PHYS2A - Exam 2 (Ch. 4-7)
A car rounds a curve at a steady 50 km/h. If it rounds the same curve at a steady 70km/h, will its acceleration be any different? Explain.
Yes the centripetal acceleration will be greater when the speed is greater since the centripetal acceleration is proportional to the square of the speed a v^2/r. When the speed is higher, the acceleration has a larger magnitude
Can a particle with constant speed be accelerating? What if it has constant velocity? Explain.
Yes, a particle with constant speed can be accelerating. A particle traveling around a curve while maintaining a constant speed is accelerating because its direction is changing. However, a particle with a constant velocity cannot be accelerating, since the velocity is not changing in magnitude or direction, and to have an acceleration the velocity must be changing.
If an object is moving, is it possible for the net force acting on it to be zero? Explain.
Yes, the net force can be zero on a moving object. If the net force is zero, the object's acceleration is zero, but the velocity is not necessarily zero.
The Sun is below us at midnight, nearly in line with the Earth's center. Are we then heavier at midnight, due to the Sun's gravitational force on us, than we are at noon? Explain.
Yes, we are heavier at midnight. At noon, the gravitational force on a person due to the Sun and the gravitational force due to the Earth are in the opposite directions. At midnight, the two forces point in the same direction. Therefore, your apparent weight at midnight is greater than your apparent weight at noon.
If a falling ball were to make a perfectly elastic collision with the floor, would it rebound to its original height? Explain.
Yes. In a perfectly elastic collision, kinetic energy is conserved. In the Earth-ball system, the kinetic energy of the Earth after the collision is negligible, so the ball has the same kinetic energy leaving the floor as it had hitting the floor. The height from which the ball is released determines its potential energy, which is converted to kinetic energy as the ball falls. If it leaves the floor with this same amount of kinetic energy and a velocity upward, it will rise to the same height as it originally had as the kinetic energy is converted back into potential energy.
Can the normal force on an object ever do work? Explain.
Yes. The normal force is the force perpendicular to the surface an object is resting on. If the object moves with a component of its displacement perpendicular to this surface, the normal force will do work. For instance, when you jump, the normal force does work on you in accelerating you vertically. And it is the normal force of the elevator floor on you that accelerates you in an elevator.
When will your apparent weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, or (d) moves upward at constant speed? (e) In which case would your apparent weight be the least? (f) When would it be the same as when you are on the ground? Explain.
Your apparent weight will be greatest in case (b), when the elevator is accelerating upward. The scale reading (your apparent weight) indicates your force on the scale, which, by Newton's third law, is the same as the normal force of the scale on you. If the elevator is accelerating upward, then the net force must be upward, so the normal force (up) must be greater than your actual weight (down). When in an elevator accelerating upward, you "feel heavy." Your apparent weight will be least in case (c), when the elevator is in free fall. In this situation your apparent weight is zero since you and the elevator are both accelerating downward at the same rate and the normal force is zero Your apparent weight will be the same as when you are on the ground in case (d), when the elevator is moving upward at a constant speed. If the velocity is constant, acceleration is zero and N = mg. (Note that it doesn't matter if the elevator is moving up or down or even at rest, as long as the velocity is constant.)
A box rests on the (frictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton's laws, as seen (a) by Mary standing on the ground beside the truck, and (b) by Chris who is riding on the truck (Fig. 4-35).
a) Mary, standing on the ground besides the truck, will see the box remain motionless while the truck accelerates out from under it. Since there is no friction, there is no net horizontal force on the box and the box will not speed up. Thus, Mary would describe the motion of the box in terms of Newton's first law - there is no force on the box, so the box does not accelerate b) Chris, standing on the truck, will see the box appear to accelerate backwards with respect to his frame of reference, which is not inertial. He might even say something about the box being "thrown" backwards in the try to invoke Newton's second law to explain the motion of the box. But the source of the force would be impossible to specify
A truck is traveling horizontally to the right. When the truck starts to slow down, the crate on the (frictionless) truck bed starts to slide. In what direction could the net force be on the crate? a) No direction. The net force is zero. b) Straight down (because of gravity) c) Straight up (the normal force) d) Horizontal and to the left e) Horizontal and to the right
a) No direction. The net force is zero The crate does not accelerate up or down, so the net force cannot be vertical. The truck bed is frictionless and the crate is not in contact with any other surface, so there are no horizontal forces. Therefore, no net force acts on the crate. As the truck slows down, the crate continues to move forward at constant speed. (How did the crate stay on the truck in the first place to be able to travel on the truck bed?)
You are trying to push your stalled car. Although you apply a horizontal force of 400N to the car, it doesn't budge, and neither do you. Which force(s) must also have a magnitude of 400N? a) The force exerted by the car on you b) The friction force exerted by the car on the road c) The normal force exerted by the road on you d) The friction force exerted by the road on you
a) The force exerted by the car on you b) The friction force exerted by the car on the road d) The friction force exerted by the road on you
Mary exerts an upward force of 40N to hold a bag of groceries. Describe the "reaction" force (Newton's third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.
a) The reaction force has a magnitude of 40N b) It points downwards c) It is exerted on Mary's hands and arms d) It is exerted by the bag of groceries
a) Why do you push harder on the pedals of a bicycle when first starting out than when moving at constant speed? b) why do you need to pedal at all when cycling at constant speed?
a) When you first start riding a bicycle you need to exert a strong force to accelerate the bike and yourself, as well as overcome friction. Once you are moving at a constant speed, you need to exert a force that will just equal the opposing forces of friction and air resistance. b) When the bike is moving at a constant speed, the net force is zero. Some friction and air resistance are present, so you would need to keep pedaling to keep the net force on the bike (and you) equal to zero
a) You pull a box with a constant force across a frictionless path using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box increase, decrease, or remain the same? Explain. b) What if there is friction?
