Download The figure above shows an 80-kilogram person standing on a 20

The figure above shows an 80-kilogram person standing on a 20-kilogram platform suspended by a
rope passing over a stationary pulley that is free to rotate. The other end of the rope is held by the
person. The masses of the rope and pulley are negligible. You may use g = 10 m/s2. Assume that
friction is negligible, and the parts of the rope shown remain vertical.
a) If the platform and the person are at rest, what is the tension in the rope?
The person now pulls on the rope so that the acceleration of the person and the platform is 2 m/s2
upward.
b) What is the tension in the rope under these new conditions?
c) Under these conditions, what is the force exerted by the platform on the person?
d) How could the force you solved for in part (c) be DIRECTLY measured in practice?
e) After a short time, the person and the platform reach and sustain an upward velocity of 0.4 m/ s.
Determine the power output of the person required to sustain this velocity.
Make sure that you define the system (as in any work, energy, or momentum
problem) AND take care to get the sign of the power correct.
What energy source provides this power?
2) AP 2009 M3: A block of mass MT rests on a frictionless horizontal table, as shown above. It is
connected to one end of a string that passes over a massless pulley and has a block of mass MH
hanging from its other end. The apparatus is released from rest.
(a) Derive an expression for the speed v h of the hanging block as a function of the distance d a s i t
descends and THEN evaluate your answer for the case when MT = MH = ½ M.
Now the block and pulley system is replaced by a uniform rope of length L and mass M, with one end
of the rope hanging slightly over the edge of the frictionless table. The rope is released from rest, and
at some time later there is a length y of rope hanging over the edge, as shown below.
Express your answers to parts (b), (c), and (d) in terms of y, L, M, and fundamental constants.
(b) Determine an expression for the force of gravity on the hanging part of the rope as a function of y.
Make sure it’s clear how you got your answer (i.e., your answer should include some logical
justification. Words may not be necessary if your equation work is logical).
(c) In your first physics course, you learned that W = F . y (yes, it’s a scalar dot product).
However, that is only true if the force is constant over the displacement. This is not true in this
problem, as your answer to the previous part (b) should show. Therefore the definition of work
becomes W = integral of F . dy (and yes, still a scalar dot product).
Derive an expression for the work done by the gravity force on the rope as a function of y, assuming y
is initially zero.
(d) Derive an expression for the speed v y of the rope as a function of y
(e) The hanging block and the right end of the rope are each allowed to fall a distance L (the length of
the rope). Assume that the string is long enough that the sliding block does not hit the pulley. Is v h
from part (a) or vy from part (d) greater after the block and the end of the rope have traveled this
distance. Justify your answer