Question

2) A window washer pulls themselves upward using a bucket pulley apparatus. A) How hard must

pull downward to raise herself slowly at a constant speed? B) If she increases this force by 15%, what
will her acceleration be? The mass of the person plus the bucket is 72 kg. Ignore friction.
How should I solve this

Answer 1

A) F = 705 N

B) a = 1.23 m/s²

Step-by-step explanation:

Given that,

The mass of the person and bucket, m = 72 Kg

The tension, T = 0

The bucket pulley apparatus works with the principle of Atwood's machine

The upward acceleration is equal to the downward acceleration. It is denoted by 'a '

The acceleration due to gravity is 'g'

The net force in the upward direction, f = T - mg ( f = ma) N

The net force in the downward direction is, F = Mg -T (F = Ma) N

The upward acceleration is equal to the downward acceleration. It is denoted by a

Adding the above equations

Mg -mg = ma + Ma

Where,

mg = 72g N

= 105 N

To remain equilibrium or to raise herself slowly at a constant speed, the upward force should be equal to the downward force.

Mg = mg

Therefore, the force required to raise herself slowly at a constant speed is 705 N

If she increases this force by 15%,

(100/72g) x 15 %

= 20.83g

Therefore, the total downward force, F = 62g+20.83g

= 92.83g N

Substituting the values in the equation

Mg -mg = Ma + ma

92.83g - 72g = (92.83g + 72g) a

a = 92.83g - 72g / 92.83 + 72g

= 0.126g

= 1.23 m/s²

Hence the acceleration will be, a = 1.23 m/s²