Question

A box with a weight of 20 newtons rest at a bottom of a ramp and is pushed to the end of the ramp with a force of 40 newtons. This ramp is an incline of 15 meters long. What is the maximum height of the ramp.

Answer 1

To move maximum height the friction force can be assumed to be

negligible.

• The height of the ramp is 15 meters

Reasons:

The component of the weight acting on the incline, w = m·g·sin(θ)

Length of the ramp = 15 m

Potential energy of the box = 15 × sin(θ) ×20 = 300·sin(θ)

F × 15 = 300·sin(θ)

F = 20·sin(θ)

Work done by net force = Potential energy gained by the box

Work done by net force = (40 - 20·sin(θ)) × 15 = 300·sin(θ)

40 = 20·sin(θ) + 20·sin(θ) = 40·sin(θ)

sin(θ) = 1

θ = arcsin(1) = 90°

The ramp is at an inclination of 90°, therefore, the ramp is oriented vertically

The height of the ramp = The length of the ramp = 15 m

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