Problem set involving Momentum and bowling balls

[Matt Poirier]

Homework Statement

Say you're bowling and you roll the ball down the lane. The bowling ball has just knocked the first bowling pin forward and that pin's forward velocity is now much larger than the bowling ball's velocity before their impact. How can the pin travel forward faster than the ball was moving without violating conservation of momentum?
Answer Choices:

• A. Since the pin has much less mass than the ball, the pin can have a larger forward velocity than the ball and still have less forward momentum than the ball had before their impact.
• B. During their impact, the ball transfers both momentum and energy to the pin and those two quantities add together to give the pin a very high forward velocity.
• C. The conservation of momentum applies only to objects that are moving in opposite directions. As long as the ball and pin move in the same direction, they aren't constrained by the conservation of momentum.
• D. The conservation of momentum applies only to an isolated object. When two objects touch, their total combined momentum is no longer a conserved quantity.

#2
The bowling ball hits another bowling pin and knocks that pin into the air. The pin travels in an arc before crashing into the back of the bowling lane. While this flying pin isn't touching anything, which of its physical quantities is constant? Note: assume that there is no air resistance.

• 
  A. The pin's momentum is constant.
• 
  B. The pin's speed is constant.
• 
  C. The pin's velocity is constant.
• 
  D. The pin's angular momentum is constant.

#3
According to bowling regulations, a newly constructed bowling lane must be flat and level to within a 1/25th of an inch. If the lane had significant hills and valleys in its surface, or if it were tilted, how would those defects affect the bowling ball's motion on the lane?

• 
  A. The ball's velocity would point in the direction that reduced its total potential energy as quickly as possible.
• 
  B. The ball would accelerate in the direction that reduced its total potential energy as quickly as possible.
• 
  C. The ball would travel directly downhill on each defect and would follow a complicated path to the pins.
• 
  D. necessarily travel directly downhill.

Homework Equations

Momentum = mass * velocity

The Attempt at a Solution

I believe the answers are A, A, and B, respectively, but I am not sure.

 

[berkeman]

I believe the answers are A, A, and B, respectively, but I am not sure.

Can you tell us your reasoning on each?

 

[FactChecker]

I disagree with one of your answers, but this sounds like a homework problem. I think that you should explain your answers to get help or comments.

 

[Matt Poirier]

Can you tell us your reasoning on each?

So the first one: the pin has less mass than the ball, which means that the change in momentum it experiences can mean that it has more velocity to make up for less mass, even if the momentum isn't the same as the ball originally had. For 2, I am really not sure, an object traveling in an arc has changing velocity (constant acceleration), as does its speed(right?), and there's no mentioning of rotation, which would mean angular momentum doesn't make sense, so this one really stumps me. And for 3, this is a general principle rule in physics that I found, an object will accelerate in the direction in which its potential energy decreases.

 

[Matt Poirier]

I disagree with one of your answers, but this sounds like a homework problem. I think that you should explain your answers to get help or comments.

Here, I tried to explain my reasoning to the best of my abilities, thank you for commenting.

 

[FactChecker]

Here, I tried to explain my reasoning to the best of my abilities, thank you for commenting.

That's better. Thanks.

So the first one: the pin has less mass than the ball, which means that the change in momentum it experiences can mean that it has more velocity to make up for less mass, even if the momentum isn't the same as the ball originally had.

Sounds right.

For 2, I am really not sure, an object traveling in an arc has changing velocity (constant acceleration), as does its speed(right?), and there's no mentioning of rotation, which would mean angular momentum doesn't make sense, so this one really stumps me.

So constant mass and changing speed should rule out some options. Even if they say nothing about angular momentum, you should know something about it.

And for 3, this is a general principle rule in physics that I found, an object will accelerate in the direction in which its potential energy decreases.

Sounds right.

 

[Matt Poirier]

That's better. Thanks.
Sounds right.So constant mass and changing speed should rule out some options. Even if they say nothing about angular momentum, you should know something about it.Sounds right.

Constant mass and changing speed basically rules out every option besides angular momentum, but I am just not sure considering nothing is said of the pin spinning.

 

[Matt Poirier]

That's better. Thanks.
Sounds right.So constant mass and changing speed should rule out some options. Even if they say nothing about angular momentum, you should know something about it.Sounds right.

but the more I think about it, the more I believe it is angular momentum.

 

[FactChecker]

but the more I think about it, the more I believe it is angular momentum.

What principles do you know that you can apply?

 

[Matt Poirier]

What principles do you know that you can apply?

None other than the other options aren't viable.

 

[FactChecker]

Have you covered conservation of angular momentum? All the basic conservation laws are extremely important.

 

[Matt Poirier]

Have you covered conservation of angular momentum? All the basic conservation laws are extremely important.

Yes just looked over them to confirm my answer, thank you so much!