Everyday Forces

We talked about weight in the lesson in inertia. Weight is the force produced when gravity acts on an object. Specifically, F=ma becomes F=mg, where g is the constant of acceleration due to gravity. Weight, in the SI system is measured in Newtons (after all, it is a force). In the British system, we measure weight in pounds.

When we draw a free-body diagram of weight, we always point weight straight down towards the center of the earth (or moon, or whatever.)

If the object is on an inclined plane, as shown to the right, the weight vector still points straight down. However, we may find it convenient to establish a different x-y axis plane and break the weight vector into different components to find forces down the plane (parallel to the plane) and on the plane (perpendicular to the plane).

Normal (Perpendicular) Force is a difficult force to understand. It is a contact force and is only present when two objects are in contact. It is the result of Newton's third law. When an object is placed on the floor, it pushes on the floor with the force of the object's weight. But from the third law, we also know that the floor pushes back on the object with the same force. This is the normal force (FN). Consider the free body diagram of an object on the floor (left). The force exerted by the object on the floor is mg, its weight. But there is a normal force exerted by the floor on the object. What is it? From the force body diagram, we add all of the forces, calling "up" positive and applying the second law:

Since there is no acceleration of the object, FN - Fg = 0, or FN = Fg. Thus, the normal force equals the weight of the object. In the picture at the left, we have a slightly different example with a ball on an inclined plane. Here, we have tilted the X-Y coordinate plane so the x-axis is parallel with the surface of the incline. As stated above, gravity still pulls straight down. Since the object is not bobbing up and down in the y-direction, there is no acceleration in that axis and the normal force is equal to the component of gravity in the y-axis, or

FN = mg cos q. As the angle increases (the plane gets steeper) this force becomes less. You can see this if you place a bathroom scale on flat ground and weigh yourself, then place the scale on an incline and weigh yourself - you will appear to weigh less. This is because the scale reads normal force.

Friction (Ff) is a force that is present when two objects are in contact with each other. It is due to molecular interactions between the two surfaces, and is present, even on very smooth surfaces. Friction is related to the normal force exerted by an object:


where Ff is the force due to friction, FN is the normal force, and m is the coefficient of friction. There are two types of coefficients, ms and mk. ms is the static coefficient of friction and is present when there is no motion between two objects. It is generally higher than mk, which is the kinetic coefficient of friction. This is the friction between two objects when there is motion and is one reason it is harder to get something starting to move than it is to keep it moving. The force of friction always opposes the direction of motion.

There are other forces that we encounter in our lives - forces from electric and magnetic fields, air resistance (drag), springs, tension on ropes, and many more. These are all forces that we will use in our problem solving, but the fundamental rules remain the same. Draw a free-body diagram, determine what forces are acting on the object and the  directions the forces are acting in, and use Newton's second law to relate forces in an axis to motion in that axis.

A note on drag. Drag is a really important force when we are dealing with the movement of objects in anything but a vacuum. Drag depends upon many variables, but two of the biggest are the surface area perpendicular to the motion and the velocity. In fact, the force of drag increases with the square of the velocity (in other words, if an object doubles its speed, the force of drag goes up by a factor of four!) This is one of the reasons that your gas mileage in your car really starts to go down as you go faster. One major effect of drag is that, in reality, falling objects do not generally accelerate past a certain point. As the velocity of the object increases, so does the force of drag on the object (opposing the force of gravity on the object) and eventually these two forces balance so that acceleration on the object is zero. When this happens, we reach something called terminal velocity.

Having said this, for 99% of our problems, we are going to ignore air resistance (drag) in solving the problems. Oddly enough, we will be able to see the effect of drag in some of our labs and we are going to quantitatively ignore it. Trust me - it will make your life easier! But it's still OK to feel cheap about doing it.

Often it is helpful to see what someone else has to say on the topic.

More on everyday forces: