Two objects are connected by a light string passing over a light, frictionless p

Question

Two objects are connected by a light string passing over a light, frictionless pulley, as shown in the figure below. The object of mass m1 is released from rest at height h above the table. Use the isolated system model to answer the following. (We assume m1 > m2.)

(a) Determine the speed of m2 just as m1 hits the table. (Use any variable or symbol stated above along with the following as necessary: g.)

v = ?

(b) Find the maximum height above the table to which m2 rises. (Use any variable or symbol stated above along with the following as necessary: g.)

hmax = ?

Explanation / Answer

a) Use conservation of energy
m1 g h = m2 g h + 1/2 m1 v² + 1/2 m2 v²
when m1 nearly hit the table both mass still have same speed.

v² = 2 (m1 - m2) g h / (m1 + m2)

b)

after m1 on the table m2 move on constant acceleration g.
H = h + v² / 2g = h + (m1 - m2) h / (m1 + m2)
H = 2 m1 h / (m1 + m2)

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