Consider a squash ball, when it hits the wall of the court the rubber compresses and the air inside also compresses causing the balls temperature to rise. This temperature rise is energy taken from the balls kinetic energy, causing the ball the hit the wall with less force.

Proof:

A ball of mass

moving with velocity

Initial velocity = −

So change in momentum of ball =

By work energy theorem,

12

Work f=done on ball by wall is 0 as force is applied by wall on ball when the ball is in contact with the wall, so no displacement.

So, 12

Heat lost to surroundings

, more heat is lost.

And impulse imparted by wall is m(v+u)

Force applied by wall=

Then from (1), 12

Meaning no heat is lost (elastic collision).

Impulse imparted by wall is 2

So, force exerted by wall = 2

We can see that force applied by wall is greater in case (2) than in case (1).

And by Newton's Third Law, ball hits the wall harder in case (2) than in case (1).

So now consider a spacecraft, inside we have a magnetic projectile inside a cylindrical chamber.

We propel this projectile inside the craft using electromagnetic acceleration, the spacecraft moves in the opposite direction, at the other end of the chamber the projectile is stopped by it hitting the end stop, in this scenario we have a very slight displacement of the craft but no net acceleration.

However,

Now think about the squash ball, kinetic energy is lost due to the heating of the rubber ball, what if at the endstop we have coils of wire which allow current to flow due to electromagnetic induction.

Lenz law will cause the projectile to slow using some of the kinetic energy to be used in the electromagnetic induction process, causing a net loss in force at the endstop. In this scenario we have an imbalance in the closed system.

Some of the initial force we used to propel the projectile will be preserved. Hence we have a small net acceleration of the craft. We return the projectile to the start position, which is a net 0 acceleration.

We then repeat the process.

Could someone please point to where I have made my error in this idea.

Proof:

A ball of mass

*m*moving with velocity

*u*in the negative x direction strikes the wall and rebounds with velocity*v*which is in the positive x direction with |*v*|<|*u*|. This change in velocity is acquired in very little time, meaning the force applied by wall is very large so the quantity of interest is impulse.Initial velocity = −

*ui*^ and final velocity =*vi*^.So change in momentum of ball =

*Favgappliedbywall*.Δ*t*=*m*(*v*+*u*)*i*^By work energy theorem,

12

*m*(*v*2−*u*2)=Heat lost to surroundings + Work done on ballWork f=done on ball by wall is 0 as force is applied by wall on ball when the ball is in contact with the wall, so no displacement.

So, 12

*m*(*v*2−*u*2)=Heat lost to surroundings

**(1)**

Case-[1]From (1), we can see that if |Case-[1]

*v*|<|*u*|, more heat is lost.

And impulse imparted by wall is m(v+u)

Force applied by wall=

*m*(*v*+*u*)Δ*t***Case-[2]**If |*v*|=|*u*|Then from (1), 12

*m*(*v*2−*u*2)=0=Heat lost to surroundingsMeaning no heat is lost (elastic collision).

Impulse imparted by wall is 2

*mu*So, force exerted by wall = 2

*mu*Δ*t*We can see that force applied by wall is greater in case (2) than in case (1).

And by Newton's Third Law, ball hits the wall harder in case (2) than in case (1).

So now consider a spacecraft, inside we have a magnetic projectile inside a cylindrical chamber.

We propel this projectile inside the craft using electromagnetic acceleration, the spacecraft moves in the opposite direction, at the other end of the chamber the projectile is stopped by it hitting the end stop, in this scenario we have a very slight displacement of the craft but no net acceleration.

However,

Now think about the squash ball, kinetic energy is lost due to the heating of the rubber ball, what if at the endstop we have coils of wire which allow current to flow due to electromagnetic induction.

Lenz law will cause the projectile to slow using some of the kinetic energy to be used in the electromagnetic induction process, causing a net loss in force at the endstop. In this scenario we have an imbalance in the closed system.

Some of the initial force we used to propel the projectile will be preserved. Hence we have a small net acceleration of the craft. We return the projectile to the start position, which is a net 0 acceleration.

We then repeat the process.

Could someone please point to where I have made my error in this idea.

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