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 = 4.40 kg is released from rest at a height h = 2.60 m above the table.

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 = 4.40 kg is released from rest at a height h = 2.60 m above the table. Using the isolated system model, determine the speed of the object of mass m2 = 3.00 kg just as the 4.40-kg object hits the table.? m/s Find the maximum height above the table to which the 3.00-kg object rises ? m

Explanation / Answer

the acceleration of the two objects is

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

where g = 9.8 m/s^2

height of mass m1 is h = 2.60 m

let v1 be the speed of mass m1 as it hits the table

we know that

v1^2 - u1^2 = 2ah

or v1^2 = u1^2 + 2ah

where u1 = 0

according to the law of conservation of energy we have

(1/2)m1v1^2 = (1/2)m2v2^2

where v2 is speed of mass m2

or v2^2 = (m1/m2) x v1^2

or v2 = (m1/m2)^1/2 x v1

let h1 be the maximum height reached by mass m2

we know that

v2^2 - u2^2 = 2ah1

or h1 = (v2^2 - u2^2/2a)

where u2 = 0

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