Prelab Preparation

Cut the sandpaper into 12" long strips.

Safety Precautions

The materials in this lab are considered nonhazardous. Please follow all laboratory safety guidelines.

Disposal

All materials may be saved and stored for future use.

Lab Hints

• This laboratory activity can be completed in two 50-minute class periods. It is important to allow time between the Introductory Activity and the Guided-Inquiry Activity for students to discuss and design the guided-inquiry procedures. Also, all student-designed procedures must be approved for safety before students are allowed to implement them in the lab. Prelab Questions may be completed before lab begins the first day, and analysis of the results may be completed the day after the lab or as homework. An additional lab period would be needed for students to complete an optional inquiry investigation (see Opportunities for Inquiry in the Further Extensions section).
• To measure static friction, pull the spring scale or force sensor gently, and subtly increase the force, until the block just begins to move. The reading taken just prior to the first sign of motion should be used to calculate the static friction. To decrease the random error inherent to this approach, increase the number of trials and average the results. If time permits, carry out standard deviation calculations to assess precision.
• To measure sliding friction, pull the spring scale or force sensor with enough force to promote constant velocity motion in the sliding object. The coefficient of friction may be calculated using the near constant value read from the spring scale or sensor.
• Small loops of thread may be tied to the eyebolts to make it easier to keep the force sensor or spring scale parallel to the table.
• It may be helpful to do some survey work before beginning the experiment proper. Practice pulling the spring scale or sensor with enough constant force to move the object at constant speed. How much space is needed? Would marking the table with masking tape to denote distance help?
• Data will vary depending on the smoothness of the tabletop. If the tabletop is too smooth to obtain good results, have students tape a sheet of notebook paper to the tabletop.
• If manufactured masses are not available, other objects, such as books, can be used as substitutes.
• If the spring scale measures in grams instead of Newtons, students should multiply their measurement in grams by 0.0098 to obtain the force in Newtons.

Teacher Tips

• This lab provides a unique context for discussions about accuracy and precision. Point out to students that the accuracy of the experimental coefficients of friction cannot be assessed because “true” values do not exist. In contrast, point out that precision may be assessed via standard deviation calculations because students can carry out limitless trials. Increasing the number of trials can mitigate the random error inherent to this type of investigation. Moreover, students may compare readings generated by different groups. If one group reports values significantly different than the other groups’ values, systematic error with the spring scale or procedure should be suspected.

Further Extensions

Opportunities for Inquiry

The coefficients of friction of everyday objects such as textbooks, calculators, and smartphones may be measured following the procedures in this investigation. In addition, the procedures detailed herein may be adapted to suit an inclined plane.

Alignment to Curriculum Framework for AP^® Physics 1

Enduring Understandings and Essential Knowledge
Classically, the acceleration of an object interacting with other objects can be predicted by using a = ΣF/m. (3B)
3B2: Free-body diagrams are useful tools for visualizing forces being exerted on a single object and writing the equations that represent a physical situation.

At the macroscopic level, forces can be categorized as either long-range (action-at-a-distance) forces or contact forces. (3C)
3C4: Contact forces result from the interaction of one object touching another object, and they arise from interatomic electric forces. These forces include tension, friction, normal, spring, and buoyant.

Learning Objectives
3B2.1: The student is able to create and use free-body diagrams to analyze physical situations to solve problems with motion qualitatively and quantitatively.
3C4.1: The student is able to make claims about various contact forces between objects based on the microscopic cause of those forces.
3C4.2: The student is able to explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and that they therefore have certain directions.

Science Practices
3.1 The student can pose scientific questions.
3.2 The student can refine scientific questions.
3.3 The student can evaluate scientific questions.
4.1 The student can justify the selection of the kind of data needed to answer a particular scientific question.
4.2 The student can design a plan for collecting data to answer a particular scientific question.
4.3 The student can collect data to answer a particular scientific question.
4.4 The student can evaluate sources of data to answer a particular scientific question.
5.1 The student can analyze data to identify patterns or relationships.
5.3 The student can evaluate the evidence provided by data sets in a particular scientific question.
6.1 The student justify claims with evidence.

