A force of 1050 N is needed to move a crate weighing 311 kg up a ramp that is 3.89 m long. If the elevated end of the ramp is 0.770 m high, what is the efficiency of the ramp?
To calculate the efficiency of the ramp, we first need to find the work input and the work output.
The work input is calculated by multiplying the force needed to move the crate by the distance over which the force is applied:
Work input = Force × Distance
Work input = 1050 N × 3.89 m
Work input = 4084.5 N·m
The work output is calculated by multiplying the weight of the crate by the vertical distance it moves up the ramp:
Work output = Weight × Height
Work output = 311 kg × 9.8 m/s^2 × 0.770 m
Work output = 2287.806 N·m
The efficiency of the ramp is then given by the ratio of the work output to the work input, multiplied by 100% to express it as a percentage:
Efficiency = (Work output / Work input) × 100
Efficiency = (2287.806 N·m / 4084.5 N·m) × 100
Efficiency = 55.99%
Therefore, the efficiency of the ramp is approximately 55.99%.