Advanced Physics Gimmell Final Exam- Semester One
A force F acts on mass M1 giving acceleration A1. The same force acts on a different mass M2 giving A2=2A1. If M1 and M2 are glued together and the same force F acts on this combination, what is the resulting acceleration. A) (3/4)A1 B) (3/2)A1 C) (1/2)A1 D) (4/3)A1 E) (2/3)A1
(2/3)A1: Mass M2 must be (1/2M1) because its acceleration was 2A1 with the same force. Adding the two masses together gives (3/2)M1, leading to an acceleration of (2/3)A1 for the same applied force
A cart starting from rest rolls down a frictionless 1.0 m high hill. It travels a distance 2.0 m along the rough bottom surface until it comes to rest. What is the coefficient of kinetic friction along the bottom surface? a) 0.25 b) 0.5 c) 1.0 d) 2.0
0.5
A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannonball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? a) 0 m/s b) 0.5 m/s to the right c) 1 m/s to the right d) 20 m/s to the right e) 50 m/s to the right
0.5m/s TO THE RIGHT
A force F acts on mass M for a time interval T, giving it a final speed v. If the same force acted for the same time on a different mass 2M, what would be the final speed of the bigger mass? a) 4v b) 2v c) v d) ½v e) ¼v
1/2v: In the first case, the acceleration acts over time T to give velocity v = aT. In the second case, the mass is doubled, so the acceleration is cut in half; therefore, in the same time T, the final speed will only be half as much
Two blocks of masses 2m and m are in contact on a horizontal frictionless surface. If a force F is applied to mass 2m, what is the force on mass m? a) 2F b) F c) 1/2F d) 1/3F e) 1/4F
1/3F: The force F leads to a specific acceleration of the entire system. In order for mass m to accelerate at the same rate, the force on it must be smaller by a factor of 3, as the mass is 1/3 of the total.
A block travels on a frictionless surface towards a spring of force constant k at a speed v. The spring is compressed a distance d before the block comes to rest. How much would a spring of force constant 9k be compressed if the block were traveling at the same speed v? a) 9d b) 1/3d c) 3d d) 1/9d
1/3d: If the force constant is increased by a factor of 9, to have the same work done on it (since W= ½kx^2), the compression distance must decrease by a factor of 3, giving a compression of 1/3d.
You tie a rope to a tree and pull on the rope with a force of 100 N. What is the tension in the rope? a) 0 N b) 50 N c) 100 N d) 150 N e) 200 N
100N: The tension in the rope is the force that the rope "feels" across any section of it (or that you would feel if you replaced a piece of the rope). Because you are pulling with a force of 100 N, that is the tension in the rope.
Two tug-of-war opponents each pull with a force of 100 N on opposite ends of a rope. What is the tension in the rope? a) 0 N b) 50 N c) 100 N d) 150 N e) 200 N
100N: This situation is the same as the previous question. The tension is not 200 N! Whether the other end of the rope is pulled by a person, or pulled by a tree, the tension in the rope is still 100 N!
You throw a ball upward with an initial speed of 10 m/s. Assuming that there is no air resistance, what is its speed when it returns to you? a) More than 10 m/s b) 10 m/s c) Less than 10 m/s d) Zero e) Need more information
10m/s: The ball is slowing down on the way up due to gravity. Eventually, it stops. Then it accelerates downward due to gravity (again). Because a = g on the way up and on the way down, the ball reaches the same speed when it gets back to you as it had when it left.
Two vectors A and B are at right angles to each other. The magnitude of A is 12 units, and the magnitude of B is 5 units. What is the magnitude of vector A minus vector B? a) 1 b) 7 c) 5 d) 13 e) 17
13: If vector B is at a right angle to vector A, then subtracting it from A will give a vector with the same magnitude as the sum though in a different direction
Two vectors A and B are at right angles to each other. The magnitude of A is 12 units, and the magnitude of B is 5 units. What is the magnitude of vector A plus vector B? a) 1 b) 7 c) 5 d) 13 e) 17
13: Two vectors at right angles have a magnitude that adds using the Pythagorean theorem. So, the magnitude of the sum is the sum of the square root of the sum of the two, which is 13.
Amy (150 lbs) and Gwen (50 lbs) are standing on slippery ice and push off each other. If Amy slides at 6 m/s, what speed does Gwen have? a) 2 m/s b) 6 m/s c) 9 m/s d) 12 m/s e) 18 m/s
18m/s: The initial momentum is zero, so the momenta of Amy and Gwen must be equal and opposite. Because p = mv, then if Amy has three times more mass, we see that Gwen must have three times more speed.
A small bug moves counterclockwise around the perimeter of a 30.0 cm diameter clock. The bug starts at 6 o'clock and moves to 3 o'clock in 10.0 seconds. What is the magnitude and direction of Vav for the bug's motion? a) 4.24 cm/s, +45º b) 4.24 cm/s, −45º c) 2.12 cm/s, −45º d) 2.12 cm/s, +45º e) 2.60 cm/s, +45º
2.12 cm/s, +45º
From rest, you step on the gas of your Ferrari, providing a force F for 4 seconds. During this time, the car moves 50 m. If the same force were applied for 8 secs, how much would the car have traveled during this time? a) 250 m b) 200 m c) 150 m d) 100 m e) 50 m
200m: In the first case, the acceleration acts over time T = 4 s to give a distance of x = -aT 2 (why is there no v the time is doubled, so the distance is quadrupled because it goes as the square of the time.
You step on the brakes of your Ferrari, providing a force F for 4 seconds. During this time, the car moves 25 m but does not stop. If the same force were applied for 8 seconds, how far would the car travel during this time? a) 100 m b) 50 m < x < 100 m c) 50 m d) 25 m < x < 50 m e) 25 m
25m<x<50m: In the first 4 seconds, the car has still moved 25 m. However, because the car is slowing down, in the next 4 seconds it must cover less distance. Therefore, the total distance must be more than 25 m but less than 50 m.
A golfer making a putt gives the ball an initial velocity of Vo, but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole? A) 2Vo B)3Vo C) 4Vo D) 8Vo E) 16Vo
2Vo: In traveling four times the distance, the resistive force will do four times the work. Thus, the ball's initial KE must be four times greater in order to just reach the hole—this requires an increase in the initial speed by a factor of 2, because KE = ½mv^2.
