How Do You Calculate Friction and Energy Loss on a Slope?

[bjarnidk]

Homework Statement

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.

Homework Equations

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

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...

 

[Chestermiller]

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

 

[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

 

[bjarnidk]

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

 

[Chestermiller]

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

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