A 6.9-kg box is being lifted by means of a light rope that is threaded through a single, light, frictionless pulley that is attached to the ceiling.Lifted at a constant speed of 2 m/s. If the box is lifted, at constant acceleration, from rest on the floor to a height of 1.5 m above the floor in 0.42 s, what average power is delivered by the person pulling on the rope?
To find the average power delivered by the person pulling on the rope, we need to use the formula:
Power = Work / Time
First, let's calculate the work done on the box. The work done on an object being lifted vertically is given by the formula:
Work = Force × Distance
The force required to lift the box is equal to its weight. The weight of an object can be calculated using the formula:
Weight = Mass × Gravity
In this case, the mass of the box is given as 6.9 kg. The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the box is:
Weight = 6.9 kg × 9.8 m/s^2
Next, we need to find the distance over which the box is lifted. The distance is given as 1.5 m.
Now that we have the force and distance, we can calculate the work done on the box:
Work = Force × Distance
Finally, we divide the work done by the time taken to find the average power:
Power = Work / Time
Substituting the known values, we can solve for average power.