Lab 03: Kinetic and Static Friction

Lab 03: Kinetic and Static Friction

Learning Objectives

Define friction, normal force, coefficient of friction, static friction, and kinetic friction.
Determine the coefficient of static friction using the minimum force required to start motion.
Determine the coefficient of kinetic friction using the force required to maintain constant velocity.
Investigate how added normal force affects friction force and coefficient of friction.
Compare wood-on-wood friction with rubber-on-wood friction.
Determine and interpret $\tan\theta$ for a block sliding at nearly uniform motion on an inclined plane.

Friction is the resistive contact force that acts between surfaces. In this experiment, a block is pulled with a spring balance to measure the force needed to start motion and the force needed to keep motion at constant velocity. The experiment also uses an inclined plane to connect the coefficient of friction with the angle of sliding.

Target Learning Outcome

TLO 3: Define friction, normal force, coefficient of friction, static friction, and kinetic friction; and determine the values of the coefficients of static and kinetic friction experimentally.

I. Discussion of Theory

Friction

Friction is a contact force that opposes relative motion or attempted relative motion between two surfaces. It acts parallel to the surfaces in contact.

Normal Force

The normal force is the perpendicular contact force exerted by a surface on an object. On a horizontal surface with a horizontal pull, the normal force is equal to the total weight supported by the surface.

Weight and normal force

W = mg

N = W_{\text{block}} + W_{\text{added load}}

Variables

Symbol	Description	Unit
$W$	weight	N
$m$	mass	kg
$g$	acceleration due to gravity	$m/s^2$
$N$	normal force	N

Static Friction

Static friction prevents an object from starting to move. It adjusts up to a maximum value. The maximum static friction is measured just before the object begins to slide.

Maximum static friction

f_{s,\max} = \mu_s N

Variables

Symbol	Description	Unit
$f_{s,\max}$	maximum static friction	N
$\mu_s$	coefficient of static friction	dimensionless
$N$	normal force	N

Kinetic Friction

Kinetic friction is the friction force acting on an object that is already sliding. It is usually less than the maximum static friction for the same surface pair.

Kinetic friction

f_k = \mu_k N

Variables

Symbol	Description	Unit
$f_k$	kinetic friction force	N
$\mu_k$	coefficient of kinetic friction	dimensionless
$N$	normal force	N

Coefficient of friction from measured force

\mu_s = \frac{f_s}{N}

\mu_k = \frac{f_k}{N}

Why constant velocity matters

When the block moves at constant velocity, its acceleration is zero. By Newton's Second Law, the net horizontal force is zero. Therefore, the spring balance reading is approximately equal to the kinetic friction force.

Inclined plane relationship

\tan\theta = \frac{V}{H}

For uniform sliding on an incline:

\mu_k \approx \tan\theta

Variables

Symbol	Description	Unit
$\theta$	angle of the inclined plane	degrees
$V$	vertical rise of the plane	cm or m
$H$	horizontal run of the plane	cm or m

Key comparison

For most dry surfaces, $\mu_s > \mu_k$ . It usually takes more force to start an object moving than to keep it moving.

II. Equipment / Materials Needed

Equipment or material	Purpose
Wooden plane	Surface on which the block is pulled or inclined.
Wooden block	Test object for wood-on-wood friction.
Wooden block with rubber sole	Test object for rubber-on-wood friction comparison.
Set of weights	Increases the normal force on the block.
Spring balance	Measures applied pulling force.
Iron stand with cross arm	Raises one end of the plane for the inclined-plane method.
Meterstick	Measures vertical rise and horizontal run of the incline.

Safety and setup reminders

Secure the wooden plane before raising it. Do not allow the block or added weights to slide off the table. Keep hands and feet clear of falling weights.

III. Diagram of Setup

Horizontal pulling setup

          Pulling direction
                ----->

  +-------------------+     +--------------------+
  | Wooden block      |-----| Spring balance     |---- pull
  +-------------------+     +--------------------+
  ________________________________________________
                 Wooden plane / table surface

Inclined plane setup

               raised end
                  /|
                 / | V
                /  |
       block   /   |
        []    /    |
             /theta|
            /______|
                H

Measure V and H, then compute tan(theta) = V/H.

Free-body diagram for horizontal pull at constant velocity

          N (Normal force)
          ^
          |
f_k <-----[]-----> F (Pulling force)
          |
          v
          W (Weight = mg)

At constant velocity: Net force = 0, so F = f_k and N = W.

IV. Procedure

Part A: Wooden block and wooden plane

STEP-BY-STEP

Hang the wooden block on the spring balance and record its weight in Table 3.1.
Place the wooden plane on a table.
Place the wooden block on one end of the wooden plane with the broader surface of the block in contact with the plane.
Connect the spring balance to the wooden block and keep the spring balance horizontal.
Pull the spring balance horizontally and slowly increase the force until the block just begins to move.
Record the minimum force $F = f_s$ needed to start motion.
Repeat the static-friction measurement for three trials and compute the average.
Pull the block so that it moves with approximately constant velocity.
Record the force $F = f_k$ required to maintain constant velocity.
Repeat the kinetic-friction measurement for three trials and compute the average.
Compute $\mu_s = f_s/N$ and $\mu_k = f_k/N$ .
Place a $100\,\text{g}$ load on top of the wooden block and repeat the measurements.
Increase the added load by $100\,\text{g}$ at a time until the total added load is $300\,\text{g}$ .
Record all results in Table 3.1.

