Ch. 8

If you dive into water, you reach greater depths than if you do a belly flop. Explain this difference in depth using the concept of conservation of energy. Explain this difference in depth using what you have learned in this chapter.

A belly flop spreads out the person's energy (and momentum) over the surface of the water causing more particles of water to absorb energy (and momentum). Therefore, the person does not have as much energy (and momentum) to move more deeply into the water than if a "dive" is used to enter the water.

Football coaches advise players to block, hit, and tackle with their feet on the ground rather than by leaping through the air. Using the concepts of momentum, work, and energy, explain how a football player can be more effective with his feet on the ground.

A player who has just leaped into the air has lost some of his energy and, therefore, momentum by pushing off on the ground.

Can momentum be conserved for a system if there are external forces acting on the system? If so, under what conditions? If not, why not?

All circumstances! Depending on how we define the system and surroundings depends on if we can actually "see" the conservation. A big surroundings, e.g. the Earth, will not show the conservation of momentum as easily as a smaller surroundings, e.g. a second car in a two-car collision.

Under what circumstances is momentum conserved?

All circumstances! Depending on how we define the system and surroundings depends on if we can actually "see" the conservation. A big surroundings, e.g. the Earth, will not show the conservation of momentum as easily as a smaller surroundings, e.g. a second car in a two-car collision.

How can a small force impart the same momentum to an object as a large force?

By traveling at a higher velocity.

What are other ways of writing ptot=constant?

DeltaU=0. Uuniverse-final - Uuniverse-initial=0.

What does a prime (') indicate?

Final momentum.

What is Newton's second law in terms of momentum? Where did this relationship come from?

Fnet=delaP/deltaT.

How can a force be less harmful? Give an example.

If it is exerted over a distance (therefore time). Car bumpers lessen the force before it reaches the actual body of the car lessoning the impact.

What is the name given to change in momentum?

Impulse.

What is an inelastic collision? What is a perfectly inelastic collision?

Inelastic collisions are those that do not conserve internal kinetic energy.

What does it mean that momentum is a vector?

It has both magnitude and direction.

While jumping on a trampoline, sometimes you land on your back and other times on your feet. In which case can you reach a greater height and why?

Landing on your feet allows a greater height to be reached because the force with which one lands is larger (same momentum in a compact area), the impact is greater.

Explain in terms of momentum and Newton's laws how a car's air resistance is due in part to the fact that it pushes air in its direction of motion.

Newton's third law is that a force has an equal and opposite force against it. The car "pushes" against the air, which is F1. The air pushes back against the car, which is F2. Therefore, 𝑭𝟏 = −𝑭𝟐. Therefore, we can also use the momentum equation of ∆𝒑𝟐 = −𝑭𝟏∆𝑡 = −∆𝒑𝟏 to show that we have conservation of momentum through air resistance.

What is an elastic collision?

One in which there is no net change in kinetic energy.

Explain in terms of impulse how padding reduces forces in a collision. State this in terms of a real example, such as the advantages of a carpeted vs. tile floor for a day care center.

Padding is like the car bumper example: the padding allows the force to begin to lessen before it reaches the bumper. In terms of the impulse formula, ∆𝒑 = 𝑭𝒏𝒆𝒕∆𝑡, the longer the time, the less the momentum the force applies. Another example is a hard bench versus a nice, soft couch. If we plop down on either, the impact is lessened by the padding on the couch.

An object that has a small mass and an object that has a large mass have the same momentum. Which object has the largest kinetic energy?

Since they both have the same momentum, the object with the larger mass has a small velocity. (Remember that mass and velocity are inversely proportional with p=mv.) Therefore, the smaller object will have the larger KE. (KE = 1/2 𝑚𝑣^2)

Tennis racquets have "sweet spots." If the ball hits a sweet spot then the player's arm is not jarred as much as it would be otherwise. Explain why this is the case.

The "sweet spot" lessens the impact.

How can objects that have equal force have larger momentums?

The force with a larger momentum will be acting on it for a longer time period.

Must the total energy of a system be conserved whenever its momentum is conserved? Explain why or why not.

The key phrase in this question is "energy of a system". The system does not have to conserve its energy because it may give (or receive) its energy to the surroundings. The energy of the universe is constant. The same principle applies to momentum.

When can Fnet=ma be used?

When mass is constant. The new form allows us to have systems where the mass is changing such as in nuclear chemistry.

Is momentum always conserved?

Yes, it is like energy. This is expressed by saying ptot=constant.

Can objects in a system have momentum while the momentum of the system is zero? Explain your answer.

Yes. Think of the two-car collision example. If we define the system to include both cars, then the momentum that one car loses is gained by the other car. This means there is a net change of momentum equal to 0, ∆𝒑𝒕𝒐𝒕 = 𝟎. But that system doesn't have a zero momentum to start with (or end with). To have a system that has zero momentum to start and end with, think of 3 cars lined up with a small space between each one. We define the system as the first two cars. A fourth car travels and hits the first car, which hits the second car, which hits the third car. The 4th, 1st, and 2nd cars all stop because they have transferred their energy to other cars. The third car moves until friction stops it. The momentum entered the system through car #4 and exited the system through car #2's collision with car #3. Therefore, the system started and ended with zero momentum while objects inside it had momentum for a time.

An object that has a small mass and an object that has a large mass have the same kinetic energy. Which mass has the largest momentum?

p=mv. Therefore, the object with larger mass will have the larger momentum.