How you can show that Newton's third law of motion follows from the Newton's second law of motion
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Answer:Originally Answered: How does Newton's third law of motion follow from the second law? Explain
Consider two bodies, I will refer to them as blue ball and red ball, in an empty space interacting with nothing else but themselves with constant velocities v blue→ and v red→ .
Their initial linear momentum is given by m bluev blue→+m red v red→ .
Now, suppose that the blue ball starts creating a force F⃗ blue→red on the red ball and so the red ball is accelerated. What happens to blue ball?
It is really important to visualize that the system’s(red ball +blue ball) momentum has NOT changed, since there are no external forces acting on them and the second law of newtonian motion states that the force is the change in linear momentum.
So we can conclude that, F⃗ =dp⃗ dt=0⃗ and, taking the second derivative dF⃗ dt=0⃗ . Or, in other words, the net force on the system does not change.
Reckoning that the force doesn’t change, the initial force is the same as the final force. Since in the beginning we said initial force is equal to zero, then so must be the final force. Hence: F⃗ final=F⃗ blue→red+F⃗ red→blue=0 . Or in other words: F⃗ blue→red=−F⃗ red→blue. There you go!
Which means that the simple fact that the blue made a force on the red ball, had the consequence (so that the momentum would be conserved) that the red ball made another force with the same intensity on the blue ball to compensate.
Explanation:
☞Rockets can propel themselves through the nothingness of space because of two fundamental laws of physics: Newton’s Third Law and the Conservation of Linear Momentum.
☞Both ideas are essential to understanding how nearly everything in the universe moves.
☞When an ice skater takes off from a dead stop, she digs her blade into the ice and the ice pushes back with an equal and opposite force, sending her gliding across the rink.
☞When a cannon is fired, the cannonball goes hurtling through the air while the cannon recoils backward in response.
☞Both of these principles stem from the same general idea: that the universe likes to keep everything in balance.