# 11.1.1. Forces

The difference between the magnitudes of two forces acting at a point is N, where the magnitude of their resultant is N. When the angle between the two forces is , find the magnitudes of the two forces.

• AN, N
• BN, N
• CN, N
• DN, N

### Example

The difference between the magnitudes of two forces acting at a point is N, where the magnitude of their resultant is N. When the angle between the two forces is , find the magnitudes of the two forces.

### Solution

Remember that when we have two forces and acting at a point and is the angle between them, we can calculate the magnitude of the resultant force using the following formula: where , , and are the magnitudes of the forces.

Using the information we have been given, we can form two simultaneous equations, then solve for the magnitudes of the two forces. Firstly, we use the equation above to form our first equation:

Let this be the first equation.

Since we know the difference between the forces is N, then

Let this be the second equation.

Substituting this into the first equation, we have

Since is a magnitude, it must be greater than or equal to zero. Hence, N. Substituting this into the second equation, we have N.

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