# Homework Help: What happens to 's' if mass changes in this situation

1. Apr 22, 2015

### Alice Saka

1. The problem statement, all variables and given/known data
A spring is used to launch a two 1kg blocks down a ramp from the top. One of the block is stack (fused) on top of the other.
If the mass of the blocks were to change, i.e. double (making it 2kg blocks). does this change the displacement of this system? This system also has friction coming from the contact between the block and the ramp.

Due to confusion, new way to read it:
Basically the block is going down the ramp via a spring launching it. The block and ramp have friction between them. After the block is launched, it will have a displacement due to the work done by the spring and (I assume) gravitation potential energy.
Now we swap the blocks out for another heavier one and repeat this procedure. Would the increase of mass have us get a different displacement than using the lighter block.

2. Relevant equations
?

3. The attempt at a solution
I was thinking F=ma and that by increasing the mass of the object, the Net Force should increase as well. Therefore the displacement should also increase as there is more force on the blocks. I've also thought about the gravitational potential energy and that it will also increase the displacement if the mass was to change due to more stored energy.

Last edited: Apr 22, 2015
2. Apr 22, 2015

### Staff: Mentor

Which displacement?
Is there a sketch?

That depends on the possible change of the acceleration, but currently I have no idea what is moving where why,

3. Apr 22, 2015

### Alice Saka

No sketch. This is why I'm confused too.
Basically the block is going down the ramp via a spring launching it. The block and ramp have friction between them. After the block is launched, it will have a displacement due to the work done by the spring and (I assume) gravitation potential energy.
Now we swap the blocks out for another heavier one and repeat this procedure. Would the increase of mass have us get a different displacement than using the lighter block.

4. Apr 22, 2015

### Staff: Mentor

Is this the exact and full problem statement? Then it is too ambiguous.
Also, where is the point in having two masses if they are fused together.

You can compare how far the blocks will slide down the ramp, assuming the ramp does not move.

5. Apr 22, 2015

### Alice Saka

This is a modified version of the problem statement due to the original being more confusing because this was given by a student teacher whose English isn't her first language.
I think saying that the two blocks being fused together might have been a mistake and she meant one block.

If you want me to keep modifying this question to find out what you're looking for,
If you were to change the mass of the block, how would this affect the displacement on the block?

Also I realised F=ma cant happen due to the spring, so the net force applied to the block doesn't change as the force given by the spring stays the same (1/2*k*x2)
If the block was being pushed horizontal, I can say for certain that the displacement goes down if mass goes up. But I don't know if that is also true for the block going down the ramp due to gravitational potential energy.

6. Apr 22, 2015

### Staff: Mentor

I'm not sure if that helps, every translation step can have errors.

F=ma is a fundamental law - it does happen. That does not mean you can use it everywhere for every question because often you do not know F, m or a.

1/2 k x^2 is not the force, it is a different (and useful) quantity.

7. Apr 22, 2015

### Alice Saka

I feel bad for wasting your time with this stupid question now.
Lets just end it here, but I'll need confirmation on my attempt.

My attempt:
Potential Energy in the spring stays the same and exerts the same amount of energy on the block. However the work done on the block is different. Since the block is heavier, the amount of energy exerted on the heavier block does not push it down the ramp as far as it did for the lighter block.
If mass increases, the displacement goes down (if we were to only look at the spring part).

Now for Gravitational Potential Energy.
Potential Energy (PE) is mass*gravity*height (PE = mgh). If mass were to increase, then the overall PE would increase as well. Even though PE increases, it doesn't increase the displacement of the block as it is proportional (I think).

Therefore, increasing the mass of the block in system will decrease the overall displacement.

8. Apr 22, 2015

### Staff: Mentor

Proportional to what?
Right. It has the same effect as weakening the spring where that result is obvious.