In one day, a 75-kg mountain climber ascends from the 1500-m level
on a vertical cli� to the top at 2400 m. The next day, she descends
from the top to the base of the cli�, 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.
To calculate the change in gravitational potential energy for the first and second day, we can use the formula:
ΔPE = m * g * Δh
where:
ΔPE is the change in gravitational potential energy
m is the mass of the mountain climber (75 kg)
g is the acceleration due to gravity (9.8 m/s^2)
Δh is the change in height
(a) Change in gravitational potential energy on the first day:
Δh = 2400 m - 1500 m = 900 m (ascend)
ΔPE1 = 75 kg * 9.8 m/s^2 * 900 m
(b) Change in gravitational potential energy on the second day:
Δh = 1350 m - 2400 m = -1050 m (descend)
Note: Since the climber is descending, the change in height is negative.
ΔPE2 = 75 kg * 9.8 m/s^2 * (-1050 m)
Now, let's calculate the change in gravitational potential energy for each day:
(a) ΔPE1 = 75 kg * 9.8 m/s^2 * 900 m
= 661,500 Joules
(b) ΔPE2 = 75 kg * 9.8 m/s^2 * (-1050 m)
= -764,250 Joules
Therefore, the change in gravitational potential energy on the first day is 661,500 Joules (positive), and on the second day is -764,250 Joules (negative).
To calculate the change in gravitational potential energy, we need to use the formula:
ΔPE = m * g * Δh
where ΔPE is the change in gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and Δh is the change in height.
(a) On the first day, the mountain climber ascends from the 1500-m level to the top at 2400 m. The change in height is Δh = 2400 m - 1500 m = 900 m. We are given the mass of the climber as 75 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Using the formula, we can calculate the change in gravitational potential energy on the first day:
ΔPE = 75 kg * 9.8 m/s^2 * 900 m
(b) On the second day, the climber descends from the top to the base of the cliff at an elevation of 1350 m. The change in height is Δh = 1350 m - 2400 m = -1050 m. Note that the change in height is negative since the climber is descending.
Using the formula again, we can calculate the change in gravitational potential energy on the second day:
ΔPE = 75 kg * 9.8 m/s^2 * (-1050 m)
Complete the calculations to find the numerical values for both (a) and (b).