Gaussian Gun, Conservation of Energy,
Kinetic and Potential Energy
The so-called Gaussian gun actually has nothing to do with the famous mathematician Carl Friedrich Gauss, but has a lot to do with magnetic fields, conservation of energy, and Newton’s laws. The idea for this experiment came to me from Josh Fair’s Dad.
; Two rare earth disc magnets – 1/2 in. in diameter and 1/8 in. thick
; Five 7/16 in. diameter chromium steel balls
; Plastic track is optional
The picture below illustrates the setup. Two disc magnets with four steel balls stuck together on one side of the magnets. I like to use five rather than four steel balls. On the other side of the magnets we have a single steel ball that we let role slowly toward the magnets. The single ball rapidly picks up speed as it moves toward the magnets. It strikes the magnets launching the last ball at high speed from the end of the stack of steel balls on the opposite side of the magnets.
Before discussing the physics of the Gaussian gun, lets first discuss the concept of potential energy. When an object is in a force field such as the Earth’s gravity, it has energy just by its
location within the field. For example, if we hold a ball in our hand, the ball has a certain amount of potential energy due to its height above the ground and the force of gravity. If we drop the ball, it falls and picks up speed. Energy of motion is called kinetic energy. As the ball falls, it looses potential energy and gains kinetic energy. In an ideal situation where no energy is lost to heat due to friction, the total amount of kinetic energy plus potential energy remains constant. This is called conservation of energy.
If an object is within a force field it can move in a repetitive way so as to constantly trade energy between potential energy and kinetic energy. The total energy must remain constant. A simple pendulum is a good example of how this happens.
As a pendulum swings it is moving the fastest at the bottom point of its trajectory where kinetic energy is at a peak. However, at the top of its swing, the pendulum’s motion is stopped altogether. Here the kinetic energy is at a minimum of zero and all of the pendulum’s energy is in the form of potential energy. Inside a gravity field, the potential energy of an object is simply calculated as its weight multiplied by its height. The simple motion of satellites in orbit can also be explained as a periodic exchange of potential and kinetic energy. The formula for computing kinetic energy depends on both the mass and speed of an object. Therefore, kinetic energy is
one-half times the mass of the object times its velocity squared. Remember squared means we 2 = 3 x 3). So, kinetic energy, KE, is computed as: multiply a number by itself ( 3
2KE = (1/2)mv.
The potential energy is just weight times height, or
PE = wh.
The weight of an object, w, is just the force of gravity on the object. As an interesting note about kinetic energy, think of a car traveling down the highway. How does its kinetic energy change with its velocity? Because kinetic energy changes as velocity squared, a car traveling at 2 miles 2per hour has 4 times the kinetic energy of one traveling at 1 mile per hour. Why? Because 2 = 24 while 1 = 1. Damage in a car crash is caused by kinetic energy. So, the amount of damage to a car that hits a wall at 2 miles per hour will be four times the amount of damage of one traveling at one mile per hour. Consider the difference between a car traveling 60 miles per hour and one 22traveling at 80 miles per hour. Let’s compute the numbers : 60 = 3600 while 80 = 6400. The
number 6400 is close to twice 3600. This means that a crash in a car going 80 miles per hour will cause almost twice the damage of one going 60 miles per hour. This is one reason why people say speed kills.
Magnetic Force and Potential Energy
We usually think of potential energy in the context of the Earth’s gravitational field, but an
object can have potential energy within just about any type of force field. The Gaussian gun works on potential energy stored by the steel ball within a magnetic field. Suppose we have a steel ball attached to a magnet, as shown. Then, pull the ball away from the magnet.
The magnet is very strong and a considerable amount of effort is needed to pull the ball and magnet apart. This effort requires us to do work to pull the steel ball and magnet apart.
Remember that work is defined as force through a distance. When the ball is close to the magnet the pulling force is very strong. Indeed, it is difficult to hold the ball close but separate from the magnet. As the distance between the ball and the magnet increases the force weakens considerably.
Recall that energy is defined as the capacity to do work. The ball now has potential energy with respect to the magnetic field due to the work we did pulling the ball off the magnet. If we release the steel ball, it accelerates toward the magnet pulled by the magnetic force field. The moving ball has kinetic energy created by the ball “falling” through the magnetic field toward the magnet. The potential energy is converted to kinetic energy. The ball is moving pretty fast when it hits the magnet.
How does this thing work? First, we have Newton’s law of conservation of momentum. We illustrate this with the desktop toy called Newton’s cradle shown below. We show five steel
balls hanging on strings. The ball on the far left is pulled back and released. As it strikes the four stationary balls the energy transfers through the four balls at the speed of sound. The ball on the far end of the stack is then lifted away. It moves to the same height away from the stack as we had initially lifted the ball on the left side to start the process.
The principles behind Newton’s cradle are the same as used when playing the game of billiards or pool.
The Gaussian Gun – How it works
We need magnetic potential energy and the principles of Newton’s cradle to make this work. Examine the photo below. It shows four steal balls attached to two disc magnets.
You can think of the magnets and attached steel balls as making a Newton’s cradle. As you
attach the balls to the magnets you notice that the farther away the ball is from the magnets, the weaker is the force holding the ball into place. I like to use five balls because the fifth ball is barely attached by the magnetic force. The single ball on the opposite side of the cradle has potential energy due to the field of the magnets. Give it only a slight nudge and the ball accelerates quickly toward the magnets. It strikes the magnets sending an impulse of energy through the balls just like the Newton’s cradle. The last ball on the row is only held weakly in place by the magnetic force and launches away just like the last ball on the Newton’s cradle. This “fires” the Gaussian gun.