Friction force on an inclined plane

[PhysicsIsKillingMe]

Homework Statement

A speed of a body of mass 8 kg is 6 m/s in position A. By the time it gets to B, the speed is measured to be 12 m/s. What is the frictional force opposing the motion?

The incline is 30 degrees, the height of the ramp is 12 meters. Position A is at the top of the ramp, position B is at the bottom.

Homework Equations

[/B]
The coefficient of static friction: µ = tan 30°

The Attempt at a Solution

[/B]
At first I tried to find the length of the ramp, let it be x.

Sin 30° = 12/X
X = 12/Sin 30°
X = 24 meters

After that I tried to find the coefficient of static friction, which turned out to be tan 1/2. After that I got lost.

 

[stockzahn]

Homework Equations

The coefficient of static friction: µ = tan 30°

This calculation would imply that the body doesn't accelerate (even doesn't move, since you call it static friction). But the (modified) equation you used to calculate it will be helpful to solve the problem.

After that I tried to find the coefficient of static friction, which turned out to be tan 1/2. After that I got lost.

So that's obviously not true.

The Attempt at a Solution

[/B]
At first I tried to find the length of the ramp, let it be x.

Sin 30° = 12/X
X = 12/Sin 30°
X = 24 meters

That's a good start, but to develop the solution I suggest to use the symbols and plug in the numbers only in the end.

How did you want to calculate the coefficient of static friction? Could you write down the formula?

 

[haruspex]

The coefficient of static friction: µ = tan 30°

Where are you getting that from? It looks like you are taking it from a quite different scenario, one in which a body is on the point of sliding down a 30° slope.
It certainly is not true here.

 

[Chandra Prayaga]

A diagram, followed by a free-body diagram is always a good place to start. As post #3 points out, you are not looking at static friction at all. The body IS sliding.