A block travels on a frictionless surface toward a spring at a speed v. The spring is compressed a distance d before the block comes to rest. How much would the same spring compress if the block was traveling at twice the speed 2v? a) 4d b) 2d c) d
2d: In traveling at twice the speed, the KE = ½mv^2 of the block has increased by a factor of 4 so to reduce it to zero the spring has to do W= -½kx^2 of 4 times as much which for the same spring means a compression of 2d.
A car starts from rest and accelerates to 30 mph. Later, it gets on a highway and accelerates to 60 mph. Which takes more energy, the 0 → 30 mph, or the 30 → 60 mph? a) 0 → 30 mph b) 30 → 60 mph c) Both the same
30 →60 mph: The change in KE (½mv^2 ) involves the velocity squared. So in the first case, we have: ½m (302 − 02) = ½m (900) In the second case, we have: ½m (602 − 302) = ½m (2700) Thus, the bigger energy change occurs in the second case.
You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? a) 0 b) 18 c) 37 d) 64 e) 100
37: The minimum resultant occurs when the vectors are opposite, giving 20 units. The maximum resultant occurs when the vectors are aligned, giving 60 units. Anything in between is also possible for angles between 0º and 180º.
You carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M), and drop these from some height h. What is the velocity of the smaller ball after the basketball hits the ground, reverses direction, and then collides with the small rubber ball? a) Zero b)v c)2v d)3v e)4v
3v: Remember that relative velocity has to be equal before and after collision! Before the collision, the basketball bounces up with v and the rubber ball is coming down with v, so their relative velocity is -2v. Therefore, after the collision, it must be +2v!
A spring-loaded gun can launch projectiles at different angles with the same launch speed. At what angle should the projectile be launched in order to travel the greatest distance before landing? a) 15º b) 30º c) 45º d) 60º e) 75º
45º: A steeper angle lets the projectile stay in the air longer, but it does not travel so far because it has a small x-component of velocity. On the other hand, a shallow angle gives a large x-velocity, but the projectile is not in the air for very long. The compromise comes at 45º, although this result is best seen in a calculation of the "range formula" as shown in the textbook.
A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector in a standard x-y coordinate system? a) 30º b) 180º c) 90º d) 60º e) 45º
45˚: The angle of the vector is given by tan θ = y/x. Thus, tan θ = 1 in this case if x and y are equal, which means that the angle must be 45º.
A box slides with initial velocity 10 m/s on a frictionless surface and collides inelastically with an identical box. The boxes stick together after the collision. What is the final velocity? a) 10 m/s b) 20 m/s c) 0 m/s d) 15 m/s e) 5 m/s
5m/s
A cart starting from rest rolls down a hill and has a speed of 4 m/s at the bottom . If the cart were given an initial push, so its initial speed at the top of the hill was 3 m/s, what would be its speed at the bottom? a) 4 m/s b) 5 m/s c) 6 m/s d) 7 m/s e) 25 m/s
5m/s
From rest, you step on the gas of your Ferrari, providing a force F for 40 m, speeding it up to a final speed of 50 km/hr. If the same force were applied for 80 m, what final speed would the car reach? a) 200 km/hr b) 100 km/hr c) 90 km/hr d) 70 km/hr e) 50 km/hr
70 km/hr: In the first case, the acceleration acts over a distance x = 40 m, to give a final speed of v2 = 2ax (why is there no v second case, the distance is doubled, so the speed increases by a factor of √2.
If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases. a) 20 m b) 30 m c) 40 m d) 60 m e) 80 m
80m: F d= Wnet= ΔKE = 0-1/2mv^2. Therefore, if the speed doubles, the stopping distance gets four times larger
The work Wo accelerates a car from 0 to 50 km/hr. How much work is needed to accelerate the car from 50 km/h to 150 km/hr? A) 2Wo B) 3Wo C) 6Wo D) 8Wo E) 9Wo
8Wo
From rest, you step on the gas of your Ferrari, providing a force F for 4 seconds, speeding it up to a final speed v. If the applied force were only ½ F, how long would it have to be applied to reach the same final speed? a) 16 s b) 8 s c) 4 s d) 2 s e) 1 s
8s: In the first case, the acceleration acts over time T = 4 s to give velocity v = aT. In the second case, the force is half; therefore, the acceleration is also half, so to achieve the same final speed, the time must be doubled.
You kick a smooth, flat stone out on a frozen pond. The stone slides, slows down, and eventually stops. You conclude that a) the force pushing the stone forward finally stopped pushing on it. b) no net force acted on the stone. c) a net force acted on it all along. d) the stone simply "ran out of steam." e) the stone has a natural tendency to be at rest.
A NET FORCE ACTED ON IT ALL ALONG: After the stone was kicked, no force was pushing it along! However, there must have been some force acting on the stone to slow it down and stop it. This would be friction!
A ball is thrown straight upward with some initial speed. When it reaches the top of its flight (at a height h), a second ball is thrown straight upward with the same initial speed. Where will the balls cross paths? a) At height h b) Above height h/2 c) At height h/2 d) Below height h/2 but above 0 e) At height 0
ABOVE HEIGHT h/2 : The first ball starts at the top with no initial speed. The second ball starts at the bottom with a large initial speed. Because the balls travel the same time until they meet, the second ball will cover more distance in that time, which will carry it over the halfway point before the first ball can reach it.
In outer space, gravitational forces exerted by a bowling ball and a Ping-Pong ball on each other are equal and opposite. How do their accelerations compare? a) They do not accelerate because they are weightless. b) Accelerations are equal, but not opposite. c) Accelerations are opposite, but bigger for the bowling ball. d) Accelerations are opposite, but bigger for the Ping-Pong ball. e) Accelerations are equal and opposite.
ACCELERATIONS ARE OPPOSITE, BUT BIGGER FOR THE PING-PONG BALL: The forces are equal and opposite—this is Newton's third law! But the acceleration is F/m, so the smaller mass has the bigger acceleration.
In the game of tetherball, the struck ball whirls around a pole. In what direction does the net force on the ball point? a) Toward the top of the pole b) Toward the ground c) Along the horizontal component of the tension force d) Along the vertical component of the tension force e) Tangential to the circle
ALONG THE HORIZONTAL COMPONENT OF THE TENSION FORCE: The vertical component of the tension balances the weight. The horizontal component of tension provides the centripetal force that points toward the center of the circle.
