Elastic collision: Help solving for unknowns

In summary, the problem is asking for the initial velocity of ball (b) and the final velocity of (a) in an elastic collision where ball (a) has a mass of 0.02kg and is moving at 3.0 m/s in the +x direction, and ball (b) has a mass of 0.035kg and a final velocity of 1.5m/s in the +x direction. There is no information given about the second ball being at rest on collision. The equation provided (mava +mbvb = mav'a + mbv'b) is not solvable without another equation. The problem is due tomorrow and the person asking for help has not been able to find a solution after
  • #1
xxtacofishxx
3
0
Is it possible to solve for an elastic collision when vb and v'a are the two unknowns? I have been trying for a few hours to solve for either unknown using the conservation of momentum and the conservation of total kinetic energy equations but have come up with nothing. Can anyone help?

mava +mbvb = mav'a + mbv'b

1/2mav2a +1/2mbv2b = 1/2mav'2a + 1/2mbv'2b
 
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  • #2
Hmmm. That equation there is not solvable unless you have another equation you can eliminate one of the unknown variables with.

Look carefully at the question and see if there any other information you can glean from it. For example, is it implied that one of the velocities is zero at any time? It might also help to write out the problem in full so someone can have a crack at it.
 
  • #3
Nothing is implied about the second ball being at rest on collision. The problem states that two balls have a head on elastic collision. Ball (a) has a mass of 0.02kg and is moving at 3.0 m/s in the +x. Ball (b) has a mass of 0.035kg and a final velocity of 1.5m/s in the +x. I'm trying to find the initial velocity of ball (b) and the final velocity of (a). I have spent hours trying to come up with an equation through substitution that will get me either of the two unknowns but have not been able to figure anything out.
 
  • #4
Anyone have any ideas? I have asked multiple friend for help and nobody seems to know how to work this problem. This assignment is due tomorrow.

Thank you in advance for any help
 

1. What is an elastic collision?

An elastic collision is a type of collision between two objects where kinetic energy is conserved. This means that the total kinetic energy of the two objects before the collision is equal to the total kinetic energy after the collision.

2. How do you calculate the velocities of two objects after an elastic collision?

The velocities of two objects after an elastic collision can be calculated using the principles of conservation of momentum and conservation of kinetic energy. This involves setting up equations using the mass, initial velocities, and final velocities of the two objects and solving for the unknowns.

3. What is the difference between an elastic collision and an inelastic collision?

An elastic collision is a type of collision where kinetic energy is conserved, while an inelastic collision is a type of collision where kinetic energy is not conserved. In an inelastic collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

4. Can an elastic collision occur in real life?

Yes, elastic collisions can occur in real life. For example, when two billiard balls collide on a pool table, the collision is close to being elastic. In reality, there may be some loss of kinetic energy due to friction, but the collision is still considered elastic.

5. What are some real-life applications of elastic collisions?

Elastic collisions have many real-life applications, including in sports such as billiards and ping pong, as well as in engineering and physics experiments. They are also used in the design of airbags for cars, where the collision between the car and an object needs to be as elastic as possible to minimize damage.

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