This is a little bit of a mouthful but any help would be greatly appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

I am building a linear accelerator similar to the one found on this site: http://www.scitoys.com/scitoys/scitoys/magnets/gauss.html This is for a physics 12 project with my friends, but only it is on a larger scale. The project involves launching a regular tennis ball as far as possible without using combustion or fuels. We are constructing it as follows: A copper pipe is cut in half to create the "grooved" barrel were the steel balls will roll. (We are using copper because it has a low coefficient for friction.) At one end is a compressed spring which will release the first steel ball towards the first magnet. (Magnets are 1.0" x .125" neodymium-iron-boron (NdFeB) rare-earth permanent magnets fixed between two washers for safety and enhanced strength.) There will be 5-6 magnets with an undetermined spacing between them. We are using 10-12 stainless steel balls with a diameter of 1.0" weighing at approximately 66.4g or 0.0664kg we think. This entire barrel will be placed in an aluminum pipe, also cut in half, so that the copper barrel will allow the last steel ball to preform an inelastic collision against the tennis ball directly (thus an oblige collision is avoided). Because of projectile motion we will be attempting to fire this at an angle (probably 45 degrees, or a little less if wind resistance occurs) to achieve a maximum distance.

My questions are as follows: 1)How can we find the resultant velocity of the tennis ball(Please supply me with formulas I won't bother you with all the exact measurements, and besides I don't have all of them.)?

2)How can we calculate the pulling force of our magnets fields (in newtons) at a distance in meters?

For question 1:

A)I know that we need to find the spring constant (k) in (newton meters)of our spring using Hook's Law (F=kx) which is easily done.

B)Then we use (K) to find the Elastic Potential Energy for our spring (EPE=1/2kx^2) were (x) is the springs compression in meters, EPE is measured in joules.

C)Then we have to deal with Static Friction. (I need help here!)

D)Followed by drawing an incline plane problem at 45 degrees, where the Elastic Potential Energy is converted into Kinetic Energy (KE)(Both in joules). The kinetic energy and the attraction force of the magnet (this is where question 2 comes in) are pulling the steel ball up the slope after the spring system is released. The kinetic friction and acceleration due to gravity are pulling the ball down the slope and into the slope resulting in a loss of velocity. [Normal force is mgcos(45) {Where m is mass (kg) and g is gravity (9.8m/s)}]

E)When the ball does hit the magnet most of the kinetic energy is transferred to the furthest ball on the other side of the magnet, where it in turn overcomes static friction. (More static friction help needed!)

F)Another incline plan problem with KE and the 2nd magnets attraction force are pulling uphill. The acceleration due to gravity, kinetic friction, and 1st magnets attraction force slowing the velocity.

G)Parts E and F repeat until the inelastic collision of the last steel ball against the tennis ball where we dip into momentum. p=mv where p is momentum in (kgm/s), m is mass in (kg) and v is velocity (m/s). Because we have to objects (one at rest) we use the equation p=(m1)(v1)+(m2)(v2) were mass 2 is at rest (the tennis ball). Using momentum we then find the resulting velocity of the tennis ball!

Other formula: Ffr=(mu)N were Ffr is force of friction in newtons, (mu) is coefficient of friction and (N) is Normal force.

Ffr=(mu)mg involving force of friction, coefficient of friction, mass and acceleration due to gravity. (But someone told me this is for objects kept horizontal?)

That really was a mouthful, it covers a lot of different physics topics too! Please inform me if I'm even approaching this right? Thanks in advance.

Kristan

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# Linear Accelerator (Gauss Rilfe)

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