A projectile is launched from the ground at an angle of 30º. At what point in its trajectory does this projectile have the least speed? a) Just after it is launched b) At the highest point in its flight c) Just before it hits the ground d) Halfway between the ground and the highest point e) Speed is always constant.
AT THE HIGHEST POINT IN ITS FLIGHT: The speed is smallest at the highest point of its flight path because the y-component of the velocity is zero.
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity? a) Klyde b) Bonnie c) They both have the same linear velocity. d) Linear velocity is zero for both of them
BONNIE: Their linear speeds v will be different because v = rω, and Bonnie is located farther out (larger radius r) than Klyde.
A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? a) Component of the gravity force parallel to the plane increased b) Coefficient of static friction decreased c) Normal force exerted by the board decreased d) Both a) and c) e) All of a) , b), and c)
BOTH A) and C): As the angle increases, the component of weight parallel to the plane increases, and the component perpendicular to the plane decreases (and so does the normal force). Because friction depends on normal force, we see that the friction force gets smaller and the force pulling the box down the plane gets bigger.
Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? a) Mike b) Joe c) Both did the same work
BOTH DID THE SAME WORK: Both exerted the same force over the same displacement. Therefore, both did the same amount of work. Time does not matter for determining the work done.
A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. Which fragment has the greater momentum? a) The heavy one b) The light one c) Both have the same momentum d) Impossible to say
BOTH HAVE THE SAME MOMENTUM: The initial momentum of the uranium was zero, so the final total momentum of the two fragments must also be zero. Thus, the individual momenta are equal in magnitude and opposite in direction.
You drop a rock off a bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their velocities? a) Both increase at the same rate. b) The velocity of the first rock increases faster than the velocity of the second rock. c) The velocity of the second rock increases faster than the velocity of the first rock. d) Both velocities stay constant.
BOTH INCREASE AT THE SAME RATE: Both rocks are in free fall. Thus, they are under the influence of gravity only. That means they both experience the constant acceleration of gravity. Since acceleration is defined as the change of velocity, both of their velocities increase at the same rate.
A small car collides with a large truck. Which experiences the greater impact force? a) The car b) The truck c) Both the same d) It depends on the velocity of each e) It depends on the mass of each
BOTH THE SAME
Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. At the bottom, whose velocity is greater? a) Paul b) Kathleen c) Both the same
BOTH THE SAME
Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second . Which box has more momentum after the force acts? a) The heavier one b) The lighter one c) Both the same
BOTH THE SAME
In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? a) Catcher has done positive work b) Catcher has done negative work c) Catcher has done zero work
CATCHER HAS DONE NEGATIVE WORK: The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F (Δr)cosθ ), because θ = 180º, then W < 0. Note that because the work done on the ball is negative, its speed decreases.
Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, the cart will a) slowly come to a stop. b) continue with constant acceleration. c) continue with decreasing acceleration. d) continue with constant velocity. e) immediately come to a stop.
CONTINUE WITH CONSTANT VELOCITY: After the cart is released, there is no longer a force in the x-direction. This does not mean that the cart stops moving! It simply means that the cart will continue moving with the same velocity it had at the moment of release. The initial push got the cart moving, but that force is not needed to keep the cart in motion.
Does the odometer in a car measure distance or displacement? A) Distance B) Displacement C) Both
DISTANCE: If you go on a long trip and then return home, your odometer does not measure zero, which is the displacement, but it records the total miles that you traveled. That means the odometer records distance
You drive for 30 minutes at 30 mi/hr and then for another 30 minutes at 50 mi/hr. What is your average speed for the whole trip? a) More than 40 mi/hr b) Equal to 40 mi/hr c) Less than 40 mi/hr
EQUAL TO 40 mi/hr: Because the average speed is distance/time and you spend the same amount of time at each speed, your average speed is 40 mi/hr.
A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder's momentum compare to the rate of change of the pebble's momentum? a) Greater than b) Less than c) Equal to
EQUAL TO: The rate of change of momentum is, in fact, the force. Remember that F = Δp/Δt. Because the force exerted on the boulder and the pebble is the same, then the rate of change of momentum is the same.
By what factor does the kinetic energy of a car change when its speed is tripled? a) No change at all b) Factor of 3 c) Factor of 6 d) Factor of 9 e) Factor of 12
FACTOR OF 9: Because the kinetic energy is ½mv2, if the speed increases by a factor of 3, then the KE will increase by a factor of 9.
A truck, initially at rest, rolls down a frictionless hill and attains a speed of 20 m/s at the bottom. To achieve a speed of 40 m/s at the bottom, how many times higher must the hill be? a) Half the height b) The same height c) √2 times the height d) Twice the height e) Four times the height
FOUR TIMES THE HEIGHT
How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? a) Same amount of work b) Twice the work c) Four times the work d) Eight times the work
FOUR TIMES THE WORK: The elastic potential energy is ½kx^2. So in the second case, the elastic PE is four times greater than in the first case. Thus, the work required to stretch the spring is also four times greater.
You drive your dad's car too fast around a curve and the car starts to skid. What is the correct description of this situation? a) Car's engine is not strong enough to keep the car from being pushed out b) Friction between tires and road is not strong enough to keep car in a circle c) Car is too heavy to make the turn d) A deer caused you to skid. e) None of the above
FRICTION BETWEEN TIRES AND ROAD IS NOT STRONG ENOUGH TO KEEP A CAR IN A CIRCLE: The friction force between tires and road provides the centripetal force that keeps the car moving in a circle. If this force is too small, the car continues in a straight line!
A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? a) Friction does no work at all b) Friction does negative work c) Friction does positive work
FRICTION DOES NEGATIVE WORK: Friction acts in the opposite direction to the displacement, so the work is negative. Or, using the definition of work (W = F (Δr)cosθ), because θ = 180º, then W < 0.
What can you say about the force of gravity Fg acting on a stone and a feather? a) Fg is greater on the stone. B) Fg is zero on both due to vacuum. C) Fg is equal on both always. D) Fg is zero on both always.
Fg IS GREATER ON THE STONE: The force of gravity (weight) depends on the mass of the object! The stone has more mass, and therefore more weight.
You tee up a golf ball and drive it down the fairway. Assume that the collision of the golf club and ball is elastic. When the ball leaves the tee, how does its speed compare to the speed of the golf club? a) Greater than b) Less than c) Equal to
GREATER THAN: If the speed of approach (for the golf club and ball) is v, then the speed of recession must also be v. Because the golf club is hardly affected by the collision and it continues with speed v, then the ball must fly off with a speed of 2v.
If each component of a vector is doubled, what happens to the angle of that vector? a) It doubles. b) It increases, but by less than double. c) It does not change. d) It is reduced by half. e) It decreases, but not as much as half.
IT DOES NOT CHANGE: The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan θ = 2y/2x, which is the same as tan θ = y/x (the original angle).
Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? a) It depends upon how much the track is tilted. b) It falls behind the cart. c) It falls in front of the cart. d) It falls right back into the cart. e) It remains at rest.
IT FALLS BEHIND THE CART: Now the acceleration of the cart is completely unrelated to the ball. In fact, the ball does not have any horizontal acceleration at all (just like the previous question), so it will lag behind the accelerating cart once it is shot out of the cannon.
The same small cart is now rolling down an inclined track and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? a) It depends upon how much the track is tilted. b) It falls behind the cart. c) It falls in front of the cart. d) It falls right back into the cart. e) It remains at rest.
IT FALLS RIGHT BACK INTO THE CART: Because the track is inclined, the cart accelerates. However, the ball has the same component of acceleration along the track as the cart does! This is essentially the component of g acting parallel to the inclined track. So, the ball is effectively accelerating down the incline, just as the cart is, and it falls back into the cart.
A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball? a) It depends on how fast the cart is moving. b) It falls behind the cart. c) It falls in front of the cart. d) It falls right back into the cart. e) It remains at rest.
IT FALLS RIGHT BACK INTO THE CART: In the frame of reference of the cart, the ball only has a vertical component of velocity, so it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocity, so the ball still returns into the cart.
When a bullet is fired from a gun, the bullet and the gun have equal and opposite momenta. If this is true, then why is the bullet deadly (whereas it is safe to hold the gun while it is fired)? a) It is much sharper than the gun. b) It is smaller and can penetrate your body. c) It has more kinetic energy than the gun. d) It goes a longer distance and gains speed. e) It has more momentum than the gun.
IT HAS MORE KINETIC ENERGY THAN THE GUN: Even though it is true that the magnitudes of the momenta of the gun and the bullet are equal, the bullet is less massive and so it has a much higher velocity. Because KE is related to v^2, the bullet has considerably more KE and therefore can do more damage on impact.
What can you say about the acceleration of gravity acting on the stone and the feather? a) It is greater on the feather. b) It is greater on the stone. c) It is zero on both due to vacuum. d) It is equal on both always. e) It is zero on both always.
IT IS EQUAL ON BOTH ALWAYS: The acceleration is given by F/m, so here, the mass divides out. Because we know that the force of gravity (weight) is mg, we end up with acceleration g for both objects.
You are driving around a curve in a narrow one-way street at 30 mph. An identical car is heading straight toward you at 30 mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head-on). What should you do? a) Hit the other car. b) Hit the wall. c) It makes no difference. d) Call your physics prof! e) Get insurance!
IT MAKES NO DIFFERENCE: In both cases, your momentum will decrease to zero in the collision. Given that the time Δt of the collision is the same, then the force exerted on you will be the same! If a truck were approaching at 30 mph, then you'd be better off hitting the wall. On the other hand, if it were only a mosquito, well, you'd be better off running him down...
A very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What happens to the truck? a) It is too heavy, so it just sits there. b) It moves backward at constant speed. c) It accelerates backward. d) It moves forward at constant speed. e) It accelerates forward.
IT MOVES BACKWARD AT CONSTANT SPEED: When the fly hits the truck, it exerts a force on the truck (only for a fraction of a second). So, in this time period, the truck accelerates (backward) up to some speed. After the fly is squashed, it no longer exerts a force, and the truck simply continues moving at constant speed.
An open cart rolls along a frictionless track while it is raining. As it rolls, what happens to the speed of the cart as the rain collects in it? (Assume that the rain falls vertically into the cart.) a) It speeds up. b) It maintains constant speed. c) It slows down. d) It stops immediately.
IT SLOWS DOWN: Because the rain falls into the cart vertically, it adds no momentum to the cart. Thus, the cart's momentum is conserved. However, because the mass of the box slowly increases with the added rain, its velocity has to decrease.
You throw a ball straight up into the air. After it leaves your hand, at what point in its flight does it have the maximum value of acceleration? a) Its acceleration is constant everywhere. b) At the top of its trajectory c) Halfway to the top of its trajectory d) Just after it leaves your hand e) Just before it returns to your hand on the way down
ITS ACCELERATION IS CONSTANT EVERYWHERE: The ball is in free fall once it is released. Therefore, it is entirely under the influence of gravity, and the only acceleration it experiences is g, which is constant at all points.
Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? a) Mike produced more power b) Joe produced more power c) Both produced the same amount of power
JOE PRODUCED MORE POWER: Because power = work/time, we see that Mike produced 0.5 W, and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower.
Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first? a) Paul b) Kathleen c) Both the same
KATHLEEN: Even though they both have the same final velocity, Kathleen is at a lower height than Paul for most of her ride. Thus, she always has a larger velocity during her ride and therefore arrives earlier!
A box sliding on a flat, rough surface runs into a fixed spring, which compresses a distance x' to stop the box. How does this distance compare with when there was no friction? a) Greater b) The same c) Less
LESS
You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip? a) More than 40 mi/hr b) Equal to 40 mi/hr c) Less than 40 mi/hr
LESS THAN 40 mi/hr: Remember that the average speed is distance/time. Because it takes longer to cover 4 miles at the slower speed, you are actually moving at 30 mi/hr for a longer period of time! Therefore, your average speed is closer to 30 mi/hr than it is to 50 mi/hr.
A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder's velocity compare to the rate of change of the pebble's velocity? a) Greater than b) Less than c) Equal to
LESS THAN: The rate of change of velocity is the acceleration. Remember that a = Δv/Δt. The acceleration is related to the force by Newton's second law (F = ma). The acceleration of the boulder is less than that of the pebble (for the same applied force) because the boulder is much more massive.
