The figure below shows a World War I cannon mounted on a railcar and set so that

Question

The figure below shows a World War I cannon mounted on a railcar and set so that it will project a shell at an angle of 28° above the horizontal. With the car initially at rest on a horizontal frictionless track, the cannon fires a 218-kg projectile at 133 m/s. (All values are for the frame of reference of the track.).


(b) If the mass of the railcar plus cannon is 4600 kg, what will be the recoil velocity of the car along the track after the firing?
_________ m/s

(c) The shell is observed to rise to a maximum height of 175 m as it moves through its trajectory. At this point, its speed is 87.4 m/s. On the basis of this information, calculate the amount of thermal energy produced by air friction on the shell from the cannon's mouth to this maximum height.
_________kJ

Explanation / Answer

Given that

M = 4600 kg

m = 218 kg

v = 133 m/s

v'' = 87.4 m/s

h = 175 m

Initial velocity of cannon, v' = 0

= 28o

(a) According to conservation of momentum we have

          m v cos + (M-m) v' = M V

==>    218 x 133 x cos28 + 0 = 4600 x V

==>    V = 5.565 m/s

(b) We know that

     Total kinetic energy of the projectile = Eth +Ek + Ep

            0.5 m v2 = Eth + 0.5 m V''2 + m g h

    0.5 x 218 x 133 x 133 = Eth + 0.5 x 218 x 87.4 x 87.4 + 218 x 9.8 x 175

   ==> Eth = 721606.16 = 721.60 kJ

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