find the resultant force 10N and 20N acting at 30¡ã
I assume that is 30 degrees. Now you have to be careful when transfering vectors to trig formulas. Vectors are added head to tail, so draw the figure, head to tail now makes the angle 150 between the vectors in the vector diagram.
Law of Cosines:
Resultant^2=10^2+20^2 -2*10*20*cos150
resultant^2= 10^2+20^2 +2*10*20*cos30
and you have it. Study the diagram you sketched and the words I wrote, be be certain you understand how to add vectors when using trig formulas.
To find the resultant force of two forces, you can use vector addition. Here are the steps to find the resultant force of 10N and 20N forces acting at 30 degrees:
Step 1: Convert the forces into their vector representation:
- The 10N force can be represented as a vector of magnitude 10N and direction of 30 degrees.
- The 20N force can be represented as a vector of magnitude 20N and direction of 30 degrees.
Step 2: Add the vectors:
- Start by drawing both force vectors tip-to-tail, ensuring that the direction and magnitude of each vector are correctly represented.
- Next, draw a vector from the tail of the first vector to the tip of the second vector.
- The resultant force is the vector that connects the tail of the first force vector to the tip of the second force vector.
Step 3: Measure the magnitude and direction of the resultant force:
- Use a ruler to measure the length of the resultant force vector.
- Use a protractor or angle measuring tool to measure the angle between the resultant force vector and the positive x-axis (or any other reference axis).
Step 4: Determine the magnitude and direction of the resultant force:
- The measured length of the resultant force vector represents the magnitude of the resultant force.
- The measured angle between the resultant force vector and the positive x-axis (or reference axis) represents the direction of the resultant force.
By following these steps, you will be able to determine the magnitude and direction of the resultant force of the given forces.