Three Blocks each of mass m are located on a frictionless track as shown above.
ID: 2066113 • Letter: T
Question
Three Blocks each of mass m are located on a frictionless track as shown above. After block A is released it makes an inelastic collision with Block B (they both stick together) and the two of them in turn collide with and stick to block C. Find the total energy converted to heat in this entire process in terms of m,g, and h. I got (1/3)(mgh) for the solution. Show me if I am correct. Thanks.
Three Blocks each of mass m are located on a frictionless track as shown above. After block A is released it makes an inelastic collision with Block B (they both stick together) and the two of them in turn collide with and stick to block C. Find the total energy converted to heat in this entire process in terms of m,g, and h. I got (1/3)(mgh) for the solution. Show me if I am correct. Thanks.Explanation / Answer
For first collision :
Velocit at point of location of block B.
0.5*m*v^2=m*g*h/3
V=(2*g*h/3)
By conservation of momentum.
m*V=(m+m)*V1
V1=V/2
Energy converted to head=U1=ke=0.5*m*2*g*h/3 - 0.5*2*m*g*h/6
=m*g*h/6
For Second collision:
Velocit at point of location of block C.
0.5*2m*v2^2=2m*g*h/6 + 0.5*2m*v1^2
v2^2=2*g*h/6 +v1^2
v2^2=2*g*h/6 +g*h/6
V2 =(g*h/3)
By conservation of momentum.
2m*V2=(2m+m)*V3
V3=2*V2/3
Energy converted to heat=U2=KE=0.5*2*m*g*h/3 - 0.5*3*m*4*g*h/27
= m*g*h/9
Total enery converted to heat = m*g*h/6+m*g*h/9
=5*m*g*h/18
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