Determine the angle of an incline that would yield a constant velocity, given the coefficient of kinetic friction is 0.10.

Explanation:

In order to solve this problem, we mus start by drawing a free body diagram of the given situation (See attached picture).

From the free body diagram we can now do a sum of forces in the x and y direction. Let's start with the y-direction:

so:

now we can go ahead and do a sum of forces in the x-direction:

the sum of forces in x is 0 because it's moving at a constant speed.

so now we solve for theta. We can start by factoring mg so we get:

we can divide both sides into mg so we get:

this tells us that the problem is independent of the mass of the object.

we now divide both sides of the equation into so we get:

so we now take the inverse function of tan to get:

so now we can find our angle:

so

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