Forces in 2D Legacy Problem #8 Guided Solution

A good problem solver will read a problem carefully and identify the known and unknown information, and begin to plot out a strategy as to how to get from the known information to the unknown information. Here we're given a problem about Renee who's pulling a 21 kilogram suitcase at a constant speed of 0.47 meters per second. She pulls on a strap with a force of 120 newtons at 38 degrees above the horizontal. It's neither a horizontal force nor a vertical force, but rather an angled force, and what we wish to do is determine the normal force and the total resistance force experienced by the suitcase. Now, you'll see here on this help page a free body diagram listed for you, and it is highly recommended, even if you didn't have this diagram, that you would organize the information in a diagram, a diagram depicting the forces acting upon the suitcase. And here, as we do this, we realize that, right away, that F applied is given, and it's 120 newtons, and the angle theta is given, and it's 38 degrees. We know the mass is equal to 21 kilograms, and we know the net force and the acceleration, even though they do not come out explicitly and tell us that it's such and such a value, we know by the phrase constant speed that the acceleration and the net force is zero. So we know that all the individual forces are going to balance each other. The problem is, at this moment, one of the forces, the 120 newtons at 38 degrees, is in a real nasty direction. So as you can see in the diagram, we need to determine the Fx, the x component of this force, and the Fy value. Finding Fx is a matter of finding the side adjacent to the 38 degrees on the little force triangle you see sketched for you, so that would be using the cosine function. 120 newtons times the cosine of 38 degrees gives me Fx, and that value is 94.56 newtons. Now the forces are balanced, and so that forward, rightward, horizontal force has got to be balanced by the sum of all the resistance forces, air friction and surface friction, and so the resistance force here is 94.56 newtons. Now if we turn our attention to the vertical forces, we can find Fy, the vertical component of the 120 newtons, by finding the side opposite the 38 degrees on the little force triangle. So we go 120 newtons times the sine of 38 degrees to find the side opposite, and it comes out to be 73.88 newtons. You should write all these numbers down as you get them, because you're going to use them in subsequent calculations. 73.88 newtons is Fy, and the F gravity force can be found, as always, by going mass times g, where g is 9.8 newtons per kilogram. When I go to 21 kilograms times the 9.8 newtons per kilogram, I get 205.8 newtons, and that's a down force, and that down force has to balance the sum of the two up forces. One of the up forces is the y component of the 120 newtons. We just calculated that as 73.88 newtons. So to find the normal force, you can say, make a mathematical statement, such as 73.88 newtons plus F norm equal 205.80 newtons. That's a matter of simply saying the two up forces equal the one down forces for a constant speed motion. When you do that, you end up getting 131.92 newtons as the normal force. Both the resistance friction force and the normal force can be rounded to the proper number of significant digits. So we have F friction equal 95 newtons, and F normal equal 130 newtons.