Physics Ch. 5 questions
Discuss the advisability of simply removing the sail in the preceding questions.
A better way to create this craft would be to not include the sail at all similar to water craft boats that have the large fans on the back. If no sail were present, then the fan would push on the air and air would push back on the fan propelling the craft backward.
To bring a supertanker to a stop, its engines are typically cut off about 25 km from port. Why is it so difficult to stop or turn a super tanker?
A super tanker has a very large mass. When it is moving, it also has a very large momentum. Since the tanker needs to stop, the change in momentum will be very large. According the impulse momentum relationship, Σf=Δp/t, by increasing the time to stop, the force required will be less.
A car is lifted a certain distance in a service station lift and therefore has potential energy relative to the floor. If it were lifted twice as high, how much potential energy would it have?
According to the definition of potential energy, PE= mgh, the potential energy is directly proportional to the height above a reference. If the height is doubled, then the potential energy must also be doubled
When a ball is hit with a given force, why does contact over a long time impart more speed to the ball?
According to the impulse momentum relationship, Δp=(ΣF)t, when force is exerted for a longer period of time, the change in momentum is greater and thus a greater final speed will be reached.
Compared with some original speed, how much work must the brakes of a car supply to stop a car that is moving four times as fast? How does the stopping distance compare?
According to the work energy theorem, the work done by the brakes is equal to the change in kinetic energy of the car.W = KEfinal - KEinitial Since the car comes to rest the final KE is equal to zero in both cases and thus W = - KEinitial. From what we learned in question 5, the work required to stop a 2 kg car moving at 1 m/s would be W = - 1 J and the work required to stop a 2 kg car moving at 4 m/s would beW = - 16 J Thus, it requires 16 times more work to stop the car that is moving four as fast. Now since the brakes apply the same force in both cases and work can also be expressed as W = F d, since the work has increased by a factor of 16 then the distance to stop the car that is traveling four times as fast would also be 16 times as large.
In terms of impulse and momentum, why are nylon ropes, which stretch considerably under tension, favored by mountain climbers?
Again, the same reason as above. If a climber falls they might be traveling quickly by the time the rope begins to stop them. When the nylon ropes stretch, they slow down the climber over a larger period of time thus changing the momentum of the climber over a great period of time. According the impulse momentum relationship, Σf=Δp/t, by increasing the time to stop, the force required will be less.
Which, if either, requires more work - lifting a 50 kg sack a vertical distance of 2 m or lifting a 25 kg sack a vertical distance of 4 m?
Both of these require the same amount of work. In order to lift a certain amount of mass, you must apply a force at least equal to the weight of the object, w=mg. Thus, the work done to lift each is (50 kg): W = (50 kg * 10 m/s2)(2 m) = 1000 J (25 kg): W = (25 kg * 10 m/s2)(4 m) = 1000 J
Why is it a good idea to have your hand extended forward when you are getting ready to catch a fast-moving baseball with your bare hand?
By extending you hand forward, you can "give" with the ball and slow the fast-moving baseball down over a longer period of time. The change in momentum when the ball is caught will be the same regardless of how the ball is caught but will a larger time, the force applied on the ball will be smaller and thus the force the ball exerts on the hand will be smaller, Σf=Δp/t
In boxing, why is it advantageous to roll with the punch?
By rolling with the punches, you are increasing the time of contact and thus reducing the force of the punch, Σf=Δp/t
If your friend pushes a lawn mower four times as far as you do while exerting only half the force, which one of you does more work? How much more?
For this question, it is easiest to put some numbers in. Suppose that you push a lawn mower with a force of 1 N for a distance of 1 m. The work that you do is W = F d = (1 N)(1 m) = 1 J. Your friend push the mower 4 times a far (4 m) while exerting ½ the force (1/2 N). The work your friend does is W = F d = (1/2 N) (4 m) = 2 J. Your friend does 2 times as much work under this circumstance.
Two people who weight the same climb a flight of stairs. The first person climbs the stairs in 30s, while the second person climbs them in 40 s. Which person does more work? Which person uses more power?
If both individuals weigh the same them they both must apply a force at least equal to their weight to get up the stairs. So let's assume that they both apple the same force over the same distance, this means that they both do the same amount of work W=fd Since power=work/time, the person who climbs the stairs in less time uses more power
Will your answer to the preceding question be different if the air is brought to a halt by the sail without bouncing?
If the air is brought to a halt without bouncing then the answer would be different. The ice sail craft would be set in motion backward. There would not be a force on the sail and thus only the force from the air on the fan would propel the craft.
When vertically falling sand lands in a horizontally moving cart, the cart slows. Ignore any friction between the cart and the tracks. Explain why the cart slows down in terms of conservation of momentum.
