A bullet of mass 1.80 x10 -3 kg, moving at 1230 m/s impacts a tree stump and pen

Question

A bullet of mass 1.80 x10-3 kg, moving at 1230 m/s impacts a tree stump and penetrates8.00 cm into the wood before coming torest. (Take the direction of the bullet to be in the positivedirection.) (a) Assuming that the acceleration of thebullet is constant, find the force (including direction) exerted bythe wood on the bullet.
kN

(b) If the same force acted on the bullet and it had the sameimpact speed but half the mass, how far would it penetrate into thewood?
cm (a) Assuming that the acceleration of thebullet is constant, find the force (including direction) exerted bythe wood on the bullet.
kN

(b) If the same force acted on the bullet and it had the sameimpact speed but half the mass, how far would it penetrate into thewood?
cm

Explanation / Answer

(a)Assuming that the acceleration of the bullet isconstant the force (including direction) exerted by the wood on thebullet F=ma acceleration a=v*t    distance d=v*t +a*t2/2 =>v2=2*|a|*d => a=-9.46*106m/s2 => F=-17020 N= -17 kN (b) If the same force acted on the bullet and it had thesame impact speed but half the mass, => acceleration =2*a => newdistance=d/2=4 cm (b) If the same force acted on the bullet and it had thesame impact speed but half the mass, => acceleration =2*a => newdistance=d/2=4 cm

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