A 7.5-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. If the box is being lifted at a constant speed of 2.0m/s, what is the power delivered by the person pulling on the ropre? If the box lifted at constant acceleration from rest on the floor to a height of 1.5m above the floor in 0.42s what average power is delivered by the person pulling the rope?

power= force*distance/time= mg*velocity

If being accelerated, then force=mg+ma

To find the power delivered by the person pulling on the rope, we need to determine the force exerted.

In the first scenario, where the box is being lifted at a constant speed of 2.0 m/s, the net force on the box is zero since it is not accelerating. Therefore, the force exerted by the person pulling on the rope is equal to the weight of the box.

Step 1: Calculate the force exerted by the person:
Force = mass x acceleration due to gravity = 7.5 kg x 9.8 m/s² = 73.5 N

Step 2: Calculate the power delivered by the person:
Power = force x velocity = 73.5 N x 2.0 m/s = 147 W

Therefore, the power delivered by the person pulling the rope in this scenario is 147 Watts.

In the second scenario, where the box is being lifted with constant acceleration, we can use the work-energy principle to calculate the average power delivered.

Step 1: Calculate the work done on the box:
Work = force x distance = (mass x acceleration due to gravity) x height = (7.5 kg x 9.8 m/s²) x 1.5 m = 110.25 J

Step 2: Calculate the time taken to lift the box:
t = 0.42 s

Step 3: Calculate the average power delivered by the person:
Average power = work / time = 110.25 J / 0.42 s ≈ 262.5 W

Therefore, the average power delivered by the person pulling the rope in this scenario is approximately 262.5 Watts.

To determine the power delivered by the person pulling the rope, we need to use the formula:

Power = Force x Velocity

In the first scenario, the box is being lifted at a constant speed of 2.0 m/s. Since the speed is constant, the net force on the box is zero. This means that the force required to lift the box is equal to the gravitational force pulling it downwards:

Force = Mass x Acceleration due to gravity
Force = 7.5 kg x 9.8 m/s^2
Force = 73.5 N

Now, we can calculate the power:

Power = Force x Velocity
Power = 73.5 N x 2.0 m/s
Power = 147 W (watts)

Therefore, the power delivered by the person pulling the rope in the first scenario is 147 watts.

In the second scenario, the box is lifted at constant acceleration. To calculate the average power, we need to use the formula:

Power = Work / Time

The work done on an object is given by:

Work = Force x Distance

The force required to lift the box is the same as in the previous scenario, 73.5 N. The distance the box is lifted is 1.5 m.

Work = 73.5 N x 1.5 m
Work = 110.25 J (joules)

The time it takes to lift the box is given as 0.42 s.

Now, we can calculate the average power:

Power = Work / Time
Power = 110.25 J / 0.42 s
Power = 262.5 W (watts)

Therefore, the average power delivered by the person pulling the rope in the second scenario is 262.5 watts.