Newton's Laws Legacy Problem #27 Guided Solution

A good problem solver typically approaches every problem the same way. They read the problem. They develop a conceptual and mental picture of what's going on. They identify what they know and what they're looking for. And they take the time to plot a strategy to get from the known information to the unknown information. Here we read about Dexterious, who's running to the cafeteria, slips on some mashed potatoes, he falls in a puddle of milk, and he skids to a stop. What our picture is, is of a person sliding across the floor and slowing down due to friction. Now I can presume that he's moving to the right, and therefore the friction acts to the left. And I'm focusing not on the running motion, but the skidding to a stop motion in the puddle of milk. And so I draw a free body diagram representing the forces acting upon old Dexter. There is a downforce of F-graph. It is 780 Newtons. I know that because in my mind I have this conceptual understanding that the weight of an object is equal to the force of gravity, which acts upon it. And so I know the downforce is 780 Newtons. There's also a support force of the floor pushing up on Dexter. That's called the normal force. So I draw an arrow up, I label it F-norm, and I know its value. It's 780 Newtons, because when an object doesn't accelerate up nor down, those up-down forces balance each other. That is, they are equal in magnitude and opposite in direction. Finally, there's the friction force, the only other force in this situation. There's no forward force. There was when he was running, but now that he's on the floor skidding, there's no more forward force. So the acceleration is 4.8 meters per second per second, and it's caused by this friction force. The friction force is the net force, and there's no other force to balance it out. So what we wish to do is we wish to determine the coefficient of friction, and the only way you can determine that mu value is to find out the friction force value. And so to get the friction, or the net force, which friction is equal to, we'll have to go M times A. But where's the M? It's missing in this problem. But fear not, because we know that the weight of the object equals mg. So take the 780 Newton weight, set it equal to mg, where g is 9.8 Newtons per kilogram, and solve for the value of M. Once you get your M, you can solve for F net as MA, and once you get your F net, you've determined the friction force. What good will that do you? Well, if you know the friction, and you know the normal, you can use the equation F friction equal mu times F norm. This problem represents a good example of how I follow the habits of a good problem solver. I read the problem, I identified known and unknown information, I constructed a diagram to represent the situation, and I thought through relationships between quantities in order to plot a strategy to get from known quantities to unknown quantities.