A 17.5 kg object moving in the + x direction at 6.0 m/s collides head-on with a

Question

A 17.5 kg object moving in the +x direction at 6.0 m/s collides head-on with a 10.5 kg object moving in the x direction at 3.5 m/s .

Part B

Find the final velocity of each mass if the collision is elastic.

Part C

Find the final velocity of each mass if the 17.5 kg object is at rest after the collision.

Part D

Is the result in part C "reasonable"? Explain.

Part E

Find the final velocity of each mass if the 10.5 kg object is at rest after the collision.

Part F

Is the result in part E "reasonable"? Explain.

Part G

Find the final velocity of each mass if the 17.5 kg object has a velocity of 3.5 m/s in the xdirection after the collision.

Part H

Is the result in part G "reasonable"? Explain.

Explanation / Answer

here,

m1 = 17.5 kg

u1 = 6 m/s

m2 = 10.5 kg

u2 = - 3.5 m/s

B)

let the final apeed be v1 and v2

when collison is elastic

m1*u1 + m2 *u2 = m1 * v1 + m2 *v2

17.5 * 6 - 10.5 * 3.5 = 17.5 * v1 + 10.5 * v2 ...(1)

using conservation of kinetic energy

0.5 * m1 * u1^2 + 0.5 * m2 * u2^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

17.5 * 6^2 + 10.5 * 3.5^2 = 17.5 * v1^2 + 10.5 * v2^2 ....(2)

from equation(1) and (2)

v1 = -1.13 m/s and v2 = 8.38 m/s

or

v1 = 6 m/s and v2 = - 3.5 m/s

c)

if m1 stops after the collsion

using conservation of momentum

m1*u1 + m2 *u2 = m2 *v2

17.5 * 6 - 10.5 * 3.5 = 10.5 * v2

v2 = 6.5 m/s , v1 = 0

d)

the result in part C is reasonablee , the mass may stop after the collison

e)

if m2 stops after the collison

using conservation of momentum

m1*u1 + m2 *u2 = m1 * v1

17.5 * 6 - 10.5 * 3.5 = 17.5 * v1

v1 = 3.9 m/s , v2 = 0

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