a) When you pull a rope at an angle, only the horizontal component of the pulling force will be accelerating the box across the table. This is a smaller horizontal force than originally used, so the horizontal acceleration of the box will decrease. b) We assume that the rope is angled upward. When there is friction, the problem is much more complicated. As the angle increases, there are two competing effects. The horizontal component of the pulling force gets smaller, which reduces acceleration. But as the angle increases, the upward part of the pulling force gets larger, which reduces the normal force. As the normal force gets smaller, the force of friction also gets smaller, which would increase the acceleration. Acceleration would increase initially, up to a certain angle , and then decrease as the angle gets higher. If the rope was instead angled downwards, then the normal force will increase, which means the force of friction will increase as well, resulting in the acceleration to decrease for all angles
In a rotating vertical cylinder (Rotor-ride) a rider finds herself pressed with her back to the rotating wall. Which is the correct free-body diagram for her?
a) force pointing downward = gravity, force pointing upwards = friction, force pointing away from wall = normal force
A car accelerates from rest to Later, on a highway it accelerates from to Which takes more energy, going from 0 to 30, or from 30 to 60? (a) 0 to 30 km/h b) 30 to 60 km/h (c) Both are the same
b) 30 to 60 km/h
A child whirls a ball in a vertical circle. Assuming the speed of the ball is constant, when would the tension in the cord connected to the ball be greatest? a) at the top of the circle b) at the bottom of the circle c) a little after the bottom of the circle when the ball is climbing d) a little before the bottom of the circle when the ball is descending quickly e) nowhere; the cord is stretched the same amount at all points
b) at the bottom of the circle (gravity opposes tension)
While driving fast around a sharp right turn, you find yourself pressing against the car door. What is happening? a) centrifugal force is pushing you into the door b) the door is exerting a rightward force on you c) both of the above d) none of the above
b) the door is exerting a rightward force on you
A golf ball is hit with a golf club. While the ball flies through the air, which forces act on the ball? Neglect air resistance. a) the force of the golf club acting on the ball b) the force of gravity acting on the ball c) the force of the ball moving forward through the air d) all of the above e) both a and c
b) the force of gravity acting on the ball
Two satellites orbit the Earth in circular orbits of the same radius. One satellite is twice as massive as the other. Which statement is true about the speeds of these satellites? a) the heavier satellite moves twice as fast as the heavier one b) the two satellites have the same speed c) the lighter satellite moves twice as fast as the heavier one d) the ratio of their speeds depends on the orbital radius
b) the two satellites have the same speed
What causes the boat to move forward? a) the force the man exerts on the paddle b) the force the paddle exerts on the water c) the force the water exerts on the paddle d) the motion of the water itself
c) The force the water exerts on the paddle Under Newton's third law, as the paddle pushes the water backwards, the water will push the paddle (and thus the boat with it) forwards
Suppose an object is accelerated by a force of 100 N. Suddenly a second force of 100 N in the opposite direction is exerted on the object, so that the forces cancel. The object a) is brought to rest rapidly b) decelerates gradually to rest c) continues at the velocity it had before the second force was applied d) is brought to rest and then accelerates in the direction of the opposite force
c) continues at the velocity it had before the second force was applied (would only go to rest if the net force was zero)
A person stands on a scale in an elevator His apparent weight will be the greatest when the elevator a) is standing still b) is moving upwards at constant velocity c) is accelerating upwards d) is moving downwards at constant velocity e) is accelerating downwards
c) is accelerating upwards
A space shuttle in orbit around the Earth carries its payload with its mechanical arm. Suddenly, the arm malfunctions and releases the payload. What will happen to the payload? a) it will fall straight down and hit the earth b) it will follow a curved path and eventually hit the earth c) it will remain in the same orbit with the shuttle d) it will drift into deep space
c) it will remain in the same orbit with the shuttle
When a skier skis down a hill, the normal force exerted on the skier by the hill is a) equal to the weight of the skier b) greater than the weight of the skier c) less than the weight of the skier
c) less than the weight of the skier Normal force is equal to the perpendicular component of the skier's weight, which is less than the weight in the case of a nonzero slope
A ping pong ball is shot into a circular tube that is lying flat (horizontal) on a tabletop. When the ping pong ball exits the tub, which path will it follow?
c) straight line path in same direction it traveled as it exited the tube
In the international space station which orbits earth, astronauts experience apparent weightlessness because a) the station is so far away from the center of the earth b) the station is kept in orbit by a centrifugal force that counteracts the earth's gravity c) the astronauts and the station are in free fall towards the center of the earth d) there is no gravity in space e) the station's high speed nullifies the effects of gravity
c) the astronauts and the station are in free fall towards the center of the earth
A penny is placed on turntable which is spinning clockwise. If the power to the turntable is turned off, which arrow best represents the direction of the acceleration of the penny at point P while the turntable is still spinning but slowing down?
