answer 4 5 and 6 C Secure https://www.flipitphysics.com/Course/ViewProblem?unitl

Question

answer 4 5 and 6

C Secure https://www.flipitphysics.com/Course/ViewProblem?unitltemlD-2896779& enrollmentlD-256152 Bumper Cars Stand Bum A burner car with mass mi = 113 kg is moving to the right with a velocity of v1-4.5 m/s. A second bumper car with mass m2 -91 kg is moving to the left with a velocity of v2 3.4 m/s. The two cars have an elastic collision. Assume theBillia surface is frictionless. 1) What is the velocity of the center of mass of the system? Interact IE Spr 975 m/s Submit 2) What is the initial velocity of car 1 in the center-of-mass reference frame? 3.52 m/s Submit 3) What is the final velocity of car 1 in the center-of-mass reference frame? 3 52 s Submit

Explanation / Answer

i) velocity of CoM = [mu + mu] / [m + m] = [113(4.5) + 91(-3.4)] / 204 = 0.976 m/s

ii) since due to conservation of momentum, the center of mass velocity remains same after impact.

the initial velocity of car 1 in the center-of-mass reference frame:

= 4.5 - 0.976 = 3.524 m/s

(and of car = -3.4 - 0.976 = - 4.376 m/s )

iii) the final velocity of car 1 in the center-of-mass reference frame:

in the CoM reference frame total momentum is 0 (cause the CoM is relatively at rest)

mv + mv = 0

total kinetic energy is conserved since it is an elastic collision:

½113(3.524)² + ½91(-4.376)² = ½113(v')² + ½98(v')²

solving gives us v' = - u' and v' = - u'

=> v' = - 3.524 m/s

(and v' = 4.376 m/s )

iv) the final velocity of car 1 in the ground (original) reference frame:

since relative to CoM v ' = -3.524 = v - velcoity of CoM = v - 0.976

=> v = 0.976 - 3.548 = -2.572 m/s

v) the final velocity of car 2 in the ground (original) reference frame:

since relative to CoM v' = 4.376 = v - velcoity of CoM = v - 0.976

=> v = 0.976 + 4.376 = 5.352 m/s

vi) in a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide.

the final speed of the two bumper cars after the collision:

equation is: 113(4.5) + 91(-3.4) = 204v

=> v = 0.976 m/s = velocity of CoM since its velocity is unchanged when momentum is conserved.

Hope this helps :)

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