A 80-g bullet is fired from a rifle having a barrel 0. 642 m long. Choose the or

Question

A 80-g bullet is fired from a rifle having a barrel 0. 642 m long. Choose the origin to be at the location where the bullet begins to move. Then the force (in newtons) exerted by the expanding gas on the bullet is 15750 + 11000x - 23750x2, where x is in meters. Determine the work done by the gas on the bullet as the bullet travels the length of the barrel. kJ If the barrel is 0. 90 m long, how much work is done? kJ How does this value compare with the work calculated in part (a)? percent difference = % A 0. 500-kg particle has a speed of 1. 80 m/s at point A and kinetic energy of 7. 90 J at point B. What is its kinetic energy at A? J What is its speed at B? m/s What is the net work done on the particle by external forces as it moves from A to B? J

Explanation / Answer

a)

W = F.dx

W = (15750 + 11000 x - 23750 x2) dx

W = 15750 x + 11000 (x2/2) - 23750 (x3/3)

W = 15750 x + 5500 (x2) - 7917 (x3)

W = 15750*(0.642) + 5500*(0.642*0.642) - 7917*(0.642*0.642*0.642)

W = 10.3 kJ

b)

W = F.dx

W = (15750 + 11000 x - 23750 x2) dx

W = 15750 x + 11000 (x2/2) - 23750 (x3/3)

W = 15750 x + 5500 (x2) - 7917 (x3)

W = 15750*(0.90) + 5500*(0.90*0.90) - 7917*(0.90*0.90*0.90)

W = 12.9 kJ

c)

percent difference = (12.86-10.28)/(10.28) * 100 = 25.1 %

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