In Investigation Four, the force of friction is measured by pulling an object along a surface using a spring scale. Students will discover that rougher surfaces and greater weight both increase frictional force.

Figure 4.1a shows a box. Its mass is pulled downward by the force of gravity. This results in the normal contact force acting in the exact opposite direction of gravity. By pulling (Figure 4.1b) or pushing (Figure 4.1c) an object at a constant speed, the forces are balanced. The vertical forces of gravity and the normal contact force are balanced. If the pull or push force is greater than the force of friction, the object will speed up in the direction of the pull or push force. If the force of friction is greater than the pull force, the object will slow down or not move.

If the object is moving at a constant speed the horizontal forces must be balanced, hence the force reading on the spring scale (pull force, Figure 4.2, below) must be equal in size and opposite in direction to the force of friction. This provides a technique to measure the frictional force between an object and any surface. As the foregoing demonstrates, it is vital that the object is not speeding up or slowing down when the spring scale force is read, otherwise, the reading will not provide a measurement of the force of friction.

Coefficient of Friction

The equation for friction shows that frictional force (F_f) is dependent on two factors: the coefficient of friction (μ) and normal contact force (R).

F_f = μR

Furthermore, the equation is in the form of a straight line, which indicates that frictional force is directly proportional to the coefficient of friction, and the normal contact force. In other words, if the coefficient of friction is doubled, the force of friction is doubled. If the normal contact force is doubled, the force of friction is doubled. The coefficient of friction (μ) is a unitless number between 0 and 1, with higher values indicating greater interaction between two surfaces. The coefficient of friction (μ) of rubber on concrete and steel on steel is shown in Table 4.1 below:

Notice, in Table 4.1, how drastically the coefficient of friction drops for rubber on concrete under wet conditions (from μ=1.0 to μ=0.2). This indicates that rubber tires on a dry road provide a great deal of frictional force when the breaks are applied. Breaking under these conditions causes the vehicle to slow down or stop rapidly. However, on the exact same road, when wet with rain, the coefficient of friction drops so much that the application of the breaks may result in sliding on the wet surface rather than slowing down or stopping.

The frictional force between steel surfaces is important in engines where steel parts rapidly move in contact with each other. Typically, one wants to reduce the amount of friction between moving metal parts of an engine. This is why we add oil to our automobile engines.

In this Investigation, a woodblock is pulled across the lab bench, masking tape, and sandpaper surfaces which give increasingly greater values of coefficient of friction. These values will only be correct for the woodblock used. If the block pulled across these surfaces was a different material (steel or rubber, for example), then the friction would differ as well. Notice that the coefficient of friction is a property of a combination of two surfaces.

Sometimes it is important to increase the coefficient of friction, such as through cleats on soccer, football, and baseball shoes. This provides the athlete with a greater frictional force for speeding up, slowing down, or changing direction. As the athlete pushes backward against the ground the frictional force with the ground pushes the athlete forward. If the frictional force was too low, the athlete’s foot would slip.

In other sports situations, it is advantageous to minimize frictional force, so that it does not slow a person or object down. For example, snowboards and ice skates have equipment that provides a low coefficient of friction with the snow and ice respectively. Modern competition swimsuits are made of or coated with materials that have very low coefficients of friction to decrease frictional force between the swimmer and the water. Skis and snowboards also wish to reduce frictional force. Waxes of various types are applied to ski and snowboard surfaces for this purpose. In each of these cases, the point of reducing friction is, of course,  to increase the speed of the athlete.

Normal Contact Force

The normal contact force also influences the force of friction. The greater the normal contact force the greater the force of friction. In many circumstances, the normal contact force is equal to the weight of the object. Students will learn that increasing weight leads to greater friction force. However, there are circumstances where the normal contact force is not equal to the weight. For example, if you try to move a heavy box by pushing downwards on it at the same time as pushing it towards the right (see Figure 4.5a below), you are increasing the downward force on the desk to be greater than its weight. This will increase the normal contact force, and therefore the force of friction so that the box will be more difficult to slide. Notice that in Figure 4.5a, the normal contact force is the length of the downward push force and force of gravity combined, and therefore greater than the normal contact force of the box alone (Figure 4.5b).

On the other hand, if you lift while pulling the box, you reduce the downward force to be less than its weight and hence decrease the normal contact force (Figure 4.5c). Notice that in Figure 4.5c the normal contact force and the upward pull force, when added together, are equal to the force of gravity, hence the forces are balanced. The frictional force will be less and the box will be easier to slide.

What is not included in the equation for friction is as informative as what is in it. The equation shows that frictional force is proportionally related to the coefficient of friction, and the normal contact force. It also indicates that other factors do not influence frictional force. Some common misconceptions are that frictional force is related to the surface area in contact, and the speed of motion. As these factors are not in the equation they do not influence friction force.

Note to Teacher: This is a perfect opportunity to point out to students that this is an example of how the application of mathematics and formulas to scientific concepts really makes them easier to understand. This is precisely the opposite of what many people think about science. How often have we heard someone say that they like science but can’t do the math?

To test this for yourself, pull an object using a spring scale and vary the surface area of the object. Note that it is important to keep the weight of the object the same, so simply turn the same object onto a smaller/larger side and repeat the friction measurement. Pull the object at different speeds and observe the spring scale reading, but be careful to only record the force when the object is moving at a constant speed. These activities should demonstrate that friction is not dependent on the surface area in contact, or the speed of the object.

In Investigation Four, students will measure sliding friction for a woodblock moving over three surfaces: the benchtop, masking tape, and sandpaper. In addition, the weight of the block will be varied for one of the surfaces.