. In each hand she holds a 1. If angular momentum is conserved, how fast will Ingrid begin to spin if she pulls her arms to a position 0.

Answer: Additional Exercises A In the Biblical tale of David and Goliath, the giant is slain when David hits him with a rock that he has spun around overhead in a sling. If Ashton sits on the fan blade at a distance of 0. How long is a strand of gold that makes one complete turn around the wheel? A A 3. A In order for Sasha in A-5 to feel weightless at the top of the ride, a at what linear speed must the Ferris wheel turn?

A Earth orbits the sun approximately once every The mass of Earth is 5. A Most doorknobs are placed on the side of the door opposite the hinges instead of in the center of the door. A Priscilla is working out in the gym with a 2. Circular Motion 95 A Leif and Paige are rearranging the heights of their movable bookshelves; they remove one of the 2.

How much force must Leif and Paige each exert to hold the shelf level? A Brewster hits a 0. If the pool ball has a radius of 3. A Rocky, a raccoon, squeezes into a 0. However, the can tips over and begins to roll. If Rocky and the can have a combined mass of The 5. What is the linear speed of the wheel? What coefficient of friction is needed between the cake pan and the truck in order to keep the pan from slipping?

If the coefficient of friction between the tires and the road is 0. B Pretending to be Tarzan, The tree branch will break if subjected to a force greater than N. What is the maximum speed with which Zach can swing in order to avoid breaking the branch?

B Hanging in front of the office of Lewis Skeirik, D. What is the tension in a supporting wire that holds the sign at an angle of Solved Examples Example 1: The gravitational force of attraction between Earth and the sun is 1.

What would this force have been if Earth were twice as massive? Solution: The gravitational force of attraction between two bodies is proportional to the mass of each of the two bodies.

As one mass increases, the gravitational force between the two bodies increases proportionally. What would this gravitational force have been if Earth had formed twice as far away from the sun? Solution: The gravitational force of attraction between two bodies is inversely proportional to the square of the distance between them.

Practice Exercises Exercise 1: When Royce was 10 years old, he had a mass of 30 kg. By the time he was 16 years old, his mass increased to 60 kg. How much larger is the gravitational force between Royce and Earth at age 16 compared to age 10? Exercise 3: Mr. Gewanter, whose mass is Exercise 4: Astrologers claim that your personality traits are determined by the positions of the planets in relation to you at birth.

Scientists argue that these gravitational effects are so small that they are totally insignificant. Compare the gravitational attraction between you and Mars to the gravitational attraction between you and your This is the average distance between Earth and Mars. This distance varies as the two planets orbit the sun. How far away is the Milky Way from our nearest neighbor, the Andromeda Galaxy, if Andromeda contains roughly the same number of stars and attracts the Milky Way with a gravitational force of 2.

Calculate the net force pulling on Earth during a a new moon, b a full moon, c a first quarter moon. The diagram is intended to help your understanding of the situation but is not drawn to scale. The m on the right side of the equation stands for this same mass, so the term cancels out of the equation.

The M on the right represents the mass of Earth or other celestial body on which the person is standing. The d in the denominator is equal to the radius of the celestial body.

On Earth you already know that this value is Solved Examples Example 4: Temba is standing in the lunch line 6. No, his acceleration due to gravity does not change because it is not dependent on his mass. What is the acceleration due to gravity on the sun? Solution: One way to solve this exercise is to actually multiply the given values by the mass and radius of Earth. However, there is an easier and much Law of Universal Gravitation neater way to come up with the correct answer.

By working with ratios, you can find an answer without any information about Earth. In other words, it is If asteroid B has a radius of only Answer: Law of Universal Gravitation Exercise 9: Black holes are suspected when a visible star is being noticeably pulled by an invisible partner that is more than 3 times as massive as the sun. What is the acceleration due to gravity on Saturn? Answer: Law of Universal Gravitation Escape Speed Vocabulary Escape Speed: The minimum speed an object must possess in order to escape from the gravitational pull of a body.

