Velocity of the roller coaster when it reaches the top of the loop. A bullet (m
ID: 1599743 • Letter: V
Question
Velocity of the roller coaster when it reaches the top of the loop. A bullet (m = 50 gram) is fired into an ice block (M = 3 KG) resting on ice. The bullet is imbedded in ice block and they move together on ice. Find the common velocity they move together. Find the initial kinetic energy of the system. Find the final kinetic energy of the system. Find the percent energy loss. Two Bowling balls are moving toward each other and collide. Assume elastic collision. M = 2 kg moving at 3 m/sec, and m = 1.8 kg moving at - 4 m/sec. Find their velocities after the collision Find their total initial kinetic energy, and total final kinetic energy. Are they equal?Explanation / Answer
Taking right as positive and left as negative.
So, the bigger ball of mass M =2 kg was moving towards the right and the smaller ball of mass m = 1.8 kg was moving towards left, initially.
let v1 and v2 be the final velocities of the bigger and smaller balls respectively.
Applying conservation of linear momentum,
total initial momentum = total final momentum
2 x 3 + 1.8 x - 4 = 2 x v1 + 1.8 x v2
- 1.2 = 2 v1 + 1.8 v2 eqn 1
also, in an eleastic collision, the velocity of approach is equal to the velocity of separation
So, 3 - (-4) = v2 - v1
7 = v2 - v1 eqn 2
putting eqn 2 in eqn 1
- 1.2 = 2 v1 + 1.8 ( v1 + 7 )
- 1.2 = 3.8 v1 + 12.6
v1 = - 3.631578947 m/s (negative sign indicates that the final direction of mass M is towards the left)
v2 = v1 + 7 = - 3.631578947 + 7 = 3.368421053 m/s towards right
total initial KE = 0.5 x 2 x 32 + 0.5 x 1.8 x (-4)2 = 23.4 J
total final KE = 0.5 x 2 x v12 + 0.5 x 1.8 x v22 = 0.5 x 2 x (- 3.631578947)2 + 0.5 x 1.8 x (3.368421053 )2 = 23.4 J
Yes, they are equal because Kinetic energy is conserved in an elastic collision.
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