### Video Transcript

In the given figure, the body is at rest under the action of a system of forces. Given that the forces are measured in newtons, find the magnitudes of š¹ and š¾.

The key piece of information thatās going to help us answer this question is spotting that weāre told that the body is at rest. Newtonās first law of motion states that an object will remain at rest unless acted upon by an external force. Another way of thinking about this is that if the net force acting upon an object is zero, then the velocity of that object is constant.

Here, the velocity is constant. It just happens to be zero. And so this means the net forces in the horizontal direction must be zero. And similarly, the net forces in the vertical direction must also be zero. Looking at our forces acting vertically, with positive being sort of upwards here, the net force is 57 minus š¹. And we know thatās going to be equal to zero.

We solve this equation for š¹ by simply adding š¹ to both sides, to get š¹ equals 57. Similarly, looking horizontally and assuming that the right is the positive direction, we get 27 plus 66 minus š¾ as the net force. And thatās equal to zero. 27 plus 66 is 93. And this time, we solve for š¾ by adding š¾ to both sides so that 93 is equal to š¾. Both of these forces weāre told are measured in newtons.

And so we see that š¹ is equal to 57 newtons and š¾ is equal to 93 newtons.