A cannon is bolted to the floor of a railway carriage, which is free to move wit
ID: 1963312 • Letter: A
Question
A cannon is bolted to the floor of a railway carriage, which is free to move without friction along a straight track. The combined mass of the cannon and the carriage is M = 1200 kg. The cannon fires a cannonball, of mass m = 1.2 kg, horizontally with velocity v = 115 m/s. The cannonball travels the length of the carriage, a distance L = 85 m, and then becomes embedded in the carriages end wall.a.What is the recoil speed of the carriage right after the cannon is fired?
b.What is the velocity of the carriage after the cannonball strikes the far wall?
c.What net distance, and in what direction, does the carriage move as a result of the firing of the cannon?
-show all work please...step by step
Explanation / Answer
Let us assume that gravity is absent in the system or the cannon is mounted high enough that the cannon ball does not reach the ground before it touches the end wall.
now the problem is all about conserving the linear momentum as there is no external force acting on the system.
therefore
M : mass of the carraige and cannon(1200kg)
m : mass of the cannon ball(1.2kg)
V : Velocity of the carraige
v : velocity of the cannon ball in horizontal direction
Conserving the linear momentum:
0 = m*v + M*V
0 = (1.2*115)+(1200*V)
=> V= -0.115 m/s
negative sign implies that it moves in the opposite direction of the cannon ball(since we have assumed its velocity in positive direction)
now we have the velocity of the ball as well as the carraige but in opposite directions.
the ball has to move a distance of 85m.
so taking the relative velocity of the ball with respect to the carraige, the time taken for the ball to reach the end would be = 85/Vr (Vr : velocity of ball relative to carraige)
Vr = v-V
= 115-(-0.115)
= 115.115m/s
therefore time taken(t) would be = 85/115.115
= 0.738 sec
after the ball gets embedded into the wall by conserving momentum; let us say the common velocity of carraige and ball is 'u' :
(M+m)*u = m*v + M*V = 0 (since the momentum is always conserved)
therefore the complete body comes to rest as the ball gets embedded into the wall.
i.e. it comes to rest after 0.738 seconds.
so the distance moved by the carraige would be = V*t
= -0.115*0.738
= 0.085m in opposite direction of cannon ball fired direction
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