Answer:
Explanation:
Given that,
Length of barrel =0.54m
Mass of bullet=125g=0.125kg
Force extend
F=16,000+10,000x-26,000x²
a. Work done is given as
W= ∫Fdx
W= ∫(16,000+10,000x-26,000x² dx from x=0 to x=0.54m
W=16,000x+10,000x²/2 -26,000x³/3 from x=0 to x=0.54m
W=16,000x+5,000x²- 8666.667x³ from x=0 to x=0.54m
W= 16,000(0.54) + 5000(0.54²) - 8666.667(0.54³) +0+0-0
W=8640+1458-1364.69
W=8733.31J
The workdone by the gas on the bullet is 8733.31J
b. Work done is given as
Work done when the length=1.05m
W= ∫Fdx
W= ∫(16,000+10,000x-26,000x² dx from x=0 to x=1.05m
W=16,000x+10,000x²/2 -26,000x³/3 from x=0 to x=1.05m
W=16,000x+5,000x²- 8666.667x³ from x=0 to x=1.05mm
W= 16,000(1.05) + 5000(1.05²) - 8666.667(1.05³) +0+0-0
W=16800+5512.5-10032.75
W=12,279.75J
The workdone by the gas on the bullet is 12,279.75J
