how much power is required to lift the crate

Power

= work done /time
If work done is in joules, and time in seconds, the power is in watts.

What crate? How far?

Use Mathmate's equation.

how much power is used to lift a 100-n bucket a distance of 10-m in 12 seconds

To determine the power required to lift a crate, you will need to consider several factors:

1. Weight of the crate: Determine the mass of the crate, typically measured in kilograms (kg) or pounds (lb).

2. Height of the lift: Determine the vertical distance the crate needs to be lifted, measured in meters (m) or feet (ft).

3. Lift speed: Determine the time it takes to lift the crate, measured in seconds (s) or minutes (min).

Once you have these values, you can calculate the power required using the following formula:

Power (P) = Work done (W) / Time (t)

The work done (W) is calculated as the product of the weight of the crate (Wc) and the height of the lift (h):

Work done (W) = Weight of the crate (Wc) × Height of the lift (h)

Now, substitute the work done (W) into the power formula:

Power (P) = Work done (W) / Time (t)

Note: Time (t) should be in seconds (s) for consistent units.

Keep in mind that this is the minimum power required to lift the crate. In reality, additional power may be needed to overcome friction and other losses in the lifting mechanism.