Two blocks of masses M_1 and M_2 are connected by a massless string that passes

Question

Two blocks of masses M_1 and M_2 are connected by a massless string that passes over a massless pulley (the figure below). M_2, which has a mass of 22.0 kg, rests on a long ramp of angle theta = 31.0 degree. Friction can be ignored in this problem. What is the value of M_1 for which the two blocks are in equilibrium (no acceleration)? (Express your answer to three significant figures.) If the actual mass of M_1 is 5.80 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.) m/s^2 In part (2) does M_2 move up or down the ramp? moves up moves down In part (2), how far does block M_2 move in 2.4 s? (Express your answer to three significant figures.)

Explanation / Answer

Apply Newton secon law to solve the problem

m2 g sin theta - T = m2 a= m2 (0) = 0

T- m1g = m1 a= m1 (0) =0

T = m1 g

m2g sin theta = m1 g

m1 = m2g sin theta/g

= 22 sin 31

=11.33 kg

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(b)

m2 g sin thea -T= m2 a

T- m1 g= m1 a

T = m1( g+a)

( m2 g sin theta - m1 ( g+a) = m2 a

m2 g sin theta - m1g = ( m2 + m1) a

a= m2 g sin theta - m1g/ m1 + m2

= 22 ( 9.8) siin 31- 5.8(9.8)/22+5.8

=1.94 m/s^2

(d)

s= ut + 1/2 at^2

= 0 ( 2.4) + 1/2 * (1.94) (2.4)^2

=5.58 m

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