In Chapter 5, you worked with gravitational potential energy and kinetic energy. When an object moves away from Earth, its gravitational potential energy increases. Since its total energy is conserved, its kinetic energy decreases. When the object is close to Earth, the gravitational force on it is a fairly constant mg. However, as you know, the gravitational force drops rapidly as you get farther from Earth. If an object moves upward from Earth with enough speed, it will never run out of kinetic energy and will escape from Earth.

Solved Examples Example 6: Earth has a mass of 5. What is the escape speed of a rocket launched on Earth? Example 7: Compare Example 6 with the escape speed of a rocket launched from the moon.

The mass of the moon is 7. Practice Exercise Exercise How fast would you need to travel a to escape the gravitational pull of the sun? When the sun becomes a red giant, will its escape speed be greater than, less than, or the same as, it is now?

Exercise How fast would the moon need to travel in order to escape the gravitational pull of Earth, if Earth has a mass of 5. If planet Apgar has a mass of 1. In this model, what is the gravitational force between a proton and an electron? A At what height above Earth would a A It is said that people often behave in unusual ways during a full moon.

The moon is 3. A The tiny planet Mercury has a radius of km and a mass of 3. A The acceleration due to gravity on Venus is 0. A The planet Mars has a mass that is 0. Describe how you might explain this phenomenon. A On October 26, , the NEAR Shoemaker spacecraft swooped within 3 miles of the asteroid Eros, taking images and collecting data from a distance closer than any spacecraft has ever come to an asteroid.

Eros has a mass of 6. The strange potato-like shape of Eros makes its diameter difficult to determine. If NASA landed a Io orbits 4. Europa: 652 Oak Road Barrington Map 6. If Jupiter and its satellites are lined up as shown, what gravitational force does the satellite Io experience?

Titan orbits Saturn at an average distance of 1. Use this information to find the mass of Saturn. However, if the car is in motion, a number of different things can happen. It is still moving in the same direction as the car but at a reduced speed with respect to the ground. Time Dilation When an object such as a spaceship is traveling near the speed of light, the time interval between two events that occur at the same place on the moving object seems longer from the perspective of a stationary observer than it does from the perspective of the moving observer.

In other words, time appears to be dilated, or stretched out. In physics, astronomical distances are often written with the unit light-years, ly. A light-year is the distance light travels in 1 year. It is equivalent to 9. With what horizontal velocity do the bales of hay hit the ground? Solution: First, consider the direction of each of the velocities and treat them as vectors.

However, relative to the ground, the speed is somewhat different, as shown. Neglecting air resistance, how fast is the Frisbee moving when his dog, Snoopy, catches it in his mouth? How long would the beam take according to Gerard, a stationary observer on Earth, if the spacecraft were moving directly overhead in a direction perpendicular to the line of sight with a speed of 0.

Solution: The number 0. The speed of light is represented with the letter c. Practice Exercises Exercise 1: Fiona is on her way home from France but she must leave her new-found love, Pierre, behind. According to Fiona, how fast are the flowers moving when she catches them? How fast is the rope moving when it is caught by the dock worker?

Answer: Exercise 3: Superman leaves Lois in Metropolis to rescue a malfunctioning space probe sent up from Earth. Flying at a speed of 0. After saying good-bye to his twin brother Henry, Albert jumps in his spacecraft and takes off for Zil traveling at a speed of 0.

The total trip takes 3. Prototyp der Alamo Manufacturing Company. Prototypen von Giuseppe Alberti. Alden Sampson. Keine Verbindung zu Alfa Romeo.

Alfa Romeo. Alger Jr. Allied Industries. Seit Prototyp Kit Car. Monaco e C. Dampfwagen-Prototyp der Alma Steam Motors [6]. Prototyp von R. Prototyp von John Alston. Prototyp von George P. Kleinstwagen-Prototyp von Antonin Majer. Prototyp der American Carriage Motor Company. Prototyp von The American Manufacturing Company. American Austin. Prototyp der Colonial Car Company.

American CGV. American Cyclecar. American De Dion. American Electric. American Locomotive Motor Car. American Mercedes. American Napier. American Populaire. American Power. American Simplex. American Steam Car. American Steamer. American Tri-Car. American Voiturette. American Waltham. Dampfwagen-Prototyp von A. Prototyp der Owatonna Manufacturing Company. Butler Ames. Prototyp der Amesbury Automobile Company [6]. Prototyp eines Supersportwagens.