If the car is moving forwards with some velocity then it has some momentum. As mass is added to the cart, the velocity of the cart must decrease in order to keep the total momentum of the system constant. p = m v. As the mass increases the velocity decreases.
When a rifle with a longer barrel is fired, the force of expanding gases acts on the bullet for a longer distance. What effect does this have on the velocity of the emerging bullet? (Do you see why long-range cannons have such long barrels?)
If the expanding gas applies a force on the bullet over a longer distance, this means that more work is done on the bullet (W = Fd). Now, according to the work energy theorem, W = KEfinal - KEinitial. Since the bullet starts from rest, KEinitial = 0 J, when more work is done by the longer barrel this means that it will impart more kinetic energy (more speed) to the bullet, KEfinal.
Cite an example in which a force is exerted on an object without doing work on the object
If the object is not in motion relative then work is not done. There must be some displacement of the object. Also, if the force is applied perpendicular to the motion then that force is not doing work on the object
A physics instructor demonstrates energy conservation by releasing a heavy pendulum bob, as shown in the sketch, allowing it to swing to and fro. What would happen, if in his exuberance, he gave the bob a slight shove as it left his nose? Explain
If the physics instructor gave the pendulum bob some initial shove, he would be imparting some initial shove, he would be imparting some initial velocity and thus initial kinetic energy. The end result would be that when the pendulum returned to the position of the instructor it would still be moving with some velocity and would thus strike the instructor. If the pendulum was simply released (with no initial velocity) then the pendulum would return to the position that it was released and then turn around
If two equal-mass sacks are lifted equal distances in the same time, how does the power required for each compare? How does the power required compare for the case in which a light sack is moved its distance in half the time?
If the sacks have equal mass and are lifted equal distances, then the work required to lift both sack is the same. Since power is work divided by time. If they are both lifted in the same amount of time then the power will be the same. For the question with the light sack, we would need to know how much lighter the same is. If the lighter sack has half the mass and is lifted half the time them the power would be the same. This is due to the fact that the work would be half as much, but also the time would be half. If the lighter sack had more that half the mass of the original sacks then the power would be greater and if it has less than half the mass of the original sacks then the power would be less
In karate, why is a force that is applied for a short time more advantageous?
If we consider a karate "chop", like that used to break a stack of wood, the hand is moving quickly and then comes into contact with the stack of wood. The change in momentum of the hand is the same regardless of the time frame of the "chop". If the force is applied for a short period, the force applied will be greater, Σf=Δp/t
Why would it be a poor idea to have the back of your hand up against the outfield wall when you catch along fly ball?
If we consider the answer to question 3, if your hand was up against the outfield wall when the ball is caught the hand does not have any time to "give" with the ball and reduce the momentum of the ball over a larger period of time thus reducing the force on the ball and in turn the force on the hand.
The momentum of an apple falling to the ground is not conserved because the external force of gravity acts on it. But momentum is conserved in a larger system. Explain.
If we include the Earth as part of the system then momentum is conserved in the apple/Earth system. We just don't see the momentum of the Earth change. The Earth exerts a force on the apple and the apple exerts an equal and opposite force back on the Earth.
If you throw a ball horizontally while standing on roller skates, you roll backward with a momentum that matches that of the ball. Will you roll backward if you go through the motions of throwing the ball, but instead hold on to it? Explain in terms of momentum conservation.
If you hold onto the ball, you will not roll backwards. The initial momentum of the ball & skater system is zero and if momentum is conserved then the total momentum after the two interact must also be zero. In order to impart momentum to the skater, the ball must be given some momentum. If the skater does not release the ball then the ball does not get momentum.
Can a machine multiple input force? Input distance? Input energy?
In a simple machine, the input energy (work) is equal to the output energy (work). Since work = force x distance, this means that a simple machine can change the input force to a different output force and can also change the input distance to a different output distance. In general if the output force is greater than the input force, then the output distance will be less than the input distance
The examples of the two previous exercises can be explained both in terms of momentum conservation and in terms of Newton's third law. Explain your answers to 7 & 8 in terms of Newton's 3rd law.
In both of the above cases, when one object exerts a force on a second object, the second object exerts an equal but opposite force back on the first according to Newton's 3rdLaw. So in the case of the person on the ice, when the person applies a force on the cloths, the cloths exert an equal force back on the person. In the case of the skater, when the skater exerts a force on the ball (throwing it), the ball exerts a force back on the skater but the skater must release the ball to apply the force.
If you push a crate horizontally with 100 N across a 10-m factory floor, and friction between the crate and the floor is a steady 70 N, how much KE is gained by the crate?