d) (arrow pointing southeast)
A car drives at a steady speed around a perfectly circular track. a) the car's acceleration is zero b) the net force on the car is zero c) both the acceleration and net force on the car point outward d) both the acceleration and net force on the car point inward d) if there is no friction, the acceleration is outward
d) both the acceleration and net force on the car point inward
A bear sling is used in some national parks for placing backpackers' food out of the reach of bears. As the backpacker raises the pack by pulling down on the rope, the force F needed: a) decreases as the pack rises until the rope is straight across b) doesn't change c) increases until the rope is straight d) increases but the rope always sags where the pack hangs
d) increases but the rope always sags where the pack hangs
The moon does not crash into the earth because: a) the net force on it is zero b) it is beyond the main pull of the earth's gravity c) it is being pulled by the sun as well as by the earth d) it is freely falling but it has a high tangential velocity
d) it is free falling but has a high tangential velocity
You are pushing a heavy box across a rough floor. When you are initially pushing the box and it is accelerating, a) you exert a force on the box, but the box does not exert a force on you b) the box is so heavy it exerts a force on you, but you do not exert a force on the box c) the force you exert on the box is greater than the force of the box pushing back at you d) the force you exert on the box is equal to the force of the box pushing back at you e) the force that the box exerts on you is greater than the force you exert on the box
d) the force you exert on the box is equal to the force of the box pushing back at you
Matt, in the foreground of, is able to move the large truck because a) he is stronger than the truck b) he is heavier in some respects than the truck c) He exerts a greater force on the truck than the truck exerts back on him d) the ground exerts a greater friction force on Matt than it does on the truck e) the truck offers no resistance because its brakes are off
d) the ground exerts a greater friction force on Matt than it does on the truck
Which of the following point towards the center of the circle in uniform circular motion? a) acceleration b)velocity, acceleration, net force c) velocity, acceleration d) velocity, net force e) acceleration, net force
e) acceleration, net force (acceleration and net force are always in the same direction)
Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more? a) the earth on the moon; the earth b) the earth on the moon; the moon c) the moon on the earth; the earth d) the moon on the earth; the moon e) both the same; the earth f) both the same; the moon
f) both the same; the moon (Newton's third law: forces must be equal; moon is smaller so it accelerates more)
In what ways is the word "work" as used in everyday language the same as it is defined in physics? In what ways is it different? Give examples of both.
"Work" as used in everyday language generally means "energy expended," which is similar to the way "work" is defined in physics. However, in everyday language, "work" can involve mental or physical energy expended and is not necessarily connected with displacement, as it is in physics. So a student could say she "worked" hard carrying boxes up the stairs to her dorm room (similar in meaning to the physics usage), or that she "worked" hard on a problem set (different in meaning from the physics usage).
A golf ball and an equal-mass bean bag are dropped from the same height and hit the ground. The bean bag stays on the ground while the golf ball rebounds. Which experiences the greater impulse from the ground? (a) The golf ball. (b) The bean bag. (c) Both the same. (d) Not enough information.
(a) The golf ball.
A car maintains a constant speed v as it traverses the hill and valley shown in Fig. 5-34. Both the hill and valley have a radius of curvature R. At which point, A, B, or C, is the normal force acting on the car (a) the largest, (b) the smallest? Explain. (c) Where would the driver feel heaviest and (d) lightest? Explain. (e) How fast can the car go without losing contact with the road at A?
(a) The normal force on the car is largest at point C. In this case, the centripetal force keeping the car in a circular path of radius R is directed upward, so the normal force must be greater than the weight to provide this net upward force.(b) The normal force is smallest at point A, the crest of the hill. At this point the centripetal force must be directed downward (toward the center of the circle), so the normal force must be less than the weight. (Notice that the normal force is equal to the weight at point B.)(c) The driver will feel heaviest where the normal force is greatest, or at point C.(d) The driver will feel lightest at point A, where the normal force is the least.(e) At point A, the centripetal force is weight minus normal force, or mg- Fn = mv^2/r. The point at which the car just loses contact with the road corresponds to a normal force of zero, which is a maximum speed without losing contact. Setting Fn = o gives mg = mv^2/ R = v = sqrt Rg
You are lying in bed and want to shut your bedroom door. You have a bouncy "superball" and a blob of clay, both with the same mass. Which one would be more effective to throw at your door to close it? (a) The superball. (b) The blob of clay. (c) Both the same. (d) Neither will work.
(a) The superball.
An astronaut is a short distance away from her space station without a tether rope. She has a large wrench. What should she do with the wrench to move toward the space station? (a) Throw it directly away from the space station. (b) Throw it directly toward the space station. (c) Throw it toward the station without letting go of it. (d) Throw it parallel to the direction of the station's orbit. (e) Throw it opposite to the direction of the station's orbit.
(a) Throw it directly away from the space station.
The space shuttle, in circular orbit around the Earth, collides with a small asteroid which ends up in the shuttle's storage bay. For this collision, (a) only momentum is conserved. (b) only kinetic energy is conserved. (c) both momentum and kinetic energy are conserved. (d) neither momentum nor kinetic energy is conserved.
(a) only momentum is conserved.
Two balls are thrown off a building with the same speed, one straight up and one at a 45° angle. Which statement is true if air resistance can be ignored? (a) Both hit the ground at the same time. (b) Both hit the ground with the same speed. (c) The one thrown at an angle hits the ground with a lower speed. (d) The one thrown at an angle hits the ground with a higher speed. (e) Both (a) and (b).
(b) Both hit the ground with the same speed.
A small boat coasts at constant speed under a bridge. A heavy sack of sand is dropped from the bridge onto the boat. The speed of the boat (a) increases. (b) decreases. (c) does not change. (d) Without knowing the mass of the boat and the sand, we can't tell
(b) decreases.
You push very hard on a heavy desk, trying to move it. You do work on the desk: (a) whether or not it moves, as long as you are exerting a force. (b) only if it starts moving. (c) only if it doesn't move. (d) never—it does work on you. (e) None of the above.
(b) only if it starts moving.
When the speed of your car is doubled, by what factor does its kinetic energy increase? (a). sqrt 2 (b) 2. (c) 4. (d) 8.
(c) 4.
Two identical billiard balls traveling at the same speed have a head-on collision and rebound. If the balls had twice the mass, but maintained the same size and speed, how would the rebound be different? (a) At a higher speed. (b) At slower speed. (c) No difference.
