Video Transcript
A force of magnitude 96 newtons acts vertically downward. It is resolved into two components as shown in the diagram. Find the magnitude of ๐น one and ๐น two, giving values to two decimal places.
In order to solve this problem, we will use Lamiโs theorem. This states that if three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two forces.
๐ด divided by sin ๐ผ is equal to ๐ต divided by sin ๐ฝ is equal to ๐ถ divided by sin ๐พ. This is because angle ๐ผ is between forces ๐ต and ๐ถ. Angle ๐ฝ is between forces ๐ด and ๐ถ. And finally, angle ๐พ is between forces ๐ด and ๐ต.
In our example, the angle between force ๐น one and 96 newtons is 90 degrees. The angle between ๐น two and 96 newtons is 42 degrees. And the angle between forces ๐น one and ๐น two is 132 degrees. This means that ๐น one divided by sin 42 is equal to ๐น two divided by sin 90, which is equal to 96 divided by sin 132.
If we consider the forces ๐น one and 96 newtons, we can rearrange the equation so that ๐น one is equal to 96 divided by sin 132 multiplied by sin of 42. This gives us an answer for ๐น one of 86.44 newtons. When we consider the two forces ๐น two and 96 newtons, we can rearrange this equation to give us ๐น two is equal to 96 divided by sin 132 multiplied by sin 90. This gives us a value of ๐น two of 129.18 newtons.
Using Lamiโs theorem, weโve proved that the force ๐น one is equal to 86.44 newtons and ๐น two is equal to 129.18 newtons.
