1. If you want to use a ramp to lift a 50 kg box up 3 m using 100 N of force, how long should the ramp be?

2. If the ramp is only 80% efficient, due to friction, how long would it need to be?

1) 14.7 m

2) 18.4 m

Explanation:

1)

Assuming that the ramp is 100%, we can apply the law of conservation of energy: this means that the work done in input to lift the box must be equal to the work done in output.

So we can write:

where

is the work in input, where

is the force applied in input

is the distance through which the input force is applied (which corresponds to the length of the ramp)

is the work in output, where

is the force in output, which corresponds to the weight of the box (m = 50 kg is the mass of the box and is the acceleration due to gravity)

is the distance through which the box has been lifted

Solving for , we find the length of the ramp:

2)

In this case, the ramp is only 80% efficient, due to the presence of friction forces. This means that only 80% of the work done in input is converted into work in output.

Therefore in this case, we can write:

Which means that the output work is only 80% of the work in input.

The equation can be rewritten as

And we have

Solving for , we find the new length of the ramp: