GATE ME 2016 Set 2 — Question 40
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Engineering Mechanics → Dynamics → Work-Energy Formulation
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Question
A mass of 2000 kg is currently being lowered at a velocity of 2 m/s from the drum as shown in the figure. The mass moment of inertia of the drum is 150 kg-m. On applying the brake, the mass is brought to rest in a distance of 0.5 m. The energy absorbed by the brake (in kJ) is __________
Correct answer
14.1 to 14.3
Solution
Given:
Mass kg
Initial velocity m/s
Drum moment of inertia kg-m
Drum diameter m radius m
Distance moved mInitial Kinetic Energy ():
Since the rope does not slip, rad/s:
JWork done by gravity () during braking:
JEnergy absorbed by the brake ():
By the work-energy principle, the energy absorbed by the brake is equal to the total initial kinetic energy plus the work done by gravity as the mass descends further during braking (since final kinetic energy is zero).
J = 14.11 kJIf m/s is used, J = 14.3 kJ.
Both values fall within the range [14.1, 14.3].
Mass kg
Initial velocity m/s
Drum moment of inertia kg-m
Drum diameter m radius m
Distance moved mInitial Kinetic Energy ():
Since the rope does not slip, rad/s:
JWork done by gravity () during braking:
JEnergy absorbed by the brake ():
By the work-energy principle, the energy absorbed by the brake is equal to the total initial kinetic energy plus the work done by gravity as the mass descends further during braking (since final kinetic energy is zero).
J = 14.11 kJIf m/s is used, J = 14.3 kJ.
Both values fall within the range [14.1, 14.3].
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