Erhalten geblieben. Prototypen der Amstutz-Osborn Company. Prototyp von N. Anderson Steam Carriage. Dampfwagen-Prototyp von Anderson Manufacturing Company.

Andrews und Herbert L. Prototyp von M. Kleinstwagen-Prototypen wie Angkor von Nhean Phaloek. Prototyp von Mathias Anheuser. Ann Arbor. Elektro-Prototyp von Earle C. Sportwagen-Prototyp von Interco Development Corp.

Prototypen VW Buggy. Prototypen von Ludwig Aper. Prototyp auf Basis Seat Prototyp der Archer Automobile Association. Prototyp von Argonaut Motor Machine. Fodrea Garage Company, Hersteller unbekannt. Prototyp von William D. Prototyp eines Elektroautos von B. Cyclecar-Prototyp der Arrow Cyclecar Company.

Arrow Locomotor. Prototyp eines Flugautos von Waldo D. Prototyp eines Sportwagen, finanziert durch Ryoji Yamazaki. Artzberger Steam. Kleinstwagen-Prototyp von Ari Antonio da Rocha. Drei Prototypen von Paul Arzens , erhalten geblieben.

Prototypen von Sport- und Rennwagen. Geplante Lizenzproduktion des Proton Persona. Einzelner Elektrowagen von L. Prototyp eines Taxis mit Elektromotor. Prototyp der Maschinenbaufabrik William Asquith Limited. Prototyp von Ray Everitt. Prototyp von Richard Abib. Prototyp, Motor von Grivel. Prototyp eines viersitzigen Cabriolets von Astron Motors. Prototyp der Atlanta Motor Company mit Vierradantrieb. Prototyp von Atlas Engine Works.

Prototyp Smart auf Basis Unimog. Prototyp der Lee J. Aubry Carriage Company. Moore auf Auburn-Fahrgestell. Sportwagen-Prototyp von Factor Aurelio Automobile. Keine Angaben. Prototyp vom Australian Car Syndicate. Einsitziger Prototyp von Albert Woods. Prototyp von F. Prototyp der Auto Acetylene Company. Auto Car.

Auto Sandal. Dampfwagen-Prototyp der Auto Supply Company. Prototyp eines Amphibienfahrzeugs von Revailler. Autocars and Accessories. Dampfwagen-Prototyp der Monarch Motor Company.

Prototyp eines Flugautos von Juan de la Cierva. Prototyp der Automatic Air Carriage Company. Automobile Construction. Automobile Fore Carriage. Prototyp eines Cyclecars. Prototyp von Ira Peavey. Zwei Prototypen von Fritz B. Busch, Michael Conrad und Pio Manzu. Prototyp einer Nachbildung des Porsche von Autonova.

Prototyp mit Einzylindermotor von De Dion-Bouton. Zwei Fahrzeuge von Wesley N. Rawson und Eigenbedarf. Prototyp eines Cyclecars von Avery Stalnaker. Prototyp von Armat Ltd. Prototypen von Antoni Wieckowski. Prototyp des Designers Gary Millard. Baby Moose. Prototyp von Bill Badsey. Einzelner Elektrowagen von F. Prototyp von Nelson M.

Prototyp der Baker Manufacturing Company. Prototypen von Robert Baker. Zwei Prototypen der Worcester Cycle Company. Prototyp von Bakrie Group. Kleinstwagen-Prototyp der Karosseriefirma Balbo. Prototyp von Frederick A. Prototyp der Charles A.

Balton Engineering Corporation. Einzelner Dampfwagen von Robert Banks. Prototypen der Banner Automobile Company. Prototyp der Barauf Motor Company. Von Barbarou et Bouvier. Prototypen der Barbour Buggy Company. Elektrowagen-Prototyp der Hartford Accumulator Company.

