# Java Math Example – Resultant of two Forces.

The program below shows how Java can be implemented in math for several applications. In this program we determine the resultant force of two different forces acting upon a body and the angle at which it is acting. At first in order to use the math functions predefined in java we need to import a java package java.lang.Math.*;

Let us see the working of this program, we first need three variables, two to store the magnitude of each force and the third to store the angle between them. Then we calculate the magnitude of the resultant and later in the second part we calculate the angle between them. So, here are the formulae for both operations:

• Resultant of two forces = √( p2 + q2 + 2 × p × q × cosθ )
• Angle made by resultant = tan-1 ( q × sinθ / p + q × cosθ )

So, now we know that we need another two variables to store each of the answers.Well this really depends on you, how precise you want to be answered, if you want your answer in decimal use double or float data-type but if you don’t want a precise one the better go with integer. Another really important thing is that Java uses angles in Radian whereas normally we use angle in Degrees. So, we also need to convert the angles in to radians before using them in the formula (or else the compiler considers 45° as 45 radians ) and convert them back again to degrees to display answer (but if you are comfortable with radians don’t include this feature).

Very well, let us get on with the program. First we declare our five variables as doubles. Then we ask the user to enter the two forces and the angle between them. Then we read and store the input data with Scanner. Also do not forget to convert the angle to radians if you are planning to enter the angle in degrees, for that we use the function Math.toRadians(a) .

Now we arrange our functions according to the formula to find out the resultant:

``     r=Math.sqrt(Math.pow(p, 2)+Math.pow(q, 2)+(2*p*q*Math.cos(a)));``

For square root we use the function Math.sqrt similarly for cosine of the angle Math.cos(a) , for power we use Math.pow(p, 2) where, in the bracket we specify the variable and its power (here its square). Then we display our answer or resultant.

Note:- Make a clever and careful use of the brackets in formula, incorrect placements of the brackets may lead to a wrong answer.

To find the angle of resultant, for time being let us neglect the tan-1 from the formula and arrange the functions accordingly.

``    t=(q*Math.sin(a))/(p+q*Math.cos(a));``

There is nothing much hard in this formula to deal with. For the sine and cosine angles we use the functions Math.sin(a) and Math.cos(a) respectively. Here now we consider the tan-1 from the formula. To display the tan inverse of a particular value we use the function Math.atan(t) .But keep in mind that Java uses angles in radians so to keep our program more user-friendly we convert the radians back to degrees by using the function Math.toDegrees() and display them. Here I have made this process a bit simpler and less time consuming:

``System.out.println("The angle at which resultant is acting on is "+ Math.toDegrees(Math.atan(t)));`` Hope this example helps you to understand how to work with Math in Java. 