In this case there is a horizontal force of 100 N forward and a 70 N frictional force acting backward. Thus the net force is (100N)+(-70N) = 30 N The work done is then W = (30 N)(10 m) = 300 J. The gained kinetic energy is thus 300 J
If the equally massive cars of the previous question stick together after colliding inelastically, how does their speed after the collision compare with the initial speed of car A?
In this case, the initial momentum of car A must be shared between the two cars after the collision. Thus, the speed of the combined system will be ½ the original speed of car A.
Your friend says that the law of conservation of momentum is violated when a ball rolls down a hill and gains momentum. What do you say?
Momentum is conserved in the absence of any external forces acting on the objects. In other words, the objects can exert forces on one another but there can not be any other forces that don't cancel out on the objects. In the case of a ball rolling down a hill, gravity is an external force that is causing the ball to speed up. Since the gravitational force is not completely canceled by the support force (as would be the case if the ball was rolling on a flat surface) then momentum is not conserved.
Two cars are raised to the same elevation on service station lifts. If one car is twice as massive as the other, how do their potential energies compare?
Once again, according to the definition of potential energy, PE = mgh, the potential energy is directly proportional to the mass of the object. If the mass is doubled, then the potential energy is also doubled
Automobiles were previously manufactured to be as rigid as possible, whereas today's autos are designed to crumple upon impact. Why?
Same reason as above, by allowing the autos to crumple the impact time has increased and thus the force has decreased.
What does it mean to say that momentum (or any quantity) is conserved?
Saying that momentum, or any quantity, is conserved means that it stays fixed for specific situations. This means that the value it starts off with will be the same as the value it ends with.
Which has greater momentum, an automobile at rest or a moving skateboard?
Since the automobile at rest has zero momentum, the moving skateboard has a larger momentum (even though it has a much smaller mass as compared to the automobile).
What is the efficiency of a machine that miraculously converts all the input energy to useful output energy?
Since the efficiency is a measure of the output energy as compared to the input energy, this would be 100% efficient.The closed the out put energy is to the input energy, the closer the efficiency is to 100%
On a playground slide, a child has potential energy that decreases by 1000 J while her kinetic energy increases by 900 J. What other form of energy is involved, and how much?
Since the loss of PE is not equal to the gain in KE, some other form of energy must be involved. This is likely heat energy due to friction between the surface of the slide and the child. Anytime friction is present, energy will not be conserved
Railroad car A rolls at a certain speed and makes a perfectly elastically collision with car B of the same mass. After the collision, car A is a rest. How does the speed of B after the collision compare the initial speed of A?
Since the railroad cars are identical and momentum is conserved. The momentum of car B must equal the momentum that car A started with. Car B will have the same speed as car A had before the collision. In elastic collisions when the cars are identical and one car starts from rest, after the collision, the car that was at rest will move at the speed of car that was moving before the collision.
If a machine multiplies force by a factor of four, what other quantity is diminished, and by how much?
Since to work remains unchanged and W=fd. If the force increases by a factor of 4 then the distance, d, must diminish by a factor of 4 or in other words 1/4 the distance of the input distance
When the mass of a moving object is doubled with no change in speed, bu what factor is its KE changed?
The KE doubles. Since KE= 1/2mv(squared), the KE is directly proportional to the mass of the object
At what point in its motion is the KE of a pendulum bob at a maximum? At what point is its PE at a maximum? When its KE is half its maximum value, how much PE does it poses?
The KE is a maximum when the PE is at a minimum which occurs at the lowest position of the pendulum. The PE is a maximum at the highest position of the pendulum. At this point, the KE is zero, Bot the KE and PE are half their maximum values when the pendulum is half way between its maximum position and minimum position
Does the KE of a car change more when it goes from 10 to 20 km/h or when it goes from 20 to 30 km/h?
The KE of the a car changes more when it goes from 20 to 30 km/h. In the formula for KE = ½ mv2 the velocity is squared and thus the larger values for the velocity will have a bigger change. (20)2 - (10)2 = 400 - 100 = 300 (30)2 - (20)2 = 900 - 400 = 500
When the velocity of an object is doubled, by what factor is its kinetic energy changed?
The KE will increase by a factor of 4. The KE is directly proportional to the velocity squared, therefore whatever happens to the velocity you must square that effect to see what happens to the KE. Double velocity = 2 squared = 4
An apple hanging from a limb has PE because of its height. If the apple falls, what becomes of this energy just before it hits the ground?
The PE is converted into KE
An ice sail craft is stalled on a frozen lake on a windless day. The skipper sets up a fan as shown. If all the wind bounces backward from the sail, will the craft be sent in motion? If so, in what direction?
The craft will not be set in motion. The fan pushes on the air and the air pushes pack on the fan. If the sail was not present, the ice sail craft would move backwards according to this picture. In this case, the air travels forward and strikes the sail pushing it forward but the sail pushes back on the air in the opposite direction. So there are two forces on the sail craft. A force from the air on the fan pushing it backward and a force from the air on the sail pushing it forward. These two forces cancel and the ice sail craft will not move.
