Problem 1- In one day, a 85 kg mountain climber ascends from the 1440 m level on a vertical cliff to the top at 2360 m . The next day, she descends from the top to the base of the cliff, which is at an elevation of 1310 m .
a) What is her gravitational potential energy on the first day? If you choose the reference level for zero potential energy at:
a. the top of the cliff. b. 1440 m level.
c. 1310 m level.
b) What is her change in gravitational potential energy on the first day?
c) What is her change in gravitational potential energy on the second day?
To answer each part of the problem, we need to use the formula for gravitational potential energy:
Gravitational Potential Energy (GPE) = mass × gravitational acceleration × height
Where:
- Mass is the mass of the climber (85 kg)
- Gravitational acceleration is approximately 9.8 m/s² (acceleration due to gravity on Earth)
a) Gravitational Potential Energy on the first day:
If we choose the reference level for zero potential energy at:
a. the top of the cliff (2360 m):
GPE = 85 kg × 9.8 m/s² × (2360 m - 2360 m) = 0 Joules
b. 1440 m level:
GPE = 85 kg × 9.8 m/s² × (2360 m - 1440 m) = 85 kg × 9.8 m/s² × 920 m = 768,560 Joules
c. 1310 m level:
GPE = 85 kg × 9.8 m/s² × (2360 m - 1310 m) = 85 kg × 9.8 m/s² × 1050 m = 868,050 Joules
b) Change in gravitational potential energy on the first day:
To calculate the change in gravitational potential energy on the first day, we can subtract the initial potential energy from the final potential energy.
Change in GPE = GPE (final) - GPE (initial)
For the reference level at the 1440 m level:
Change in GPE = GPE (at 1440 m) - GPE (at the top of the cliff)
Change in GPE = 768,560 J - 0 J = 768,560 Joules
c) Change in gravitational potential energy on the second day:
The second day involves descending from the top to the base of the cliff (1310 m).
Change in GPE = GPE (at 1310 m) - GPE (at the top of the cliff)
Change in GPE = 868,050 J - 0 J = 868,050 Joules