(a) Assuming that the mass of the cannon and its carriage is 4,500 kg, find the
ID: 1373169 • Letter: #
Question
(a) Assuming that the mass of the cannon and its carriage is 4,500 kg, find the recoil speed of the cannon.
m/s
(b) Determine the maximum extension of the spring.
m
(c) Find the maximum force the spring exerts on the carriage.
N
(d) Consider the system consisting of the cannon, carriage, and projectile. Is the momentum of this system conserved during the firing?
YesNo
Why or why not?
Explanation / Answer
We can apply cons of momentum to the cannon and the projectile in the horizontal direction. the initial momentum is 0, and the final is mvcos(45) - MV
so mvcos(45) - MV =0, or V = m/M vcos(45)
b) now we apply cons of energy to the cannon and the spring. Ei = 1/2MV^2 V from answer a
Ef = 0 + 1/2kx^2 where x is the extension of the spring
Ei = Ef
1/2MV^2 = 1/2 kx^2, solve for x
c) The maximum force exerted by the spring occurs at the max displacment |F| = k x use x from b
d) We can consider the momentum for the cannon, carriage and projectile conserved in the x direction since there are no external forces. However, since there is a normal force and gravity in the y direction, the momentum in the y direction is not conserved.
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