(c) No difference.
A bowling ball is dropped from a height h onto the center of a trampoline, which launches the ball back up into the air. How high will the ball rise? (a) Significantly less than h. (b) More than h. The exact amount depends on the mass of the ball and the springiness of the trampoline. (c) No more than h—probably a little less. (d) Cannot tell without knowing the characteristics of the trampoline
(c) No more than h—probably a little less.
A satellite in circular orbit around the Earth moves at constant speed. This orbit is maintained by the force of gravity between the Earth and the satellite, yet no work is done on the satellite. How is this possible? (a) No work is done if there is no contact between objects. (b) No work is done because there is no gravity in space. (c) No work is done if the direction of motion is perpendicular to the force. (d) No work is done if objects move in a circle.
(c) No work is done if the direction of motion is perpendicular to the force.
A bowling ball hangs from a 1.0-m-long cord, Fig. 7-30: (i) A 200-gram putty ball moving hits the bowling ball and sticks to it, causing the bowling ball to swing up; (ii) a 200-gram rubber ball moving hits the bowling ball and bounces straight back at nearly causing the bowling ball to swing up. Describe what happens. (a) The bowling ball swings up by the same amount in both (i) and (ii). (b) The ball swings up farther in (i) than in (ii). (c) The ball swings up farther in (ii) than in (i). (d) Not enough information is given; we need the contact time between the rubber ball and the bowling ball.
(c) The ball swings up farther in (ii) than in (i).
A baseball is pitched horizontally toward home plate with a velocity of 110 km h. In which of the following scenarios does the baseball have the largest change in momentum? (a) The catcher catches the ball. (b) The ball is popped straight up at a speed of 110 km h. (c) The baseball is hit straight back to the pitcher at a speed of 110 km h. (d) Scenarios (a) and (b) have the same change in momentum. (e) Scenarios (a), (b), and (c) have the same change in momentum.
(c) The baseball is hit straight back to the pitcher at a speed of 110 km h.
A railroad tank car contains milk and rolls at a constant speed along a level track. The milk begins to leak out the bottom. The car then (a) slows down. (b) speeds up. (c) maintains a constant speed. (d) Need more information about the rate of the leak
(c) maintains a constant speed.
A car traveling at a velocity v can stop in a minimum distance d. What would be the car's minimum stopping distance if it were traveling at a velocity of 2v? (a) d. (b)sqrt 2 d (c) 2d. (d) 4d. (e) 8d.
(d) 4d.
Two children float motionlessly in a space station. The 20-kg girl pushes on the 40-kg boy and he sails away at 1.0 m/s. The girl (a) remains motionless; (b) moves in the same direction at 1.0 m/s (c) moves in the opposite direction at 1.0 m/s (d) moves in the opposite direction at 2.0 m/s (e) none of these.
(d) The girl moves in the opposite direction at 2.0 m/s. Since there are no external forces on the pair, momentum is conserved. The initial momentum of the system (boy and girl) is zero. The final momentum of the girl must be the same in magnitude and opposite in direction to the final momentum of the boy so that the net final momentum is also zero.
Engines, including car engines, are rated in horsepower. What is horsepower? (a) The force needed to start the engine. (b) The force needed to keep the engine running at a steady rate. (c) The energy the engine needs to obtain from gasoline or some other source. (d) The rate at which the engine can do work. (e) The amount of work the engine can perform.
(d) The rate at which the engine can do work.
A truck going has a head-on collision with a small car going Which statement best describes the situation? (a) The truck has the greater change of momentum because it has the greater mass. (b) The car has the greater change of momentum because it has the greater speed. (c) Neither the car nor the truck changes its momentum in the collision because momentum is conserved. (d) They both have the same change in magnitude of momentum because momentum is conserved. (e) None of the above is necessarily true.
(d) They both have the same change in magnitude of momentum because momentum is conserved.
A small car and a heavy pickup truck are both out of gas. The truck has twice the mass of the car. After you push both the car and the truck for the same amount of time with the same force, what can you say about the momentum and kinetic energy (KE) of the car and the truck? Ignore friction. (a) They have the same momentum and the same KE. (b) The car has more momentum and more KE than the truck. (c) The truck has more momentum and more KE than the car. (d) They have the same momentum, but the car has more kinetic energy than the truck. (e) They have the same kinetic energy, but the truck has more momentum than the car.
(d) They have the same momentum, but the car has more kinetic energy than the truck.
A ball is thrown straight up. At what point does the ball have the most energy? Ignore air resistance. (a) At the highest point of its path. (b) When it is first thrown. (c) Just before it hits the ground. (d) When the ball is halfway to the highest point of its path. (e) Everywhere; the energy of the ball is the same at all of these points.
(e) Everywhere; the energy of the ball is the same at all of these points.
A small car and a heavy pickup truck are both out of gas. The truck has twice the mass of the car. After you push both the car and the truck for the same amount of time with the same force, what can you say about the momentum and kinetic energy (KE) of the car and the truck? Ignore friction. (a) They have the same momentum and the same KE. (b) The car has more momentum and more KE than the truck. (c) The truck has more momentum and more KE than the car. (d) They have the same momentum, but the car has more kinetic energy than the truck. (e) They have the same kinetic energy, but the truck has more momentum than the car. Choose the best answer in the previous Question (# 9) but now assume that you push both the car and the truck for the same distance with the same force. [Hint: See also Chapter 6.]
(e) They have the same kinetic energy, but the truck has more momentum than the car.
A skier starts from rest at the top of each of the hills shown in Fig. 6-34. On which hill will the skier have the highest speed at the bottom if we ignore friction: (a), (b), (c), (d), or (e) c and d equally?
