Determine the velocity after collision

In summary, sphere A moves with a velocity of 4u towards sphere B, which then collides. After the collision, sphere C moves to the right with a velocity of u. The elastic coefficient between A and B is 0.75, and B and C are 0.5. After the first collision, sphere A and B have a velocity of 3u and 12u, respectively.
  • #1
goldfish9776
310
1

Homework Statement


three small spheres, A , B and C with mass of 3kg , 4kg , 7kg respectively are arranged as shown in the figure. Initially , sphere B is placed in static condition,while the sphere A is moving with a velocity of 4u towards B and collides . Then , sphere C move to right with velocity u , the elastic coefficient between A and B is 0.75 , and B and C is 0.5, determine

the velocity of sphere A and B after the first collision . How to do this ?

3(4u) +4(0) = 3V1 +4V2

12u = 3V1 +4V2

V2 - V1 / ( U1 -U2 ) = 0.75

since U2 = 0 ,

V2 - V1 = 0.75 u

12u - 3( V2- 0.75u ) +4V2

14.25u = 7V2 , V2 = 2.035 u , V1 = 1.29u ,

is my ans correct ? i don't have the ans btw
 

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  • #2
I think that elastic coefficient refers to kinetic energy loss ratio.
 
  • #3
goldfish9776 said:

Homework Statement


three small spheres, A , B and C with mass of 3kg , 4kg , 7kg respectively are arranged as shown in the figure. Initially , sphere B is placed in static condition,while the sphere A is moving with a velocity of 4u towards B and collides . Then , sphere C move to right with velocity u , the elastic coefficient between A and B is 0.75 , and B and C is 0.5, determine

the velocity of sphere A and B after the first collision . How to do this ?

3(4u) +4(0) = 3V1 +4V2

12u = 3V1 +4V2

V2 - V1 / ( U1 -U2 ) = 0.75

since U2 = 0 ,

V2 - V1 = 0.75 u

12u - 3( V2- 0.75u ) +4V2

14.25u = 7V2 , V2 = 2.035 u , V1 = 1.29u ,

is my ans correct ? i don't have the ans btw
what will occur after that ? sphere A and B sticked together and collide with C or ?
 
  • #4
Take all together in one step with 3 bodies.
 
  • #5
theodoros.mihos said:
Take all together in one step with 3 bodies.
can you show how to do that ?
 
  • #6
Sorry, I'm wrong. IP ask two steps, 1st A collides B and 2nd by B and C are collides.
Take momentum conservation for every step combined with the correct energy relation.
 
  • #7
theodoros.mihos said:
I think that elastic coefficient refers to kinetic energy loss ratio.
I would think it refers to the coefficient of restitution. This relates to velocity ratios. The fraction of KE retained will be the square of this.
 
  • #8
I would think it refers to the coefficient of restitution. This relates to velocity ratios. The fraction of KE retained will be the square of this.

For this reason, if we divide velocities after with the same factor, the momentum conservation is not correct.
 

FAQ: Determine the velocity after collision

1. What is the definition of velocity after collision?

Velocity after collision refers to the speed and direction of an object immediately after it collides with another object. It takes into account the momentum and energy of the objects involved in the collision.

2. How is velocity after collision calculated?

Velocity after collision can be calculated by using the conservation of momentum equation, which states that the total momentum before the collision is equal to the total momentum after the collision. This can be expressed as: m1v1 + m2v2 = m1v1' + m2v2', where m represents mass and v represents velocity.

3. What factors can affect the velocity after collision?

The velocity after collision can be affected by factors such as the mass and velocity of the objects involved, the angle of collision, and the presence of external forces such as friction or air resistance.

4. Can the velocity after collision be greater than the initial velocity?

Yes, in certain cases, the velocity after collision can be greater than the initial velocity. This can happen when there is an external force acting on the objects, or if the collision is perfectly elastic, meaning that there is no loss of energy during the collision.

5. How does the type of collision affect the velocity after collision?

The type of collision can greatly affect the velocity after collision. In an elastic collision, where there is no loss of energy, the velocity after collision will be equal to the initial velocity. In an inelastic collision, where there is some loss of energy, the velocity after collision will be less than the initial velocity. In a completely inelastic collision, where the objects stick together after the collision, the velocity after collision will be zero.

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