A 15 g marble moves to the right at 3.5 m/s and makes an elastic head-on collision with a 22 g marble. Thefinal velocity of the 15 g marble is 5.4 m/s to the left, and the final velocity of the 22 g marble is 2.0 m/s tothe right. What is the initial kinetic energy of the two marble system?

Question
Asked Oct 6, 2019
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A 15 g marble moves to the right at 3.5 m/s and makes an elastic head-on collision with a 22 g marble. The
final velocity of the 15 g marble is 5.4 m/s to the left, and the final velocity of the 22 g marble is 2.0 m/s to
the right. What is the initial kinetic energy of the two marble system?

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Expert Answer

Step 1

Let the marbles are m1, m2 and u1, u2 are initial velocity and v1, v2 are final velocity respectively.

и,
у
и,
т
т,
т,
т
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и, у и, т т, т, т

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Step 2

Given,

m, 15 g 0.015 kg
m 22 g 0.022 kg
u 3.5 m/s
= 5.4 m/s
2 2.0 m/s
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m, 15 g 0.015 kg m 22 g 0.022 kg u 3.5 m/s = 5.4 m/s 2 2.0 m/s

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Step 3

By the conservation ...

ти + т,и, — ту, + тv,
0.015x3.5 0.022u, 0.015x (- 5.4) +0.022 x 2.0
0.05250.022u, =- 0.081+0.044
0.022u
- 0.0895
4.068 m/s
и,
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ти + т,и, — ту, + тv, 0.015x3.5 0.022u, 0.015x (- 5.4) +0.022 x 2.0 0.05250.022u, =- 0.081+0.044 0.022u - 0.0895 4.068 m/s и,

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