Average power (counterweight, tension, motor)

[jamesweston0]

Homework Statement

The material hoist and the load have a total mass of 600 kg and the counterweight C has a mass of 150 kg. If the upward speed of the hoist increases uniformly from to 0.9 m/s to 2.3 m/s in 2 s, determine the average power generated by the motor M during this time. The motor operates with an efficiency of e = 0.8.

Homework Equations

F = ma

P = Fv

e = energy output / energy input

The Attempt at a Solution

This question doesn't seem like it's too hard but I still am stuck! I feel like I am close though so I would appreciate some insight. Great forum this is!

I first figured out the acceleration of the system by using this:

(Vf - Vi)/t = a

(2.3 - 0.9)/2 = a = 0.7

I then looked at the counterweight and figured out the tension in the left rope. Equation looked like this:

W - Tc = ma

(150*9.8) - Tc = (150*0.7)

Tc = 1365 N

I then looked at the main weight. I think I screwed up on the tension forces. I used the 600kg for the masses. This is what I did:

Tc + 2Tm - mg = ma

1375 + 2Tm - (600*9.8) = (600*0.7)

-4515 + 2T = 420

T = 2467.5 N

I multiplied this by the average velocity, which I found by adding the initial and final velocities, and then dividing by 2.

2467.5*1.6 = 3948 N

I then took this number and divided by 0.8 to get the amount generated. I'm also not sure if I'm supposed to multiply here or divide because I'm confused by what generated means. Silly thing I know. But it doesn't really make a difference whether I multiply or divide by 0.8 at this point because I have already messed up earlier on somewhere.

Can someone explain where I am flawed in my thinking? I really want and need to understand this stuff thoroughly. Thanks a ton!

 

[nasu]

The unit for power is Watt and not Newton.
In rest it seems OK.

 

[jamesweston0]

The unit for power is Watt and not Newton.
In rest it seems OK.

Oops yeah I screwed up there. But the answer is actually 10.1 kW.