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Ravenatic20
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Homework Statement
A 2000-kg car moving with a speed of 20 m/s collides with and sticks to a 1500-kg car at rest. Show that because momentum is conserved in the rest frame, momentum is also conserved in a reference frame moving with a speed of 10 m/s in the direction of the moving car.
Homework Equations
Not sure
The Attempt at a Solution
Let's have the larger (2000-kg) car be mass M, and the smaller (1500-kg) car to be mass m. Car M is traveling at speed v. After the collision, the two cars become one mass (M+m) and its velocity we will call v'.
To an observer on the ground...
mv + 0 = (M+m) v'
v' = MV/(M+m)
To an observer in a moving frame...
M is moving at speed V-v (towards the smaller car, m) and m is moving at speed -v (towards the larger vehicle, M). After the collision, (M+m) is moving at speed v'-v.
M(V-v) - mv = (M+m)(v'-v)
MV - Mv - mv + Mv + mv = (M+m)v'
v' = MV/(M+m)
These two equations are the same, meaning the final speed of the indecent is v' from any observer. Does this mean momentum is also conserved in a reference frame? If I'm on the right track, what good would it do plugging in numbers?