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

Answer:

A) F = 705 N

B) a = 1.23 m/s²

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