# Sliding Friction

 Materials: Computer and School Network Time Allotment: 4 Class Days

### Purpose:

The purpose of this lab is to analyze the relationships between the variables associated with the frictional forces acting upon a skidding automobile.

### Pre-Lab Analysis:

In this lab, the skidding of a car to a stop will be simulated and a variety of relationships associated with the phenomenon will be explored. Such relationships include:

• the effect of normal force upon the force of friction acting on a skidding car (Part 1).
• the effect of mass or weight upon the acceleration of the car (Part 2).
• the effect of mass or weight upon the skidding distance of the car (Part 3).
• the effect of the coefficient of friction upon the acceleration of the car (Part 4).
• the effect of the coefficient of friction upon the skidding distance of the car (Part 5).

To prepare for the investigation of these relationships, we will begin with an analysis of the physical situation of a car skidding (with wheels locked) across a level roadway to a stop.

1. Draw a free-body diagram showing all the forces (neglecting air resistance) acting upon a rightward-moving car which is skidding to a stop. Label the forces according to type.

2. How do the up and down forces compare to each other for this situation? Explain.

3. State the equation discussed in class which relates the force of friction to the normal force. Define the symbols which you use in your equation.

4. Which force supplies the unbalanced force (i.e., the Fnet) which casues the acceleration (or deceleration) of the car? Explain.

5. Use Newton's second law to help you write an equation relating the acceleration of the car to the coefficient of friction, the weight of the car, and the mass of the car. (Hint: you will need to use some information from the above questions.)

6. Substitute the expression for weight (m*g) into the above equation and simplify.

7. Based on your equation above, do you believe that the accelaration of a skidding car will be dependent upon its ...
1. mass? ______________
2. coefficient of friction? ______________
3. acceleration of gravity? ______________

### Procedure:

To begin this lab:

1. Log on to the student server in the usual manner
2. Open the Multimedia folder; then open the Hypercard application.
3. Once the Hypercard is opened, chose Open... from the File menu.
4. A directory dialogue box should appear. Navigate through the Physics Stacks directory and find the file titled Sliding Friction; open this stack by double-clicking on its icon.

Click anywhere on the first card in order to navigate to the simulation card.

Running the Simulations:

Near the bottom of the monitor are three input fields for entering values for the mass, speed, and the coefficient of friction for a car which is braking to a stop. Clicking on these fields allows the user to enter desired values. Accepted values of mass, speed, and coefficient of friction are:

• Mass: 600 kg to 1400 kg
• Initial Speed: 10 m/s to 30 m/s
• Coefficient of Friction: 0.3 to 1.0 (a unitless quantity)

Clicking on the Run Simulation button will run the simulation with the current values of mass, speed, and coefficient of friction. Once the car reaches the 0-mark, the brakes are applied and the car slows down with the designated acceleration. As the simulation runs, values of acceleration, skidding distance, and force are shown in the top section of the card. Your task involves conducting a systematic study to explore the relationships discussed in the Analysis section above. To accomplish this task you will have to run multiple simulations and systematically vary one of the quantities at a time. Gather data from the top section of the card and record all your data in the tables below. Once you have collected some data, you will have to answer several questions; some questions require the use of the Graphical Analysis program.

### Data Table:

Part 1: Effect of Normal Force Upon the Force of Friction

 Init. Speed = _________ m/s Coefficient of Frict.= ________

 Mass (kg) Normal Force (N) Force of Friction (N) __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________

Part 2: Effect of Car Mass Upon Acceleration

 Init. Speed = ________ m/s Coefficient of Frict. = ________

 Mass (kg) Acceleration (m/s/s) __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________

Part 3: Effect of Car Mass Upon Skidding Distance

 Init. Speed = ___________m/s Coefficient of Frict.= ________

 Mass (kg) Skidding Distance (m) __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________

Part 4: Effect of Coefficient of Friction Upon Acceleration

 Init. Speed = ________ m/s Mass = ________ kg

 Coefficient of Frict. Acceleration (m/s/s) __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________

Part 5: Effect of Coefficient of Friction Upon Skidding Distance

 Init. Speed = ________ m/s Mass = ________ kg

 Coefficient of Frict. Skidding Distance (m) __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________

### Qualitative Analysis:

1. What effect (direct, inverse or none) does varying normal force have upon the force of friction acting upon the car? ________________ Support your answers by making actual reference to the collected data.

2. What effect (direct, inverse or none) does varying mass have upon the acceleration of the car? ________________ Support your answers by making actual reference to the collected data.

3. What effect (direct, inverse or none) does varying mass have upon the skidding distance of the car? ________________ Support your answers by making actual reference to the collected data.

4. What effect (direct, inverse or none) does varying coefficient of friction have upon the skidding distance of the car? ________________ Support your answers by making actual reference to the collected data.

5. What effect (direct, inverse or none) does varying coefficient of friction have upon the acceleration of the car? ________________ Support your answers by making actual reference to the collected data.

### Qualitative Analysis:

1. Determine the mathematical relationship for the data set collected in Part 1 of this lab - the force of friction and the normal force. Use the Graphical Analysis program (on the school's server) to plot force of friction vs. normal force (normal force is plotted along the horizontal axis). Once the data is entered, turn on the Statistics and the Regression Line. (Consult the Graphical Analysis Manual if necessary.) With the statistics turned on, make a note of the COR, the slope and the y-intercept as shown in the bottom of the Graph window.
1. In the space below, write an equation for the data set in slope-intercept form; use the symbol Ffrict for the force of friction and the symbol Fnorm for the normal force.

2. Print your graph (with Statistics showing) and include with your lab report.

3. Propose what physical quantity the slope of the line represents. Support your answer with good reasoning.

2. Survey your data for Part 4 of this lab. What is the relationship between the coefficient of friction and the acceleration of a skidding car? State the relationship and explain why it exists using information from the Pre-Lab Analysis section.

3. Does the relationship between coefficient of friction and skidding distance (Part 5) appear to be linear to the -1 power or linear to the -2 power?________________ To find out, use the Graphical Analysis program (on the school's server) to plot distance vs. coefficient of friction (coefficient of friction is plotted along the horizontal axis). Once the data is entered, raise coefficient of friction to the -1 power. (Consult the Graphical Analysis Manual if necessary.) With the statistics turned on, make a note of the COR as shown in the bottom of the Graph window. Now raise the coefficient of friction to the -2 power. Compare the COR of the new graph with that of the old. Print your two graphs (with Statistics showing) and include with your lab report. Now make an exhaustive explanation of the original question, using your graphs to support your answer.

### Conclusion:

Use several well-written and complete sentences to summarize the relationships disconvered in this lab.