Part B: Wooden block with rubber sole and wooden plane

STEP-BY-STEP

Replace the ordinary wooden block with the block that has a rubber sole.
Repeat the same procedure used in Part A.
Measure $f_s$ and $f_k$ for no added load, $100\,\text{g}$ , $200\,\text{g}$ , and $300\,\text{g}$ added loads.
Compute the coefficients $\mu_s$ and $\mu_k$ for each trial.
Record all results in Table 3.2.

Part C: Inclined plane method

STEP-BY-STEP

Place the wooden block on one end of the wooden plane with the broader surface of the block in contact with the plane.
Slowly raise that end of the wooden plane using the iron stand and cross arm.
Adjust the height until the block slides down the plane with approximately uniform motion.
Measure the vertical distance $V$ and horizontal distance $H$ .
Repeat the measurement for three trials.
Compute $\tan\theta = V/H$ for each trial.
Interpret the average value of $\tan\theta$ as an estimate of the coefficient of kinetic friction for uniform sliding on an incline.

Pulling technique

The spring balance should be pulled horizontally and steadily. If the spring balance is angled upward, the normal force decreases and the calculated friction coefficient becomes unreliable.

V. Student Information

Field	Entry
Name
Schedule
Group No.
Date Performed

VI. Data and Results

Table 3.1. Wooden Block and Wooden Plane

Weight of wooden block: ________ N

Added Mass	Trial	Total Normal Force, $N$	Static friction, $f_s$	$\mu_s=f_s/N$	Kinetic friction, $f_k$	$\mu_k=f_k/N$
0 g	1
0 g	2
0 g	3
$100\,\text{g}$ added	1
$100\,\text{g}$ added	2
$100\,\text{g}$ added	3
$200\,\text{g}$ added	1
$200\,\text{g}$ added	2
$200\,\text{g}$ added	3
$300\,\text{g}$ added	1
$300\,\text{g}$ added	2
$300\,\text{g}$ added	3
Overall Average

Table 3.2. Wooden Block with Rubber Sole and Wooden Plane

Weight of rubber-soled block: ________ N

Added Mass	Trial	Total Normal Force, $N$	Static friction, $f_s$	$\mu_s=f_s/N$	Kinetic friction, $f_k$	$\mu_k=f_k/N$
0 g	1
0 g	2
0 g	3
$100\,\text{g}$ added	1
$100\,\text{g}$ added	2
$100\,\text{g}$ added	3
$200\,\text{g}$ added	1
$200\,\text{g}$ added	2
$200\,\text{g}$ added	3
$300\,\text{g}$ added	1
$300\,\text{g}$ added	2
$300\,\text{g}$ added	3
Overall Average

Table 3.3. Wooden Block and Inclined Wooden Plane

Trial	Vertical distance, $V$	Horizontal distance, $H$	$\tan\theta=V/H$	Interpretation
1
2
3
Average

Observation Prompt

What do you observe regarding the value of $\tan\theta$ ? How does it compare with the value of $\mu_k$ obtained using the spring balance method?

Graphing Section

Plotting Friction Data

STEP-BY-STEP

On a sheet of graphing paper or using graphing software, create a plot of friction force vs. normal force.
Place the Normal Force ( $N$ ) on the x-axis.
Place the Friction Force ( $f_s$ or $f_k$ ) on the y-axis.
Plot the data points for static friction and draw a line of best fit. The slope of this line represents the coefficient of static friction ( $\mu_s$ ).
On the same graph, plot the data points for kinetic friction and draw a line of best fit. The slope of this line represents the coefficient of kinetic friction ( $\mu_k$ ).
Repeat this process for both the wood-on-wood and rubber-on-wood data.

Interpreting the Graph

Since $f = \mu N$ , the relationship is linear and passes through the origin (y-intercept is zero). The slope of the line ( $\Delta f / \Delta N$ ) directly gives the experimental coefficient of friction.

VII. Computations

Required computations

STEP-BY-STEP

Convert each added mass to weight using $W=mg$ .
Compute the normal force for each load condition.
Compute $\mu_s=f_s/N$ for each static-friction trial.
Compute $\mu_k=f_k/N$ for each kinetic-friction trial.
Compute the average $\mu_s$ and average $\mu_k$ for each surface pair.
Compute $\tan\theta=V/H$ for each inclined-plane trial.
Compare the spring-balance method and inclined-plane method.
State whether $\mu_s$ is greater than $\mu_k$ based on your measured data.

Sample computation: converting mass to weight

If a $100\,\text{g}$ mass is added to the block, you must convert it to weight (force) in Newtons.

