User:Guy vandegrift/Current project

From Wikiversity
Jump to navigation Jump to search

euler summation formula[edit]

https://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Maclaurin_formula&oldid=626918816

In the end, we get the following simple formula ([1]):

.

Where 'N' is the number of points in the interval of integration, from to .

This is just the trapezoid rule with correction terms ([2]).



Ballistic pendulum lab[edit]

In this lab we shall investigate the ballistic pendulum by taking measurements and using a computer program to analyze the results. The formulas used in this analysis will be developed from first principles (Newton's laws).

Ballistic pendulum device[edit]

Student ballistic pendulum.jpg

Make a hand drawn sketch of the ballistic pendulum and label the important parts. For now we shall use the following names:

  • The 'cannonball' is a small ball of mass m
  • The 'cannon' shoots the 'cannonball' using a spring mechanism that is attached to the cannon rod
  • The 'target' is a device that captures the cannonball. It has mass M (which includes a portion of the attached aluminum rod in a way that only calculus students could understand).
  • The 'cart' is the name we shall use for the combined 'cannonball' and 'target'. It has has mass '(m+M)'
  • The 'ramp' is not a physical component but the path taken by the 'cart' as it moves
  • The 'rachet' is the device that catches the cart at a final height.

All heights are measured from the center of the cannonball as it leaves the cannon rod.

Ballistic pendulum theory[edit]

Computer code[edit]

% This tests the pre hml option
% it should be two lines
  • Write instructions for opening MATLAB on a campus computer, pasting and running this code.
MatLab code
clear all;clc;close all;
x='hello'
% ball mass was 68.5 grams
% mass of thing with rod was 275.6 g
% use cgs units
g=980;%cm/s/s
m=68.5;
M=275.6;
h_big=16.3;
h_small=9;
h=h_big-h_small;
v_1=sqrt(2*g*h)%119.6161cm/s This is the speed of the ball and receiver put 
% together when they were at the bottom
% (m+M)*v_1 = m*v_0  (we want v_0)
v_0=v_1*(m+M)/m %muzzle speed of cannon
R_observed=211.5%cm range
theta=asin(12/40.5);%
% the formula for range is d = 2v_0^2*sin(theta)/g
R_calc = 2*v_0^2*sin(theta)/g

bigoversmall=R_calc/R_observed

display('How high does the cannon shoot?')
height=    v_0^2   /   (2*g)

References[edit]

  1. DEVRIES, Paul L. ; HASBUN, Javier E. A first course in computational physics. Second edition. Jones and Bartlett Publishers: 2011,p.156)
  2. DEVRIES, Paul L. ; HASBUN, Javier E. A first course in computational physics. Second edition. Jones and Bartlett Publishers: 2011,p.156)