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physics
mechanics

Questions and Answers of Mechanics

NASA often uses the gravity of a planet to “slingshot” a probe on its way to a more distant planet. The interaction of the planet and the spacecraft is a collision in which the objects do not
The Moon revolves around the Earth. Model its orbit as circular. Is the Moon’s linear momentum conserved? Is its kinetic energy conserved?
A raw egg dropped to the floor breaks upon impact. However, a raw egg dropped onto a thick foam rubber cushion from a height of about 1 m rebounds without breaking. Why is this possible? If you try
Can the center of mass of an object be located at a position at which there is no mass? If so, give examples.
A juggler juggles three balls in a continuous cycle. Any one ball is in contact with his hands for one fifth of the time. Describe the motion of the center of mass of the three balls. What average
Does the center of mass of a rocket in free space accelerate? Explain. Can the speed of a rocket exceed the exhaust speed of the fuel? Explain.
Early in the twentieth century, Robert Goddard proposed sending a rocket to the moon. Critics objected that in a vacuum, such as exists between the Earth and the Moon, the gases emitted by the rocket
Explain how you could use a balloon to demonstrate the mechanism responsible for rocket propulsion.
On the subject of the following positions, state your own view and argue to support it. (a) The best theory of motion is that force causes acceleration. (b) The true measure of a force’s
Is it possible to calculate the torque acting on a rigid object without specifying an axis of rotation? Is the torque independent of the location of the axis of rotation?
Is the triple product defined by A . (B X C) a scalar or a vector quantity? Explain why the operation (A.B) X C has no meaning.
Vector A is in the negative y direction, and vector B is in the negative x direction. What are the directions of? (a) A X B (b) B X A?
If a single force acts on an object and the torque caused by the force is nonzero about some point, is there any other point about which the torque is zero?
Suppose that the vector velocity of a particle is completely specified. What can you conclude about the direction of its angular momentum vector with respect to the direction of motion?
If a system of particles is in motion, is it possible for the total angular momentum to be zero about some origin? Explain.
If the torque acting on a particle about a certain origin is zero, what can you say about its angular momentum about that origin?
A ball is thrown in such a way that it does not spin about its own axis. Does this mean that the angular momentum is zero about an arbitrary origin? Explain.
For a helicopter to be stable as it flies, it must have at least two propellers. Why?
A particle is moving in a circle with constant speed. Locate one point about which the particle’s angular momentum is constant and another point about which it changes in time.
Why does a long pole help a tightrope walker stay balanced?
Often when a high diver wants to turn a flip in midair, she draws her legs up against her chest. Why does this make her rotate faster? What should she do when she wants to come out of her flip?
In some motorcycle races, the riders drive over small hills, and the motorcycle becomes airborne for a short time. If the motorcycle racer keeps the throttle open while leaving the hill and going
Stars originate as large bodies of slowly rotating gas. Because of gravitation, these clumps of gas slowly decrease in size. What happens to the angular speed of a star as it shrinks? Explain.
If global warming occurs over the next century, it is likely that some polar ice will melt and the water will be distributed closer to the Equator. How would this change the moment of inertia of the
A mouse is initially at rest on a horizontal turntable mounted on a frictionless vertical axle. If the mouse begins to walk clockwise around the perimeter, what happens to the turntable? Explain.
A cat usually lands on its feet regardless of the position from which it is dropped. A slow-motion film of a cat falling shows that the upper half of its body twists in one direction while the lower
As the cord holding a tether ball winds around a thin pole, what happens to the angular speed of the ball? Explain.
If you toss a textbook into the air, rotating it each time about one of the three axes perpendicular to the textbook, you will find that it will not rotate smoothly about one of these axis. (Try
A scientist arriving at a hotel asks a bellhop to carry a heavy suitcase. When the bellhop rounds a corner, the suitcase suddenly swings away from him for some unknown reason. The alarmed bellhop
Stand with your back against a wall. Why can’t you put your heels firmly against the wall and then bend forward without falling?
Can an object be in equilibrium if it is in motion? Explain.
Can an object be in equilibrium when only one force acts upon it? If you believe the answer is yes, give an example to support your conclusion.
(a) Give an example in which the net force acting on an object is zero and yet the net torque is nonzero. (b) Give an example in which the net torque acting on an object is zero and yet the net force
Can an object be in equilibrium if the only torques acting on it produces clockwise rotation?
