Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. if the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

The mass released from the top of the 60º incline.

Explanation:

The external forces acting upon any of the masses, are the same for both (not numerically): the gravity, the normal force and the friction force.

As the gravity is always directed downward, we can decompose it in a component normal to the surface (that is equal to the normal force as the body is not accelerating in this direction), and another which is parallel to the incline, and which is the responsible for the acceleration of the object along the incline (opposed by the friction force).

So, we can write the following:

Fx = mg sin θ - μk .Fn = m.g. sin θ - μk. mg cos θ= m a

We can easily see, that if the angle is larger, the acceleration component due to gravity will be larger, and at the same time, the friction force will be smaller, so the acceleration for the 60º will be the larger one.

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