Question

A 50- kg mountain climber moves 30 m up a vertical slope. If the muscles in her body convert chemical energy into gravitational potential energy with an efficiency of no more than 5%, what is the chemical energy used to climb the slope?

Answer 1

To calculate the chemical energy used by the climber, one must first calculate the potential energy gained during the climb and then divide it by the efficiency of energy conversion.

Step-by-step explanation:

The student is asking about the chemical energy used by a mountain climber to ascend a vertical slope when the efficiency of converting that energy into gravitational potential energy is given. To determine the chemical energy used by the climber, we first calculate the increase in potential energy (PE) when the climber moves up a slope. The potential energy change is calculated using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. So, the potential energy gained by the climber is PE = 50 kg × 9.8 m/s² × 30 m. Then, we take into account the efficiency of the conversion, which is 5%. The chemical energy used (CE) is then found using CE = PE/efficiency. By calculating these values, we can find out the total chemical energy exerted by the climber during the ascent.

Answer 2

Chemical energy:

Wch = 294 kJ

Step-by-step explanation:

Given:

m = 50 kg

h = 30 m

μ = 5% (μ = 0.05)

_______________

Wch - ?

Potential energy:

Wp = m·g·h = 50·9.8·30 = 14 700 J

Chemical energy:

Wch = Wp / μ = 14 700 / 0.05 = 294 000 J or 294 kJ