# Momentum & speed changes?

• clevername

## Homework Statement

A truck moves on its own horizontally on a frictionless road. A big box is dropped in the bed of the truck, and they continue to coast.

a) Does the horizontal momentum of the system(truck+box) change? Justify answer with relevant theorems.
b)Does the speed of the truck change? If so, what is the new speed?

p=mv

## The Attempt at a Solution

I posted this somewhere else and need a second opinion. I personally thought that since the combined mass would be larger, then it would have a larger momentum. Here's the answer I received from someone else. -

a)Momentum remains same. The speed of the truck decreases so that the momentum remains same.

b)As mentioned above, the speed decreases.

What do you think?

a)Momentum remains same. The speed of the truck decreases so that the momentum remains same.

What do you think?

More Importantly, what do you think? What is the speed of the box? Does the mass of the truck remain the same to validate your logic?

Well, I stated what I thought. It doesn't match with the thoughts of a person who was more seasoned in physics, so I'm trying to get some more input here.

Well, I stated what I thought. It doesn't match with the thoughts of a person who was more seasoned in physics, so I'm trying to get some more input here.

That's very good. Now if you answer the questions I have asked, you will gain the input you are looking for yourself; that's the right way to learn. We are all here to help you.

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I'm not really sure what you mean by what is the speed of the box. If it's dropped into the truck, I would guess it's the same as the truck. Also, I think you are misreading my initial post, and referring to the 3rd partys logic as my own. I think - according to the problem... that the mass will increase, therefore making momentum(p=mv) larger. Adding mass to the system doesn't seem like it would change the speed unless another force was acting on it like friction or wind resistance. Maybe I'm reading the problem wrong. I'm pretty sure I'm making an adequate effort on my end here

I'm not really sure what you mean by what is the speed of the box. If it's dropped into the truck, I would guess it's the same as the truck.
That is obvious, but what I meant was does the speed of the truck plus box system the same as the initial speed of the truck?
I think - according to the problem... that the mass will increase, therefore making momentum(p=mv) larger. Adding mass to the system doesn't seem like it would change the speed unless another force was acting on it like friction or wind resistance.
Use conservation of linear momentum. Now do you think that the speed will change?
I personally thought that since the combined mass would be larger, then it would have a larger momentum.
To change the momentum, you would need a force in the line of motion of the truck. Is any such force acting on the truck?

The really key thing here nobody's made enough of a point of is the speed of the box BEFORE it was dropped into the moving truck. It it was hanging motionless from a crane the truck drove under the result, and equations, would be very different than if it was dropped from a helicopter traveling at the same speed of the truck!