Elastic collision problem?
A cart with mass 400 g moving on a frictionless linear air track at an initial speed of 0.9 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart continues in its original direction at 0.51 m/s.
(a) What is the mass of the second cart?
(b) What is its speed after impact?
(c) What is the speed of the two-cart center of mass?
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Verified answer
Equate the 'before' and 'after' states:
400*0.9+m*0=400*0.51+m*v.................conservation of momentum
0.5*400*0.9^2+0.5*m*0^2=0.5*400*0.51^2+0.5*m*v^2...conservation of energy
a) & b) solve the simultaneous equations for m and v.
For (c) consider the mass 'after' as (400+m) in the original equation for momentum.