If one cart was at rest, and was struck by another cart of equal mass, what would the final velocities be for a perfectly elastic collision? For a perfectly inelastic collision?
2 Answers
For a perfectly elastic collision, the final velocities of the carts will each be 1/2 the velocity of the initial velocity of the moving cart.
For a perfectly inelastic collision, the final velocity of the cart system will be 1/2 the initial velocity of the moving cart.
Explanation:
For an elastic collision, we use the formula
In this scenario, momentum in conserved between the two objects.
In the case where both objects have equal mass, our equation becomes
We can cancel out m on both sides of the equation to find
For a perfectly elastic collision, the final velocities of the carts will each be 1/2 the velocity of the initial velocity of the moving cart.
For inelastic collisions, we use the formula
By distributing out the
This shows us that the final velocity of the two cart system is 1/2 the velocity of the initial moving cart.
For a perfectly elastic collision, the cart that was initially moving comes to a halt, while the other cart moves with velocity
For a perfectly inelastic collision both carts move with a shared velocity of
Explanation:
Momentum conservation leads to
Since, in this problem
This holds for both elastic and inelastic collision.
Perfectly elastic collision
In a perfectly elastic collision, the relative velocity of separation is the same as that of approach (with a negative sign)
So.
Thus
**Perfectly inelastic collision#
For a perfectly inelastic collision, the two bodies stick together, so that