(e) c and d equally?(c has steepest slope and d has longest hill)
When a golf ball is dropped to the pavement, it bounces back up. a) is a force needed to make it bounce back up? b) if so, what exerts the force?
A) a force is needed to bounce the ball back up, because the ball changes direction, so the ball accelerates. If the ball is accelerating then there must be a force b) The pavement exerts force on the golf ball
Explain, on the basis of conservation of momentum, how a fish propels itself forward by swishing its tail back and forth
As the fish swishes its tail back and forth, it moves some water backward, away from the fish. If we consider the system to be the fish and the water, then, from conservation of momentum, the fish must move forward.
If you walk along a log floating on a lake, why does the log move in the opposite direction?
As you take a step on the log, your foot exerts a force on the log in the direction opposite to the direction in which you want to move, causing the log to be pushed backwards. If the log was on the ground, friction between the ground and the log would have prevented the log from moving, but because the log is on water, a frictionless surface, there is little resistance to the movement of the log to prevent it from moving backwards.
What would your bathroom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle.
Assume your weight is W. If you weighed yourself on an inclined plane that is inclined at angle x, then the bathroom scale would read the magnitude of the normal force between you and the plane, which would be Wcosx.
A bucket of water can be whirled in a vertical circle without the water spilling out even at the top of the circle when the bucket is upside down. Explain.
At the top of the bucket's arc, the gravitational force and normal forces from the bucket, both pointing downward, must provide the centripetal force needed to keep the water moving in a circle. In the limiting case of no normal force, Newton's second law would give Fnet = mg = m v^2/r which means that the bucket must be moving with a tangential speed of v > sqrt gr or the water will spill out of the bucket. At the top of the arc, the water has a horizontal velocity. As the bucket passes the top of the arc, the velocity of the water develops a vertical component. But the bucket is traveling with the water, with the same velocity, and contains the water as it falls through the rest of its path.
Analyze the motion of a simple swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock has to be wound up.
At the top of the pendulum's swing, all of its energy is gravitational potential energy; at the bottom of the swing, all of the energy is kinetic.(a) If we can ignore friction, then energy is transformed back and forth between potential energy and kinetic energy as the pendulum swings.(b) If friction is present, then during each swing energy is lost to friction at the pivot point and also to air resistance. During each swing, the kinetic energy and the potential energy decrease, and the pendulum's amplitude decreases. When a grandfather clock is "wound up," the amount of energy that will eventually be lost to friction and air resistance is stored as potential energy (either elastic or gravitational, depending on the clock mechanism), and part of the workings of the clock is to put that stored energy back into the pendulum at the same rate that friction is dissipating the energy.
Compare the effort (or force) needed to lift a 10kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2kg object horizontally with a given speed on the Moon and on Earth.
Because the acceleration due to gravity on the moon is less than it is on earth, an object with a mass of 10kg will weigh less on the moon than it does on earth. Therefore, it will be easier to lift on the Moon. (When you lift something, you exert a force to oppose its weight)/ However, when throwing the object horizontally, the force needed to accelerate it to the desired horizontal speed is proportional to the object's mass, F = ma. Therefore, you would need to exert the same force to throw the 2kg object with a given speed on the moon as you would on earth.
A father and his young daughter are ice skating. They face each other at rest and push each other, moving in opposite directions. Which one has the greater final speed?
Both the father and daughter will have the same magnitude force acting on them as they push each other away, by considering Newton's third law. If we assume that the young daughter has less mass than the father, her acceleration will be greater (a = F/m). Both forces, and therefore both accelerations, act over the same time interval (while the father and daughter are in contact), so the daughter's final speed will be greater than her father's.
When a person jumps from a tree to the ground, what happens to the momentum of the person upon striking the ground?
Consider this problem as a very light object hitting and sticking to a very heavy object. The large object-small object combination (earth + jumper) would have some momentum after the collision, but due to the very large mass of the Earth, the velocity of the combination is so small that it is not measurable. Thus the jumper lands on the Earth, and nothing more happens.
The mass of the "planet" Pluto was not known until it was discovered to have a moon. Explain how this enabled an estimate of Pluto's mass.
For Pluto's moon, we can equate the gravitational force from Pluto on the moon to the centripetal force needed to keep the moon in orbit: m = v^2r/G = 4pi^2r^2/GT^2. This allows us to solve for the mass of Pluto if we know G, the radius of the moon's orbit, and the velocity of the moon, which can be determined from the period T and orbital radius. Note that the mass of the moon cancels out.
In Fig. 6-31, water balloons are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed when it hits the ground? Ignore air resistance. Explain your answer.
For each of the balloons, the initial energy (kinetic plus potential) equals the final energy (all kinetic). Since the initial energy depends on only the speed and not on the direction of the initial velocity, and all balloons have the same initial speed and height, the final speeds are all the same.
We claim that momentum is conserved. Yet most moving objects eventually slow down and stop. Explain.
For momentum to be conserved, the system under analysis must be "closed"—not have any forces on it from outside the system. A coasting car has air friction and road friction on it, for example, which are "outside" or "external" forces and thus reduce the momentum of the car. If the ground and the air were considered part of the system and their velocities analyzed, then the momentum of the entire system would be conserved, but not necessarily the momentum of any single component, like the car.
Astronauts who spend long periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5-33). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.
