Questions: Since the elevator in the previous problem travels with constant velocity v=4.0 m/s, it takes a total time Δt=7.5 s to travel the full 30 m. Using your answer from the previous question for the work done, calculate the average power that the motor must deliver to lift the elevator and the passenger. (Round your answer to the first decimal place). P=81619.2 W P=97619.2 W P=76285.9 W P=65619.2 W

Since the elevator in the previous problem travels with constant velocity v=4.0 m/s, it takes a total time Δt=7.5 s to travel the full 30 m. Using your answer from the previous question for the work done, calculate the average power that the motor must deliver to lift the elevator and the passenger. (Round your answer to the first decimal place).
P=81619.2 W
P=97619.2 W
P=76285.9 W
P=65619.2 W

Transcript text: Since the elevator in the previous problem travels with constant velocity $v=4.0 \frac{\mathrm{~m}}{\mathrm{~s}}$, it takes a total time $\Delta t=7.5 \mathrm{~s}$ to travel the full 30 m . Using your answer from the previous question for the work done, calculate the average power that the motor must deliver to lift the elevator and the passenger. (Round your answer to the first decimal place). $P=81619.2 \mathrm{~W}$ $P=97619.2 \mathrm{~W}$ $P=76285.9 \mathrm{~W}$ $P=65619.2 \mathrm{~W}$

Solution

Solution Steps

Step 1: Understanding the Problem

We need to calculate the average power delivered by the motor to lift the elevator and the passenger. We are given the work done from a previous problem and the time taken for the elevator to travel a certain distance.

Step 2: Recall the Formula for Power

The average power $ P $ is given by the formula: \[ P = \frac{W}{\Delta t} \] where $ W $ is the work done and $ \Delta t $ is the time taken.

Step 3: Use Given Values

We are given that the work done $ W $ is from a previous problem, and the time $ \Delta t = 7.5 $ seconds. We need to use the given options to find the correct power value.

Step 4: Calculate Power for Each Option

We will check each option to see which one matches the given work done when divided by the time $ \Delta t = 7.5 $ seconds.

$ P = 81619.2 \, \text{W} $ \[ W = P \times \Delta t = 81619.2 \times 7.5 = 612144 \, \text{J} \]
$ P = 97619.2 \, \text{W} $ \[ W = P \times \Delta t = 97619.2 \times 7.5 = 732144 \, \text{J} \]
$ P = 76285.9 \, \text{W} $ \[ W = P \times \Delta t = 76285.9 \times 7.5 = 572144.25 \, \text{J} \]
$ P = 65619.2 \, \text{W} $ \[ W = P \times \Delta t = 65619.2 \times 7.5 = 492144 \, \text{J} \]

Step 5: Determine the Correct Option

Assuming the work done from the previous problem is known, we compare the calculated work for each power option to find the correct one. Without the exact work value, we assume the correct power is the one that matches the work done.