an initially stationary 15.0 kg crate of cheese wheels is pulled via a cable a distance d = 5.70 m up a frictionless ramp to a height of h = 2.5 m, where it stops. What is its potential energy of the crate after it is lifted? how much work is done during the lift? If it takes 10 seconds to lift the cheese, what is the power rating of the lifting device?

If the ramp is frictionless, the work done equals the potential energy change, P.E. = W = M g h.

The distance d doesn't matter.

Divide that work by 10 seconds for the power rating in watts.

To find the potential energy of the crate after it is lifted, we can use the formula:

Potential energy (PE) = mass (m) * gravitational acceleration (g) * height (h)

Given:
Mass of the crate (m) = 15.0 kg
Gravitational acceleration (g) ≈ 9.8 m/s^2
Height (h) = 2.5 m

Substituting the values:
PE = 15.0 kg * 9.8 m/s^2 * 2.5 m
PE = 367.5 Joules

Therefore, the potential energy of the crate after it is lifted is 367.5 Joules.

To find the work done during the lift, we can use the formula:

Work (W) = force (F) * distance (d)

Since the ramp is frictionless, the only force acting on the crate is the force of gravity. The force of gravity can be calculated using the mass and gravitational acceleration:

Force (F) = mass (m) * gravitational acceleration (g)

Given:
Mass of the crate (m) = 15.0 kg
Gravitational acceleration (g) ≈ 9.8 m/s^2

Substituting the values:
F = 15.0 kg * 9.8 m/s^2
F = 147.0 N

Now we can calculate the work done:
W = 147.0 N * 5.70 m
W = 838.8 Joules

Therefore, the work done during the lift is 838.8 Joules.

To find the power rating of the lifting device, we can use the formula:

Power (P) = work (W) / time (t)

Given:
Work (W) = 838.8 Joules
Time (t) = 10 seconds

Substituting the values:
P = 838.8 Joules / 10 seconds
P = 83.88 Watts

Therefore, the power rating of the lifting device is 83.88 Watts.