Help: Apply tension into equation for multiple pulleys

[ziptrickhead]

I have this problem for homework.

Find the magnitude of the minimum force F that allows the window washer to move upward.
Express your answer in terms of the mass M and the magnitude of the acceleration due to gravity g.

The professor didn't go over multiple pulleys though so I am confused.

Now, what I thought was that the force required would be the force of the window washer. Since the pulleys and cables are frictionless and have no mass and the platform has no mass, the man would just have to pull down his own mass times gravity.

So with only one pulley I thought that the forces required would just be the mass times acceleration due to gravity (Mg).

With 2 pulleys in the system, the force required from the man would be half of that of the system with just one pulley (Mg/2).

When I put in that for the answer it was wrong and the feedback was: "The upward force on the platform from the lower pulley is 2T, since the pulley feels an upward force of T from each of two cables."

Right now I'm stuck at this point.

 

[Doc Al]

Hint: The tension is the same throughout the rope.

How many times does the rope pull up on the "man + platform" system? (Think of that lower pulley as part of the platform, since it's attached.)

 

[ziptrickhead]

Well, you would have the force pulling on the platform from the first pulley and then tension from the bracket so the rope would pull twice on the platform/man? That would go with the feedback statement and because there are 2 forces pulling the platform/man then the force required would be halved again: Mg/4?

 

[Doc Al]

Draw an imaginary box around the "man + platform + bottom pulley". How many ropes stick out?

 

[ziptrickhead]

Well, 3 ropes would stick out.

Obviously I'm thinking in the wrong direction because i tried Mg/6 and it said I was off by a multiplicative factor.

I checked online and saw a picture of a 2 pulley system that showed that the tension of each rope would be 1/2T. If I were to add up the tension of the 3 ropes it would be 3/2.

Right now I'm just pulling stuff out of nowhere and trying it and I just don't understand where it's going...

 

[Doc Al]

Well, 3 ropes would stick out.

Right! So, if the tension in the rope is F, what upward force do the ropes exert on the system in terms of F?

 

[ziptrickhead]

If tension equals F then: F=3T so tension would equal F/3. So then the force required to pull the man up would be Mg/3.

I think I'm starting to understand, just that the Tension=Force part I was missing.

 

[Doc Al]

If tension equals F then: F=3T so tension would equal F/3. So then the force required to pull the man up would be Mg/3.

I think you've got it.

I'll rephrase it in my own words: The force that the man exerts on the rope must equal the tension in the rope. That force is called "F". So the upward force on the system equals 3F. Since the system is in equilibrium, 3F=mg, so F = mg/3.

 

[ziptrickhead]

Thank you very much!

I see what I was doing wrong now. I didn't even understand how one pulley works let alone try to figure out 2 pulleys.

 

[kenau_reveas]

would you mind sharing your answer with me?