Question

a 55kg student runs up a flight of stairs in 20s. the distance and height of the stairs are shown. neglect loss. list the energy types at the initial and final time and whether work and loss (due to non - conservative forces) occur as well as the corresponding amounts of energy. what was her average power output?

Explanation:

Step1: Determine initial energy

The student starts from rest at the bottom - no kinetic energy and at reference level - no potential energy. So initial energy $E_i = 0$ J.

Step2: Calculate work done

Work done $W$ is equal to the change in gravitational potential energy. The formula for gravitational potential energy is $U = mgh$, where $m = 55$ kg, $g=9.8$ m/s², and $h = 13$ m. So $W=mgh=55\times9.8\times13$ = $7007$ J.

Step3: Determine loss

Since we are neglecting loss, loss $L = 0$ J.

Step4: Calculate final energy

The final energy $E_f$ is equal to the gravitational potential energy at the top of the stairs, which is the same as the work done (because no loss), so $E_f=7007$ J.

Step5: Calculate average power

The formula for power $P=\frac{W}{t}$, where $W = 7007$ J and $t = 20$ s. So $P=\frac{7007}{20}=350.35$ W.

Answer:

Initial: none = 0 J
Work: yes = 7007 J
Loss: no = 0 J
Final: gravitational potential energy = 7007 J
Average power output: 350.35 W