Answer:
Ek = 156.25 J
Explanation:
Given:-
- The moment of inertia of the grinding wheel I = 2.0 kg-m2
- The torque applied T = 2.5 N-m
Find:-
What is its final kinetic energy 10 seconds after starting from rest?"
Solution:-
- The relationship between applied torque and the angular acceleration α of the grinding wheel is can be expressed as:
T = I*α
- Solve for α , using the given data:
2.5 = 2.0*α
α = 1.25 rad / s^2
- Assuming constant acceleration ( constant applied torque T ) we can determine the angular velocity of the grinding wheel after time t = 10 sec using rotational kinematic equation of motion.
wf = wi + α*t
Where, wf = Final angular velocity (rad/s)
wi = Initial angular velocity (rad/s)
- Assuming the grinding wheel was initially at rest wi = 0 rad /s. We have:
wf = 0 + 1.25*10
wf = 12.5 rad/s
- The kinetic energy (Ek) of the grinding wheel after 10 seconds can b determined in rotational kinematics terms as follows:
Ek = 0.5*I*wf^2
Ek = 0.5*2.0*12.5^2
Ek = 156.25 J
- The kinetic energy of the grinding wheel after 10 seconds is Ek = 156.25 J
