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According to Newton's Third Law, a force in one direction produces an equal force in the opposite direction
According to Newton's Third Law, a force in one direction produces an equal force in the opposite direction. If the force that acts on a cannonball and the recoiling cannon are equal in magnitude, why does the cannon not recoil with the same velocity at the cannonball?
Expert Solution
Yes, the forces are the same. Now we assume there is no resistance from the air and the ground. So that force is the only force. Then accroding to Newton's second law
F=m_ball*a_ball
-F=m_cannon*a_cannon.
where m_ball, and m_cannon are the mass of the cannonball and cannon respectively.
a_ball and a_cannon are the acceleration of the cannonball and cannon.
It is obvious that the mass of cannon is much greater than the mass of the cannonball, so the acceleration of the cannon is much smaller than that of the ball.
v=at.
Since the acceleration of cannon is smaller, then at the same time, the speed of the cannon is much smaller than the speed of the cannon.
This problem can be solved easily thy Conservation of Momentum. To keep the total momentum of the system at zero, the cannon must then recoil with an equal momentum
m_ball*v_ball+m_cannon*v_cannon=0
v_cannon=-(m_ball/m_cannon)*v_ball.
so the speed of cannon is much smaller than the speed of the cannonball.
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