Two vehicles are travelling along a straight stretch of road. The first
vehicle, mass ml = 1200 kg, abruptly stops. The vehicle
behind, mass m2 =
1000 kg, is unable to stop in time and hits the first vehicle at a speed
of 15 m/s. After the collision the first vehicle is moving forward at 10
m/s. Find the velocity of the second vehicle after the collision.
(b)Draw a diagram showing the two vehicles immediately after the collision. (See above)
Put the x-axis along the direction that both vehicles are moving.
(d) Calculate the momentum of the system of two vehicles in the before and after states. How many
Use an algebraic symbol for any unknown quantities.
|component||Vehicle 1||Vehicle 2||Total||Vehicle 1||Vehicle 2||Total|
Set totals equal
m2vi = m1v1 + m2v2
Solve for the velocity of vehicle 2. Comment on your result.
v2 = vi - m1v1 /m2 = 15 m/s- (10 m/s)(1200 kg / 1000 kg) = 15 m/s - (10 m/s)12/10 = 3 m/s
Car #2 is moving in the plus x- direction at 3 m/s. This seems like a reasonable result.
If you got everything done, then estimate the force exerted on the first car by the second.
Car 1#s momentum changes by an amount pf - pi
= m1(10 m/s - 15 m/s ) = -( 1200 kg)(5 m/s) = -6000 N.s.
Estimating that the collision lasts about one half second, we estimate the force to be about:
F = I/t = 6000 N.s / 1/2 s = 12000 N. (We used the magnitudes of the vectors here, not the components.)
This is about 10 times the weight of the car - enough to do some damage.