Part A) Two masses of 5 kg and 2.4 kg are suspended by a pulley with a radius of 11 cm and a mass of 4 kg as shown in the figure. The cord has negligible weight and causes the pulley to rotate without slipping. What is the angular acceleration of the pulley? Treat the pulley as a uniform disk. The acceleration of gravity is 9.8 m/s^2.
Answer in units of rad/s^2
Part B) What is the magnitude of the tension in the cord on the right-hand side?
Answer in units of N
Part C) The masses start from rest 2.45 m vertically apart.
What is the speed of the right-hand mass when the two masses pass each other?
Answer in units of m/s
Answer in units of rad/s^2
Part B) What is the magnitude of the tension in the cord on the right-hand side?
Answer in units of N
Part C) The masses start from rest 2.45 m vertically apart.
What is the speed of the right-hand mass when the two masses pass each other?
Answer in units of m/s
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What figure?? Hard to answer part b and c without it. For part a
T2 x r - T1 x r = I alpha where I = 1/2 Mr^2 for the pulley
5g - T2 = 5 a
T1 - 2.4 g = 2.4 a where a = r alpha
so T2 = 5g - 5 x .11 x alpha
T1 = 2.4 x 0.11 x alpha + 2.4g
Plug in first equation to eliminate T1 and T2 and solve for alpha
(2.6 g - 7.4 x 0.11 x alpha)(0.11) = 1/2 x 4 x 0.11^2 alpha
2.6 g - 7.4 x 0.11 x alpha = 2 x 0.11^2 alpha
2.6 g = alpha( 7.4 x 0.11 + 2 x 0.11^2)
T2 x r - T1 x r = I alpha where I = 1/2 Mr^2 for the pulley
5g - T2 = 5 a
T1 - 2.4 g = 2.4 a where a = r alpha
so T2 = 5g - 5 x .11 x alpha
T1 = 2.4 x 0.11 x alpha + 2.4g
Plug in first equation to eliminate T1 and T2 and solve for alpha
(2.6 g - 7.4 x 0.11 x alpha)(0.11) = 1/2 x 4 x 0.11^2 alpha
2.6 g - 7.4 x 0.11 x alpha = 2 x 0.11^2 alpha
2.6 g = alpha( 7.4 x 0.11 + 2 x 0.11^2)