Two blocks of mass M1 and M2 (M1>M2) slide on a frictionless floor and have the same kinetic energy when they hit a long rough stretch (µ > 0), which slows them down to a stop. Which one goes farther? a) M1 b)M2 c) they will go the same distance
M2: With the same ΔKE, both blocks must have the same work done to them by friction. The friction force is less for m must be greater.
A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system? a) Momentum of the system is positive b) Momentum of the system is negative c) Momentum of the system is zero d) You cannot say anything about the momentum of the system
MOMENTUM OF THE SYSTEM IS ZERO: Because the total kinetic energy is zero, this means that all of the particles are at rest ( v = 0). Therefore, because nothing is moving, the total momentum of the system must also be zero.
A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block? a) N>mg b)N=mg c)N<mg (but not zero) d)N=0 e)Depends on the size of the elevator
N=mg: The block is moving at constant speed, so it must have no net force on it. The forces on it are N (up) and mg (down), so N = mg, just like the block at rest on a table.
A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block? a) N>mg b)N=mg c)N<mg (but not zero) d)N=0 e)Depends on the size of the elevator
N>mg: The block is accelerating upward, so it must have a net upward force. The forces on it are N (up) and mg (down), so N must be greater than mg in order to give the net upward force!
Alice and Bill are at the top of a building. Alice throws her ball downward. Bill simply drops his ball. Which ball has the greater acceleration just after release? a) Alice's ball b) It depends on how hard the ball was thrown. c) Neither—they both have the same acceleration. d) Bill's ball
NEITHER-THEY BOTH HAVE THE SAME ACCELERATION: Both balls are in free fall once they are released; therefore, they both feel the acceleration due to gravity (g). This acceleration is independent of the initial velocity of the ball.
You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? a) A net force acted on it. b) No net force acted on it. c) It remained at rest. d) It did not move, but only seemed to. e) Gravity briefly stopped acting on it.
NO NET FORCE ACTED ON IT: The book was initially moving forward (because it was on a moving bus). When the bus stopped, the book continued moving forward, which was its initial state of motion, and therefore it slid forward off the seat.
A box sits in a pickup truck on a frictionless truck bed. When the truck accelerates forward, the box slides off the back of the truck because a) The force from the rushing air pushed it off. b) The force of friction pushed it off. c) No net force acted on the box. d) The truck went into reverse by accident. e) None of the above.
NO NET FORCE ACTED ON THE BOX: Generally, the reason that the box in the truck bed would move with the truck is due to friction between the box and the bed. If there is no friction, there is no force to push the box along, and it remains at rest. The truck accelerated away, essentially leaving the box behind!
If the average velocity is non-zero over some time interval, does this mean that the instantaneous velocity is never zero during the same interval? A)yes B)no C)it depends
NO: For example, your average velocity for a trip home might be 60 mph, but if you stopped for lunch on the way home, there was an interval when your instantaneous velocity was, in fact, zero.
Two objects are known to have the same momentum. Do these two objects necessarily have the same kinetic energy? a) Yes b) No
NO: If object 1 has mass m and speed v, and object 2 has mass 1/2m and speed 2v, they will both have the same momentum. However, because KE = 1/2mv^2, we see that object 2 has twice the kinetic energy of object 1, due to the fact that the velocity is squared.
A system of particles is known to have a total momentum of zero. Does it necessarily follow that the total kinetic energy of the system is also zero? a) Yes b) No
NO: Momentum is a vector, so the fact that Ptot does not mean that the particles are at rest! They could be moving such that their momenta cancel out when you add up all of the vectors. In that case, because they are moving, the particles would have non-zero KE.
Engine 1 produces twice the power of engine 2. Can we conclude that engine 1 does twice as much work as engine 2? a) Yes b) No
NO: No! We cannot conclude anything about how much work each engine does. Given the power output, the work will depend upon how much time is used. For example, engine 1 may do the same amount of work as engine 2, but in half the time.
Is it possible for the kinetic energy of an object to be negative? a) Yes b) No
NO: The kinetic energy is ½mv^2. The mass and the velocity squared will always be positive, so KE must always be positive.
Is it possible to do work on an object that remains at rest? A) yes B) no
NO: Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done.
Does the displacement of an object depend on the specific location of the origin of the coordinate system?
NO: because the displacement is the DIFFERENCE between two coordinats, the orgin does not matter
If the position of a car is zero, does its speed have to be zero?
NO: the speed does not depend on position; it depends on the change of position. Because we know that the displacement does not depend on the origin of the coordinate system, an object can easily start at x = -3 and be moving by the time it gets to x = 0.
A mass attached to a vertical spring causes the spring to stretch and the mass to move downward. What can you say about the spring's potential energy (PEs) and the gravitational potential energy (PEg) of the mass A) Both PEs and PEg decrease B) PEs increases and PEg decreases C) both PEs and PEg increase D) PEs decreases and PEg increases E) PEs increases and PEg is constant
PEs increases and PEg decreases: The spring is stretched, so its elastic PE increases, because PEs= ½kx^2. The mass moves down to a lower position, so its gravitational PE decreases, because PEg=mgh
A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child? a) Positive work was done b) Negative work was done c) Zero work was done
POSITIVE WORK WAS DONE: The kinetic energy of the child increased because her speed increased . This increase in KE was the result of positive work being done. Or, from the definition of work, because W = ΔKE = KE - KEi and we know that KEf>KEi in this case, then the work W must be positive
Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this? a) Pushing her from behind b) Pulling her from the front c) Both are equivalent d) It is impossible to move the sled e) Tell her to get out and walk
PULLING HER FROM THE FRONT: In case 1, the force F is pushing down (in addition to mg), so the normal force is larger. In case 2, the force F is pulling up, against gravity, so the normal force is lessened. Recall that the opposing frictional force is proportional to the normal force.
We just decided that the cart continues with constant velocity. What would have to be done in order to have the cart continue with constant acceleration? a) Push the cart harder before release b) Push the cart longer before release c) Push the cart continuously d) Change the mass of the cart e) It is impossible to do that.
PUSH THE CART CONTINUOUSLY: In order to achieve a non-zero acceleration, it is necessary to maintain the applied force. The only way to do this would be to continue pushing the cart as it moves down the track. This will lead us to a discussion of Newton's second law
You drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will a) quickly lag behind the plane while falling. b) remain vertically under the plane while falling. c) move ahead of the plane while falling. d) not fall at all.