Which undergoes the greatest change in momentum: (1) a baseball that is caught, (2) a baseball that is thrown, or (3) a baseball that is caught and then thrown back, if all of the baseballs have the same speed just before being caught and just after being thrown?
The greatest change in momentum comes from the ball that is caught and then thrown again with the same speed. Let's consider a simple example. Suppose the ball has a mass of 1 kg and the speed of the ball is 1 m/s. For each case above, let's consider the change in momentum. Assume a ball that is coming at the person has negative velocity in terms of direction and a ball the is thrown has positive velocity as compared to the person. (1)Δp = (mv)final -(mv)initial= 0 -(1kg)(-1m/s) = 1 kg m/s (2)Δp = (mv)final -(mv)initial= (1kg)(1m/s) -0 = 1 kg m/s (3)Δp = (mv)final -(mv)initial= (1kg)(1m/s) -(1kg)(-1m/s) = 2 kg m/s Because the ball changes direction in the last case, the change in momentum is greater. You can also think about this in terms of forces. You have to have force to catch the ball and then also force to throw it. This is different than just catching or just throwing.
In terms of impulse and momentum, why do airbags in cars reduce the chances of injury in accidents?
This is very similar to the question above. According the impulse momentum relationship, Σf=Δp/t , by increasing the time to stop, the force required will be less.
A moving car has kinetic energy. If it speeds up until it is going four times as fast, how much kinetic energy does it have in comparison?
This question is easiest to consider by giving some numbers to mass and velocity. Let's assume the mass of the object is 2 kg and the starting speed is 1 m/s. The starting kinetic energy is then KE = ½ m v squared = ½ (2 kg)(1 m/s)2 = 1 J Now, let's consider what happens when the speed increase to 4 times as fast so that v = 4 m/s. In this case the kinetic energy isKE = ½ m v squared = ½ (2 kg)(4 m/s)2 = 16 J The kinetic energy increases by a factor of 16. Basically, however must the velocity increases, you must square that value to see how the KE increase (4)squared = 16.
Why does the force of gravity do work on a car that rolls down a hill, but no work when it rolls along a level part of the road.
When a car rolls down a hill, some of the motion is in the downward direction which is also the direction of the force. (Gravity is helping the car move). When part of the force is directed along the motion, work is done. In the case of a car traveling on a level road, the force of gravity is perpendicular to the motion and any for that is perpendicular to the motion does not do work on the object.
In the absence of air resistanc, a ball thrown vertically upward with a certain initial KE returns to its original level with the same KE. When air resistance is a factor affecting the ball, does it return to its original level with the same, less, or more KE?
When air resistance is present, the ball will return to the position that it was thrown will less KE. The ball will not reach the same maximum height when air resistance is present since the air resistance is opposing the motion. In the same regard, as it falls back to the level it was thrown, air resistance opposes the motion and thus it will not be traveling fast
A boxer can punch a heavy bag for more than an hour without tiring, but tires quickly when boxing with an opponent for a few minutes. Why? (Hint: When the boxer's fist is aimed at the bag, what supplies the impulse to stop the punches? When the boxer's fist is aimed at the opponent, what or who supplies the impulse to stop the punches that don't connect?)
When the boxer punches a heavy bag, the bag supplies the impulse to stop the punch. The boxer pushes on the bag but the bag also pushes back on the boxer. When the boxer aims at an opponent but the punch doesn't make contact, the boxer must supply the force to stop the punch. In the case of the heavy bag, the impact time to stop thepunch is very short and thus the force is relatively large. On the other hand, when the boxer does not make contact with the opponent, the boxer must stop the punch over a longer period of time. The force is less than the case of the heavy bag but the force must be supplied by the boxer.
If you throw a raw egg against a wall, you'll break it; but, it you throw it with the same speed into a sagging sheet, it won't break. Explain, using concepts from this chapter.
When the egg is thrown against a wall, it stops very quickly in comparison to when the egg is thrown into a sagging sheet where the time to stop is larger. There will be less force on the egg that is caught in the sheet due to the time of impact being larger.
A fully dressed person is at rest in the middle of a pond on perfectly frictionless ice and must get to shore. How can this be accomplished? Explain in terms of momentum conservation.
When the person is standing on the pond at rest, the initial momentum of the person is zero. If the person were to take off some of his/her cloths and toss the cloths quickly away from his/her body, the cloths would have momentum in one direction. Since momentum is conserved, the person would get equal and opposite momentum in the other direction. The person might not travel very fast but if the ice were frictionless, they would eventually reach the other end of the pond.
