It is well known that bullets and other missiles fired at Supermansimply bounce

Question

It is well known that bullets and other missiles fired at Supermansimply bounce off his chest. Suppose that a gangster spraysSuperman's chest with 10 g bullets at the rate of 100 bullets/min,the speed of each bullet being 700 m/s. Suppose too that thebullets rebound straight back with no change in speed. What is themagnitude of the average force on Superman's chest from the streamof bullets?

where does the 2*m*v come from..

i don't particularly like the wording of the question either.. isit 1 bullet or a stream.. and what constitutes a stream..

Each bullet has a change of momentum of 2*m*v=2*0.01kg*700 m/s = 14kgm/s.

In 60 sec, the total impulse from the 100 bullets is 1400kgm/s.

The average force is then 1400 kgm/s /60 s = 23 N. Notmuch!

However, if a single bullet applies its force in 1ms, the avg forceof a single bullet is 14000 N!

Explanation / Answer

The initial momentum, Pi is m*v The final momentum , Pf is -m*v So the change in momentum is Pf - Pi =(-m*v) - (m*v) = -2m*v. This is where the factor 2 comes in. The question is only considering the magnitude of momentumchanges, and ignores direction altogether; hence the - sign doesnot matter. The change is momentum is then 2*m*v Further since the question refers to a number of bullets thatare being shot continuously ( at a rate of 100 bullets/s precisely,as per question), the word stream is used ( graphically) torepresent this continuous shooting of bullets.

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