# Mass on the wedge

1. Jan 22, 2013

### Gloyn

1. The problem statement, all variables and given/known data
We have a body of mass M placed in a kind of sledge like on the picture:

Coefficient of fristion between the mass and the sledge is zero, but the coefficient of friction between the wedge and the sledge is μ. Angle of the wedge is α. The sledge is massles. The slegde is pushed with some initial velocity up the wedge. What are the forces that the mass M acts with on the plates at the sides of the sledge?

2. Relevant equations

Inertial force: F_I=-ma
2nd Newten s Law F=ma

3. The attempt at a solution

If the sledge was not moving, the force acting on the left plate would be F=mg*sinα, but since it is moving, we calculate the acceleration down the wedge, which is:

ma=mg*sinα+mgμ*cosα -> a= g(sinα+μ*cosα)

So the resultant force is:

F=mg*sinα-(mg*sinα+mgμ*cosα)=-mgμ*cosα

and it points up the wedge. Is that right?

2. Jan 22, 2013

### apelling

I sort of agree with you but would quibble over the wording.

The resultant force is always given by ma.

When going up the slope a=g(sinα+μ*cosα)
But when going down a=g(sinα-μ*cosα)
Resultant F=ma=mg*sinα+ reaction force from plates.
Reaction force from plates=±mgμ*cosα
So when going up the slope the mass is pushing on the plate to the right in your diagram, but when sliding down pushes on the left hand plate.

3. Jan 22, 2013

### Gloyn

You're right of course :) Thanks for help!

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