Collision of 2 balls of different masses traveling opposite direction

[_Mayday_]

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

$$Ft=mv-mu$$

My Attempt

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

$$Ft=mv-mu$$

$$(0.5\times3.0)-(0.2\times2.0)=(0.5\times1.5)-(0.2\times x)$$

$$1.1=0.75-(0.2\timesx)$$

$$x=11.3m/s$$

(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 $$Ft$$?


Any help would be great

 

[Hootenanny]

You might want to check your arithmetic on question (a). Yes, (b) is just asking you for the impulse which is the quantity Ft.

 

[_Mayday_]

Sorry let me do that

first bit again.

(a)

$$1.1=0.75-0.2x$$

$$1\frac{7}{15} = 0.26$$

$$x = 7.3m/s$$

I hope that's a bit better

(b)

$$Ft=mu-mv$$

$$Ft=0.2\times2-0.2\times7.3 = 1.06Ns$$

Does that look a bit better?

 

[Hootenanny]

Sorry let me do that

first bit again.

(a)

$$1.1=0.75-0.2x$$

Good

$$1\frac{7}{15} = 0.26$$

Not so good, where's your x gone?

$$x = 7.3m/s$$

Take a sanity check, does this seem reasonable to you?

 

[_Mayday_]

Sorry let me do that

first bit again.

(a)

$$1.1=0.75-0.2x$$

$$\frac{1.1}{0.75} = 1\frac{7}{15} = 0.2x$$

$$x = \frac{1\frac{7}{15}}{0.2} = 7\frac{1}{3}$$

I would have thought th answer to be around 3.5 as that would make all the initial and final figures equal...

 

[Hootenanny]

Your making your mistake between this step,

$$1.1=0.75-0.2x$$

And this one,

$$\frac{1.1}{0.75} = 1\frac{7}{15} = 0.2x$$

Let me show you step by step,

1.1=0.75-0.2x

1.1-0.75 = -0.2x

$$x = \frac{1.1-0.75}{-0.2}$$

Do you follow?

 

[_Mayday_]

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 =]

 

[Hootenanny]

Cheers I follow that, and now with that I will get the correct answer for (b) thanks =]

A pleasure as always