Question

In: Physics

A block slides down a frictionless inclined ramp. If the ramp angle is 26° and its...

A block slides down a frictionless inclined ramp. If the ramp angle is 26° and its length is 29 m, find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

Expert Solution

There are two forces acting on the block: mg is the gravitational force of the Earth, N is the normal force of the ramp on the incline. The free body diagram of the block is shown below:

The gravitational force is resolved into components parallel and perpendicular to the ramp. The block is not allowed to move in the direction perpendicular to the ramp, the net force on the block in this direction is zero.

The net force along the ramp accelerates the block, the acceleration is given by Newton's second law of motion.

Substituting we get

The acceleration of the block along the incline is constant, the motion of the block along the incline is governed by the kinematics equations for uniformly accelerated motion. To find the final speed of the block we use

where u is the initial velocity, L is the length of the ramp.

Given the block starts from rest u=0, substituting L=29m, a=4.296m/s² we get

genius_generous answered 4 months ago

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