In 35s, Samsonite lifts his 8kg case from the floor to .8m above the ground (in his arms), carries it 24m across the room ( at the same height), and puts it on a conveyor belt 1.8m above the floor. At this point, the machine raises the bag 13 more meters in a mere 2s. Compare the man's power to the machine's power.

To compare the man's power to the machine's power, we need to calculate the work done by each of them.

Work is defined as the force applied over a distance, and can be calculated using the formula:

Work = Force x Distance

First, let's calculate the work done by Samsonite:

1. The work done to lift the case:
Work = Force x Distance
Work = mgh, where m is the mass of the case, g is the acceleration due to gravity, and h is the height lifted.
Here, m = 8kg, g = 9.8 m/s^2, and h = 0.8m
Work = 8kg x 9.8 m/s^2 x 0.8m = 62.72 Joules

2. The work done to carry the case:
Work = Force x Distance
Work = 0J, as the case is carried at the same height, so there is no change in potential energy.

Next, let's calculate the work done by the machine:

1. The work done to raise the bag:
Work = Force x Distance
As we already know the time and distance, we can calculate the force required using the formula:
Force = (2 x m)/(t^2), where m is the mass of the case and t is the time taken.
Here, m = 8kg and t = 2s
Force = (2 x 8kg) / (2s)^2 = 2.0 N

Now, let's calculate the work done using this force:
Work = Force x Distance
Work = 2.0 N x 13m = 26 Joules

To compare the man's power to the machine's power, we need to calculate their respective powers.

Power is defined as the rate at which work is done, and can be calculated using the formula:

Power = Work / Time

Let's calculate the respective powers:

1. Man's power:
Power = Work / Time
Power = 62.72 Joules / 35s = 1.79 Watts

2. Machine's power:
Power = Work / Time
Power = 26 Joules / 2s = 13 Watts

Therefore, the machine's power is approximately 13 Watts, while the man's power is approximately 1.79 Watts.

To compare the man's power to the machine's power, we need to calculate the work done by each and divide by the respective time taken.

Step 1: Calculate the work done by Samsonite in lifting the case.
Work = Force x Distance x Cosine(theta)
where
Force = mass x acceleration due to gravity
Distance = height lifted
Cosine(theta) = angle between the direction of force and displacement

Given:
Mass of the case (m) = 8 kg
Height lifted (h1) = 0.8 m

The force exerted by Samsonite is given by:
Force = 8 kg x 9.8 m/s^2 (acceleration due to gravity)
Force = 78.4 N

The work done by Samsonite is:
Work_Samsonite = Force x Distance x Cosine(theta)
Where theta is the angle between the force and displacement, which is 0 degrees in this case (vertical direction).
Cosine(0) = 1

Work_Samsonite = 78.4 N x 0.8 m x 1 = 62.72 Joules

Step 2: Calculate the work done by Samsonite in carrying the case across the room.
Work_Samsonite = Force x Distance x Cosine(theta)
Distance (d) = 24 m
theta = 0 degrees (as the case is carried at the same height)

Work_Samsonite = 78.4 N x 24 m x 1 = 1881.6 Joules

Step 3: Calculate the work done by Samsonite in placing the case on the conveyor belt.
Work_Samsonite = Force x Distance x Cosine(theta)
Distance (d) = 1.8 m
theta = 0 degrees (as the case is placed at the same height)

Work_Samsonite = 78.4 N x 1.8 m x 1 = 141.12 Joules

Step 4: Calculate the work done by the machine in lifting the case further.
Work_Machine = Force x Distance x Cosine(theta)
Force = mass x acceleration due to gravity
Mass of the case (m) = 8 kg
Height lifted (h2) = 13 m
theta = 0 degrees (vertical direction)

Force = 8 kg x 9.8 m/s^2
Force = 78.4 N

Work_Machine = Force x Distance x Cosine(theta)
Work_Machine = 78.4 N x 13 m x 1 = 1019.2 Joules

Step 5: Calculate the power for both Samsonite and the machine.

Power_Samsonite = Work_Samsonite / Time
Time taken for the tasks = 35s + 2s (lifting by the machine)
Time = 37s

Power_Samsonite = (62.72 + 1881.6 + 141.12) Joules / 37 s
Power_Samsonite = 2085.44 Joules / 37 s
Power_Samsonite ≈ 56.35 Watts

Power_Machine = Work_Machine / Time (lifting by the machine)
Power_Machine = 1019.2 Joules / 2 s
Power_Machine = 509.6 Watts

So, the man's power is approximately 56.35 Watts, while the machine's power is approximately 509.6 Watts.