The figure shows a man sitting in a bosun\'s chair that dangles from a massless
ID: 1580961 • Letter: T
Question
The figure shows a man sitting in a bosun's chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man and chair is 90.4 kg. With what force magnitude must the man pull on the rope if he is to rise (a) with a constant velocity and (b) with an upward acceleration of 1.40 m/s2? (Hint: A free-body diagram can really help.) Problem continues below.
If the rope on the right extends to the ground and is pulled by a co-worker, with what force magnitude must the co-worker pull for the man to rise (c) with a constant velocity and (d) with an upward acceleration of 1.40 m/s2? What is the magnitude of the force on the ceiling from the pulley system in (e) part a (f) part b, (g) part c, and (h) part d?
Explanation / Answer
a)
when the man is pulling the force with atension T the total upward force on the man and chair due to its two contact
points with the rope is 2T
2T - mg = ma
when a = 0
T = mg/2
T = (90.4 x 9.81 m/s) / 2
T = 443.412 N
b)
a = 1.40 m /s^2
2T - mg = ma
2T = m[g + a]
T = m[g +a ] /2
T = 90.4 x [9.81 + 1.40] / 2
T = 506.692 N
c)
from newtons law of motion
T - mg = ma
now a = 0
T = mg
T = 90.4 kg x 9.81 m/s^2
T = 886.824 N
d)
when the acceleration is a = 1.40 m/s^2 then
T = m[g + a]
T = 90.4 x [9.81 x 1.40]
T = 1013.384 N
e)
the rope comes into contact at the left edge abdthe ruight edge of the pulley producing a total downward force of
F = 2T
F = 2 x 443.412
F = 886.824 N
f)
F = 2T
F = 2 x 506.692 N
F = 1013.384 N
g)
F = 2 x 886.824 = 1773.648 N
h)
F = 2 x 1013.384 N = 2026.768 N
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.