Window washer pulley system acceleration

[Hailcanadien]

Homework Statement

A window washer pulls herself upward using the bucket-pulley apparatus shown in Fig. 4-48. The mass of the person plus the bucket is 61 kg.

(a) How hard must she pull downward to raise herself slowly at constant speed?
298.9 N
(b) If she increases this force by 12%, what will her acceleration be?
? m/s²

Homework Equations

F=ma
U_kF_n=f_fr

The Attempt at a Solution

I tried...
298.9 x 1.12=334.8
and put it in the equation...
334.8N=(30.5kg)(a)
and got 10.976 m/s²...
which wasn't right...

I used 30.5 instead of 61 because a pulley makes the weight half...

 

[kuruman]

In part (b) the upward force is twice the tension and the downward force is the weight. What is the net force? Once you have the net force, what is the acceleration?

 

[Hailcanadien]

the net force comes out to be 35.9N
so then would you do it like...
35.9N = 30.5a
a = 1.18?

 

[kuruman]

How do you get 35.9 N? That's not twice the tension minus the weight. Also, 30.5 kg is not the mass of the system. The mass is 61.5 kg.

 

[Hailcanadien]

the 35.9 is 334.8 - 298.9, the net force, b/c 334.8 is the force she is pulling upwards and 298.9 is the force of gravity, and in this pulley system, the bucket she is in tied to a rope which is thrown over a pulley and back down to her hand, sorry if that was confusing, but in this case, with the pulley, she only has to pull half her weight.

 

[kuruman]

Your way of looking at the problem gives the correct answer, but may lead you into pitfalls with other problems like it. It is best to draw a free-body diagram and get that

2T - mg = ma

from it where T = 334.8N. Basically, your solution divides the above equation by 2.