Question

Two blocks of masses Mi and M2 are connected by a massless string that passes over a massless pulley (the figure below). M2, which has a mass of 20.0 kg, rests on a long ramp of angle 428.0°. Friction can be ignored in this problem. 1) What is the value of Mi for which the two blocks are in equilibrium (no acceleration)? (Express your answer to three significant figures.) 5.4 Submit Your submissions: 15.4 Computed value: 5.4 Feedback: Submitted: Friday, January 26 at 8:58 PM 2) If the actual mass of Mi is 5.40 kg and the system is allowed to move, what is the magnitude of the acceleration of the two blocks? (Express your answer to three significant figures.) 0.68 m/s2 Submit Your submissions: .08 Computed value: 0.68 Feedback: X Submitted: Friday, January 26 at 8:59 PM 3) In part (2) does M2 move up or down the ramp? moves up moves down Submit 4) In part (2), how far does block M2 move in 2.2 s? (Express your answer to three significant figures.) m Submit

Answer 1

Few body diagram for m_1, and m_2 apply equilibrium condition of force for m, m_1, g = T Apply equilibrium condition of force from m_2 m_29 sin theta = T m_2 9 sin theta = m_1 9 m_1 = m_2 sin theta = (20) sin 28 degree = 9.38N apply equilibrium conditions of forces for masses m_1 and m_2 T - m_1 9 = m_1 a m_2 9 sin theta - m_1 9 - m-1 a = m_2 a a = (m_2 - sin theta - m_2) 9/m_1 + m_21 = [(20) sin 28 - 5.4](9.8)/20 + 5.4 = 1.53 m/s^2 since m_2 sin theta greaterthan m_1, the mass will move down words. The distance moved by mass is S = 1/2 at^2 = 1/2 (1 - 53) (2.2)^2 = 3.70m