A window washer pulls herself upward using the bucket-pulley apparatus..
Part A) How hard must she pull downward to raise herself slowly at constant speed? The mass of the person plus the bucket is 80 kg .
Part B) If she increases this force by 16 %, what will her acceleration be? The mass of the person plus the bucket is 80 kg .
this depends on the mechanical advantage of the pulley system.
To solve Part A, we can start by analyzing the forces involved. When the window washer pulls downward on the bucket, there are two opposing forces at play:
1. Force of gravity pulling the window washer and the bucket downward.
2. Force applied by the window washer, pulling upward with the bucket to raise herself.
To maintain a constant speed while pulling herself upward, the force applied by the window washer must exactly balance the force of gravity pulling her down.
Let's denote the force applied by the window washer as F_applied and the force of gravity as F_gravity.
The force of gravity is given by the formula F_gravity = mass * acceleration due to gravity, which is approximately equal to 9.8 m/s^2 on Earth.
Part A) How hard must she pull downward to raise herself slowly at constant speed?
To find the force applied by the window washer, we can set up the equation:
F_applied = F_gravity
F_applied = mass * acceleration due to gravity
Given the mass of the person plus the bucket is 80 kg, we can substitute this value into the equation:
F_applied = 80 kg * 9.8 m/s^2
F_applied = 784 N (Newtons)
Therefore, the window washer must pull downward with a force of 784 N to raise herself slowly at a constant speed.
Moving on to Part B:
Part B) If she increases this force by 16%, what will her acceleration be?
To calculate the new force applied by the window washer, we can multiply the original force by 1 plus the percentage increase (16% in this case).
New force applied = Original force applied * (1 + percentage increase)
New force applied = 784 N * (1 + 0.16)
New force applied = 784 N * 1.16
New force applied = 908.24 N
Now, using Newton's second law, we can find the new acceleration.
Force applied = mass * acceleration
Rearranging the equation to find acceleration:
Acceleration = Force applied / mass
Substituting the values:
Acceleration = 908.24 N / 80 kg
Acceleration ≈ 11.35 m/s^2
Therefore, if the window washer increases her force by 16%, her acceleration will be approximately 11.35 m/s^2.