   Chapter 6, Problem 63AP

Chapter
Section
Textbook Problem

A 2.0-g particle moving at 8.0 m/s makes a perfectly elastic head-on collision with a resting 1.0-g object. (a) Find the speed of each particle after the collision. (b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g. (c) Find the final kinetic energy of the incident 2.0-g particle in the situations described in parts (a) and (b). In which case does the incident particle lose more kinetic energy?

(a)

To determine
The speed of each particle after collision.

Explanation

Explanation

Given Info:

Mass of the moving particle is 2.0g , speed of the moving particle is 8.0ms1 , mass of the particle which is at rest is 1.0g , the initial speed of particle at rest is zero.

Apply conservation of momentum for both particles before and after collision,

m1v1+m2v2=m1v1+m2v2

• m1 is the mass of the moving particle
• v1 is initial the speed of the particle
• m2 is the mass of the particle which is at rest
• v2 is the speed of particle at rest.
• v1 is the speed of m1 after collision
• v2 is the final speed of m2 after collision

Use 0m/s for v2 in the above equation and rewrite in terms of v2 .

v2=(m1m2)(v1v1) (I)

Apply conservation of mechanical energy for both particles,

12m1v12+12m2v22=12m1(v1)2+12m2(v2)2

Use 0m/s for (v2)2 in the above equation and rewrite in terms of v2 .

(v2)2=(m1m2)(v12(v1)2) (II)

Use (m1/m2)(v1v1) for v2 in the above equation and rewrite in terms of v1

(b)

To determine
The speed of each particle after collision.

(c)

To determine
The magnitude of kinetic energy of the moving particle for given velocities.

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