A construction crew pulls up an 87.5 kg load using a rope thrown over a pulley and pulled by an electric motor. They lift the load 15.5 m and it arrives with a speed of 15.6 m.s having started from rest. Assume that acceleration was not constant.
How much work was done by the motor?
Potential Energy change PLUS kinetic energy change
To find the work done by the motor, we can use the work-energy principle. According to the principle, the work done on an object is equal to the change in its kinetic energy.
The initial speed of the load is zero, so its initial kinetic energy is zero. The final speed of the load is 15.6 m/s, so its final kinetic energy is given by:
Final Kinetic Energy = (1/2) * mass * (final velocity)^2
Final Kinetic Energy = (1/2) * 87.5 kg * (15.6 m/s)^2
Final Kinetic Energy = 0.5 * 87.5 kg * 243.36 m^2/s^2
Final Kinetic Energy = 10659 J
Since the initial kinetic energy is zero, the work done by the motor is given by:
Work done by motor = Final Kinetic Energy - Initial Kinetic Energy
Work done by motor = 10659 J - 0 J
Work done by motor = 10659 J
Therefore, the work done by the motor is 10659 Joules.