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 𝐹 and 𝐾.
The key piece of information that’s going to help us answer this question is spotting that we’re told that the body is at rest. Newton’s 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 𝐹. And we know that’s going to be equal to zero.
We solve this equation for 𝐹 by simply adding 𝐹 to both sides, to get 𝐹 equals 57. Similarly, looking horizontally and assuming that the right is the positive direction, we get 27 plus 66 minus 𝐾 as the net force. And that’s equal to zero. 27 plus 66 is 93. And this time, we solve for 𝐾 by adding 𝐾 to both sides so that 93 is equal to 𝐾. Both of these forces we’re told are measured in newtons.
And so we see that 𝐹 is equal to 57 newtons and 𝐾 is equal to 93 newtons.