I do not see Fig. 4-42, and do not know how the rope is "wired", how many pulleys, etc. If possible, describe the figure in words, or post a link to the figure.
there is only one pulley
So the total mass of the bucket and the window-washer is 69 kg.
It is supported by two ropes. If the bucket moves at constant speed, what is the tension T, in each rope, in order to support the weight?
If the tension is increased by 11%, i.e. T1=1.11T, the additional force will casue the bucket to accelerate upwards.
The total force F, for acceleration is 2(T1-T). The mass is 69 kg.
What is the acceleration?
to get T would you just do 69(9.8)
Does your figure show two rops supporting the bucket?
So the two tensions should add up to 69g.
no since there is only one pulley then there is only one rope and if there is only one pulley and one rope there is only one tension
One end of the rope must be held by the window washer, is the other end of the rope attached to a fixed wall the bucket?
If it is attached to the bucket, there are two ropes, and 2T=W. If the other end is attached to a wall, I don't see how the pulley is useful.
Another way to look at it is to draw the free body diagram of the bucket (and the window-washer).
okay well i am confused about the way you can figure out the acceleration if the tension is increased by 11%
All you do is multiply your percentage by gravity...so 0.11*9.8
so what is the force???