Question

A truck with a mass of 1800 kg traveling 32 miles per hour collides with a car (mass = 1100 kg) sitting at a stop sign. The two lock together and both cars slide into the intersection. Both drivers slam on the brakes in desperation. The coefficient of friction between the tires and the road is 0.58.

a. What is the momentum of each car before the collision?

b. What is their combined momentum after the collision? Justify your answer.

c. How fast are they travelling together after the collision?

d. We assume this is an inelastic collision, since they are stuck together. PROVE it is an inelastic collision, using energy.

e. How far do the two cars slide into the intersection?

Answer 1

(A) v = 32 x 1609 m / 3600 s

v = 14.3 m/s

p = (1800 x 14.3) + (1100 x 0)

p = 25744 kg m/s

(B) momentum will be conserved during collision,

pf = pi = 25744 kg m/s

(C) 25744 = (1800 + 1100) v

v = 8.88 m/s

(D) Ki = 1800 x 14.3^2 /2 = 184041 J

Kf = (1800 + 1100) (8.88^2)/2 = 114339 J

Kf is not equal to ki. (some energy is lost)

this is inelastic collision.

(E) a = - fk/m = - uk g = - 0.58 x 9.8 = - 5.68 m/s^2

vf^2 - vi^2 = 2 a d

0^2 - 8.88^2 = 2(-5.68) d

d = 6.94 m