Prototyp von Mohamed Ahmed Barkia. Barnes, produziert bei Autocar. Dampfwagen-Prototyp der Frontenac Manufacturing Company. Barnhart und C. Prototyp eines Mittelmotorsportwagens von Design Performance. Prototyp von Edward F. Bartholomew, nach eigenen Angaben auch einige verkauft. Dreirad-Prototypen von Alexander Basilewski. Anleitung zum Bau von Kleinstwagen von Karlheinz Basse. Prototyp einer Voiturette. Batchelder und William H.

Prototyp von John W. Prototyp von George Bateup. Einzelner Dampfwagen des Joseph Battin. Seit Prototypen von Bavina Cars India. Prototyp der Bayer AG.

Prototyp der Universal Car Equipment Company. Dreirad-Prototyp Bech Drabebil, erhalten geblieben. Prototyp der Otto Becker Automobilfabrik. Prototyp von James R. Bede mit Propeller am Heck. Prototyp nach Belcar-Lizenz. Dampfwagen-Prototyp von James E. Belger und Samuel Bowker. Englisch Bjelka.

Prototypen der Bell Automobile Corporation. Zwei Prototypen der Belmont Motor Company. Prototyp von Andrew und John B. Prototyp der Berger Manufacturing Company. Zwei Prototypen von Peter Berlo. Prototyp eines Kleinstwagens. Prototyp der Bertzchy Motor Company. Prototyp der Berwick Automobile Company. Zwei Prototypen der Best Manufacturing Company.

Prototypen der Detroit Bi-Car Company. Prototyp der Biddle Manufacturing Company. Vier Prototypen von Henry H. Prototyp der Bison Motor Company. Prototyp eines Elektroautos der Bissell Electric Company. Black Diamond. Dampfwagen von Seth C. Black, Vermarktung unklar. Dampfwagen-Prototyp der Blair Light Company.

Prototyp von James E. Blank und G. Prototyp der Blaurock Carriage Company. Elektromobil-Prototyp von H. Prototypen von Sebastian Blimline. Prototyp von Gordon Bloomquist auf Kaiser-Basis. Blue Light. Bluff Climber. Prototyp als Nachfolger des Lassale. Prototyp von Thomas H. Prototyp der Bonebrake-Roberts Company. Prototyp von Clarence Bonner.

Etwa Prototyp eines Roadsters mit Lada-Motor. Prototyp der Borbet GmbH. Dampfwagen-Prototypen von Virgilio Bordino.

Zwei Sportwagen-Prototypen von Richard Bosley. Boston High Wheel. Prototyp von George B. Prototyp von Charles Boyden. Prototyp von Hi-Tech Car Company. Prototyp der Braddon Motors Company. Prototypen der Commercial Motor Car Company. Nachbau des Porsche , Vermarktung unklar. Prototyp der Bremac Motor Car Corporation. Prototypen von Arthur J. Elektro-Prototypen von Brenning Brothers.

Prototypen der Brewster Motor Car Company. Prototyp der Brictson Manufacturing Company. Dampfwagen-Prototyp der Bridgeport Boiler Works. Prototypen der Briggs Manufacturing Company. Eines ist erhalten geblieben. Prototyp der Brooks Motor Company. Dampfwagen-Prototypen von Joe Brown.

Prototypen von George D. Prototyp der Brown Auto Company. Prototyp von Samuel Brown. Zwei Prototypen von Edwin F. Drei Prototypen der F. Brownell Motor Company. Ward LaFrance und Edgar Wemple. Prototyp 12055 Point Oak Road 63131 Review der Brunswick Motor Car Company. Elektrowagen-Prototyp der Brush Electric Company. Von P. Prototyp von Klasse Chassis.

Prototyp von Don Bruce. Buckley Co. Prototypen eines Cabriolets mit Frontmotor. Prototyp der Buffalo Cycle Supply Company. Prototyp einer Luxuslimousine im Auftrag von Gianni Bulgari.

Dampfwagen-Prototypen von James Herbert Bullard. Edward Burgett und William S. Prototyp der Burns Typewriter Company. Das zweite Fahrzeug hatte Vierradantrieb. Prototyp von George Burwell. Prototyp von Charles W. Prototyp der Butler Company. Zwei Dreirad-Prototypen von Edward G.

