a toy car of mass 0.01 kg, gets into an elastic collision with a toy train mass 0.35 kg. if the train is at rest and the car is moving at 2 m/s initially. how fast is the train moving after the collision? Use the equation ((2*m)/(m+t))*v
Initial momentum = 2 * .01 = .02
= final momentum
= .01 cv + .35 tv
so
cv = 2 - 35 tv
Initial Ke = (1/2)(.01)(4) = .02
= final Ke
= (1/2)(.01) cv^2 + (1/2)(.35) tv^2
4 = cv^2 + 35 tv^2
4 = (2 - 35 tv)^2 + 35 tv^2
4 = 4 - 140 tv + 1225 tv^2 + 35 tv^2
140 tv = 1260 tv^2
tv = 140/1260 = 0.111 m/s
To find the speed of the train after the collision, we can use the equation you provided:
((2 * m) / (m + t)) * v
where:
m = mass of the car
t = mass of the train
v = initial velocity of the car
Plugging in the given values:
m = 0.01 kg (mass of the car)
t = 0.35 kg (mass of the train)
v = 2 m/s (initial velocity of the car)
((2 * 0.01) / (0.01 + 0.35)) * 2
Simplifying:
(0.02 / 0.36) * 2
0.0556 * 2
0.1112 m/s
So, the train is moving at approximately 0.1112 m/s after the collision.