GATE ME 2014 Set 3 — Question 47
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Engineering Mechanics → Dynamics → Dynamics of Rigid Bodies
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Question
A four-wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in 10 s, the braking torque (in N.m) on each wheel is _______
Correct answer
9 to 11
Solution
Given:
Mass of the vehicle, kg
Angular velocity of wheels, rad/s
Radius of wheels, m
Time to stop, s
Number of wheels, Step 1: Calculate the initial linear velocity () of the vehicle.
m/sStep 2: Calculate the deceleration () required to stop the vehicle in 10 s.
m/sStep 3: Calculate the total braking force () required.
NStep 4: Calculate the total braking torque ().
N.mStep 5: Calculate the braking torque on each wheel ().
N.mThus, the braking torque on each wheel is 10 N.m.
Mass of the vehicle, kg
Angular velocity of wheels, rad/s
Radius of wheels, m
Time to stop, s
Number of wheels, Step 1: Calculate the initial linear velocity () of the vehicle.
m/sStep 2: Calculate the deceleration () required to stop the vehicle in 10 s.
m/sStep 3: Calculate the total braking force () required.
NStep 4: Calculate the total braking torque ().
N.mStep 5: Calculate the braking torque on each wheel ().
N.mThus, the braking torque on each wheel is 10 N.m.
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