For objects (including astronauts) on the inner surface of the cylinder, the normal force provides a centripetal force, which points inward toward the center of the cylinder. This normal force simulates the normal force we feel when on the surface of Earth.(a) Falling objects are not in contact with the floor, so when released they will continue to move with constant velocity until they reach the shell. From the frame of reference of the astronaut inside the cylinder, it will appear that the object "falls" in a curve, rather than straight down.(b) The magnitude of the normal force on the astronaut's feet will depend on the radius and speed of the cylinder. If these are such that (so that for all objects), then the normal force will feel just like it does on the surface of Earth.(c) Because of the large size of Earth compared to humans, we cannot tell any difference between the gravitational force at our heads and at our feet. In a rotating space colony, the difference in the simulated gravity at different distances from the axis of rotation could be significant, perhaps producing dizziness or other adverse effects. Also, playing "catch" with a ball could be difficult since the normal parabolic paths as experienced on Earth would not occur in the rotating cylinder.
It is said that in ancient times a rich man with a bag of gold coins was stranded on the surface of a frozen lake. Because the ice was frictionless, he could not push himself to shore and froze to death. What could he have done to save himself had he not been so miserly?
He could have thrown the coins in the direction opposite the shore he was trying to reach. Since the lake is frictionless, momentum would be conserved and he would "recoil" from the throw with a momentum equal in magnitude and opposite in direction to the coins. Since his mass is greater than the mass of the coins, his speed would be less than the speed of the coins, but, since there is no friction, he would maintain this small speed until he hit the shore.
Only one force acts on an object. Can the object have zero acceleration. Can it have zero velocity? Explain.
If only one force acts on an object, the net force cannot be zero, so the object cannot have zero acceleration, by Newton's second law. It is possible for the object to have zero velocity, but only for an instant. Ex: A ball thrown only has the force of gravity acting on it, but when it reaches its highest point, its velocity is zero.
The source of the Mississippi River is closer to the center of the Earth than is its outlet in Louisiana (because the Earth is fatter at the equator than at the poles). Explain how the Mississippi can flow "uphill."
If the Earth were a perfect, nonrotating sphere, then the gravitational force on each droplet of water in the Mississippi would be the same at the headwaters and at the outlet, and the river wouldn't flow. Since the Earth is rotating, the droplets of water experience a centripetal force provided by a part of the component of the gravitational force perpendicular to the Earth's axis of rotation. The centripetal force is smaller for the headwaters, which are closer to the North Pole, than for the outlet, which is closer to the equator. Since the centripetal force is equal to mg - N (apparent weight) for each droplet, N is smaller at the outlet, and the river will flow. This effect is large enough to overcome smaller effects on the flow of water due to the bulge of the Earth near the equator.
If the acceleration of an object is zero, are no forces acting on it? Explain.
If the acceleration of an object is zero, the vector sum of the forces acting on the object is zero, so there can be forces on an object that has no acceleration (forces of same magnitude but opposite direction are present but will result in a net force or zero). Ex: a book resting on a table is acted on by normal force and gravity, but has zero acceleration.
An antenna loosens and becomes detached from a satellite in a circular orbit around the Earth. Describe the antenna's subsequent motion. If it will land on the Earth, describe where; if not, describe how it could be made to land on the Earth.
If the antenna becomes detached from a satellite in orbit, the antenna will continue in orbit around the Earth with the satellite. If the antenna were given a component of velocity toward the Earth (even a very small one), it would eventually spiral in and hit the Earth. If the antenna were somehow slowed down, it would also fall toward the Earth.
When you stand still on the ground, how large a force does the ground exert on you? Why doesn't this force make you rise up into the air?
If you are at rest, the net force on you is zero. Hence the ground exerts a force on you exact equal to your weight. The two forces acting on you sum to zero, so you don't accelerate. If you squat down and then push with a larger force against the ground, the ground then pushes back on you with a larger force by Newton's third law, and you can then rise into the air
According to Newton's third law, each team in a tug of war pulls with equal force on the other team, What then, determines which team will win?
In a tug of war, the team that pushes hardest against the ground wins. It is true that both teams have the same force on them due to the tension in the rope. But the winning team pushes harder against the ground and thus the ground pushes harder on the winning team, making a net unbalanced force.
Why is the stopping distance of a truck much shorter than for a train going the same speed?
In a very simple analysis, the net force slowing the moving object is friction. If we consider that the moving object is on a level surface, then the normal force is equal to the weight. Combining these ideas, we get the following: Fnet = ma = umg -> a = ug The coefficient of friction of the train (steel on steel) is smaller than the coefficient of friction of the truck (rubber on dry concrete). Thus the acceleration of the train will be smaller than that of the truck and therefore, the truck's stopping distance will be smaller.
A boy stands on the back of a rowboat and dives into the water. What happens to the boat as he leaves it? Explain.
In order to conserve momentum, when the boy dives off the back of the rowboat the boat will move forward.
Will the acceleration of a car be the same when a car travels around a sharp curve at a constant 60km/h as when it travels around a gentle curve at the same speed?
No the acceleration will not be the same. The centripetal acceleration is inversely proportional to the radius a = v^2/r. Traveling around a sharp curve, with a smaller radius, will require a large centripetal acceleration than traveling a gentle curve, with a larger radius
Can a centripetal force ever do work on an object? Explain.
No, not if the object is moving in a circle. Work is the product of force and the displacement in the direction of the force. Therefore, a centripetal force, which is perpendicular to the direction of motion, cannot do work on an object moving in a circle.
Sometimes it is said that water is removed from clothes in the spin dryer by centrifugal force throwing the water outward. Is this correct?
No. The barrel of the dryer provides a centripetal force on the clothes to keep them moving in a circular path. A water droplet on the solid surface of the drum will also experience this centripetal force and move in a circle. However, as soon as the water droplet is at the location of a hole in the drum there will be no centripetal force on it and it will therefore continue moving in a path i n the direction of the tangential velocity, which will take it out of the drum. There is no centrifugal force throwing the water outside; there is rather a lack of centripetal force to keep the water moving in a circular path.
child on a sled comes flying over the crest of a small hill, as shown in Fig. 5-32. His sled does not leave the ground, but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton's second law.
