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 1.19 m, its speed is 3.18 m/s. If the total mass of the two blocks is 14.5 kg, what is the mass of each block? (Enter your answers from smallest to largest.

Answer 1

Let the mass of the heavier block = M kg

and the mass of the lighter block = m kg

Total mass M+m = 14.5kg or m=14.5-M

Now according to the problem the blocks start from rest thus

initia velocity u=0 m/s, final velocity v=3.18m/s and the distance travelled by block during this is s=1.19m

using the third equation of motion, we get

by plugging all the values in above equation, we get

Now the equation of motions will be

For massive mass

eq-1

for lighter block

eq-2

solving eq-1 and eq-2

by plugging all the values we get

therefore   

Hence,

the lighter mass is 4.1kg whereas the heavier mass is 10.4kg