Answer :
Final answer:
The potential energy of the crate at the top of the ramp is approximately 8,492.35 Joules.
Explanation:
Given:
- Mass of the crate (m) = 500 N
- Length of the ramp (d) = 5.00 m
- Inclination angle (θ) = 20.0°
The potential energy (PE) of an object at a height h above the ground is given by the formula:
PE = m.g.h
where:
m is the mass of the object,
g is the acceleration due to gravity (9.81 m/s² on Earth),
h is the height of the object above a reference point.
In this case, we need to find the potential energy of the crate at the top of the ramp. The height h can be calculated using trigonometry as follows:
h= d⋅sin (θ)
Substitute the given values into the equations:
h = 5.00 m × sin (20.0°)
h ≈ 5.00 m × 0.3420 ≈ 1.71 m
Now, calculate the potential energy:
PE = 500 N × 9.81 m/s² × 1.71 m ≈ 8,492.35 J
