Physics 220 Class Exercise October 16 2000

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.

(a) Draw a diagram showing the two vehicles immediately before the collision.

(b)Draw a diagram showing the two vehicles immediately after the collision. (See above)

(c) Choose a coordinate system.

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

components do you need to consider here?

Only one

Use an algebraic symbol for any unknown quantities.
Momentum  Before  After
component  Vehicle 1 Vehicle 2 Total  Vehicle 1 Vehicle 2 Total 
Px 0 m2vi m1vi m1v1 m2v2 m1v1+m2v2

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.