Mechanical Advantage The pulley system shown in the figure is used to lift a m=
ID: 1791835 • Letter: M
Question
Mechanical Advantage The pulley system shown in the figure is used to lift a m= 67-kg crate. Note that one chain connects the upper pulley to the ceiling and a second chain connects the lower pulley to the crate. Assume the masses of the chains, pulleys, and ropes are negligible.
Figure 1 of 1
a) Determine the force F required to lift the crate with constant speed. Express your answer using two significant figures.
b) Determine the tension in the upper chain. Express your answer using two significant figures.
c) Determine the tension in the lower chain. Express your answer using two significant figures.
Explanation / Answer
Since this is a pulley system, we have to count the number of “ropes” involved. There are two halves of rope on the pulley holding up the block, so the amount of force required for each is one half the total. The total force is just mass times gravity
the force F required to lift the crate is
F = 2T - mg
since crate moving with constant speed
so, acceleration a = 0 m/s2
ma = 2T - mg
0 = 2T - mg
2T = mg
T = mg/2
= 67(9.8)/2
=328.3 N
rounding to two significant digits
T = 330 N
(b)
T _upper= mg
T _upper= 67(9.8)
=656.6 N
rounding to two significant digits
T_upper = 660 N
(c)
T_ upper = T_ lower = 660 N