REMAIN VERTICALLY UNDER THE PLANE WHILE FALLING: Both the plane and the package have the same horizontal velocity at the moment of release. They will maintain this velocity in the x-direction, so they will stay aligned.
If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B? a) Same magnitude, but can be in any direction b) Same magnitude, but must be in the same direction c) Different magnitudes, but must be in the same direction d) Same magnitude, but must be in opposite directions e) Different magnitudes, but must be in opposite directions
SAME MAGNITUDE, BUT MUST BE IN OPPOSITE DIRECTIONS: The magnitudes must be the same, but one vector must be pointing in the opposite direction of the other in order for the sum to come out to zero. You can prove this with the tip-to-tail method.
A bowling ball and a Ping-Pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest? a) The bowling ball b) Same time for both c) The Ping-Pong ball d) Impossible to say
SAME TIME FOR BOTH
Consider two elastic collisions: 1) a golf ball with speed v hits a stationary bowling ball head-on. 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision? a) Situation 1 b) Situation 2 c) Both the same
SITUATION 2: In case 1, the bowling ball will almost remain at rest, and the golf ball will bounce back with a speed close to v. In case 2, the bowling ball will keep going with a speed close to v, hence the golf ball will rebound with a speed close to 2v.
You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for y = 0 in this problem. Which of the following quantities will you and your friend agree on? a) Skier's change in PE b) Skier's final KE c) Skier's PE, change in PE, and final KE d) Skier's PE and final KE e) Skier's change in PE and final KE
SKIER'S CHANGE IN PE AND FINAL KE: The gravitational PE depends upon the reference level, but the difference ΔPE does not! The work done by gravity must be the same in the two solutions, so ΔPE and ΔKE should be the same.
A mass m is placed on an inclined plane (µ > 0) and slides down the plane with constant speed. If a similar block (same µ) of mass 2m were placed on the same incline, it would a) not move at all. b) slide a bit, slow down, then stop. c) accelerate down the incline. d) slide down at constant speed. e) slide up at constant speed.
SLIDE DOWN AT CONSTANT SPEED: The component of gravity acting down the plane is double for 2m. However, the normal force (and hence the friction force) is also double (the same factor!). This means the two forces still cancel to give a net force of zero.
Does the speedometer in a car measure velocity or speed? a) Velocity b) Speed c) Both d) Neither
SPEED: The speedometer clearly measures speed, not velocity. Velocity is a vector (depends on direction), but the speedometer does not care what direction you are traveling. It only measures the magnitude of the velocity, which is the speed.
Three blocks of mass 3m, 2m, and m are connected by strings and pulled with constant acceleration a. What is the relationship between the tension in each of the strings? A) T1>T2>T3 B)T1<T2<T3 C) T1=T2=T3 D) All tensions are zero E) Tensions are random
T1>T2>T3: T1 pulls the whole set of blocks along, so it must be the largest. T2 pulls the last two masses, but T3 only pulls the last mass
A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension? a) Tension does no work at all b) Tension does negative work c) Tension does positive work
TENSION DOES NO WORK AT ALL: No work is done because the force acts in a perpendicular direction to the displacement. Or, using the definition of work (W = F (Δr)cosθ), because θ = 180º, then W < 0.
In the previous problem, which ball has the greater velocity at ground level? a) The "dropped" ball b) The "fired" ball c) Neither—they both have the same velocity on impact. d) It depends on how hard the ball was thrown.
THE "FIRED" BALL: Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the "fired" ball also has a horizontal velocity. When you add the two components vectorially, the "fired" ball has a larger net velocity when it hits the ground.
A box of weight 100 N is at rest on a floor where µs= 0.4. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? a) To the left b) To the right c) Up d) Down e) The box does not move
THE BOX DOES NOT MOVE: the static friction force has a maximum of μsN= 40N. The tension in the rope is only 30N. So the pulling force is not big enough to overcome friction
In the collision between the car and the truck, which has the greater acceleration? a) The car b) The truck c) Both the same d) It depends on the velocity of each e) It depends on the mass of each
THE CAR: We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m, so the car has the larger acceleration, because it has the smaller mass.
During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening? a) Centrifugal force is pushing you into the door. b) The door is exerting a leftward force on you. c) Both of the above d) Neither of the above
THE DOOR IS EXERTING A LEFTWARD FORCE ON YOU: The passenger has the tendency to continue moving in a straight line. There is a centripetal force, provided by the door, that forces the passenger into a circular path.
In outer space, a bowling ball and a Ping-Pong ball attract each other due to gravitational forces. How do the magnitudes of these attractive forces compare? a) The bowling ball exerts a greater force on the Ping-Pong ball. b) The Ping-Pong ball exerts a greater force on the bowling ball. c) The forces are equal. d) The forces are zero because they cancel out. e) There are actually no forces at all.
THE FORCES ARE EQUAL
A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. Which fragment has the greater speed? a) The heavy one b) The light one c) Both have the same speed d) Impossible to say
THE LIGHT ONE: We have already seen that the individual momenta are equal and opposite. In order to keep the magnitude of momentum mv the same, the heavy fragment has the lower speed and the light fragment has the greater speed .
In the previous question, which box has the larger velocity after the force acts? a) The heavier one b) The lighter one c) Both the same
THE LIGHTER ONE: The force is related to change in momentum, so as indicated, the same force gives the same change in momentum. However, momentum is p = mv, so the smaller mass will have the larger velocity after the force acts.
A bowling ball and a Ping-Pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, for which is the stopping distance greater? a) The bowling ball b) Same distance for both c) The Ping-Pong ball d) Impossible to say
THE PING-PONG BALL: Use the work-energy theorem: W = ΔKE. The ball with less mass has the greater speed (why?), and thus the greater KE. In order to remove that KE, work must be done, where W = Fd. Because the force is the same in both cases, the distance needed to stop the less massive ball must be bigger.
When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that? a) This slows your initial velocity, which is already upward. b) You don't go up; you're too heavy. c) You're not really pulling down—it just seems that way. d) The rope actually pulls you up. e) You are pulling the ceiling down.
THE ROPE ACTUALLY PULLS YOU UP: When you pull down on the rope, the rope pulls up on you! It is actually this upward force by the rope that makes you move up! This is the "reaction" force (by the rope on you) to the force that you exerted on the rope. And voilá, this is Newton's third law.
