# Calculating Rail Gun Distance for Escape Velocity

• lylos
In summary, the problem involves a conducting bar sliding over horizontal rails connected to a voltage source that maintains a constant current and a uniform magnetic field. It is suggested that this principle could be used to accelerate payloads into Earth orbit. To find the distance the bar must travel to reach the escape speed for Earth, the magnetic force and kinematics equations are used. After correcting for incorrect formulas, the correct answer is found using the kinematics equation that relates velocity to distance.
lylos

## Homework Statement

A conducting bar with mass=25.0 kg and length L=51.0 cm slides over horizontal rails that are connected to a voltage source. The voltage source maintains a constant current I= 2400A in the rails and bar, and a constant, uniform, vertical magnetic field B = 0.480 T fills the region between the rails.
See figure:

It has been suggested that rail guns based on this principle could accelerate payloads into Earth orbit or beyond. Find the distance the bar must travel along the rails if it is to reach the escape speed for the Earth (11.2 km/s).
For simplicity, assume the net force on the object is equal to the magnetic force, as in parts A and B, even though gravity plays an important role in an actual launch into space.

## Homework Equations

I know the magnetic force is 588N.
F=ma
V = at
X = at^2

## The Attempt at a Solution

588/25 = 23.52 m/s^2
11200 m/s = 23.52 m/s^2 * t
t = 476.190

x = 23.52 m/s^2 * 476.19^2
5333322.666672 m

Am I missing something, it says that is incorrect...

I think the best approach here might be with the kinematics eqn that relates velocity to distance along which body is uniformly accelerated, since Vi=0 (body at rest): V^2=2a*x

ah, my formulas were wrong... it's x=1/2at^2 and v=at... I should've caught that...

you miss my point maybe. there is no need to mess with time, but certainly you can get the right answer using that approach. Try it both ways!

## 1. What is a rail gun and how does it work?

A rail gun is a type of weapon that uses electromagnetic forces to accelerate a projectile to high velocities. It works by passing a large electrical current through two parallel conductive rails, creating a strong magnetic field. A conductive projectile is placed between the rails and the magnetic field exerts a force on it, propelling it forward at incredibly high speeds.

## 2. How fast can a rail gun shoot?

Rail guns have the potential to shoot projectiles at speeds of over Mach 7 (7 times the speed of sound), which is much faster than traditional firearms. The exact speed depends on the design and power of the rail gun, but they are capable of reaching hypersonic velocities.

## 3. What are the advantages of using rail guns over traditional firearms?

There are several advantages to using rail guns. One of the main advantages is their high muzzle velocity, which results in increased range and accuracy. Rail guns also have lower recoil compared to traditional firearms, making them easier to handle. They also do not require any chemical propellants, making them more environmentally friendly and less prone to malfunctions.

## 4. Are there any limitations to rail gun technology?

While rail guns have many advantages, there are also some limitations to the technology. One of the main limitations is the high amount of power required to accelerate the projectile to high speeds. This can be difficult to achieve and requires advanced power sources. Additionally, rail guns are currently quite large and heavy, making them difficult to use in certain situations.

## 5. What are some potential applications of rail gun technology?

Rail guns have a variety of potential applications, including military and defense purposes, space launch systems, and even as a potential method for launching spacecraft. They are also being developed for use in transportation, such as launching trains or accelerating ships at sea. Additionally, their high velocities and precision could make them useful in scientific research and experimentation.

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