How to Solve Pulley and Normal Force Problems Using Newton's Laws

[starprincess]

Homework Statement

An 80.0 kg student stands on a 20.0 kg platform and applies a steady downwards force of 300 N on a long rope; the rope extends up from the students hands passes over pulley#1 at the top and then under pulley #2; finally the rope is attached to the bottom of pulley #1, as shown in the figure. Assume that the ropes and pulleys have negligible mass and that the pulleys are ideal and frictionless. The top pulley remains at rest.

Homework Equations

See figure.

The Attempt at a Solution

I tried doing the weight of the student which equals 784 N - the force (300 N) = 484.
However, the correct answer is 420... I do not know how to arrive at that value.

Another similar problem:

Need to find the normal force which the platform exerts on the student's feet:

My attempt same as first problem: 784 N - 160 = 624.
However, the correct answer is 480 N.

 

[pat666]

Normal force should just be 80*9,81- the upward force the person is exerting-the weight of the block(i get 440)??,

 

[pat666]

looking at the first problem and the solution i get with my method makes me think that what i just said is wrong... do you know what the pulleys are there for... have you been doing anything with pulleys that I am missing.

 

[starprincess]

No, I only know as much as what the given information states.

 

[starprincess]

Help please?

 

[pat666]

OK sorry for the long reply time, this problem had me screwed for a while..
Problem 1:
Fnet=100*10-300 this was a big problem for me to solve your text takes g as 10 not 9.81 (should say if not 9.81)
Fnet=700
therefore they both have a downward acceleration of 7m/s^2
but...
the block has a force of 7*20 and the person 80 * 7 (F=ma with a being 7 not 10)
so Normal force equals 560-140 = 420N!

please tell me if you need more help and if this is useful to you

 

[PhanthomJay]

You have to draw free body diagrams and properly apply Newton's laws when solving these problems. You should also note that the cable tensions T1, T2, and T3 must be equal when frictionless, massless, ideal pulleys are used. Thus, when you look at the man/platform system, 900N pulls up on the system, and the weight of the system, 980 N, acts down. That's a net force on the system of 80N down. Calculate the downward acceleration of the system using Newton 2, then look at the forces acting on the man alone, to solve for the Normal force, again using Newton 2 and the same acceleration for the man as was determined for the system. Use a similar approach in the 2nd problem.