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 1.10 m , its speed is 4.00 m/s .

part A)If the total mass of the two blocks is 18.0 kg , what is the mass of the more massive block?

Take free fall acceleration to be 9.80 m/s2 .

part B)

What is the mass of the lighter block?

Take free fall acceleration to be 9.80 m/s2

Explanation / Answer

Let the mass of massive block be M, then mass of lighter is m=18.0 - M

As the blocks start from rest, u=0 and velocity v =4 m/s at distance s= 1.10 m

using v^2 - u^2 =2as

a=v^2 /2s

a =7.27 m/s^2

Writing equations of motion

For massive going down

Mg T= Ma..............................(1)

for lighter block

T -mg=ma..........................(2)

solving (1) and (2)

a=(M-m)g/(M+m) =(2M-18)g/18

but a= 7.27

(2M -18)g/18=7.27

Heavier mass M is 15.676 kg
______________________________________...
(B)lighter mass is 2.233 kg

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