Question

A rail gun uses electromagnetic forces to accelerate a projectile to very high velocities. The basic mechanism of acceleration is relatively simple and can be illustrated in the following example. A metal rod of mass 30.0 g and electrical resistance 0.400 ? rests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 9.00 cm apart. (Figure 1) The rails are also connected to a voltage source providing a voltage of V = 5.00 V . The rod is placed in a vertical magnetic field. The rod begins to slide when the field reaches the value B = 0.131 T . Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s2 for the magnitude of the acceleration due to gravity. Find the coefficient of static friction between the rod and the rails.

Answer 1

Answer:

$u_s=0.0802$

Explanation:

To find the coefficient of static friction between the rod and the rails first must find the current

Using law ohm:

$V=I*R$

$I=\frac{V}{R}=5.0v/0.40$

$I=2A$

Now using the Gauss Law of magnetic field solve to us'

$u_s=\frac{I*L*\beta}{m*g}$

Replacing given:

$\beta=0.131T$,$L=9.00cm*\frac{1m}{100cm}=0.09m$, $m=30.0g*\frac{1kg}{1000g}=0.03kg$

$u_s=\frac{2A*0.09m*0.131T}{0.030kg*9.8m/s^2}$

$u_s=0.0802$

Answer 2

The coefficient of static friction between the metal rod and the rails is 0.5.

Given the following data:

• Mass of metal rod = 30.0 grams to kg = 0.03 kg

• Resistance = 0.4 Ohms

• Distance, L = 9 cm to m = 0.09 m

• Voltage = 5 Volts

• Magnetic flux, B = 0.131 Tesla

• Acceleration due to gravity = 9.8 $m/s^2$

To find the coefficient of static friction between the metal rod and the rails, we would apply Gauss's law of magnetic field:

First of all, we would determine the current flowing through the rails:

$Current = \frac{Voltage}{Resistance} \\\\Current = \frac{5}{0.4}$

Current = 12.5 Amps

Mathematically, the magnetic force on a current-carrying conductor is given by the formula:

$F_m = BIL$

Where:

• $F_m$ is the magnetic force.

• B is the magnetic flux.

• I is the current.

• L is the length.

Substituting the given parameters into the formula, we have;

$F_m = 0.131 \times 12.5 \times 0.09\\\\F_m = 0.147 \;Newton$

The limiting frictional force acting on the metal rod is given by:

$F_r = umg$

Also, the magnetic force must be equal to the limiting frictional force before the metal rod starts the motion:

$F_m = F_r\\\\0.147 = u\times 0.03 \times 9.80\\\\0.147 = u0.294\\\\u = \frac{0.147}{0.294}$

Coefficient of static friction = 0.5

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