A motor is used to turn the pulley A which is connected to the wheel B by a tran
ID: 1997056 • Letter: A
Question
A motor is used to turn the pulley A which is connected to the wheel B by a transmission belt. The system starts from rest. The motor begins to rotate the pulley A with a constant angular acceleration of = 2.4 rad/s2. Assume the transmission belt does not slip on the pulley or the wheel.
1.Determine the linear speed of point P after wheel B has turned one revolution.
(include units with answer)
2.Determine the time for wheel B to complete the second revolution.
Note: this answer does not include the time for the first revolution.
(include units with answer)
A motor is used to turn the pulley A which is connected to the wheel B by a transmission belt. The system starts from rest. The motor begins to rotate the pulley A with a constant angular acceleration of = 2.4 rad/s2. Assume the transmission belt does not slip on the pulley or the wheel.
1.Determine the linear speed of point P after wheel B has turned one revolution.
(include units with answer)
2.Determine the time for wheel B to complete the second revolution.
Note: this answer does not include the time for the first revolution.
(include units with answer)
Explanation / Answer
Herem
aA = 2.4 rad/s^2
for the angular acceleration of B
aB * rB = aA * rA
2.4 * 0.17 = aB * 0.37
aB = 1.103 rad/s^2
a) after 1 revolution, theta = 2pi radian
angular speed of B , wB = sqrt(2 * aB * theta)
wB = sqrt(2 * 1.103 * 2pi)
wB = 3.72 rad/s
linear speed of P = 0.37 * wB
linear speed of P = 3.72 * 0.37
linear speed of P = 1.38 m/s
2)
let the time taken is t
using second equation of motion
theta = wB * t + 0.5 * a * t^2
2pi = 3.72 * t + 0.5 * 1.103 * t^2
solving for t
t = 1.39 s
the time taken to complete the second revolution is 1.39 s
the time taken for B to complete t
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