2. A 0.500 kg car is pulled by a 2 k block cart is R= 0.10a attached to a flywhe
ID: 3308518 • Letter: 2
Question
2. A 0.500 kg car is pulled by a 2 k block cart is R= 0.10a attached to a flywheel (pulley,-12MR) with a mass of 2 kg and radius of 10 cm Assume that the rolling cart is essentially sliding at zero friction. 2kg at is the acceleration, a, of the system? Please show all work, including Newton's second law equations for the 2 kg block, the cart, and the flywheel. A) Wh B) Find the two tensions in the string. C) What is the angular acceleration of the pulley? D) Assuming the system started from rest, what is the speed of the dropping block when the flywheel has turned through one rotation?Explanation / Answer
on 2kg:
Fnet = m a
2g - T1 = 2 a ....... (i)
on flywheel, Net torque = I alpha
R (T1 - T2) = (M R^2 / 2) (a / R)
T1 - T2 = M a / 2 = a ..... (ii)
on 0.5 kg :
T2 = 0.5 a .... (iii)
(i) +(ii) +(iii) =>
2 g = (2 + 1 + 0.5) a
a = 5.6 m/s^2 .......Ans
(B) T2 = 0.5 a = 2.8 N ....Tension in rope connected to 0.5 kg block.
rope that is attacted to 2 kg.
T1 = 2( g - a) = 8.4 N .....Ans
(C) alpha = a / R = 5.6 / 0.10
= 56 rad/s^2
(D) wf^2 - wi^2 = 2 alpha theta
w^2 - 0 = 2(56)(2pi)
w = 26.5 rad/s
v = w r = 2.65 m/s
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