You can think of the workkinetic energy theorem as a second theory of motion, pa

Question

You can think of the workkinetic energy theorem as a second theory of motion, parallel to Newton's laws in describing how outside influences affect the motion of an object. In this problem, solve parts (a), (b), and (c) separately from parts (d) and (e) so you can compare the predictions of the two theories. A 13.5-g bullet is accelerated from rest to a speed of 814 m/s in a rifle barrel of length 66.2 cm.

(a) Find the kinetic energy of the bullet as it bullet as it leaves the barrel. ___kJ

(b) Use the work-kinetic energy theorem to find the net work that is done on the bullet. ___kJ

(c) Use the result to part (b) to find the magnitude of the average net force that acted on the bullet while it was in the barrel. ___kN

(d) Now model the bullet as a particle under constant acceleration. Find the constant acceleration of the bullet that starts from rest and gains a speed of 814 m/s over a distance of 66.2 cm. ___km/s2

(e) Modeling the bullet as a particle under a net force, find the net force that acted on it during its acceleration. ___kN

(f) What conclusion can you draw from comparing your results of parts (c) and (e) ________

Explanation / Answer

a) Kinetic energy of bullet as it leaves the barrel = 0.5*0.0135*8142 = 4472.5 J=4.472 kJ

b)net work done on the bullet=kinetic energy gained by bullet=4.472 kJ

c)let avegrage foce that acted on bullet be F

F*0.662=4472.5

F=6756.1 N=6.756 kN

d)let the acceleration be a

a=8142/(2*0.662)=500450 m/s2=500.45 km/s2

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