First, convert mass to kilograms: $m = 100\,\text{g} = 0.100\,\text{kg}$

Then multiply by acceleration due to gravity ( $g = 9.8\,\text{m/s}^2$ ): $W_{\text{added}} = mg = (0.100)(9.8) = 0.98\,\text{N}$

This $0.98\,\text{N}$ is added to the block's weight to find the total normal force.

Sample computation: spring balance method

Suppose the wooden block weighs $4.0\,\text{N}$ and the measured force needed to start motion is $1.6\,\text{N}$ .

\mu_s = \frac{f_s}{N} = \frac{1.6}{4.0} = 0.40

If the force needed to keep the block moving at constant velocity is $1.2\,\text{N}$ , then:

\mu_k = \frac{f_k}{N} = \frac{1.2}{4.0} = 0.30

Sample computation: inclined plane method

Suppose the block slides uniformly when the vertical rise is $18\,\text{cm}$ and the horizontal run is $60\,\text{cm}$ .

\tan\theta = \frac{V}{H} = \frac{18}{60} = 0.30

For uniform sliding, this suggests $\mu_k \approx 0.30$ .

Expected Trends

Key Expected Results

Static vs. Kinetic: The static friction force ( $f_s$ ) is generally greater than the kinetic friction force ( $f_k$ ) for the same normal force. Therefore, $\mu_s > \mu_k$ .
Surface Material: Rubber-on-wood typically has a higher coefficient of friction than wood-on-wood.
Normal Force Dependence: The friction force ( $f_s$ and $f_k$ ) increases proportionally as the normal force increases.
Constant Coefficient: The calculated coefficients of friction ( $\mu_s$ and $\mu_k$ ) should remain roughly constant across different normal forces for the same two contact surfaces.

VIII. Error Analysis

Common sources of error

Pulling the spring balance at an upward or downward angle instead of horizontally.
Jerking the block instead of pulling slowly and steadily.
Reading the spring balance while the pointer is oscillating.
Uneven or dirty contact surfaces.
Added weights shifting while the block moves.
Misreading the vertical rise $V$ or horizontal run $H$ in the inclined-plane setup.
Raising the plane too quickly, causing accelerated rather than uniform motion.

Ways to improve accuracy

Keep the pulling force horizontal.
Take at least three trials for every load condition.
Use the average of repeated readings.
Clean the wooden plane and block contact surfaces before testing.
Pull slowly for static friction and smoothly for kinetic friction.
Use the same contact surface orientation for all trials unless intentionally testing area effects.

IX. Observations and Conclusions

Conclusion guide

A strong conclusion should state the average coefficients of static and kinetic friction for each surface pair, identify which surface pair produced greater friction, compare $\mu_s$ and $\mu_k$ , and explain whether $\tan\theta$ from the inclined-plane method agrees with the kinetic-friction result.

Lab Report Format

Your formal lab report should include the following sections:

Objective: State the purpose of the experiment.
Apparatus: List the equipment used.
Theory: Briefly explain the concepts of static and kinetic friction, normal force, and the inclined plane method.
Data: Present the completed tables with all trials and averages. Include your graphs.
Computations: Show at least one complete set of sample calculations (converting mass to weight, computing normal force, $\mu_s$ , $\mu_k$ , and $\tan\theta$ ).
Error Analysis: Discuss potential sources of error and how they might have affected the results.
Conclusion: Summarize findings, stating the final average coefficients and verifying the expected trends.

X. Questions and Problems

A dictionary is pulled to the right at constant velocity by a $10\,\text{N}$ force acting $30^\circ$ upward above the horizontal. The coefficient of kinetic friction between the book and the horizontal surface is $0.5$ . What is the weight of the book?
A sled system is pulled by a rope at $30^\circ$ above the horizontal with a force of $50\,\text{N}$ . The total mass of the sled system is $20\,\text{kg}$ and it is already in motion. Using $\mu_k = 0.02$ , calculate the acceleration.
Using the same sled system, what minimum pulling force is required to start motion from rest if $\mu_s = 0.4$ ?
Why is the coefficient of static friction usually greater than the coefficient of kinetic friction?
Does increasing the normal force increase the coefficient of friction, the friction force, or both? Explain using your data.

Selected Answer Key

Weight of the book $\approx 22.3\,\text{N}$ (Normal force is approx $17.3\,\text{N}$ ).
Acceleration $\approx 1.9\,\text{m/s}^2$ .
Minimum pulling force $\approx 73.6\,\text{N}$ (requires solving the system $F\cos\theta = \mu_s N$ and $N = W - F\sin\theta$ ).

XI. References

Bueche, F. J., & Hecht, E. (1997). Schaum's Outline of Theory and Problems of College Physics (9th ed.). New York: McGraw-Hill.

Instructor note

The original HTML worksheet has been converted into MDX and expanded with theory, formulas, setup diagrams, corrected data tables, computation guidance, error analysis, observation prompts, and additional post-lab questions. HTML-only features such as dark-mode toggles and input fields were converted into printable MDX content that fits the existing CE content renderer.

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