# Collision of 2 balls of different masses traveling opposite direction

• _Mayday_
So a simple typo. I was worried that my teaching had suddenly got very bad!So, to summarise then, (a) is asking for the speed of B after the collision, which is equal to 7.3m/s, and (b) is asking for the impulse exerted on B, which is equal to 1.06Ns. In summary, the speed of B immediately after the collision is 7.3m/s and the magnitude of the impulse exerted on B is 1.06Ns.
_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

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

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?

_Mayday_ said:
Sorry let me do that

first bit again.

(a)

$$1.1=0.75-0.2x$$
Good
_Mayday_ said:
$$1\frac{7}{15} = 0.26$$
Not so good, where's your x gone?
_Mayday_ said:
$$x = 7.3m/s$$
Take a sanity check, does this seem reasonable to you?

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...

_Mayday_ said:
$$1.1=0.75-0.2x$$
And this one,
_Mayday_ said:
$$\frac{1.1}{0.75} = 1\frac{7}{15} = 0.2x$$
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?

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 =]

_Mayday_ said:
Cheers I follow that, and now with that I will get the correct answer for (b) thanks =]
A pleasure as always

## 1. What is the outcome when two balls of different masses traveling in opposite directions collide?

The outcome of a collision between two balls of different masses traveling in opposite directions depends on the relative masses and velocities of the balls. Generally, the larger and faster-moving ball will impart more force on the smaller and slower-moving ball, causing it to change direction and potentially accelerate or decelerate.

## 2. How do the masses of the balls affect the collision?

The mass of each ball affects the amount of force that is imparted during the collision. The larger mass will typically have a greater impact on the smaller mass, causing it to accelerate or decelerate more significantly.

## 3. Are there any factors besides mass that can affect the collision?

Yes, the velocity of each ball also plays a role in the collision. The faster-moving ball will have a greater impact on the slower-moving ball, causing it to change direction and potentially accelerate or decelerate.

## 4. How can we calculate the outcome of a collision between two balls of different masses traveling in opposite directions?

To calculate the outcome of a collision, we can use principles of conservation of momentum and conservation of energy. By examining the masses and velocities of the balls before and after the collision, we can determine the resulting velocities and directions of each ball.

## 5. Can the collision between two balls of different masses traveling in opposite directions be completely elastic?

In theory, a collision between two balls of different masses traveling in opposite directions could be completely elastic, meaning there is no loss of kinetic energy during the collision. However, this is unlikely in real-world scenarios due to factors such as friction and deformation of the balls upon impact.

• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
15
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
3K
• Introductory Physics Homework Help
Replies
13
Views
6K
• Introductory Physics Homework Help
Replies
19
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
3K
• Introductory Physics Homework Help
Replies
16
Views
4K
• Introductory Physics Homework Help
Replies
2
Views
4K
• Introductory Physics Homework Help
Replies
9
Views
3K
• Introductory Physics Homework Help
Replies
16
Views
2K