question 7 7. You decide to build a small rail gun as we discussed in class. You

Question

question 7

7. You decide to build a small rail gun as we discussed in class. You connect a 30.ov power source to your two rails and find a small piece of metal to use as a projectile. The projectile has a mass of 0.010kg and a length of 0.o5m. The resistance in your rails and projectile are 2.00 ohms. (a) what is the current going to be in your circuit? (b) Find the magnetic field at the center of your projectile due to each rail (we'll neglect the magnetic field that the projectile uces (c) Calculate the acceleration of the projectile. (d) if prod the projectile starts at rest, determine the speed the projectile leaves the rail gun if your rails are 2.00 meters long. (Ans length projectile rail

Explanation / Answer

given

V_battery = 30 V

m = 0.01 kg

L = 0.05 m

R = 2 ohms

a) I = V_battery/R

= 30/2

= 15 A

b)

B = B_upperrail + B_lowerrail

= mue*I/(2*pi*r) + mue*I/(2*pi*r)

= mue*I/(pi*r)

= 4*pi*10^-7*15/(pi*0.05/2)

= 2.4*10^-4 T

c) F = B*I*L*sin(90)

m*a = B*I*L

a = B*I*L/m

= 2.4*10^-4*15*0.05/0.01

= 0.018 m/s^2

d)

use, v^2 - u^2 = 2*a*d

==> v^2 - 0^2 = 2*A*d

==> v = sqrt(2*a*d)

= sqrt(2*0.018*2)

= 0.268 m/s

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