Question

a. How much work does an elevator motor do to lift a $1000$kg elevator a height of $100$m?

b. How much power must the motor supply to do this in$50$ s at constant speed?

Short answer

a). work done by elevator motor is $9.8·{10}^5$J

b). power is$19620$W

Step-by-step solution

Step 1. Given information

mass $m=1000$kg

height$h=100$m

Step 2. Work done by elevator motor

work that elevator motor does to elevator is equal to difference in potential energy

$$\begin{gathered} E_{motor}=∆E_{potential} \\ =mg∆h \\ =1000kg·9.8m/s^2·100m \\ =9.81·{10}^{5}J \end{gathered}$$

Step 3. Find the power

power is defined as the rate at which transfer energy(in our case work done by elevator motor) Then we have,

$P=\frac{E_{motor}}{∆t}=\frac{9.81·{10}^{5}J}{50s}=19620W$