Two blocks with different mass are attached to either end of a light rope that p

Question

Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended a distance 1.40 m , its speed is 2.00 m/s .

A-

If the total mass of the two blocks is 12.0 kg , what is the mass of the more massive block?

Take free fall acceleration to be 9.80 m/s2 .

B-What is the mass of the lighter block?

Take free fall acceleration to be 9.80 m/s2 .

Explanation / Answer

Let us consider mass of larger>

Let us consider mass of lighter>

From given data (m1+m2) = 12 kg

initial velocity of m1 is u =0 , final velocity =2 m/s , s = 1.4 m

From kinematic equation

v^2 -u^2 =2as

(2*2) - 0 =(2*a*1.4)

a = 1.429 m/s^2

Let us consider T is in the rope.

From Newton second law net force on larger mass along y direction

T - m1g = -m1a

T = m1g -m1a ...(2)

From Newton second law net force on smaller mass along y direction

T - m2g = m2a

T = m2g +m2a ...(3)

From (2) and (3)

m1g -m1a =m2g +m2a

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

1.429(m1+m2) = 9.8(m1-m2)

m1+m2 = 6.86 (m1-m2) ...(4)

By solving (1) and (4) equaitons we get

A) mass of larger mass m1 = 6.875 kg

B) mass of smaller mass m2 = 5.125 kg

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