A bumper car with mass m 1 = 117 kg is moving to the right with a velocity of v
ID: 1283037 • Letter: A
Question
A bumper car with mass m1 = 117 kg is moving to the right with a velocity of v1 = 4.2 m/s. A second bumper car with mass m2 = 81 kg is moving to the left with a velocity of v2 = -3.3 m/s. The two cars have an elastic collision. Assume the surface is frictionless.
1)
What is the velocity of the center of mass of the system?
m/s
Your submissions:
2)
What is the initial velocity of car 1 in the center-of-mass reference frame?
m/s
Your submissions:
3)
What is the final velocity of car 1 in the center-of-mass reference frame?
m/s
Your submissions:
4)
What is the final velocity of car 1 in the ground (original) reference frame?
m/s
Your submissions:
5)
What is the final velocity of car 2 in the ground (original) reference frame?
m/s
Your submissions:
6)
In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide.
What is the final speed of the two bumper cars after the collision?
A bumper car with mass m1 = 117 kg is moving to the right with a velocity of v1 = 4.2 m/s. A second bumper car with mass m2 = 81 kg is moving to the left with a velocity of v2 = -3.3 m/s. The two cars have an elastic collision. Assume the surface is frictionless. 1) What is the velocity of the center of mass of the system? m/s Your submissions: 2) What is the initial velocity of car 1 in the center-of-mass reference frame? m/s Your submissions: 3) What is the final velocity of car 1 in the center-of-mass reference frame? m/s Your submissions: 4) What is the final velocity of car 1 in the ground (original) reference frame? m/s Your submissions: 5) What is the final velocity of car 2 in the ground (original) reference frame? m/s Your submissions: 6) In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide. What is the final speed of the two bumper cars after the collision?Explanation / Answer
1) vcm = m1 v1 + m2 v2 / (m1 + m2)
= (117*4.2 + 81(-3.3)) / (117+ 81)
= 1.132 m/s
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2) initial velocity of car1 v1i cm= v1 - vcm
= 4.2 - 1.132
= 3.07 m/s
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3) After collision direction of first car is opposite to its initial direction
v1f cm = - v1i cm = -3.07 m/s
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4) v1f ground = v1f cm + vcm
= -3.07 + 1.132
= -1.938 m/s
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5) v2f cm = -v2i cm = - (v2 - vcm)
= - (-3.3 - 1.132) = 4.432 m/s
v2f ground = 4.432 + 1.132
= 5.564 m/s
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6) v = m1 v1 + m2 v2 / (m1 + m2)
= (117*4.2 + 81(-3.3)) / (117+ 81)
= 1.132 m/s
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