Byrider Electric. Prototyp von Alonzo R. Caffrey Steam. Prototyp eines Elektro-Kleinstwagens. Prototyp eines Avant-Train. Prototyp der Kinsey-McAlvay Company. Prototyp der California Cycle Car Company. California Component Cars. California Custom Coach. California Touring. Californian Six. Prototypen der Calumet Motors Corporation. Prototyp von Camelot Classics Corporation. Prototyp der F.

Bultman Company. Prototyp eines Elektroautos. Canadian Motor Syndicate. Canadian Standard. Prototyp der Cannon Motor Car Company. Cantono Electric. Dampfwagen-Prototyp, vergebens angeboten, erhalten geblieben. Prototyp der Carey Motor Car Company. Dampfwagen Carhart Steam. Prototyp eines Flugautos von Matthias Klug.

Einzelner Elektrowagen von H. Prototyp von John Carroll. Prototyp der Carroll Motor Car Company. Zwei Prototypen von Humberto Malzoni Casella. Prototyp von Henrique Casini. Prototyp eines Dampfwagens von Don Pedro Ribera.

Caswell und Harold Caswell. Dreirad-Dampfwagen der Herren Catley und Ayres. Prototyp der Cavalier Motor Associates. Prototyp von C. Cecil, erhalten geblieben.

Prototypen von J. Prototyp der Central Motor Car Company. Prototyp der Central Automobile Company. Prototyp der Central Manufacturing Company. Prototyp der Century Motor Car Company. Century Steamer. Century Tourist. Prototyp von Chameleon Car Company. Prototyp der Champion Motor Car Company. Dampfwagen-Prototyp von P.

Prototyp von Harry Eugene Luck. Einzelner Dampfwagen von Odell M. Prototyp auf Basis des Heinkel Kabinenrollers. Kleinstwagen-Prototyp von Philippe Charbonneaux.

Prototyp von James A. Prototyp von Eastern Motors Syndicate. Einzelner Dampfwagen von F. Chautauqua Steamer. Prototyp von Jaime Muniz. Von E. Prototyp von Herbert W. Prototyp der Chicago Cyclecar Company. Chicago Electric. Chicago Light Six. Chicago Motor Buggy. Prototyp von Henry Nehrybecki. Prototypen der Christensen Engineering Company. Kleinstwagen-Prototyp von Ezio Cingolani.

Kleinstwagen-Prototyp, erhalten geblieben. Prototyp eines Dreirad-Kleinstwagens von City Mobile. Prototyp von Henry W. Wiliam G. Clark bot an, seine Motoren in Fahrgestelle einzubauen. Prototyp der E.

Clark Machine Company. Clark Electric. Prototypen der Clark Motor Company. Classic Chassis Services. Classic Glass. Prototyp der Cleaver Motor Vehicle Company. Zwei einzelne Dampfwagen von John Clegg.

Prototyp von H. Prototypen der Cleveland Motor Carriage Company. Cleveland Three-Wheeler. Einzelner Dampfwagen von Enos Merrill Clough. Prototyp der Cluts Manufacturing Company. Buggy mit Frontantrieb, Vermarktung unklar.

Cyclecar-Prototyp von Paul Coats. Sportwagen-Prototyp von Cobra International. Prototyp der Coburn Bunting Motor Corporation. Einzelner Dampfwagen von Adelbert Brown Coe. Dampfwagen-Prototyp von Howard E.

Coffin, erhalten geblieben. Colen und Andrew Lang. Elektro-Prototypen von Clyde J. Prototyp der Collinet Motor Company. Prototyp von Collins Motors. Prototyp der Collins Motor Car Company. Prototyp der Mechanical Development Corporation. Colonial Electric. Prototyp von Colonial Motors.

Prototyp von Columbia Machine Works. Cyclecar-Prototyp der American Cyclecar Company. Columbia Motor Buggy. Elektro-Prototypen der Columbia Perambulator Company. Cyclecar-Prototyp der Columbus Brass Company. Von V.

Prototyp der Commander Motors Corporation. Commercial Electric. Prototyp der Compressed Air Power Company. Prototyp der Conger Manufacturing Company.

