Newton's Laws Legacy Problem #24 Guided Solution

This is an example of a problem that would be abnormally difficult if a student isn't practicing the habits of a good problem solver. In this problem, what we should do is read the problem carefully and get a mental picture of what's going on, and even construct a free body diagram representing the forces acting upon our car. We read about Dawson's Ford Coupe, which is skidding to a stop across the pavement. So our picture is of a car moving across a roadway and slowing down. Let's just suppose for a moment the car is moving to the right as we view it, and it's slowing down. So what we would expect is a leftward net force and a leftward acceleration to cause the slowing down motion. If I were to think of the forces acting upon the car, I would come up with three. Certainly there's a force of gravity, as there always is, straight down. I would draw a picture of a car or a box, and I would draw an arrow straight down, label it F-grab. That's the weight of the object. We know the mass, 1,300 kilograms, so we should be able to calculate the F-grab value as 1,300 times 9.8 mg. Now there's also a support force from the roadway that pushes up upon the car to balance the downward force of gravity. That up force is called F-norm, so I draw an arrow up, I label it F-norm, and its value is the same as F-grab, so if you've calculated F-grab, you have also, in effect, calculated F-norm. Finally, there's the friction force that opposes the motion of this car across the pavement. That's a backwards or leftward force on a rightward moving car. I would draw an arrow to the left and label it F-friction, and what I wish to calculate is the acceleration of our car. Now if you understand Newton's laws, then what you understand is that to calculate acceleration, you must know two things. The net force, which we don't know, and the mass, which is given here as 1,300 kilograms. So how are you going to calculate the net force? Well, as always, you're going to use your freedom of body diagram, and you're going to add up all the forces, and there's three. The ups and the downs are opposite and equal in magnitude, so they add up to zero, which means the only force left is the friction force. The friction force is the net force. So how do you calculate it? Well, as always, friction is mu times F-norm. Mu, the coefficient of friction, is given here as 0.85. The F-norm, you just calculate it. Same as the F-grab value. So go mu times F-norm, and you get your friction force. That friction force is the net force, and if you divide its value by mass, 1,300 kilograms, you get the acceleration. This problem solution was based, again, upon visualizing the situation, drawing a free body diagram, and strategizing how I can get from known values to unknown values. One last comment. There's a shortcut here. Let's just suppose the mass wasn't even given, and what you would have for the down force is M, unknown, times G, whatever that is. The up force would be the same value, MG. The friction force would be mu times MG. Mu times normal, and normal happens to be MG. So your friction force is mu MG, and your acceleration is this friction force value, or net force, mu MG, divided by M. The M's cancel out, and your acceleration is mu times G. When you multiply mu times G, 0.85, times 9.8, you get the same answer you do with my log solution.