What Is the Wagon's Speed After an Elastic Collision?

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In summary, a 150 kg cart moving at 13 m/s east collided with a 420 kg wagon moving at 5.0 m/s east. The cart rebounded westward with a speed of 3.0 m/s. Using the conservation of momentum,
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Homework Statement



A 150 kg cart moving at 13 m/s east collided with a 420 kg wagon moving at 5.0 m/s east.
The cart rebounded westward with a speed of 3.0 m/s . What was the speed of the wagon after the collision? Observe standard Cartesian coordinates.

Homework Equations



KE1+KE2=KE1'+KE2'
conservation of momentum
conservation of kinetic energy in elastic collisions

The Attempt at a Solution


(0.5)(150)(13)2+(0.5)(420)(5)2=(0.5)(150)(-3)2+(0.5)(420)v2
v=9.0m/s

Answer as given is 11m/s
 
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  • #2
the problem itself doesn't say that the collision is elastic. so just use conservation of momentum here.
 
  • #3
canicon25 said:

Homework Statement



A 150 kg cart moving at 13 m/s east collided with a 420 kg wagon moving at 5.0 m/s east.
The cart rebounded westward with a speed of 3.0 m/s . What was the speed of the wagon after the collision? Observe standard Cartesian coordinates.

Homework Equations



KE1+KE2=KE1'+KE2'
conservation of momentum
conservation of kinetic energy in elastic collisions


The Attempt at a Solution


(0.5)(150)(13)2+(0.5)(420)(5)2=(0.5)(150)(-3)2+(0.5)(420)v2
v=9.0m/s

Answer as given is 11m/s

IssacNewton is right !
Conservation of kinetic energy is valid only when coefficient of restitution(e) is 1
here its not specified, so you must use momentum conservation.

ALSO:
if e is given and is ≠1 then you may use:
(v2 - v1) = e(u1 - u2)
 

FAQ: What Is the Wagon's Speed After an Elastic Collision?

What is an elastic collision with rebound?

An elastic collision with rebound is a type of collision that occurs between two objects in which both kinetic energy and momentum are conserved. This means that after the collision, the objects will bounce off each other and continue moving with the same total energy and speed as before the collision.

How is an elastic collision with rebound different from an inelastic collision?

In an inelastic collision, some kinetic energy is lost during the collision, resulting in a decrease in the total energy of the system. This means that the objects involved will not rebound and may stick together after the collision. In contrast, an elastic collision with rebound involves no loss of kinetic energy, resulting in the objects bouncing off each other.

What factors affect the rebound in an elastic collision?

The rebound in an elastic collision is affected by the elasticity of the objects involved, the angle of collision, and any external forces acting on the objects. Objects with higher elasticity will experience a greater rebound, while objects with lower elasticity will have a lower rebound.

Can an elastic collision with rebound occur between objects of different masses?

Yes, an elastic collision with rebound can occur between objects of different masses. The mass of an object does not affect the conservation of energy and momentum in an elastic collision. However, the velocity of the objects after the collision will be different due to the difference in their masses.

How is the coefficient of restitution used to describe an elastic collision with rebound?

The coefficient of restitution is a measure of the elasticity of a collision. In an elastic collision with rebound, the coefficient of restitution will have a value of 1, indicating that there is no loss of kinetic energy during the collision. A lower value for the coefficient of restitution indicates a less elastic collision, while a value of 0 indicates a perfectly inelastic collision.

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