Question

Collisions in 1-D

One cart with some mass Mc travels without friction on a 1-D tack at a speed of 1.75 m/s. Another cart sits at rest some distance along the track. The two cars will collide in a perfectly elastic collision. Calculate the final speed of each cart in the following scenarios:

A) The stationary cart has a mass equal to that of the moving cart, Mc

B) The stationary cart has a mass equal to half that of the moving cart, .5xMc

C) The stationary cart has a mass equal to 10 times that of the moving cart, 10xMc

Answer 1

A)

Initial speed of first cart with mass is

Initial speed of second cart with mass is ( stationary)

Final speed of first cart is , and final speed of second cart is

Conserving the momentum of the two carts before and after collision,

-----(1)

The collision is perfectly elastic, Coefficient of restitution

-------(2)

adding (1) and (2) , and  

Final speed of first cart is , final speed of second cart is

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B)

Initial speed of first cart with mass is

Initial speed of second cart with mass   is ( stationary)

Final speed of first cart is , and final speed of second cart is

Conserving the momentum of the two carts before and after collision,

-----(1)

The collision is perfectly elastic, Coefficient of restitution

-------(2)

solving equations (1) and (2) , and  

Final speed of first cart is , final speed of second cart is

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C)

Initial speed of first cart with mass is

Initial speed of second cart with mass   is ( stationary)

Final speed of first cart is , and final speed of second cart is

Conserving the momentum of the two carts before and after collision,

-----(1)

The collision is perfectly elastic, Coefficient of restitution

-------(2)

solving equations (1) and (2) , and  

Final speed of first cart is (negative sign indicates the direction is opposite to initial direction)

final speed of second cart is

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