To a close approximation the pressure behind a rifle bullet varies inversely wit

Question

To a close approximation the pressure behind a rifle bullet varies inversely with the position x of the bullet along the barrel. Thus, the acceleration of the bullet may be written a=k/x where k is a constant. If the bullet starts from rest at x=7.5 mm and if the muzzle velocity of the bullet is 600 m/s at the end of the 750mm barrel, compute the acceleration of the bullet as it passes the midpoint of the barrel at x = 375 mm. Answer is 104.3 km/s^2. To a close approximation the pressure behind a rifle bullet varies inversely with the position x of the bullet along the barrel. Thus, the acceleration of the bullet may be written a=k/x where k is a constant. If the bullet starts from rest at x=7.5 mm and if the muzzle velocity of the bullet is 600 m/s at the end of the 750mm barrel, compute the acceleration of the bullet as it passes the midpoint of the barrel at x = 375 mm. Answer is 104.3 km/s^2.

Explanation / Answer

let a = acceleration = k/x, xo = 7.5 mm, vo = 0 from the condition given x1 = 750 mm, v1 = 600 m/s, find a when x = 750/2 mm = 0.375 m Again, a = dv/dt = dv/dx dx/dt = v dv/dx = k/x v dv = k dx/x integrate, v2/2 = k lnx + C use xo = 7.5 mm, vo = 0, vo2/2 = klnxo + C so C = -k lnxo v2/2 = k (lnx - lnxo) use x1 = 750 mm, v1 = 600 m/s, v12/2 = k (lnx1 -lnxo) ?k = v12/[2(lnx1 -lnxo)] = 3.91*10 3 m2/s2 a(x) = k/x = 1.043*10 5 m/s2 = 104.3km/s2 .........................ans

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.