Question

Calculate the energy in kJ used by a 55.0-kg person who does 50 deep knee bends in which their center of mass is lowered and raised 0.400 m. (They do work in both directions.) You may assume their efficiency is 20%.

A. 60 kJ
B. 70 kJ
C. 80 kJ
D. 90 kJ

Answer 1

The energy used by a 55.0-kg person for 50 deep knee bends can be calculated by determining the work done per bend, multiplying by 50 (for both directions), and dividing by the efficiency of 20%. The average power consumption rate is then found by dividing this energy by the time taken in seconds.

Step-by-step explanation:

To calculate the energy used by a 55.0-kg person doing 50 deep knee bends, we use the following steps:

1. Calculate the work done in one knee bend to lift the center of mass by 0.400 m, which equals to the change in potential energy:
2. Work (W) = mgh = 55.0 kg × 9.8 m/s2 × 0.400 m
3. Calculate the total work done for 50 bends, remembering that work is done both lowering and raising:
4. Total work for 50 bends (Wtotal) = 2 × 50 × Work for one bend
5. Since the person's efficiency is 20%, only 20% of the energy used does this work. Thus, the total energy used (Eused) will be:
6. Eused = Wtotal / Efficiency
7. Convert this to kilojoules (kJ) for the final answer.

The average power consumption rate in watts is calculated by dividing the total energy used in kilojoules by the time in seconds and then converting kilojoules to joules since power is measured in joules per second (watts).

1. Convert time from minutes to seconds.
2. Calculate power:
3. Power (P) = Eused / Time (seconds)