# mathematical problem in Physics

• October 24th 2009, 10:12 AM
mars shaw
mathematical problem in Physics
The total work done by the force as the object moves from position x1 to xn can be approximated by the formula
http://www.staff.amu.edu.pl/%7Eroman...7/image004.gif
What is meant by (i) in this?
Is it first middle or last value? Below the sigma it is (i=1) but in graph it is in middle.
kindly explain.
http://www.staff.amu.edu.pl/~romango...work-graph.gif
http://www.staff.amu.edu.pl/~romangoc/M7-work-variable-force.html
• October 24th 2009, 11:04 AM
The i value runs from 1 and n (in this example) and you substitute whatever i value you're on into the part to the right of the $\sum$ symbol.
The $\sum$ symbol is a way of simplifying a long addition problem.
Lets say n=5. This means that there will be 5 values of $\Delta W$ to consider.
Let the first one be called $\Delta W_1$, the second $\Delta W_2$ etc up to $\Delta W_n$.
Then what $\sum_{i=1}^n \Delta W_i$ does is we start at i=1 and add together all $\Delta W$ values from $\Delta W_1$ up to $\Delta W_n$ which in this case is 5.
So we get $\sum_{i=1}^n \Delta W_i = \sum_{i=1}^5 \Delta W_i = \Delta W_1 + \Delta W_2 + \Delta W_3 + \Delta W_4 + \Delta W_5$.