If you measure the net force and the net torque on a system to be zero, (a) Could the system still be rotating with respect to you? (b) Could it be translating with respect to you?
The center of gravity of an object may be located outside the object. Give a few examples for which this is the case.
Assume you are given an arbitrarily shaped piece of plywood, together with a hammer, nail, and plumb bob. How could you use these items to locate the center of gravity of the plywood? Suggestion: Use
For a chair to be balanced on one leg, where must the center of gravity of the chair be located?
A girl has a large, docile dog she wishes to weigh on a small bathroom scale. She reasons that she can determine her dog’s weight with the following method: First she puts the dog’s two front
A tall crate and a short crate of equal mass are placed side by side on an incline, without touching each other. As the incline angle is increased, which crate will topple first? Explain.
A ladder stands on the ground, leaning against a wall. Would you feel safer climbing up the ladder if you were told that the ground is frictionless but the wall is rough, or that the wall is
When you are lifting a heavy object, it is recommended that you keep your back as nearly vertical as possible, lifting from your knees. Why is this better than bending over and lifting from your
What kind of deformation does a cube of Jell-O exhibit when it jiggles?
Ruins of ancient Greek temples often have intact vertical columns, but few horizontal slabs of stone are still in place. Can you think of a reason why this is so?
If the gravitational force on an object is directly proportional to its mass, why don’t objects with large masses fall with greater acceleration than small ones?
The gravitational force exerted by the Sun on you is downward into the Earth at night, and upward into the sky during the day. If you had a sensitive enough bathroom scale, would you expect to weigh
Use Kepler’s second law to convince yourself that the Earth must move faster in its orbit during December, when it is closest to the Sun, than during June, when it is farthest from the Sun.
The gravitational force that the Sun exerts on the Moon is about twice as great as the gravitational force that the Earth exerts on the Moon. Why doesn’t the Sun pull the Moon away from the Earth
A satellite in orbit is not truly traveling through a vacuum. It is moving through very, very thin air. Does the resulting air friction cause the satellite to slow down?
How would you explain the fact that Jupiter and Saturn have periods much greater than one year?
If a system consists of five particles, how many terms appear in the expression for the total potential energy? How many terms appear if the system consists of N particles?
Does the escape speed of a rocket depend on its mass? Explain.
Compare the energies required to reach the Moon for a 105-kg spacecraft and a 103-kg satellite. Explain why it takes more fuel for a spacecraft to travel from the Earth to the Moon than for the
Explain why it takes more fuel for a spacecraft to travel from the Earth to the Moon than for the return trip. Estimate the difference.
A particular set of directions forms the celestial equator. If you live at 40° north latitude, these directions lie in an arc across your southern sky, including horizontally east, horizontally
Why don’t we put a geosynchronous weather satellite in orbit around the 45th parallel? Wouldn’t this be more useful in the United States than one in orbit around the equator?
Is the absolute value of the potential energy associated with the Earth–Moon system greater than, less than, or equal to the kinetic energy of the Moon relative to the Earth?
Explain why no work is done on a planet as it moves in a circular orbit around the Sun, even though a gravitational force is acting on the planet. What is the net work done on a planet during each
Explain why the force exerted on a particle by a uniform sphere must be directed toward the center of the sphere. Would this be the case if the mass distribution of the sphere were not spherically
At what position in its elliptical orbit is the speed of a planet a maximum at what position is the speed a minimum?
If you are given the mass and radius of planet X, how would you calculate the free-fall acceleration on the surface of this planet?
If a hole could be dug to the center of the Earth, would the force on an object of mass m still obey Equation 13.1 there? What do you think the force on m would be at the center of the Earth?
In his 1798 experiment, Cavendish was said to have “weighed the Earth.” Explain this statement.
The Voyager spacecraft was accelerated toward escape speed from the Sun by Jupiter’s gravitational force exerted on the spacecraft. How is this possible?
How would you find the mass of the Moon?
