A crane lifts a concrete hopper of mass 370 kg from the ground to the top of a 38 m building that is under construction. The hopper moves with a constant speed during the lift. The power rating of the crane motor is 8.2 kiloWatts.
How much work does the crane do in lifting the hopper to the top of building?
You don't need the power rating of the motor to calculate the work required to lift one.
It is W = M g H
H = 38 m
g = 9.8 m/s^2
M = 370 kg
The answer will be in joules
To find the work done by the crane in lifting the hopper to the top of the building, we can use the formula:
Work = Force x Distance
First, we need to find the force exerted by the crane. The force can be calculated using the formula:
Force = Mass x Gravity
We know the mass of the hopper is 370 kg, and the acceleration due to gravity is approximately 9.8 m/s². Therefore:
Force = 370 kg x 9.8 m/s²
Now that we have the force, we can calculate the work done by the crane. The distance is given as 38 m. Therefore:
Work = Force x Distance
Substituting the values, we get:
Work = (370 kg x 9.8 m/s²) x 38 m
Calculating this expression will give us the work done by the crane in lifting the hopper to the top of the building.
Now, let's calculate it: