Answer to Question #102110 in Mechanics | Relativity for Deanne

Question

2.Inelastic Collision. Two automobiles of 540 and 1400 kg collide head-on while

moving at 80 km/h in opposite directions. After the collision the automobiles remain locked together.

(a)Find the velocity of the wreck immediately after the collision.

(b)Find the kinetic energy of the two-automobile system before and after the collision.

(c)The front end of each automobile crumples by 0.60 m during the collision. Find the acceleration (relative to the ground) of the passenger compartment of each automobile;
make the assumption that these accelerations are constant during the collision.

Answer 1

a) From the conservation of momentum:

$$-mv+Mv=(M-m)v=(m+M)u$$

$$u=\frac{80}{3.6}\frac{1400-540}{1400+540}=9.85\frac{m}{s}$$

b)

$$K_i=0.5(mv^2+Mv^2)=0.5(m+M)v^2$$

$$K_i=0.5(540+1400)\frac{80^2}{3.6^2}=479000\ J$$

$$K_f=0.5(540+1400)9.85^2=94000\ J$$

c)

$$u^2=2ad\to 9.85^2=2(0.6)a$$

$$a=81\frac{m}{s^2}$$