The Apollo 13 spacecraft developed trouble in the oxygen system about halfway to the Moon. Why did the mission continue on around the Moon, and then return home, rather than immediately turn back to
Two drinking glasses having equal weights but different shapes and different cross-sectional areas are filled to the same level with water. According to the expression P = P0+ pgh, the pressure is
Figure Q14.2 shows aerial views from directly above two dams. Both dams are equally wide (the vertical dimension in the diagram) and equally high (into the page in the diagram). The dam on the left
Some physics students attach a long tube to the opening of a hot water bottle made of strong rubber. Leaving the hot water bottle on the ground, they hoist the other end of the tube to the roof of a
If the top of your head has a surface area of 100 cm2, what is the weight of the air above your head?
A helium-filled balloon rises until its density becomes the same as that of the surrounding air. If a sealed submarine begins to sink, will it go all the way to the bottom of the ocean or will it
A fish rests on the bottom of a bucket of water while the bucket is being weighed on a scale. When the fish begins to swim around, does the scale reading change?
Will a ship ride higher in the water of an inland lake or in the ocean? Why?
Suppose a damaged ship can just barely keep afloat in the ocean. It is towed toward shore and into a river, heading toward a dry dock for repair. As it is pulled up the river, it sinks. Why?
Lead has a greater density than iron, and both are denser than water. Is the buoyant force on a lead object greater than, less than, or equal to the buoyant force on an iron object of the same volume?
The water supply for a city is often provided from reservoirs built on high ground. Water flows from the reservoir, through pipes, and into your home when you turn the tap on your faucet. Why is the
Smoke rises in a chimney faster when a breeze is blowing. Use the Bernoulli effect to explain this phenomenon.
If the air stream from a hair dryer is directed over a Ping- Pong ball, the ball can be levitated. Explain.
When ski jumpers are airborne (Fig Q14.13), why do they bend their bodies forward and keep their hands at their sides?
When an object is immersed in a liquid at rest, why is the net force on the object in the horizontal direction equal to zero?
Explain why a sealed bottle partially filled with a liquid can float in a basin of the same liquid.
When is the buoyant force on a swimmer greater—after exhaling or after inhaling?
A barge is carrying a load of gravel along a river. It approaches a low bridge and the captain realizes that the top of the pile of gravel is not going to make it under the bridge. The captain orders
A person in a boat floating in a small pond throws an anchor overboard. Does the level of the pond rise, fall, or remain the same?
An empty metal soap dish barely floats in water. A bar of Ivory soap floats in water. When the soap is stuck in the soap dish, the combination sinks. Explain why.
A piece of unpainted porous wood barely floats in a container partly filled with water. If the container is sealed and pressurized above atmospheric pressure, does the wood rise, fall, or remain at
A flat plate is immersed in a liquid at rest. For what orientation of the plate is the pressure on its flat surface uniform?
Because atmospheric pressure is about 105 N/m2 and the area of a person’s chest is about 0.13 m2, the force of the atmosphere on one’s chest is around 13 000 N. In view of this enormous force,
How would you determine the density of an irregularly shaped rock?
Why do airplane pilots prefer to take off into the wind?
If you release a ball while inside a freely falling elevator, the ball remains in front of you rather than falling to the floor, because the ball, the elevator, and you all experience the same
Two identical ships set out to sea. One is loaded with a cargo of Styrofoam, and the other is empty. Which ship is more submerged?
A small piece of steel is tied to a block of wood. When the wood is placed in a tub of water with the steel on top, half of the block is submerged. If the block is inverted so that the steel is under
Prairie dogs (Fig. Q14.28) ventilate their burrows by building a mound around one entrance, which is open to a stream of air when wind blows from any direction. A sec second entrance at ground level
An unopened can of diet cola floats when placed in a tank of water, whereas a can of regular cola of the same brand sinks in the tank. What do you suppose could explain this behavior?
Figure Q14.30 shows a glass cylinder containing four liquids of different densities. From top to bottom, the liquids are oil (orange), water (yellow), salt water (green), and mercury (silver). The
In Figure Q14.31, an air stream moves from right to left through a tube that is constricted at the middle. Three Ping-Pong balls are levitated in equilibrium above the vertical columns through which
You are a passenger on a spacecraft. For your survival and comfort, the interior contains air just like that at the surface of the Earth. The craft is coasting through a very empty region of space.
A motorboat going downstream overcame a raft at a point A; τ = 60 min later it turned back and after some time passed the raft at a distance l = 6.0 km from the point A. Find the flow velocity
A point traversed half the distance with a velocity v0. The remaining part of the distance was covered with velocity v1 for half the time, and with velocity v2 for the other half of the time. Find

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