On level ground, the normal force on the child would be the same magnitude as his weight. This is a typical situation, but as the child and sled come over the crest of the hill, they are moving on a curved path, which can at least be approximated by a circle. There must be a centripetal force., pointing inward towards the center of the arc. The combination of gravity and the normal force n the body provides this centripetal force, which must be greater than zero. At the top of the hill, if downward is the positive direction, Newton's second law says F = mg - Fn = m v^2/r. Thus the normal force must be less than the child's weight.
A block is given a brief push so that it slides up a ramp. After the block reaches its highest point, it slides back down, but the magnitude of its acceleration is less on the descent than on the ascent. Why?
On the way up, there are two forces on the block that are parallel to each other causing the deceleration - the component of weight parallel to the plane and the force of friction on the block. Since the forces are parallel to each other, both pointing down the plane, they add, causing a larger magnitude force and a larger acceleration. On the way down, those same two forces are opposite of each other, because the force of friction is now directed up the plane. With these two forces being opposite of each other, the new force is smaller, so the acceleration is smaller.
A girl is whirling a ball on a string around her hand in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?
She should let go of the string at the moment that the tangential velocity vector is directed exactly at the target. This would be when the string is perpendicular to the desired direction of motion of the ball.
Why is more fuel required for a spacecraft to travel from the Earth to the Moon than to return from the Moon to the Earth?
Since the Earth's mass is much greater than the Moon's mass, the point at which the net gravitational pull on the spaceship is zero is closer to the Moon. It is shown in Problem 30 that this occurs at about 90% of the way from the Earth to the Moon. So, a spaceship traveling from the Earth toward the Moon must therefore use fuel to overcome the net pull backward for 90% of the trip. Once it passes that point, the Moon will exert a stronger pull than the Earth and accelerate the spacecraft toward the Moon. However, when the spaceship is returning to the Earth, it reaches the zero point at only 10% of the way from the Moon to the Earth. Therefore, for most of the trip toward the Earth, the spacecraft is "helped" by the net gravitational pull in the direction of travel, so less fuel is used.
A heavy crate rests on the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?
Static friction between the crate and the truck bed causes the crate to accelerate
The Earth moves faster in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons—the main factor is the tilt of the Earth's axis relative to the plane of its orbit.]
The Earth is closer to the Sun in January. See Fig. 5-29 and the accompanying discussion about Kepler's second law. The caption in the textbook says: "Planets move fastest when closest to the Sun." So in the (greatly exaggerated) figure, the time between points 1 and 2 would be during January, and the time between points 3 and 4 would be July.
The force of gravity on a 2kg rock is twice as great as that on a 1kg rock. Why then doesn't the heavier rock fall faster?
The acceleration of both rocks is found by dividing their weight (the force of gravity on them) by their mass. The 2kg rock has a force of gravity on it that is twice as great as the force of gravity on the 1kg rock, but also twice as great a mass on the 1kg rock, so the acceleration is the same for both.
According to Eq. 7-4, the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.
The air bag greatly increases the amount of time over which the stopping force acts on the driver. If a hard object like a steering wheel or windshield is what stops the driver, then a large force is exerted over a very short time. If a soft object like an air bag stops the driver, then a much smaller force is exerted over a much longer time. For instance, if the air bag is able to increase the time of stopping by a factor of 10, then the average force on the person will be decreased by a factor of 10. This greatly reduces the possibility of serious injury or death.
Is the centripetal acceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth? Explain.
The centripetal acceleration of Mars in its orbit around the Sun is smaller than that of the Earth. For both planets, the centripetal force is provided by gravity, so the centripetal acceleration is inversely proportional to the square of the distance from the planet to the Sun: a = v^s/r = Gm/r^2. Since Mars is at a greater distance from the Sun than is Earth, it has a smaller centripetal acceleration. Note that the mass of the planet does not appear in the equation for the centripetal acceleration.
What happens to the gravitational potential energy when water at the top of a waterfall falls to the pool below?
The initial potential energy of the water is converted first into the kinetic energy of the water as it falls. When the falling water hits the pool, it does work on the water already in the pool, creating splashes and waves. Additionally, some energy is converted into heat and sound.
If the speed of a particle triples, by what factor does its kinetic energy increase?
The kinetic energy increases by a factor of 9, since the kinetic energy is proportional to the square of the speed.
A light object and a heavy object have the same kinetic energy. Which has the greater momentum? Explain.
The momentum of an object can be expressed in terms of its kinetic energy, as follows: p = mv = sqrt m^2v^2 = sqrt 2m(1/2 mv^2) = sqrt 2mKE. Thus if two objects have the same kinetic energy, then the one with more mass has the greater momentum.
Would it require less speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth's rotation direction and explain your choice.
The satellite needs a certain speed with respect to the center of the Earth to achieve orbit. The Earth rotates toward the east so it would require less speed (with respect to the Earth's surface) to launch a satellite (a) toward the east. Before launch, the satellite is moving with the surface of the Earth so already has a "boost" in the right direction.
People sometimes ask, "What keeps a satellite up in its orbit around the Earth?" How would you respond?
The satellite remains in orbit because it has a velocity. The instantaneous velocity of the satellite is tangent to the orbit. The gravitational force provides the centripetal force needed to keep the satellite in orbit, acting like the tension in a string when twirling a rock on a string. A force is not needed to keep the satellite "up"; a force is needed to bend the velocity vector around in a circle. The satellite can't just have any speed at any radius, though. For a perfectly circular orbit, the speed is determined by the orbit radius, or vice versa, through the relationship v = sqrt rg, where r is the radius of the orbit and g is the acceleration due to gravity at the orbit position.