A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits? a) The beanbag b) The rubber ball c) Both the same
THE RUBBER BALL: Both objects reach the same speed at the floor. However, while the beanbag comes to rest on the floor, the ball bounces back up with nearly the same speed as it hit. Thus, the change in momentum for the ball is greater, because of the rebound. The impulse delivered by the ball is twice that of the beanbag.
An astronaut on Earth kicks a bowling ball and hurts his foot. A year later, the same astronaut kicks a bowling ball on the Moon with the same force. His foot hurts a) more. b) less. c) the same amount.
THE SAME AMOUNT: The masses of both the bowling ball and the astronaut remain the same, so his foot feels the same resistance and hurts the same as before.
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every 2 seconds. Klyde's angular velocity is a) the same as bonnie's. b) twice bonnie's. c) half of bonnie's. d) one-quarter of bonnie's. e) four times bonnie's.
THE SAME AS BONNIE'S: The angular velocity ω of any point on a solid object rotating about a fixed axis is the same. Both Bonnie and Klyde go around one revolution (2π radians) every 2 seconds.
In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? a) Quarter as much b) Half as much c) The same d) Twice as much e) Four times as much
THE SAME: All freely falling objects fall at the same rate, which is g. Because the acceleration is the same for both, and the distance is the same, then the final speeds will be the same for both stones.
Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you took the longer path? a) The same b) Twice as much c) Four times as much d) Half as much e) You gain no PE in either case
THE SAME: Because your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same.
You drop a rock off a bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their separation? a) The separation increases as they fall. b) The separation stays constant at 4 m. c) The separation decreases as they fall. d) It is impossible to answer without more information.
THE SEPARATION INCREASES AS THEY FALL: At any given time, the first rock always has a greater velocity than the second rock. Therefore, it will always be increasing its lead as it falls. Thus, the separation will increase.
Suppose that the speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck, how will that affect the speedometer reading as compared to the true linear speed of the truck? a) The speedometer will read a higher speed than the true linear speed. b) The speedometer will read a lower speed than the true linear speed c) The speedometer will still read the true linear speed
THE SPEEDOMETER WITH READ A LOWER SPEED THAN THE TRUE LINEAR SPEED: The linear speed is v = ωR. So, when the speedometer measures the same angular speed ω as before, the linear speed v is actually higher, because the tire radius is larger than before.
You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it? a) The superball b) The blob of clay c) It doesn't matter—they will be equally effective. d) You are just too lazy to throw anything.
THE SUPERBALL: The superball bounces off the door with almost no loss of speed, so its Δp (and that of the door) is 2mv. The clay sticks to the door and continues to move along with it, so its Δp is less than that of the superball, and therefore it imparts less Δp to the door.
A book is lying at rest on a table. The book will remain there at rest because a) there is a net force but the book has too much inertia. b) there are no forces acting on it at all. c) it does move, but too slowly to be seen. d) there is no net force on the book. e) there is a net force, but the book is too heavy to move.
THERE IS NO NET FORCE ON THE BOOK: There are forces acting on the book , but the only forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force.
Given that A + B = C, and that | A | + | B | = | C |, how are vectors A and B oriented with respect to each other? a) They are perpendicular to each other. b) They are parallel and in the same direction. c) They are parallel but in the opposite direction. d) They are at 45º to each other. e) They can be at any angle to each other.
THEY ARE PARALLEL AND IN THE SAME DIRECTION: The only time vector magnitudes will simply add together is when the direction does not have to be taken into account (i.e., the direction is the same for both vectors). In that case, there is no angle between them to worry about, so vectors A and B must be pointing in the same direction.
Given that A + B = C, and that | A |^2 + | B |^2 = | C |^2, how are vectors A and B oriented with respect to each other? a) They are perpendicular to each other. b) They are parallel and in the same direction. c) They are parallel but in the opposite direction. d) They are at 45º to each other. e) They can be at any angle to each other.
THEY ARE PERPENDICULAR TO EACH OTHER: Note that the magnitudes of the vectors satisfy the Pythagorean theorem. This suggests that they form a right triangle, with vector C as the hypotenuse. Thus, A and B are the legs of the right triangle and are therefore perpendicular
A small car and a large truck collide head-on and stick together. Which one has the larger momentum change? a) The car b) The truck c) They both have the same momentum change. d) Can't tell without knowing the final velocities
THEY BOTH HAVE THE SAME MOMENTUM CHANGE: Because the total momentum of the system is conserved, that means that Δp = 0 for the car and truck combined. Therefore, ΔPcar be equal and opposite to that of the truck (-ΔPtrucktotal momentum change to be zero. Note that this conclusion also follows from Newton's third law.
From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? a) The "dropped" ball b) The "fired" ball c) They both will hit at the same time. d) It depends on how hard the ball was fired. e) It depends on the initial height.
THEY BOTH WILL HIT AT THE SAME TIME: Both of the balls are falling vertically under the influence of gravity. They both fall from the same height. Therefore, they will hit the ground at the same time. The fact that one is moving horizontally is irrelevant—remember that the x and y motions are completely independent!
A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box? a) One force b) Two forces c) Three forces d) Four forces e) No forces are doing work
THREE FORCES: Any force not perpendicular to the motion will do work: N does no work T does positive work f does negative work mg does negative work
You and a friend can each pull with a force of 20 N. If you want to rip a rope in half, what is the best way to do so? a) You and your friend each pull on opposite ends of the rope b) Tie the rope to a tree, and you both pull from the same end c) It doesn't matter—both of the above are equivalent d) Get a large dog to bite the rope
TIE THE ROPE TO A TREE, AND YOU BOTH PULL FROM THE SAME END: Take advantage of the fact that the tree can pull with almost any force (until it falls down, that is!). You and your friend should team up on one end, and let the tree make the effort on the other end.
A box sliding on a frictionless flat surface runs into a fixed spring, which compresses a distance x to stop the box. If the initial speed of the box were doubled, how much would the spring compress? a) Half as much b) The same amount c) √2 times as much d) Twice as much e) Four times as much
TWICE AS MUCH
Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? a) Quarter as much b) Half as much c) The same d) Twice as much e) Four times as much
TWICE AS MUCH: Consider the work done by gravity to make the stone fall distance d: ΔKE = W ΔKE = mgd Thus, the stone with the greater mass has the greater KE, which is twice as big for the heavy stone.
