# 12.3.1: Friction Forces and Equilibrium

- Page ID
- 17819

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

## Friction Forces and Equilibrium

### Materials:

- lab sheet and writing untensil
- calculator
- small board, box, book, or other object to slide across the table
- string
- pulley with clamp
- set of known masses
- spreadsheet and graphing software
- force sensor + computer with control and analysis software

### Observation

We observe that it is more difficult to start an object sliding than it is to keep it sliding.

### Question

Why is it that more force is required to start an object sliding than is required to keep it sliding?

### Search Existing Knowledge

Find an equation that shows what factors the frictional force depends on. Write it down below and list your source.

### Hypothesis

You should have found that frictional force depends on the static and kinetic friction coefficients. Provide a hypothesis about which is larger. Explain how you used your observation and the information you found to inform your hypothesis.

### Test

To test your hypotheses we determine the static and kinetic friction coefficients between an object and the table.

Our method will be to use the force sensor to measure the weight of the object. Then use the force sensor to measure the force needed to slide the object, and keep it sliding at the same speed. Be sure to **zero the force probe** in the orientation you will use it before making each one of your measurements.

Use the string to hang your object from the force probe and record the weight of your object here:________________.

Use the concepts of tension force and static equilibrium to explain how you know that the reading on the force probe was equal to the weight of the object.

What is the normal force on the object from the table when it is sitting on the table? Explain how you know using the concept of static equilibrium.

Does the normal force change if the book is sliding across the table? [Hint: Does the book ever start moving vertically?]

Now you will use the string to connect the object to the force probe and then gradually increase how hard you pull horizontally on the object until it finally begins to slide. After it begins to slide, keep pulling the object at a constant speed for at least five seconds. Practice this a few times before you begin taking data.

Now that you have practiced, zero the force probe in the horizontal orientation that you will pull, and record the force measured by the probe while you pull horizontally on the object until it finally begins to slide and continues at a constant speed for at least five seconds.

Record the maximum force registered by the force probe:_______________

This is the size of the maximum frictional force applied before the object started to move, or the static frictional force. Explain how the concept of static equilibrium tells us that the maximum reading on the probe is the static frictional force.

Use the static friction force and your known normal force from above to calculate a static friction coefficient. Show your work.

Record the average force registered by the force probe after the object started to slide:_______________

You pulled the book with a constant speed and direction so it was in dynamic equilibrium and the forces must be balanced. Therefore the pull force you measured with the force probe must have been equal to the kinetic frictional force.

Use the kinetic friction force and your known normal force from above to calculate a kinetic friction coefficient. Show your work.

Repeat the experiment 6 more times, calculating a static and kinetic friction coefficient each time. Create a chart to keep track of your data. You may want to create a spreadsheet to calculate the coefficients from the force measurements so that you don’t need to do it by hand each time and because you will be calculating average and standard deviations of your measurements.

Calculate the average static friction coefficient and average kinetic friction coefficient and record these below:

Also calculate a standard deviation for each set of coefficient measurements. Record this below:

Using the standard deviation as the uncertainty in your measurements, do the average static and kinetic coefficients differ by more than the uncertainty? Explain.

### Conclusion

Do you conclude that the static coefficient is larger, the kinetic coefficient is larger, or they are the same? Explain.

Was your qualitative hypothesis correct? Explain.