A hand exerts a constant horizontal force on a block that is free to slide on a frictionless surface (Fig. 6-30). The block starts from rest at point A, and by the time it has traveled a distance d to point B it is traveling with speed When the block has traveled another distance d to point C, will its speed be greater than, less than, or equal to Explain your reasoning
The speed at point C will be less than twice the speed at point B. The force is constant and the displacements are the same, so the same work is done on the block from A to B as from B to C. Since there is no friction, the same work results in the same change in kinetic energy. But kinetic energy depends on the square of the speed, so the speed at point C will be greater than the speed at point B by a factor of sqrt 2, not a factor of 2.
How many "accelerators" do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleration do they produce?
The three main "accelerators" are the accelerator pedal, the brake pedal, and the steering wheel. The accelerator pedal can be used to increase speed (depress pedal) or to decrease speed in combination with friction (release pedal). The brake pedal can be used to decrease pedal by depressing it. The steering wheel is used to change directions which also is an acceleration.
Describe all the forces acting on a child riding a horse on a merry-go-round. Which of these forces provides a centripetal acceleration of the child?
The three main forces on the child are the downward force of gravity (child's weight), the normal force up on the child from the horse, and the static frictional force on the child from the surface of the horse. The frictional force provides centripetal acceleration. If there are other forces, such as contact horses between the child's hands or legs to the horse, which has a radial component, then that will also contribute to the centripetal acceleration
You lift a heavy book from a table to a high shelf. List the forces on the book during this process, and state whether each is conservative or nonconservative.
The two forces on the book are the applied force upward (nonconservative) and the downward force of gravity (conservative). If air resistance is not negligible, it is nonconservative.
Whiplash sometimes results from an automobile accident when the victim's car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?
The victim's head is not really thrown backward during the car crash. If the victim's car was initially at rest, or even moving forward, the impact from the rear suddenly pushes the car, the seat, and the person's body forward. The heat, being attached by the somewhat flexible neck to the body, can momentarily remain where it was, thus lagging behind the body. The neck muscles must eventually pull the head forward, and that causes the whiplash. To avoid this, use the car's headrests.
Why do airplanes bank when they turn? How would you compute the banking angle given the airspeed and radius of the turn? [Hint: Assume an aerodynamic "lift" force acts perpendicular to the wings. See also Example 5-7.
When an airplane is in level flight, the downward force of gravity is counteracted by the upward lift force, analogous to the upward normal force on a car driving on a level road. The lift on an airplane is perpendicular to the plane of the airplane's wings, so when the airplane banks, the lift vector has both vertical and horizontal components (similar to the vertical and horizontal components of the normal force on a car on a banked turn). Assuming that the plane has no vertical acceleration, then the vertical component of the lift balances the weight and the horizontal component of the lift provides the centripetal force
A heavy ball is hung from the ceiling by a steel wire. The instructor pulls the ball back and stands against the wall with the ball against his chin. To avoid injury the instructor is supposed to release the ball without pushing it (Fig. 6-33). Why?
When the ball is released, its potential energy will be converted into kinetic energy and then back into potential energy as the ball swings. If the ball is not pushed, it will lose a little energy to friction and air resistance. It will return almost to the initial position but will not hit the instructor. If the ball is pushed, it will have an initial kinetic energy, and will, when it returns, still have some kinetic energy when it reaches the initial position, so it will hit the instructor on the chin. (Ouch!)
A stone hangs by a fine thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4-36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.
When you give a sharp pull, the suddenness of the application of the force is key. When a large sudden force is applied to the bottom string, the bottom string will have a large amount of tension in it. Because of the stone's inertia, the upper string does not immediately experience the large force. The bottom string must have more tension in it and will break first. If a slow and steady pull is applied, the tension in the bottom string increases. Because the upper string has the weight of the stone on it, it will have a larger tension than the bottom string, and therefore break first.
Why does a child in a wagon seem to fall backwards when you give the wagon a sharp pull forward?
When you give the wagon a sharp pull forward, the force of friction between the wagon and the child acts on the child to move her forward. But the force of friction acts as a contact point between the child and the wagon - we assume the child is sitting in the wagon The lower part of the child begins to move forward, while the upper part, following Newton's law (law of inertia) remains almost stationary, making it seem as if the child falls backwards. The backwards motion is relative to the wagon, not the ground.
When you release an inflated but untied balloon, why does it fly across the room?
When you release an inflated but untied balloon at rest, the gas inside the balloon (at high pressure) rushes out the open end of the balloon. That escaping gas and the balloon form a closed system, so the momentum of the system is conserved. The balloon and remaining gas acquire a momentum equal and opposite to the momentum of the escaping gas, so they move in the opposite direction to the escaping gas
Does an apple exert a gravitational force on the Earth? If so, how large a force? Consider an apple (a) attached to a tree and (b) falling.
Whether the apple is (a) attached to a tree or (b) falling, it exerts a gravitational force on the Earth equal to the force the Earth exerts on it, which is the weight of the apple (Newton's third law). That force is independent of the motion of the apple.
When an object falls freely under the influence of gravity there is a net force mg exerted on it by the earth. Yet by Newton's third law the object exerts an equal and opposite force on the earth. Does the earth move? Explain.
Find acceleration: F(earth) = F(object) -> Ma(earth) = mg -> a(earth) = mg/M. Since earth has a mass with order of 10^25 kg the acceleration of the earth must be in the order of 10^-25 g, which is too small of an acceleration to be detectable.
