# Power by Motor on Pulley System

1. Nov 20, 2015

### k_squared

1. The problem statement, all variables and given/known data

2. Relevant equations
P = T*V
F=ma
3. The attempt at a solution

My approach was this: Using the pin at C as a datum, I figured that DB=CD and thus 2CD + AC = l. Thus I figured that at 3 ft/s, A was rising 3/2 feet per second.

However, I also figured the it would just be (3/2=v)(F=force required to keep box from accelerating, as the speed is constant.)

T1 - 100 = 0
100 + 100 -T2 = 0

...I take it T2 is on the motor, but, I'm not sure. Could someone please give me a hint about the tensions? These pulley problems have been killing me even where everything else is easy!

2. Nov 20, 2015

### Mister T

Evidently T1 is the tension in the piece of rope between A and C.

T2 is the tension in the piece of rope between B and E.

So the motor is exerting a force of 200 lb.

I don't follow. I think you meant BC=BD?

Anyway, the work done by the motor on the rope has to equal the work done on the load by the rope.

3. Nov 20, 2015

### k_squared

Why is the tension 200... is is because the pulling is from both sides?

4. Nov 20, 2015

### Mister T

When you solve the equation

100 + 100 -T2 = 0

for T2, you get 200 lb.

It's because there are two ropes pulling upward on the pulley B, and each rope has a tension of 100 lb.

5. Nov 20, 2015

### k_squared

Ahh... I understand. The tension in the rope attached to the load is uniformly 100 pounds, and the motor is pulling against *two* such segments. That kinda makes sense. I have no problem whatsoever computing the work power on systems without pulleys... I seem generically bad at getting the tension, though.

So technically... no, the last thing you said was the only thing that didn't help me! So basically, this set up is backwards, because the load has mechanical advantage on the motor?

Would that mean that if the load and the motor were switched, the motor would only have to develop 50 lbs of tension in the rope to be in equilibrium?

6. Nov 20, 2015

### Mister T

The statement I referred to was an attempt to get you to understand the speed of the load. You have it wrong in your attempted solution. I also asked you about a typo you may have made in labeling the rope segments?

7. Nov 21, 2015

### k_squared

Yes, I meant BC=BD.... I'm still not sure I understand the speed of the load, I'm going to review that section if I can find it.

8. Nov 21, 2015

### Mister T

The work done by the motor on the rope has to equal the work done on the load by the rope. Work equals force times distance. If the force on rope BE is two times the force on rope AC then what does that tell you about the distance traveled by each section of rope?

9. Nov 21, 2015

### k_squared

...BE travels half the distance as AC?

10. Nov 21, 2015

### Mister T

Right, so that tells you the relationship between the speeds. You had it backwards originally!