A stationary object with mass m B is struck head-on by an object with mass m A t

Question

A stationary object with mass mB is struck head-on by an object with mass mA that is moving initially at speed v0.

Part A

If the collision is elastic, what percentage of the original energy does each object have after the collision?

Part B

Part C

What does your answer in parts A and B give for the special case mA=mB?

Part D

Part E

What does your answer in parts A and B give for the special case mA=5mB?

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Part F

Part G

For what values, if any, of the mass ratio mAmB is the original kinetic energy shared equally by the two objects after the collision?

Express your answer numerically. If there is more than one answer, enter each answer, separated by a comma.

A stationary object with mass mB is struck head-on by an object with mass mA that is moving initially at speed v0.

Part A

If the collision is elastic, what percentage of the original energy does each object have after the collision?

KA2K1 =

Part B

KB2K1 =

Part C

What does your answer in parts A and B give for the special case mA=mB?

KA2K1 =

Part D

KB2K1 =

Part E

What does your answer in parts A and B give for the special case mA=5mB?

KA2K1 =

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Part F

KB2K1 =

Part G

For what values, if any, of the mass ratio mAmB is the original kinetic energy shared equally by the two objects after the collision?

Express your answer numerically. If there is more than one answer, enter each answer, separated by a comma.

mAmB =

Explanation / Answer

PartA

by using conservation of momentum

MaVa1 + MbVb1 = MaVa2 + MbVb2

then

the velocity after the collision is

Va2 = (Ma-Mb/Ma+Mb)*V0
Vb2 = (2Ma/Ma+Mb)*V0

Then, using equations for kinetic energy of the system

Kinetic energy = 0.5 * m * v^2

K1 = 0.5*Ma*V0^2

The kinetic energy of either mass after the collision can be found by substituting the final velocity into the kinetic energy equation:
Ka2 = 0.5*Ma*[(Ma-Mb/Ma+Mb)*V0]^2
Ka2= 0.5*Ma*Vo^2*(Ma-Mb/Ma+Mb)^2
Ka2 = K1 (Ma - Mb / Ma +Mb)^2

PART B

then here also

putting the value of Vb2

Kb2 = 0.5*Ma*V0^2 (4MbMa/(Ma+Mb)^2 )

Kb2 = K1 (4MbMa/(Ma+Mb)^2 )

Kb2/K1 = 4MbMa/(Ma+Mb)^2

PART C

when the mass is Ma = Mb

then

Ka2 = K1 (Ma - Mb / Ma +Mb)^2

Ka2/ K1 = (Ma - Ma / Ma +Ma )^2

Ka2/K1 = 0

PART D

Kb2/K1 = 4MbMa/(Ma+Mb)^2

when Ma = Mb

then

Kb2/K1 = 4Ma*Ma / ( Ma +Ma)^2

Kb2/K1 = 4*Ma^2 / 2Ma^2

Kb2/K1 = 1

Part E

Ka2 = K1 (Ma - Mb / Ma +Mb)^2

when Ma=5Mb

then

Ka2/K1 = ( 5Mb - Mb / 5Mb + Mb)^2

Ka2/K1 = 4 / 9

PART F

Kb2/K1 = 4MbMa/(Ma+Mb)^2

when Ma = 5Mb

then

Kb2/K1 = 4* Mb * 5 * Mb / ( 5Mb + Mb)^2

Kb2/K1 = 5 / 9

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