# Magnitude and direction

• Jul 30th 2010, 09:28 AM
RosieLaird
Magnitude and direction
Forces of 85 pounds and 50 pounds act on a single point. The angle between the forces is 15 degrees. Find the direction and the magnitude of the resultant force
• Jul 30th 2010, 09:34 AM
Unknown008
Draw a diagram. This is important to let you see what angles you'll use and what sides you are looking for.

Then, use the cosine rule to find the magnitude of the resultant, and the sine rule to find the direction of the resultant.

Post what you come up with.
• Jul 30th 2010, 09:38 AM
RosieLaird
Quote:

Originally Posted by Unknown008
Draw a diagram. This is important to let you see what angles you'll use and what sides you are looking for.

Then, use the cosine rule to find the magnitude of the resultant, and the sine rule to find the direction of the resultant.

Post what you come up with.

Problem is we don't know how to find the magnitude and direction. What are the steps?
• Jul 30th 2010, 09:53 AM
Unknown008
Okay, what you need to find is the magnitude of the red arrow.

Attachment 18383

To do this, you make use of the cosine rule.

This gives the length of one side of a triangle, provided you know the lengths of the other two sides, and the angle between those two sides. In this case, we have 85, 50 and 165 degrees.

So, magnitude of resultant, 'A' is given by:

$A^2 = 85^2 + 50^2 - 2(85)(50)cos(165)$

You can calculate A now.

For the direction, you'll need to find the angle between the resultant and one of the lines, I propose the horizontal line. Let's call the angle theta.

So, the sine rule says that the ratio of the sine of an angle in a triangle to the length of the opposite side is always constant in a triangle.

So,

$\frac{sin(\theta)}{50} = \frac{sin(165)}{A}$

Solve for theta once you got the value of A.

The angle is the direction of the resultant, with respect to the 85 lbs force.