Forces in 2D Legacy Problem #24 Guided Solution

A good problem solver will read a problem carefully and develop a mental picture of what's going on. We'll identify the known and the unknown quantities and plot a strategy for getting from the known to the unknown. In this problem, the strategy plotting in the organization of known information is best done with a free body diagram, like you see here on this page. What I know about our object is it's a wagon with a mass of 23 kilograms, and it's being moved up the hill at a constant speed. Now, the fact that it's being moved in the same direction at the same speed means that all the forces must be balanced, that the net force is zero and the acceleration is zero. As you see on the diagram, there's three forces acting upon an object. There's the force of gravity, there's the normal force, and there's the applied force. These three forces have to balance each other out. Now, it's difficult to see that they're balancing when you have the gravity force not going in the same or the opposite direction of the other two forces. What we typically do is we take a force like gravity and we resolve it into components, components which are parallel to the inclined plane and perpendicular to the inclined plane. Equations for finding the components of the force of gravity are given on the overview page. First, we want to go m times g to get the force of gravity value. 23 times 9.8 is 225.40 newtons. That's the force of gravity, the down force. But what I want to do is find the parts of this force that are parallel and perpendicular to the plane. To find the perpendicular component, I would go this mg value, 225.40 newtons, and multiply it by the cosine of 16 degrees. That gives me 216.67 newtons, and that's the perpendicular component of the force. The normal force will balance this, and it's really inconsequential to the solution of the problem. Now I need to find the parallel component of the gravity force, and I do that by going mg of 225.40 newtons multiplied by the sine of 16 degrees. That gives me 16.13 newtons. That's the force of gravity that pulls the cart down the hill, and what we wish to do is determine the force that must be applied up the hill in order to pull the child and the wagon at a constant speed. So the force must be 62.13 newtons to balance the parallel component of gravity, and that would be your answer.