Mu+Shoe+Lab


 * Lab Title:** Mu Shoe Lab


 * Primary Authors:** Paul and Anna


 * Contributing Authors:** Megan


 * Abstract:** The goal of this experiment was to determine the factors which influence the amount of friction it takes to move a shoe across a table at a constant rate. Two different shoes were used in this experiment: a leather boot and a tennis shoe. By adding weights to the inside of the shoe the force of gravity on them changed, which caused increased applied force values. The normal force and the force of gravity are opposites, and the applied force from pulling the shoe across the table and the force of friction are also opposites.


 * Introduction:** Shoes have different types of soles and weights which affect the amount of friction that it normally acts on them during everyday life. Athletic shoes tend to have rubber soles and treads to resist slipping during running and jumping, while shoes meant for fashion can have lighter soles made of other materials because they're not meant to undergo strenuous physical activity. Additionally, different surfaces can have different amounts of friction: bumpy roads have more friction than an ice rink, for example. Because of this, the surface in the experiment was kept constant throughout so that the results were accurate in determining how the mass of a shoe and the type of shoe affect frictional values. We used a force probe and added weights with masses ranging from nothing to 1 kg inside the shoes.


 * Methods:** The program LoggerPro was used to show the force of gravity on the shoe by hanging it from the force probe and noting the amount of force it read. We knew that this was the same as the normal force, as long as it was a positive value, and we recorded it in our data table. The shoe was then dragged across the surface of the table at a constant speed and pulled by either a string that was wrapped around the shoe or by the shoelace. In both methods we made sure to pull the shoe so that the string or shoelace was parallel to the surface of the lab table. While pulling, the applied force that the force probe read was noted. Like before, we knew that this was the same value as the force of friction in the opposite direction, so we made sure that we recorded it in our data table as a positive value. After we had done this for an empty shoe, a shoe with a 200 g weight, a shoe with a 500 g weight, and a shoe with a 1000 g weight, we switched shoes and repeated the whole process to get new data. After collecting enough data points, Graphical Analysis was used to plot the points on the same graph in two different lines, one for each shoe, and since they appeared to be linear, linear regression was used to find lines of best fit for our data.

Data: The first normal force is the object with no added weight, the second row is the object with an added weight of 200 grams, the third is an added 500 grams, and the last is an added 1 kilogram. Even though new normal force could have theoretically been found after adding the weights, we continued to find them experimentally. For shoe one (Anna's boot): For shoe two (Paul's gym shoe): (again, +0 grams, + 200 grams, + 500 grams, + 1 kilogram). These values were then entered into Graphical Analysis to find the line of best fit for the data:
 * Results:**
 * Weight Added (g) || Normal Force (N) || Force of Friction (N) ||
 * none || 4.25 || 0.6 ||
 * 200 || 6.1 || 1.0 ||
 * 500 || 8.3 || 1.5 ||
 * 1000 (1 kg) || 12.45 || 2.6 ||
 * Weight Added (g) || Normal Force (N) || Force of Friction (N) ||
 * none || 3.845 || 2.1 ||
 * 200 || 5.8 || 2.8 ||
 * 500 || 8.4 || 5.2 ||
 * 1000 (1 kg) || 12.322 || 8.3 ||

The slope for trial one was 0.2450, and the slope for trial two was 0.7592. The slope is the ratio of the force of friction to the normal force on the shoe. In general the shoe from trial one had a larger normal force than the shoe from trial two. So this means that the force of friction should be greater for the shoe from trial one. However, this is not the case, even when the shoe from trial one had a normal force of 12.5 N the shoe from trial two had a larger force of friction with a normal force of only 5.8 N. This means that there must be some other factor, and there is. The other factor affecting the shoes were the treads on the shoes. Treads increase the force of friction by making the bottom of the shoe less smooth and more jagged so it can catch onto the ground more. The shoe from trial one had barely any treads and was easily pulled across the table. However the shoe from trial two had a lot more treading on the bottom, and this treading is a possible factor that could have increased the force of friction without affecting the normal force.

1. The investigation with the first shoe was different than the one with the second shoe because we used a slightly different method to pull the shoes because of their shape. Also, obviously, the two different shoes gave back very different data. 2. The slope of the graph represents the ratio of the change in frictional force to the change in normal force, which is represented by the Greek letter μ (mu). This is also known as the coefficient of friction or the percent "stickiness". As the slope increases, the percent "stickiness" also increases. 3. To maximize the force of friction the surface may be changed to a rougher surface. Also, additional weights can be added to the shoe and it is best if the shoe had good grips on the bottom of them to grip the surface. For example, sandals would not suffice on a soccer field, but soccer cleats have grips on the bottom so they can dig into the ground and have a strong force of friction. To win tug-of-war, it would be helpful to choose a gravelly surface to play on, and wear heavy, rubber-soled athletic shoes with treads on the bottom. 4. Assuming the person has a mass of 60 kg, it would take 143.58 N to move this person in the first pair of shoes (boots) and 445.26 N to move this person in the second pair of shoes (gym shoes). These numbers were calculated using the lines of best fit for the graphs of the data for each shoe.
 * Analysis Questions:**


 * Conclusion:** Through the experiment, it is found that the factors which affect the amount of friction on a shoe are the weight of the shoe, the material of the sole and whether or not it has treads, and the surface of the ground (inferred from physics observation throughout life). To to increase the amount of friction needed, one should increase the weight of or inside the shoe, increase the treading, use rubber soles, or roughen the surface along which the shoe is dragged. These factors will make a significant impact on the amount of friction on a shoe based on the results in this lab.