Question on problem in TBR Physics Ch4

[Abe468]

I had a problem with Q#48 (passage 7). It was basically like there is a car moving north and then a larger truck moving south each at the same speed. They collide. After collision, the car moves east with the same speed pre-collision. What direction is the truck moving in?

I originally thought it was west, but TBR says southwest.

My first problem with this question is if they're are only moving on a north-south axis, how does the car end up going east in the first place? The explanation says that by conservation of momentum the truck must gain some westward direction, but also since the car is no longer moving on a north-south axis, the truck must have all the movement in that direction and so it's moving southwest. I don't know, for some reason the explanation just didn't make sense to me. Any help is appreciated!

Oh if someone has time in looking at Question #26 for Passage IV in that same chapter, I could use a little help in understanding that diagram and what the question is saying too. When they say spindle radius R, do they mean the radius of the lower spindle wheel in the figure, or do they mean the thicker top wheel so that the masses are held farther apart?

Thanks,
Abe

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[austinap]

I had a problem with Q#48 (passage 7). It was basically like there is a car moving south and then a larger truck moving north each at the same speed. They collide. After collision, the car moves east with the same speed pre-collision. What direction is the truck moving in?

I originally thought it was west, but TBR says southwest.

My first problem with this question is if they're are only moving on a north-south axis, how does the car end up going east in the first place? The explanation says that by conservation of momentum the truck must gain some westward direction, but also since the car is no longer moving on a north-south axis, the truck must have all the movement in that direction and so it's moving southwest. I don't know, for some reason the explanation just didn't make sense to me. Any help is appreciated!

Oh if someone has time in looking at Question #26 for Passage IV in that same chapter, I could use a little help in understanding that diagram and what the question is saying too. When they say spindle radius R, do they mean the radius of the lower spindle wheel in the figure, or do they mean the thicker top wheel so that the masses are held farther apart?

Thanks,
Abe

This is a classic conservation of momentum problem. A good way to do these is to think about each axis separately.

To start with, there is no momentum in the east-west axis, so the same must be true after any collision. Since the car is moving east after the collision, the truck must have some momentum in the west direction to cancel this. Since the truck weighs more, west velocity of the truck must be less than the east velocity of the car.

Now think about the north-south axis. Since they are moving at the same speeds but the truck weighs more, there is more momentum in the truck's direction of travel (north). After the collision, the car has no north-south momentum, so all of the original momentum on this axis must now belong to the truck. Thus, the truck must still have some northern velocity.

So, the truck has some velocity in the north direction, and some velocity in the west direction. The truck is moving northwest. I think you switched the initial directions of travel in your explanation.

How can the car now have an eastern velocity when initially there was only north south? It 'took' it from the truck. Think about bouncing a ball off of a wall at an angle. it's the same idea.

 

[loveoforganic]

The answer is actually southwest. I think it's a mistake, and agree with austinap's explanation.

Edit: nvm, you did switch the directions

 

[Abe468]

Oh sorry about that...I did switch the truck and car directions. Truck was actually going south and the car was going north. I'll edit that in a second. Thanks for the response! I think I have a better understanding of it after reading your explanation.