Solve Pulley Problem: Force Magnitudes & Ceiling Force

[csquared5]

Ok, here is the problem:

A man is sitting in a bosun's chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man and chair is 89.6 kg. With what force magnitude must the man pull on the rope if he is to rise (a) with a constant velocity and (b) with an upward acceleration of 1.41 m/s2? (Hint: A free-body diagram can really help.) If the rope on the right extends to the ground and is pulled by a co-worker, with what force magnitude must the co-worker pull for the man to rise (c) with a constant velocity and (d) with an upward acceleration of 1.41 m/s2? What is the magnitude of the force on the ceiling from the pulley system in (e) part a (f) part b, (g) part c, and (h) part d?

So I'm getting (a), (b), (c), (d), and (g) right, but I can't figure out how to go (e), (f), and (g)

For (a), I'm using 2Ftension=m(g+a), a being 0, and getting 439.04
For (b), I'm using 2Ftension=m(g+a), a being 1.41, and getting 502.208
For (c), it's 2x (a), which is 878.08
For (d), it's 2x (b), which is 1004.416

For (e) ?
For (f) ?

For (g), I simply used the equation (Tension (the answer for (c)) plus m1g, the mass of the man and bucket times gravity.

For (h) ?

Any help on how to determine (e), (f), and (h) would be greatly appreciated, this is due by 7am tomorrow! =[

 

[learningphysics]

Find out the force exerted on the pulley by the ceiling (by Newton's 3rd law, this is the same force you need)... examine the freebody diagram of the pulley.

 

[csquared5]

would the tension be acting downwards on the pulley twice because of the two different ends of the rope? i have no idea what the free body diagram for the pulley would look like

 

[learningphysics]

would the tension be acting downwards on the pulley twice because of the two different ends of the rope? i have no idea what the free body diagram for the pulley would look like

yes... the forces acting on the pulley are the two tensions below... and the contact force at the ceiling...

What is ma for the pulley?

 

[csquared5]

how do you know ma for the pulley if it is supposedly massless in this problem?

 

[learningphysics]

how do you know ma for the pulley if it is supposedly massless in this problem?

by massless they mean mass = 0. plus the pulley is fixed to the ceiling, so acceleration = 0... ma definitely equals 0 for the pulley.

 

[csquared5]

ok, so if ma is 0 for the pulley, then the only forces acting on it are the two tensions? is this the same for (e), (f), and (h), and if it is is that the answer to the problem? as simple as that?

 

[learningphysics]

ok, so if ma is 0 for the pulley, then the only forces acting on it are the two tensions? is this the same for (e), (f), and (h), and if it is is that the answer to the problem? as simple as that?

The two tensions and the force in the ceiling.

yes, the ceiling exerts 2*tension to balance the two tensions below, and make the net force on the pulley 0.

 

[csquared5]

so the force of the pulley on ceiling is two times the tension and in order to achieve equilibrium, the force of the ceiling on the pulley is the same, right?

so (e) would be 878.08, (f) would be 1004.416, and (h) would be the same again (2008.832?) even though there's another person involved in pulling the pulley?

 

[csquared5]

ok i got it =] thank you for all your help!

 

[learningphysics]

so the force of the pulley on ceiling is two times the tension and in order to achieve equilibrium, the force of the ceiling on the pulley is the same, right?

Well... you want the pulley to be in equilbrium... so the ceiling exerts 2 times tension to balance the two tensions below the pulley. So that's the force of the ceiling on the pulley...

the question asks for the force of the pulley on the ceiling... which is just an equal force in the opposite direction, by Newton's 3rd law.

 

[learningphysics]

ok i got it =] thank you for all your help!

cool. no prob.