Video Transcript
In the given figure, the body is subject to the action of a system of forces. Given that it is moving at a constant speed 𝑣 and that the forces are measured in newtons, find 𝐹 and 𝐾.
The key to answering this question is spotting that the object itself is moving at a constant speed. Newton’s first law of motion states that if the net force or the vector sum of all forces acting on an object is zero, then the velocity of the object will remain constant. The opposite here is therefore true. Since it’s moving at a constant speed, the net sum of the forces must be equal to zero. And once we can consider these forces as vectors, we can also split them into their horizontal and vertical components.
So let’s begin by considering the horizontal components of the force acting on this body. We’ll take the direction to the right to be positive. Then, the net sum of the forces acting in this direction, let’s call that the sum of 𝐹 sub 𝑥, is 31 plus two 𝐹 minus 35. And in fact we subtract 35 because that’s acting in the negative direction. That simplifies to two 𝐹 minus four. And remember, since the net sum of the forces is zero, we can form and solve an equation for 𝐹. We add four to both sides of this equation, and we get four equals two 𝐹. Then we divide both sides by two. And we get 𝐹 is equal to four divided by two, which is two, or two newtons.
Next, we’ll consider the vertical direction. And we take upwards to be positive. Then, the net sum of the forces in this direction is eight 𝐾 minus 56. But of course, once again, we know the net sum of these forces is zero. So eight 𝐾 minus 56 equals zero. We solve for 𝐾 by adding 56 to both sides. Then, finally, we divide by eight, and we find 𝐾 is equal to seven, or seven newtons. So 𝐹 is equal to two newtons, and 𝐾 is equal to seven newtons.