Conservation of momentum, elastic collision problem? Help

By solving both equations, we can find the final velocity of the second sphere (v2) which is equal to twice the initial velocity (u) before the collision. This means that the second sphere has the same speed as the first sphere before the collision. Therefore, its mass (m2) must be one third of the first sphere's mass (m1). In summary, the mass of the second sphere is one third of the mass of the first sphere.
  • #1
nchin
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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 = (m1 - m2)u

The solution:

v2 = 2u

m2(2u) = (m1-m2)u
2m2 = m1 - m2
3m2 = m1
m2 = m1/3

What I do not understand:

Why is v2 = 2u?? Is it because when m1 collides with m2, it transfers its speed to m2 so then m2 has twice its speed now? So then it's speed is the same as the initial speed times two?
 
Last edited:
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  • #2
This is an elastic collision, so kinetic energy is conserved as well. There are two equations to solve, momentum and kinetic energy.
 

1. What is conservation of momentum?

The conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system (where no external forces are acting) remains constant over time. This means that the total momentum before an event must equal the total momentum after the event.

2. What is an elastic collision?

An elastic collision is a type of collision where the total kinetic energy of the system is conserved. This means that the objects involved in the collision bounce off of each other without any loss of energy.

3. How is conservation of momentum applied in elastic collision problems?

In elastic collision problems, the total momentum before the collision is equal to the total momentum after the collision. This allows us to set up equations using the mass and velocity of the objects involved in the collision to solve for unknown variables.

4. What are the key principles to remember when solving elastic collision problems?

The key principles to remember when solving elastic collision problems are the conservation of momentum and the conservation of kinetic energy. Additionally, the direction and magnitude of the velocities of the objects before and after the collision must also be taken into account.

5. Can the conservation of momentum be applied to other types of collisions?

Yes, the conservation of momentum can be applied to all types of collisions, including inelastic collisions where some energy is lost due to deformation or heat. However, the conservation of kinetic energy may not hold true in these types of collisions.

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