A rail gun is a devic that propels a projectile using magnetic force. A simplifi

Question

A rail gun is a devic that propels a projectile using magnetic force. A simplified diagram of this device is shown above. The projectile in the picture is a bar of mass M and lenth D, which has a constant current I flowing through the +y-direction, as shown. The space between the thin frictionless rails contains a uniform magnetic field exerts a constant force F on the projectile, as shown.

Express all algebraic answers to the following parts in terms of the magnitude F of the constant magnetic force, other quantities given above, and fundamental constants.

a) Determine the position x of the projectile as a function of time t while it is on the rail in the projectile starts from rest at x=0 when t=0.

b) Determine the speed of the projectile as it leaves the right-hand end of the track.

c) Determine the energy supplied to the projectile by the rail gun.

d) In what direction must the magnetic field B point in order to create the force? Explain your reasoning.

e) calculate the speed of the bar when it reaches the end of the rail given the following values.

B= 5 T   L= 10 m   I= 200 A    M= .5 Kg     D= 10 cm

A rail gun is a devic that propels a projectile using magnetic force. A simplified diagram of this device is shown above. The projectile in the picture is a bar of mass M and lenth D, which has a constant current I flowing through the +y-direction, as shown. The space between the thin frictionless rails contains a uniform magnetic field exerts a constant force F on the projectile, as shown. Express all algebraic answers to the following parts in terms of the magnitude F of the constant magnetic force, other quantities given above, and fundamental constants. a) Determine the position x of the projectile as a function of time t while it is on the rail in the projectile starts from rest at x=0 when t=0. b) Determine the speed of the projectile as it leaves the right-hand end of the track. c) Determine the energy supplied to the projectile by the rail gun. d) In what direction must the magnetic field B point in order to create the force? Explain your reasoning. e) calculate the speed of the bar when it reaches the end of the rail given the following values. B= 5 T L= 10 m I= 200 A M= .5 Kg D= 10 cm

Explanation / Answer

Given that the magnetic force on the bar is F Then the acceleration is a = F /M (a) From equation of motion displacement is                 x - xo = ut + (1/2) at2                 x - 0 = 0 + (1/2) at2                       x = (1/2)at2                       x = (1/2)(F/M)t2 (b)      Now the final velocity is                v2 = u2 + 2aL                v2 = 0 + 2(F/M)L                v = 2FL/M (c) energy supplied is              E = (1/2) Mv2 - (1/2) Mu2                   = (1/2) Mv2 - 0                        (Since u = 0 m/s)                 = (1/2)M(2FL / M)                 = FL (d)       From right hand rule the magnetic field direction must be out of the page. (e)       Speed of the rod is                   v = 2FL/M                   v = 2(BID)L/M                   v = 2BIDL/M                     = 2*5T*200A*0.10m*10m / 0.5kg                     = 63.24 m/s                                                                                                                                                     

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