a 85 kg man lowers himself down to the ground from a height of 10 meters by holding a rope that runs over a frictionless pulleyto a 65 kg sand bag.With what speed does the man hit the ground if he started from rest?
Answers
Answer:
Viewing the man-rope-sandbag as a system means that we should be careful to choose a consistently positive direction of motion (though there are other ways to proceed, say, starting with individual application of Newton’s law to each mass). We take down as positive for the man’s motion and up as positive for the sandbag’s motion and, without ambiguity, denote their acceleration as a. The net force on the system is the difference between the weight of the man and that of the sandbag.
The system mass is m
sys
=85kg+65kg=150kg.
Thus, Eq. 5-1 leads to
(85kg)(9.8m/s)(65kg)(9.8m/s
2
)m
sys
a
which yields a=1.3m/s
2
. Since the system starts from rest, Eq. 2-16 determines the speed (after traveling Δy=10m) as follows:
v=
2aΔy
=
2(1.3m/s
2
)(10m)
=5.1m/s