p09_072.pdf

72. (a) We denote the mass of the car (and cannon) as M (excluding that of the cannonballs) and the mass

of all the cannonballs as m . For concreteness, we assume that before ﬁring all the cannonballs are

at the front (left side of Fig. 9-52) of the car, which we choose to be the origin of the x axis;we

choose + x rightward. The coordinate of the center of mass of the car-cannonball system is

x com =

(0) m + 2 M

M + m

2( M + m )

After the ﬁring, we assume all the cannonballs are at the other end of the car;the train will have

moved (in the negative x direction) by a distance d ,atwhichtime

x com = 2 −

d M +( L

−

d ) m

M + m

Equating the two expressions, we obtain d =

M + m <L. If m

M , the distance d can be very

close to (but can never exceed) L .Thus d max = L .

(b) After each impact, there is no relative motion in the system;thus, the ﬁnal speed of the car is equal

to that of the center of mass of the system, which is zero.