Question

A 1500-kg air conditioning unit is being lifted by a crane onto the roof of a building. The unit starts on the ground and is raised straight up to a height of 12.0 m by a cable attached to the crane. The tension in the cable during the lift is 1.54 × 104 N. (Reminders: a free body diagram will probably be helpful, and work can be positive or negative.) (a) How much work is done on the air conditioning unit by the tension force? (b) How much work is done on the unit by gravity? (c) What is the speed of the unit when it reaches 12.0 m above the ground? Show how you use work and energy to find your answer. Do not use kinematics (although this would be good way to double-check your answer).

Answer 1

a) the tension is in the same direction of displacement, meaning that the work is positive:

$W=Td=1.54\cdot 10^{4}\cdot 12=18.48\cdot 10^{4}\, J$

b) the weight is in the opposite direction of displacement, meaning that the work is negative:

$W=Wd=-1500\cdot 9.8\cdot 12=-176400\, J$

c) using work energy principle:

$W=\Delta K=\frac{mv^2}{2}$assuming it starts from rests

$18.48\cdot 10^{4}-176400=\frac{1500v^2}{2}$

solving for v we have that: