A cannon is rigidly attached to a carriage, which can move along horizontal rail
ID: 1581248 • Letter: A
Question
A cannon is rigidly attached to a carriage, which can move along horizontal rails, but is connected to a post by a large spring, initially unstretched and with force constant k = 2.37 104 N/m, as in the figure below. The cannon fires a 200-kg projectile at a velocity of 112 m/s directed 45.0° above the horizontal. (a) If the mass of the cannon and its carriage is 5000 kg, find the recoil speed of the cannon. Your response differs from the correct answer by more than 10%. Double check your calculations. m/s (b) Determine the maximum extension of the spring. m (c) Find the maximum force the spring exerts on the carriage. (Enter the magnitude of the force.) N (d) Consider the system consisting of the cannon, the carriage, and the shell. Is the momentum of this system conserved during the firing? Yes No Why or why not?
Explanation / Answer
(a)
From conservation of momentum ,
mp*vp = mc*vc
200 * 112*cos45 = 5000*v
v = 3.16 m/s
(b)
From conservation of energy,
(1/2)mv^2 = (1/2)kx^2
5000*3.16^2 = 2.37*10^4*x^2
x = 1.45 m
(c)
Maximum force,
F = kx = 2.37*10^4*1.45
F = 34484.35 N
(d)
No, the momentum of this system is not conserved during the firing. because some of the momentum is transferred to the ground.
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