When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path? a) Both v = 0 and a = 0 b) v ≠ 0, but a = 0 c) v = 0, but a ≠ 0 d) Both v ≠ 0 and a ≠ 0 e) Not really sure
V=0, but a≠0: clearly v = 0 because the ball has momentarily stopped. But the velocity of the ball is changing, so its acceleration is definitely not zero! Otherwise, it would remain at rest!
Alice and Bill are at the top of a cliff of height H. Both throw a ball with initial speed Vo; Alice straight down, and Bill straight up. The speeds of the balls when they hit the ground are Va and Vb, respectively. If there is no air resistance, which is true? a)Va<Vb b)Va=Vb c)Va>Vb d) Impossible to tell
Va=Vb: Bill's ball goes up and comes back down to Bill's level. At that point, it is moving downward with v ball. Thus, it will hit the ground with the same speed as Alice's ball.
A person stands under an umbrella during a rainstorm. Later, the rain turns to hail. The number of "drops" hitting the umbrella per time, as well as their speed, remains the same. Which case requires more force to hold the umbrella? a) When it is hailing b) When it is raining c) Same in both cases
WHEN IT IS HAILING: When the raindrops hit the umbrella, they tend to splatter and run off, whereas the hailstones hit the umbrella and bounce back upward. Thus, the change in momentum (impulse) is greater for the hail. Because Δ p = F Δt, more force is required in the hailstorm. This is similar to the situation with the bouncy rubber ball in the previous question.
You are on the street, trying to hit a friend with a water balloon. He is sitting in his dorm room window above your position. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the water balloon hit him? a) Yes, it hits. b) Maybe—it depends on the speed of the shot. c) The shot is impossible. d) No, it misses. e) Not really sure
YES, IT HITS: This is really the same situation as before! The only change is that the initial velocity of the water balloon now has a y-component as well. But both your friend and the water balloon still fall with the same acceleration—g!
You are trying to hit a friend with a water balloon. He is sitting in the window of his dorm room directly across the street. You aim straight at him and shoot. Just when you shoot, he falls out of the window! Does the water balloon hit him? a) Yes, it hits. b) Maybe—it depends on the speed of the shot. c) No, it misses. d) The shot is impossible. e) Not really sure
YES, IT HITS: Your friend falls under the influence of gravity, just like the water balloon. Thus, they are both undergoing free fall in the y-direction. Since the slingshot was accurately aimed at the right height, the water balloon will fall exactly as your friend does, and it will hit him!!
You are on the street, trying to hit a friend with a water balloon. He is sitting in his dorm room window above your position and is aiming at you with HIS water balloon! You aim straight at him and shoot and he does the same in the same instant. Do the water balloons hit each other? a) Yes, they hit. b) Maybe—it depends on the speeds of the shots. c) The shots are impossible. d) No, they miss. e) Not really sure
YES, THEY HIT: This is still the same situation! Both water balloons are aimed straight at each other and both still fall with the same acceleration—g!
If the velocity of a car is non-zero ( v ≠ 0), can the acceleration of the car be zero? a) Yes b) No c) Depends on the velocity
YES: An object moving with constant velocity has a non-zero velocity, but it has zero acceleration because the velocity is not changing.
Can friction ever do positive work? a) Yes b) No
YES: Consider the case of a box on the back of a pickup truck. If the box moves along with the truck , then it is actually the force of friction that is making the box move.
Is it possible for the gravitational potential energy of an object to be negative? a) Yes b) No
YES: Gravitational PE is mgh , where height h is measured relative to some arbitrary reference level where PE = 0. For example, a book on a table has positive PE if the zero reference level is chosen to be the floor. However, if the ceiling is the zero level, then the book has negative PE on the table. Only differences (or changes) in PE have any physical meaning.
You and your dog go for a walk to the park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement?
YES: you have the same displacement. Because you and your dog had the same initial position and the same final position, then you have (by definition) the same displacement.
You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you? a) You are thrown to the right. b) You feel no particular change. c) You are thrown to the left. d) You are thrown to the ceiling. e) You are thrown to the floor.
YOU ARE THROWN TO THE RIGHT: The passenger has the tendency to continue moving in a straight line. From your perspective in the car, it feels like you are being thrown to the right, hitting the passenger door.
A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? a) More than its weight b) Equal to its weight c) Less than its weight but more than zero d) Depends on the speed of the puck e) Zero
ZERO: The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must be no net force acting on the puck.
You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book? a)mg•Δr b)Fhand•Δr c)(Fhand + mg)•Δr d)Zero e)None of the above
ZERO: The total work is zero because the net force acting on the book is zero. The work done by the hand is positive, and the work done by gravity is negative. The sum of the two is zero. Note that the kinetic energy of the book does not change either!
An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in the time t, through what angle did it rotate in the time ½t? a) ½θ b) ¼θ c) ¾θ d) 2θ e) 4θ
¼θ: The angular displacement is θ = αt2 (starting from rest), and there is a quadratic dependence on time. Therefore, in half the time, the object has rotated through one-quarter the angle.
An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity ω at time t, what was its angular velocity at the time ½t? a) ½ω b) ¼ω c) ¾ω d) 2ω e) 4ω
½ω: The angular velocity is ω = αt (starting from rest), and there is a linear dependence on time. Therefore, in half the time, the object has accelerated up to only half the speed.
Antilock brakes keep car wheels from locking and skidding during a sudden stop. Why does this help slow the car down? A) μk> μs so sliding friction is better B) μk> μs so static friction is better C) μs> μk so sliding friction is better D) μs> μk so static friction is better E) none of the above
μs> μk SO STATIC FRICTION IS BETTER: Static friction is greater than sliding friction , so by keeping the wheels from skidding, the static friction force will help slow the car down more efficiently than the sliding friction that occurs during a skid.
Car 1 has twice the mass of car 2, but they both have the same kinetic energy. How do their speeds compare? A) 2V1=V2 B) √2 V1= V2 C) 4V1=V2 D) V1=V2 E) 8V1=V2
√2 V1= V2: Because the kinetic energy is ½mv2, and the mass of car 1 is greater, then car 2 must be moving faster. If the ratio of m ratio of v2 values must also be 2. This means that the ratio of v must be the square root of 2.
