# Box sliding down frictionless incline

1. Jan 10, 2010

### pewpew23

1. The problem statement, all variables and given/known data

A box initially at rest at the top of a frictionless ramp is allowed to slide to the bottom. At the bottom its speed is 4 m/s. Next, the box is again slid down the ramp, but this time it does not start from rest. It has an initial speed of 3 m/s at the top. How fast is it going when it gets to the bottom?

2. Relevant equations

No idea....

3. The attempt at a solution

Since the lenght of the ramp, mass of the block, nor the time it takes to get from the top of the ramp to the bottom is given... I don't know where to start with this one.

2. Jan 10, 2010

### jegues

EDIT: What I had done was wrong :).

Matterwave is correct, just use conservation of energy.

Last edited: Jan 10, 2010
3. Jan 10, 2010

### pewpew23

I'm not sure I understand your equation...
vf meaning velocity and ?
vi is initial velocity, correct?

4. Jan 10, 2010

### jegues

Yes, I'm just using a subscript to denote the initial and final states of the velocity.

5. Jan 10, 2010

### Matterwave

Perhaps Jegues' method is simpler, but I would approach this in terms of energy conservation. Potential energy at top = kinetic energy at bottom. The m's will cancel out.

6. Jan 10, 2010

### pewpew23

so a=(vf-vi)/t

a=4/t

a=(vf-3)/t

set them equal to eachother
4/t = vf-3/t

t's cancel out and we get 4= vf-3
and vf=7 :)

7. Jan 10, 2010

### jegues

Bump, I edited my post above. As Matterwave suggested conservation of energy is what you're looking for.

EDIT:
This is what I had initially suggested. It is wrong. Use conservation of energy, sorry in advance for any confusion.

8. Jan 10, 2010

### pewpew23

KE= 1/2mv^2
GPE= mgh

and that would give us h= .81716
but how would I use that solve for vf is vi=3?

9. Jan 10, 2010

### jegues

You generated the height using the first case good!

Now for second case, in the intial state what types of energy are there? In the final state what types of energy are there?

10. Jan 10, 2010

### pewpew23

At the top of the ramp, all energy is in Gravitational Potential (mgh) and KE.
and at the bottom there is only KE.

1/2vi^2 + gh = 1/2vf^2
12.499 = 1/2vf^2
and vf = 4.9

11. Jan 10, 2010

### jegues

Looks correct to me!