Motion, Power, Energy Questions

[ZorAxe]

Homework Statement

A load of 2,5kN is hoisted by means of a rope and a lifting machine with a rotational frequency of 40r/min and a drum diameter of 700mm.

Calculate the following:

1. The torque

2. The speed of the rope or load in m/s

3. The work done per minute

4. The power required to lift the load

5. The efficiency of the lifting machine if an electric motor of 5kW is required to drive the lifting machine

Homework Equations

See below

The Attempt at a Solution

This is my first time posting, so I hope I have got the format right. Here's my attempt at the equations

1. T = F x r
T = 2500N x 0.35m
T = 875Nm

2. V = π x d x N/60
V = π x 0.7m x 40/60
V = 1.465m/s

3. WD = F x s
WD = 2500N x (1.465 x 60)
WD = 2500N x 87.9
WD = 219750 joules
WD = 219.75 kJoules

4. P = F x V
P = 2500N x 1.465m/s
P = 3662.5watts
P = 3.663kWatts

5. Eff = OUT PWR/IN PWR %
Eff = 3662.5w/5000w
Eff = 0.7325
Eff = 73.25%

Those were the answers I got. Please correct me if I am wrong, or just give me some guidance and I can re attempt the questions.

Thanks guys :D

 

[BruceW]

For question 1, technically the total torque on the drum is zero. But I think they are asking for the torque which must be applied by some external motor. So I think you do have the right answer for question 1.

 

[BruceW]

And your answer for question 2 looks good too.

 

[BruceW]

3,4,5 all look correct as well. nice!

 

[ZorAxe]

Thanks BruceW, I appreciate it :D