A 52 kg skier is at the top of a slope, as in the
figure. At the initial point A, the skier is 17.7
m vertically above the final point B.
The acceleration of gravity is 9.81 m/s2 .
Find the difference in gravitational po-
tential energy associated with the skier at the
points A and B if the zero level for gravita-
tional potential energy is at point B.
Answer in units of J.
It doesn't matter where the zero of PE is when you are talking about differences in PE, as you are here.
difference in PE = M g (H2 - H1)
= 52* 9.81 * 17.7 = __ J
The gravitational potential energy (PE) of an object is given by the formula:
PE = m * g * h
where m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical distance above the reference point.
Given:
m = 52 kg
g = 9.81 m/s^2
h = 17.7 m
Using the formula, we can calculate the gravitational potential energy at points A and B.
At point A:
PE_A = m * g * h_A
At point B:
PE_B = m * g * h_B
Since the zero level for gravitational potential energy is at point B, the gravitational potential energy at point B is zero (PE_B = 0).
Therefore, the difference in gravitational potential energy between points A and B can be calculated as:
Delta PE = PE_A - PE_B
= m * g * h_A - m * g * h_B
= m * g * (h_A - h_B)
Substituting the given values:
Delta PE = 52 kg * 9.81 m/s^2 * (17.7 m - 0 m)
Simplifying:
Delta PE = 9746.32 kg·m^2/s^2
= 9746.32 J
The difference in gravitational potential energy is 9746.32 Joules.
To find the difference in gravitational potential energy, we need to first calculate the gravitational potential energy at point A and point B and then find the difference between the two.
The gravitational potential energy (PE) is given by the formula:
PE = m * g * h
Where:
m = mass of the skier = 52 kg
g = acceleration due to gravity = 9.81 m/s^2
h = height (vertical distance) above the reference level
First, let's calculate the gravitational potential energy at point A:
PE_A = m * g * h_A
Since the skier is 17.7 m vertically above point B, the height at point A (h_A) will be 17.7 m.
PE_A = 52 kg * 9.81 m/s^2 * 17.7 m
Now, let's calculate the gravitational potential energy at point B:
PE_B = m * g * h_B
As the zero level for gravitational potential energy is at point B, the height at point B (h_B) will be zero.
PE_B = 52 kg * 9.81 m/s^2 * 0 m
Now, we can find the difference in gravitational potential energy:
Difference = PE_A - PE_B
Difference = (52 kg * 9.81 m/s^2 * 17.7 m) - (52 kg * 9.81 m/s^2 * 0 m)
Simplifying the equation gives us:
Difference = 52 kg * 9.81 m/s^2 * 17.7 m
Calculating this gives the answer in units of Joules (J).