Continental Roadster. Dampfwagen von Peregrine Cook. Dampfwagen-Prototyp von James M. Dampfwagen von Frank P. Prototypen von Robert L. Dampfwagen-Prototypen von John F.

Prototypen der Cooper Motor Company. Prototypen von Lucius D. Kleinstwagen-Prototyp von Corat. Etwa bis Umbauten auf Fiat-Basis. Prototyp eines Strandwagens, der auch in Deutschland vertrieben werden sollte.

Seit Elektroauto-Prototypen. Prototyp der Union Automobile Company. Prototyp von Craig-Hunt. Dreirad-Dampfwagen von Postie Lawson, erhalten geblieben. Prototyp der Crandall Machine Company.

Prototyp von J. Prototyp der Crescent Automobile Manufacturing Company. Prototyp von Charles R. Drei Prototypen von Samuel Eliot. Einzelner Dampfwagen von Alonzo T. Zwei Prototypen von Harry E. Cross Lander. Cross Ranger. Prototyp Replika Porsche Ab Cull und A. Einzelner Dampfwagen der Cullman Wheel Company. Einzelnes Elektroauto von G. Einzelner Dampfwagen von Francis Curtis.

Custom Design Associates. Prototyp der Cycleplane Company. Prototyp von Henry E. Neal Jr. Zwei Dampfwagen von Dr. Ludwig Czischek-Christens. Dreirad-Prototyp von Franz Wiesinger. Prototyp, Hersteller unbekannt. Prototyp eines Dreirades mit Tandemsitzen von David Arthur.

Prototyp von James Scripps-Booth. Prototyp der Daisy Cyclecar Company. Prototyp eines Einspurautos von Jan Anderle. Dan Patch. Dreirad-Prototyp von Jens Nilson. Prototyp der L. Damann Motor Company. Prototyp von Stuart Darrow. Prototyp eines Roadsters von Dart Cars. Daryl Holliday.

Dreirad-Einsitzer von M. Daulon und dem Karosseriehersteller Gordia. Prototyp von William T. Prototyp von William Norris Davis. Prototyp von Dick Davis. Davis und Webster. Prototyp der Dayton Autoelectric Company. Dreirad-Prototyp von Dazin. Prototyp von Diego Grullon und Juan Ovalle. Prototyp der De Cross Cyclecar Company. De Dietrich. Angebot von De Haven Brothers, Produktion unklar. Prototyp eines Fahrzeugs im Stile der er Jahre.

De La Vergne. Prototypen von H. De Loura. De Mars. De Palma. De Schaum. De Vecchi. Prototyp der Decatur Gasolene Engine Company. Prototyp von Charles Dechaux. Prototyp von Deering Works. Prototyp der Miller Machine Company. Kleinwagen-Prototyp nach Lizenz von Chausson. Prototyp von American Motors Inc. Prototypen von Delta Design. Prototyp von Eric H. Demars, Hersteller unbekannt. Des Moines. Prototyp der Motor Components Manufacturing Company.

Prototyp der Nevada Motor Car Company. Prototypen von Desmania Design. Prototyp der P. Detroit Electric. Detroit Taxicab. Prototyp der Devac Automobile Company. Prototyp von G. Dickinson Morette. Strandwagen, Vermarktung unklar. Prototyp von Diecasters. Kleinstwagen-Prototyp von G. Prototyp der Ditwiler Manufacturing Company. Prototyp von S. Daraus wurde der DKR. Zwei Prototypen von Spartaco Dobelli.

Prototypen eines Kleinstwagens von Jaime Lerner. Dreirad-Prototyp mit hinterem Einzelrad. Prototypen der Dodgeson Motors. Prototyp von Clemar Bucci.

Einzelner Elektrowagen von Clarence W. Prototyp der A. Prototyp eines Kleinwagens. Prototyp Triboo 43 von Don Foster Technologies. Dampfwagen-Prototyp von Thomas B.

Dreirad-Prototyp mit Heckmotor. Prototyp der Dovetail Carriage Company. Prototyp der Dow Portable Electric Company.

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