Two blocks are connected by a light string that passes over a frictionless pulle

Question

Two blocks are connected by a light string that passes over a frictionless pulley as in the figure below. The system is released from rest while m2 is on the floor and m1 is a distance h above the floor. (a) Assuming m1> m2, find an expression for the speed of mi just as it reaches the floor. (Use any variable or symbol stated above along with the following as necessary: g.) (b) Taking m1 = 6.3 kg, m2 = 3.5 kg, and h = 3.1 m, evaluate your answer to part (a). m/s (c) Find the speed of each block when m1 has fallen a distance of 1.8 m. m/s Need Help? Read it

Explanation / Answer

a) m1 g -T = m1 a

T - m2 g = m2 a

equating the above equations

m1 g - m1 a = m2 a + m2 g

a = (m1 - m2) g / (m1 + m2)

velocity = sqrt (2 a d)

vf = sqrt [2 (m1 - m2) g h / (m1 + m2) ]

b) vf = sqrt [2 (6.3- 3.5) 9.8 * 3.1 / (6.3+ 3.5) ]

= 4.17 m/s

c) acceleration = (6.3- 3.5) 9.8 / (6.3+ 3.5) = 2.8 m/s2

speed v = sqrt(2 * 2.8 * 1.8)

speed = 3.17 m/s

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