Object sliding down a slope

1. Feb 15, 2014

bjarnidk

1. The problem statement, all variables and given/known data
An object slides down a slope of 30° to the horizontal with CONSTANT VELOCITY.
Find the force of friction and the energy lost on the way down.

2. Relevant equations
$$\mu m g \cos \theta$$
$$\mu m g \cos \theta - m g \sin \theta = 0$$
$$W = K_2 + U_2 - (K_1 + U_1)$$

3. The attempt at a solution
I tried the following:

$$\mu mg \cos30 = mg \sin30 = \mu = tan30 \cdot m = 3,3 \cdot m$$

So the ratio is $$3,3m$$? It doesn't sound right...
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 15, 2014

Staff: Mentor

In your force balance equation, the two terms are equal to one another, so they must both be representations of the force of friction (Actually, the second term is the component of the body's weight along the incline, which, as you showed, is equal to the force of friction). Which of these two representations of the force of friction do you think will be easier to work with in the second part of your problem, given that one of them contains μ, and the other term contains only quantities that you know in advance?

Chet

3. Feb 15, 2014

BvU

Doesn't look right either! You divide left and right by cos 30, which is good. Why then divide by m only on the left and not on the right ?

Then: tan 30° is definitely not 3.3

4. Feb 15, 2014

bjarnidk

Sorry, $$\mu$$ is tan30, but the force of friction is 3,3m, would that be correct?

5. Feb 15, 2014

Staff: Mentor

No. As I said in my previous post, the friction force is mgsin30=5m Newtons