Question

In one day, a 75-kg mountain climber ascends from the 1500-m level on a vertical cliff to the top at 2400 m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 1350 m. What is her change in gravitational potential energy (a) on the first day and (b) on the second day?

a) (a) Gain; (b) Loss
b) (a) Loss; (b) Gain
c) (a) Gain; (b) No Change

Answer 1

The mountain climber experiences a gain in gravitational potential energy on the first day when ascending from 1500 m to 2400 m and a loss in gravitational potential energy on the second day when descending from 2400 m to 1350 m(option a).

Step-by-step explanation:

The change in gravitational potential energy (GPE) for a mountain climber can be calculated using the formula GPE = mgh, where m is the mass of the climber, g is the acceleration due to gravity (9.8 m/s2), and h is the change in height.

(a) On the first day, the climber ascends from 1500 m to 2400 m, a difference in elevation of 900 m. So, the change in GPE is:
GPE = m × g × h = 75 kg × 9.8 m/s2 × 900 m
Calculating this gives a gain in GPE.

(b) On the second day, the climber descends from 2400 m to 1350 m, a difference in elevation of 1050 m. The change in GPE is:
GPE = 75 kg × 9.8 m/s2 × (-1050 m)
Calculating this gives a loss in GPE, since the climber is moving in the opposite direction of the gravitational force.

Therefore, the answer is (a) Gain; (b) Loss.