Please help me with this question, but only answer id you know how to do it 100% and please write big and clear.
(a) Consider here, m1 = 4m mass
and, m2 = m
Now, for determining the velocity of this mass at the collision point,
(1/2)*m1*v1^2 = m1*g*h
=> v1 = sqrt(2gh) towards right.(+ve sign consider)
for the second mass, m2 -
(1/2)*m2*v2^2 = m2*g*4h
=> v2 = sqrt(8gh) (-ve sign consider)
Now suppose the velocity of the combined mass is v.
apply conservation of momentum -
m1v1 + m2v2 = (m1+m2)v
=> 4m*sqrt(2gh) - m*sqrt(8gh) = (4m+m)*v
=> 4*sqrt(2gh) - 2*sqrt(2gh) = 5v
=> 2*sqrt(2gh) = 5v
=> v = 0.4*sqrt(2gh)
Now suppose h1 is the height attained by the combined mass in the right direction -
so -
(1/2)*(m1+m2)*v^2 = (m1+m2)*g*h1
=> h1 = v^2/2g = [0.4*sqrt(2gh)]^2 / 2g = 0.16*(h)
(b) Total initial KE energy, KE1 = 4mgh + mg(4h) = 8mgh
Final KE, KE2 = (1/2)*(m1+m2)*v^2 = 0.5*5m*[0.4*sqrt(2gh)]^2 = 2.5m*0.16*2gh = 0.8mgh
Loss in KE = Energy converted into thermal energy = 8mgh - 0.8mgh = 7.2mgh
So, the fraction of energy that is converted into thermal energy = (7.2mgh) / (8mgh) = 0.90.
Please help me with this question, but only answer id you know how to do it...
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