Newton's Laws Legacy Problem #23 Guided Solution

Physics students often view physics problems as mathematical exercises, and indeed they are mathematical exercises. And oftentimes such students even view their difficulties with physics problems as being mathematical in nature. But for certain, many times the problems are conceptual in nature. And in this problem, that's likely the case if you're having difficulty solving it. What we observe is that Alejandra is attempting to drag her golden retriever across the wooden floor, and she does so at a constant speed of 0.95 meters per second. So the big concept in this problem that must be applied is that if an object's moving in a straight line at a constant speed, then all the forces on the object are balanced. And here for this golden retriever, there are four forces. There's always the gravity force. That's downwards. There's the normal support force, which is directed upwards. There's the applied force on the dog, which is exerted forwards. And there's the friction force, which is exerted backwards. Now the force we wish to determine is the forward applied force. And that forward applied force is balanced by the backwards friction force. We know that the coefficient of friction, what we commonly call mu, in the equation F frict equals mu F norm, that mu value is 0.72. If we can determine the friction value, we can determine the applied force, because it's got to be the same if all the forces balance. So how do you determine this friction force? You simply find the normal force and multiply it by the coefficient of friction. Well, how do you find the normal force? Once more, you go back to your concept. All the forces balance, meaning the up is equal to down and the right is equal to the left. So the up force, the normal force, is equal to the down force, the force of gravity. And that can be calculated if you know the mass. F graph equals m times g, where the m is 32.6 kilograms and the g is 9.8 newtons per kilogram. So once you get the gravity force, the normal force up is the same value as F. And once you get the normal force, the friction force can be calculated as mu 0.72 times F norm. Now that you've found the friction force, the applied force is the same value, and you have your answer. Now if you think about what we just did there, we thought through the problem conceptually, thinking in terms of the forces acting up on the object in a free body sort of diagram depicting those forces. It wasn't a strangely difficult mathematical exercise that involved a few equations. The equations we figured out by having a conceptual understanding of the situation.