Collision of 2 balls of different masses traveling opposite direction

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Question

Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposited directions on a smooth horizontal table when they collide directly. Immediately before the collision, the spped of A is 3m/s and the speed of B is 2m/s. The speed of A immediately after the collision is 1.5m/s. The direction of the motion of A is unchanged as a result of the collision.

By modelling the balls as particles, find

(a) The speed of B immediately after the collision


(b) The magnitude of the impulse exerted on B after the collision

Equations

[tex]Ft=mv-mu[/tex]

My Attempt

(a) Conservation of momentum would mean that the initial momentum must be equal to the final momentum.

[tex]Ft=mv-mu[/tex]

[tex](0.5\times3.0)-(0.2\times2.0)=(0.5\times1.5)-(0.2\times x)[/tex]

[tex]1.1=0.75-(0.2\timesx)[/tex]

[tex]x=11.3m/s[/tex]

(b) I have no Idea where to start here, I think it's more a question of now knowing what it is asking for. Is it asking for my value for [tex]Ft[/tex]?


Any help would be great :cool:
 

Answers and Replies

  • #2
Hootenanny
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You might want to check your arithmetic on question (a). Yes, (b) is just asking you for the impulse which is the quantity Ft.
 
  • #3
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Sorry let me do that

first bit again.

(a)

[tex]1.1=0.75-0.2x[/tex]

[tex]1\frac{7}{15} = 0.26[/tex]

[tex]x = 7.3m/s[/tex]

I hope thats a bit better o:)

(b)

[tex]Ft=mu-mv[/tex]

[tex]Ft=0.2\times2-0.2\times7.3 = 1.06Ns[/tex]

Does that look a bit better?
 
  • #4
Hootenanny
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Sorry let me do that

first bit again.

(a)

[tex]1.1=0.75-0.2x[/tex]
Good :smile:
[tex]1\frac{7}{15} = 0.26[/tex]
Not so good, where's your x gone?
[tex]x = 7.3m/s[/tex]
Take a sanity check, does this seem reasonable to you?
 
  • #5
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Sorry let me do that

first bit again.

(a)

[tex]1.1=0.75-0.2x[/tex]

[tex]\frac{1.1}{0.75} = 1\frac{7}{15} = 0.2x[/tex]

[tex] x = \frac{1\frac{7}{15}}{0.2} = 7\frac{1}{3}[/tex]

I would have thought th answer to be around 3.5 as that would make all the initial and final figures equal...
 
  • #6
Hootenanny
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Your making your mistake between this step,
[tex]1.1=0.75-0.2x[/tex]
And this one,
[tex]\frac{1.1}{0.75} = 1\frac{7}{15} = 0.2x[/tex]
Let me show you step by step,

1.1=0.75-0.2x

1.1-0.75 = -0.2x

[tex]x = \frac{1.1-0.75}{-0.2}[/tex]

Do you follow?
 
  • #7
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Oh my word! I can't believe I did that! Thats a shocker haha. Cheers I follow that, and now with that I will get the correct answer for (b) thanks =]
 
  • #8
Hootenanny
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Cheers I follow that, and now with that I will get the correct answer for (b) thanks =]
A pleasure as always :smile:
 

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