As shown in the figure on the right, a string is wrapped around a solid cylindri
ID: 1614444 • Letter: A
Question
As shown in the figure on the right, a string is wrapped around a solid cylindrical pulley of m_2 = 5.0 kg and radius R = 0.2 m. A block of m_1 = 1.5 kg is attached to the end of the string. Let T denote the tension in the string, and radius let a denote the linear acceleration of the 1.5-kg block. The moment inertia of the pulley is given by: (1/2) m_2 R^2. (a) Write down the equation of motion for the 1.5-kg block using symbols: m_1, g, T a (b) Write down an expression for the torque acting on the pulley using symbols: R, T (c) Write down the equation of motion for the pulley using symbols: m_2, R, T, a. Show all intermediate steps clearly. (d) Find the linear acceleration of the 1.5 kg block. (e) Find the angular acceleration of the pulley. (f) Find the tension T in the string.Explanation / Answer
A) m1a = m1g - T
B) net torque is TR
C) i alpha = torque
0.5 m2*R^2 *alpha = TR and a=alpha R
0.5 m2*a= T
D) adding equation A and C
(m1+0.5m2)*a = m1g
(1.5+0.5*5)a = 1.5*9.8
a = 14.7/4
= 3.675 m/s^2
E) alpha= a/R = 3.675/0.2
= 18.375 rad/s^2
F) T = 0.5*5*3.675
= 9.1875 N
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