Question

prove linear momentum conservation law from
Newton's third Law​

Answer 1

Explanation:

Conservation of Linear Momentum and Newton's Third Law

If space is a vacuum—that is, if it contains absolutely nothing—then how does a rocket move? Doesn’t it need something to push against?

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

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$Problem$

• Demonstrate how Newton’s Third Law and the Conservation of Momentum affect movement.

$Materials$

• Two skateboards
• Medicine ball
• Procedure
• Have two people sit on the skateboards a few feet apart, facing each other and with their feet off the ground.

Have one person throw the ball to the other. How does the person who threw the ball move after the ball is thrown? What about the person who catches the ball?

$Results$

The person who throws the ball will roll backwards. When the second person catches the ball, she will move in the direction the ball was going.

Answer 2

Answer:

The law of conservation of linear momentum easily follows from the third law of motion. 

Consider a system of two particles, A and B. Let's say they interact with each other and 'A' experts a Force Fba on 'B' and in reaction, 'B' exerts a force Fab on 'A'.

Now, according to the second law of motion,

Fba= Mb x d/dt(Vb) = d/dt(Mb x Vb)

Fab= Ma x d/dt(Va) = d/dt(Ma x Va)

where Mb and Ma are masses of 'B' and 'A' respectively, and similarly Vb and Va their velocities in that order. d/dt denotes the derivative.

Now, adding the above two equations,

Fab + Fba = d/dt (Ma x Va) + d/dt(Mb x Vb)

Note that according to the third law of motion, these forces Fab and Fba are equal and opposite, so Fab= -Fba 

Hence, 0= d/dt(Ma x Va) + d/dt(Mb x Vb) = d/dt(Pa + Pb)

where Pa and Pb are the linear momenta of 'A' and 'B' respectively. 

Hence, Pa + Pb= constant (since the derivative is zero)

Therefore, The sum of the linear momenta of the bodies is constant. 

The above calculations assume no external forces act upon the system. Hence, if there is zero net external force, the linear momentum of a system remains conserved, i.e. unchanged. 

Explanation:

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