# Conservation of momentum, elastic collision, find other mass? help

• nchin
In summary, we are trying to find the mass of one titanium sphere after an elastic collision with another titanium sphere. By using the conservation of momentum and kinetic energy, we can set up equations and solve for the unknown mass. The collision is elastic, so the relative speeds of approach and separation are equal. Using the fact that the spheres approach each other with the same speed, we can set the final velocity of one sphere equal to the initial velocity of the other sphere.
nchin
conservation of momentum, elastic collision, find other mass? help!

Two titanium spheres approach each other head-on with the same speed and collide elastically After the collision, one of the spheres, whose mass is 300 g, remains at rest.

What is the mass of the other sphere?

What i did:

m1v1 + m2v2 = m1u1 + m2u2
v1 = 0 b/c at rest

m2v2 = m1u1 + m2u2

m2v2 - m2u2 = m1u1

m2(v2 - u2) = m1u1 ? This is where I got stuck!

nchin said:
Two titanium spheres approach each other head-on with the same speed and collide elastically

What is the relationship between u1 and u2?

The collision is elastic. What can you say about the relative speeds of approach and separation?

Fightfish said:
What is the relationship between u1 and u2?

The collision is elastic. What can you say about the relative speeds of approach and separation?

Momentum is the same so initial speed equals final speed?

So I looked up the solution and it uses v=2u
(m1-m2)u = m2(2u)

So why is it 2u? I know that m1v1 is at rest. Is it because when m1 collides with m2 it gave its speed to m2 so you multiply by 2?

You applied momentum conservation. What else is conserved in an elastic collision?

Also, redo your momentum conservation equation. The spheres approach each other with the same speed, thus they move in opposite directions.

Doc Al said:
You applied momentum conservation. What else is conserved in an elastic collision?

Also, redo your momentum conservation equation. The spheres approach each other with the same speed, thus they move in opposite directions.

I know that p and ke is comserved. I'm not sure what else.

m2v2 = m1u1 - m2u2

nchin said:
I know that p and ke is comserved. I'm not sure what else.
Make use of the fact that KE is conserved.

m2v2 = m1u1 - m2u2
Better. Note that the speeds of the balls before colliding are the same. Use that fact.

Doc Al said:
Make use of the fact that KE is conserved.

Better. Note that the speeds of the balls before colliding are the same. Use that fact.

How can we use ke in this?

m2v2 = (m1 - m2)u?

nchin said:
How can we use ke in this?
Calculate the KE before and after. Set them equal to each other.

m2v2 = (m1 - m2)u?
OK.

There's a quicker way to solve this (hinted at by Fightfish), but I suggest doing it this way.

1/2m1vi + 1/2m2vi = 1/2m2vf

1/2vi(m1 + m2) = 1/2m2vf --> mult each side by two

vi(m1 + m2) = m2vf ??

nchin said:
1/2m1vi + 1/2m2vi = 1/2m2vf

1/2vi(m1 + m2) = 1/2m2vf --> mult each side by two

vi(m1 + m2) = m2vf ??
Two things:
(a) KE = 1/2 mv2, not 1/2 mv.
(b) Use the same symbols for the speeds that you used in the momentum equation.

## 1. What is the law of conservation of momentum?

The law of conservation of momentum states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. This means that the total amount of momentum in a system remains constant, even if there are changes in the velocities of individual objects.

## 2. How does an elastic collision differ from an inelastic collision?

In an elastic collision, both kinetic energy and momentum are conserved. This means that the objects involved in the collision bounce off each other and maintain their original shapes and velocities. In an inelastic collision, kinetic energy is not conserved as some of it is converted into other forms of energy, such as heat or sound. The objects may also stick together after the collision.

## 3. Can you explain the equation used to find the mass of an object in a collision?

The equation used to find the mass of an object in a collision is m1v1 + m2v2 = (m1 + m2)v, where m1 and m2 are the masses of the two objects, v1 and v2 are their velocities before the collision, and v is their combined velocity after the collision. This equation is based on the principle of conservation of momentum.

## 4. How do you determine the mass of an object in a collision if the other mass is unknown?

To find the mass of an object in a collision if the other mass is unknown, you can use the conservation of momentum equation mentioned above. Rearranging the equation to solve for the unknown mass, you get m2 = (m1v1 - (m1 + m2)v) / v2. This allows you to substitute in the known values for m1, v1, and v, and solve for m2.

## 5. Are there any real-life applications of conservation of momentum and elastic collisions?

Yes, conservation of momentum and elastic collisions have many real-life applications. They are used in car safety features, such as airbags, to reduce the impact of collisions. They are also used in sports equipment, such as helmets and padding, to protect athletes from injuries. In addition, these principles are important in the design and operation of machines, such as cranes and rockets.

• Introductory Physics Homework Help
Replies
15
Views
2K
• Introductory Physics Homework Help
Replies
16
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
21
Views
1K
• Introductory Physics Homework Help
Replies
22
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
16
Views
2K
• Introductory Physics Homework Help
Replies
10
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
527