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Newton third law? so to stop a rocket we should generate thrust (from thrusters mounted on front of the rocket) in opposite direction?

If so then if a tank in motion shoots from cannon then recoil will slow down tank speed to some degree? or what about hitting back of the moving car from inside using a baseball bat?

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For the rocket, yes, Newton's third law applies. However, also look at it by considering the conservation of momentum of the center of mass. Before the rocket fires it's thrusters forward, it's center of mass has a certain momentum (given by p = m*v). When the rocket fires the thrusters, gasses are ejected forward.

The gas has mass and a velocity, and because center of mass is conserved (because there are no external, unbalanced forces), the rocket body will decrease it's velocity.

Think about it this way: the gas was originally moving at the rocket's speed when it was in its tanks. When the gas is ejected, the gas (which has mass) has an increased velocity. This alone would violate the conservation of mass, because now the faster moving gas would result in the increase in velocity of the center of mass. But when the gas is fired, the system conserves momentum as the rocket body decreases velocity, so that the momentum of center of mass is still the same as before firing.

Now, when the tank fires a projectile, the same ideas apply. The projectile increases velocity, therefore the tank decreases (or increase it in the negative direction to the projectile) its velocity, so overall, the momentum of the center of mass is still equal. Starting to see a pattern?

Optional read: This brings up a simple, yet interesting, classical mechanics problem to learn: the mass of the projectile is very small compared to the tank (let's say it's 1 kg), but it's velocity is very large (let's say 10 m/s). The momentum of the projectile is p = m*v = 1 kg * 10 m/s = 10 kg m/s.

Since before, the system was at rest (so v = 0) therefore momentum = 0. After firing, the momentum must still be zero. But the projectile, we calculated, has 10 kg m/s of momentum. So, to "counter" this, the tank (lets say mass = 10 kg) must have -10 kg m/s of momentum (so the addition of the two momentums [or momenti?] = 0).

By using p = m*v, we get -10 kg m/s = 10 kg * v ... thus the velocity of the tank will be v = -1 m/s. Isn't math so wonderful?

In a moving car, it's even more interesting. When you initially throw the ball backward, the car will still conserve it's momentum of center of mass: the decrease in velocity of the ball is countered by the increased velocity of the car. Then, when the ball hits the back and stops, the ball is actually increasing velocity (because it decreased velocity in the negative direction). Now, to not violate conservation of momentum, the car will decrease in velocity.

So overall, the center of mass is always conserved, as long as no external, unbalanced forces act on the system. And to follow this rule, the masses that make up a system increase/decrease in velocity, while the center of mass velocity doesn't change.

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The reason that the rocket slows down is due to conservation of momentum. When you activate the thrusters pushing forwards, you are pushing forwards some amount of mass (in the form of gas) at a velocity larger than that of the rocket. If the rocket did not slow down, this would increase the total momentum of the rocket since the mass was initially in the rocket as fuel. So the rocket slows down. The same applies to the other cases you listed where you release a cannon or ball from a moving vehicle. In order to conserve momentum, the motion of the vehicle must have an acceleration opposite the direction you launch the projectile.

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  • $\begingroup$ So, the velocity will decrease in all mentioned cases? and what about let's say, a slowly moving bicycle? if a cyclist would hit with his hands (with a great force) bicycle handlebars, then the bicycle should slown down? or in other words, how to stop a bicycle without using it's breaks. I just want to be 100% sure. $\endgroup$
    – szufla
    Commented Jul 19, 2018 at 6:35

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