Velocity change due to load dropped vertically onto trolley

[Maka42]

A trolley is moving at a constant speed down a track, with no net force acting upon it. A heavy load is dropped vertically on top of the moving trolley. What happens to the trolley's speed?

a) It stays the same,
b) It decreases,
c) It becomes zero,
d) It is impossible to say,
e) It increases (x)

I thought that it would increase as when you increase the mass the component of weight acting to pull the trolley down the slope would increase and so it would begin to accelerate, unfortunatley the computer told me I was wrong. The question doesn't really say if there is still no net force after the mass was added.

I only have one try left on this question and I can't find any relevant information anywhere!

Any help would be greatly appreciated! :)

 

[NascentOxygen]

Hi Maka42.

moving at a constant speed down a track

This doesn't say it's sliding down a slope; it just means the trolley is moving along a track.

In future, please retain and make use of the template headers that are provided when posting to the homework forum.

 

[Maka42]

I interpreted it that way at first as well, I feel like "down a track" can mean its both going down a slope and a flat surface. If it was a flat surface would that mean the kinetic force of friction would increase and thus make it go slower?

 

[NascentOxygen]

You are not told there is friction.

 

[Maka42]

Hmm, well if there is no friction then I guess that means the velocity would stay the same. Thanks for your help! I guess my problem was more with the English rather than the physics, good thing I'm doing a physics degree rather than an English one!

 

[NascentOxygen]

if there is no friction then I guess that means the velocity would stay the same.

You don't get marked for guesses! You need to justify you answer soundly based on physics principles.

 

[Maka42]

That's very true, well I suppose since there is no friction in the horizontal direction, the increase in weight would simply be balanced by the reaction force and so there would still be no net force meaning velocity would be unchanged.

 

[haruspex]

As it happens, it doesn't matter which way you interpret it, as horizontal without friction or down a slope with friction exactly matching the downslope component of gravity. The increased mass would increase both forces in proportion, so no gain in speed from that.

 

[Maka42]

Oh, It never occurred to me that it both the forces would change proportionally. Thanks for your reply, I definitely won't be making these mistakes again!

 

[gneill]

<Mentor's note: Thread title changed to be more descriptive of problem>

 

[NascentOxygen]

That's very true, well I suppose since there is no friction in the horizontal direction, the increase in weight would simply be balanced by the reaction force and so there would still be no net force meaning velocity would be unchanged.

So you're saying the load would speed up so it exactly matches the horizontal speed of the trolley before it became loaded?

 

[Maka42]

Well I thought that the speed would remain constant throughout because there is no net force horizontally and due to Newton's first law the speed would remain unchanged. I feel as though I'm missing something important though.

 

[NascentOxygen]

If the cargo is going to acquire the speed of the unloaded trolley, you'll need to explain where the energy to do this will come from.

Newton's Law is written as applying to "a body", whereas in the situation here we have two bodies that combine into one.

 

[haruspex]

Well I thought that the speed would remain constant throughout because there is no net force horizontally and due to Newton's first law the speed would remain unchanged. I feel as though I'm missing something important though.

I encourage students to develop a feel for mechanics problems by thinking themselves into it. While running, you grab a heavy package off a table next to you. Does it affect your speed? What force do you feel?
If that doesn't do it for you, what conservation laws can you quote that might be relevant?

 

[NascentOxygen]

Note: I have reset the "solved" tag in this thread's subject line, because I see no indication that the problem has been solved.

 

[Maka42]

Hmm, well now that I think about it, the total momentum before and after are different, as the load is moving vertically and the cart is moving horizontally. Which means an external force is acting.

 

[haruspex]

Hmm, well now that I think about it, the total momentum before and after are different, as the load is moving vertically and the cart is moving horizontally. Which means an external force is acting.

Consider those two directions separately.
In each direction, how do you know that total momentum (of the cart+load system) has changed; what external force might account for it?

 

[Maka42]

Hmm, all I can think of is the normal force adjusting due to the momentum of the weight. But then I'm not really sure how that would change the velocity if there's no friction.

 

[haruspex]

Hmm, all I can think of is the normal force adjusting due to the momentum of the weight. But then I'm not really sure how that would change the velocity if there's no friction.

You mean the momentum of the dropped load. Viewing the cart plus load as a system, the vertical momentum story is a bit complicated. It isn't really relevant to the problem, but here goes. While the load is falling, the total gravitational force exceeds the the normal force (which is only matching the cart's weight), so the system is gaining downward momentum. On landing, there is a sudden, very large increase in the normal force for a fraction of a second. The extra momentum implied matches the momentum gained while the load was falling, leaving the system with no net vertical momentum.

So, back to the horizontal. You agree there is no horizontal force on the system. So what does conservation of momentum in that direction tell you?