Two parallel forces are acting in the same direction, where one of them is twice the other in terms of magnitude and the magnitude of their resultant is 76.98 newtons. Determine the magnitude of the smaller one.
Let’s begin by sketching this out. We have two parallel forces acting in the same direction. And we’re told that one of these forces is twice the other in terms of magnitude. So if we define the size of our first force to be 𝑥 newtons, then the size of our larger force must be two 𝑥 newtons. We’re also told that the magnitude of their resultant force is 76.98 newtons. Well, their resultant is simply the sum of these. So it’s 𝑥 plus two 𝑥. So we can say that 𝑥 plus two 𝑥 is equal to 76.98 newtons.
Now, in fact, we have been given information about the magnitude of our forces. But since we’re modeling them as all acting in the same direction to the right, we can essentially say that they’re all positive. So this equation still holds. Simplifying the left-hand side, and we get three 𝑥 equals 76.98. To solve for 𝑥, we simply divide through by three. So 𝑥 is 76.98 divided by three, which is 25.66. Since 𝑥 newtons is the smaller force, then we’re finished. 𝑥 is 25.66 newtons. And of course, we could check our answer by calculating the resultant of our two forces. They are 25.66 and two times 25.66. So the resultant is the sum of these. That is indeed 76.98 newtons as required. So the magnitude of the smaller force is 25.66 newtons.