On a frictionless horizontal air table, puck A (with mass 0.247 kg ) is moving toward puck B (with mass 0.375 kg ), which is initially at rest. After the collision, puck A has velocity 0.118 m/s to the left, and puck B has velocity 0.655 m/s to the right.What was the speed vAi of puck A before the collision?Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

Question
Asked Dec 2, 2019
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On a frictionless horizontal air table, puck A (with mass 0.247 kg ) is moving toward puck B (with mass 0.375 kg ), which is initially at rest. After the collision, puck A has velocity 0.118 m/s to the left, and puck B has velocity 0.655 m/s to the right.

What was the speed vAi of puck A before the collision?

Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

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Expert Answer

Step 1

Let the mass of puck A be denoted as mA and the mass of puck B be denoted as mB

Let the initial and final velocities of the puck A be denoted as vAi and vAf and the initial and final velocities of the puck B be denoted as vBi  and vBf

 

Using the Law of conservation of linear momentum as,

my m = mVf
mB
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my m = mVf mB

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Step 2

Make the necessary substitutions and solve for vAi as,

 

(0.247kg)v+(0.375kg) (0) = (0.247kg)(-0.1 18m/s)+
(0.375kg)(0.655m/s)
0.2165 kg m/s
0.247kg
0.88 m/s
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(0.247kg)v+(0.375kg) (0) = (0.247kg)(-0.1 18m/s)+ (0.375kg)(0.655m/s) 0.2165 kg m/s 0.247kg 0.88 m/s

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Step 3

Thus the velocity vAi is equal to 0.88 m/s directed towards the right.

b)

The kinetic energy of puck A before collision denoted by KA and puck B...

КА
2
1
극(0.247kg)(0.88m/s)'
=0.095 J
1
KB
2
1
(0.375kg) (0)
2
=0 J
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КА 2 1 극(0.247kg)(0.88m/s)' =0.095 J 1 KB 2 1 (0.375kg) (0) 2 =0 J

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