How is the coefficient of restitution zero for this problem?

In summary, the coefficient of restitution is calculated by dividing the relative speed after collision by the relative speed before collision, and in this problem, it is equal to 0. The objects collide and stick together, meaning the relative velocity after collision is 0. To find the values for RV_after and RV_before, you need to know the relative velocity after collision.
  • #1
Benjamin_harsh
211
5
Homework Statement
A mass ##m_{1}## of 100kg travelling with a uniform velocity of 5m/sec
along a line collides with a stationary mass ##m_{2}## of 1000kg. After the
collision,both the masses travel together with the same velocity.
The coefficient of restitution is zero.
Relevant Equations
##coefficient\; of \;restitution = \large\frac{Relative\; speed \;after \;collision}{Relative\; speed\; before\; collision} \normalsize= 0##
##coefficient\; of \;restitution = \large\frac{Relative\; speed \;after \;collision}{Relative\; speed\; before\; collision} \normalsize= 0##
 
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  • #2
There is enough information in the problem to explicitly calculate. Think of what the relative speed after collision is.
 
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  • #3
Benjamin_harsh said:
How is the coefficient of restitution zero for this problem?
1- The question tells you it is zero.
2- The relative velocity after collision is zero. So the formula, ##CR=\frac{RV_{after}}{RV_{before}}## also tells you CR is zero.

The two objects collide and stick together.
 
  • #4
Merlin3189 said:
2- The relative velocity after collision is zero. So the formula, ##CR=\frac{RV_{after}}{RV_{before}}## also tells you CR is zero.
What values should I substitute in ##RV_{after}## and ##RV_{before}##?
 
  • #5
Sorry, I don't like to do maths :rolleyes:.
The value you should substitute for ##RV_{after}## is the relative velocity after they collide.
So the physics question is, "what is the relative velocity after collision?"
If you know what relative velocity means, then the question tells you this explicitly (in different words.)

Do you understand relative velocity?
 

1. What is the coefficient of restitution?

The coefficient of restitution is a measure of the elasticity of a collision between two objects. It is a dimensionless quantity that represents the ratio of the relative velocity of separation to the relative velocity of approach between the two objects.

2. How is the coefficient of restitution calculated?

The coefficient of restitution is calculated by dividing the relative velocity of separation by the relative velocity of approach. It can also be calculated using the kinetic energy before and after the collision.

3. Why is the coefficient of restitution important in physics?

The coefficient of restitution is important in physics because it helps us understand how objects behave during collisions. It is a crucial factor in determining the outcome of a collision and can be used to predict the motion of objects after a collision.

4. Can the coefficient of restitution be negative?

No, the coefficient of restitution cannot be negative. It is a dimensionless quantity and represents a ratio, so it will always be positive or zero. A negative value would imply that the objects are moving towards each other after the collision, which is not physically possible.

5. How is the coefficient of restitution related to the elasticity of a collision?

The coefficient of restitution is directly related to the elasticity of a collision. A higher coefficient of restitution indicates a more elastic collision, while a lower coefficient of restitution indicates a more inelastic collision. A coefficient of restitution of zero represents a perfectly inelastic collision where the objects stick together after the collision.

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