Answers to Prelab Questions

1. A box of mass m is dragged across a floor by a 50.0 N force, parallel to the floor. The box is accelerating at a rate of 3.00 m/s².
   1. Draw a free-body diagram of the box assuming the floor is frictionless.
      {13784_PreLabAnswers_Figure_1}
   2. Calculate the mass m of the box.
      {13784_PreLabAnswers_Equation_1}

      50.0 N = m x 3.00 m / s²

      {13784_PreLabAnswers_Equation_2}
2. The same box now encounters a rough surface and moves with a constant velocity.
   1. Draw a free-body diagram of the box, and identify the force opposing the motion.
      {13784_PreLabAnswers_Figure_2}

      The force opposing motion is sliding (kinetic) friction.

   2. Determine the coefficient of friction between the box and the surface.
      {13784_PreLabAnswers_Equation_3}

      a = 0 m/s²

      {13784_PreLabAnswers_Equation_4}

      F = f_kF = μ_k x NF = μ_k x mg

      {13784_PreLabAnswers_Equation_5}
3. The same box is then pulled over an especially rough surface and comes to a stop. The pulling force is still applied and the box does not move.
   1. Draw a free-body diagram of the box, and identify the force opposing the motion
      {13784_PreLabAnswers_Figure_3}

      The force opposing motion is static friction.

   2. The applied pulling force is increased to 70.0 N. The box remains stationary. Determine the coefficient of friction between the box and the floor.
      {13784_PreLabAnswers_Equation_6}

      a = 0 m/s²

      {13784_PreLabAnswers_Equation_7}

      F = f_sF = μ_s × NF = μ_s x mg

      {13784_PreLabAnswers_Equation_8}
   3. The applied pulling force is steadily increased. Just before the box moves forward, the force is recorded to be 144.0 N. Determine the maximum coefficient of friction between the box and the surface.
      {13784_PreLabAnswers_Equation_9}

      a = 0 m/s²

      {13784_PreLabAnswers_Equation_10}

      F = f_{s, max}F = μ_{s, max} x NF = μ_{s, max} x mg

      {13784_PreLabAnswers_Equation_11}
4. The same box is being pulled by a force, F, at an angle, θ, above the horizontal, across a rough surface at a constant velocity.
   1. Draw a free-body diagram of the box.
      {13784_PreLabAnswers_Figure_4}
   2. Identify the forces acting on the box in the x- and y-axes.

      In the x-direction, the forces acting on the box are the x-component of the force, F, (to the right) and kinetic friction in the opposite direction (to the left). Because the box is moving with a constant velocity (not accelerating), these forces are equal: F_x = F_f.
      In the y-direction, the forces acting on the box are the weight (mg), the normal force (N), and the y-component of the force, F. The weight is acting downward, while the normal force and y-component are acting upward. Because the box is not accelerating in the y-direction, the forces are equal: mg = N + F_y.

   3. Will the frictional force increase or decrease as θ is increased from 0° to 45°? Explain your reasoning.

      The force of friction will decrease as the angle of the pull force, θ, increases. As the angle increases, the y-component of the pull force increases. Consequently, the normal force, N, decreases, because N = mg – F_y. There is a direct relationship between the normal force and frictional force, F_f = μ_k x N. So as the normal force decreases, the frictional force decreases.

5. Considering your answers to Prelab Questions 2, 3 and 4, and the provided materials, write a procedure for how you would determine the coefficient of kinetic (sliding) friction and the coefficient of static friction. Be sure to define the conditions of the system in your procedure.

   To measure static friction: A spring scale or force sensor is attached to the wood block. The scale or sensor should read 0 N before any force is applied to the block. A force is slowly and gradually applied, parallel with the tabletop, until the block jerks forward and slides. The force measured immediately before the block moves is the static friction force. Trials should be repeated until the maximum force is consistent. The coefficient of friction can then be calculated using Equation 1 and the mass of the block.
   To measure sliding (kinetic) friction: A spring scale or force sensor is attached to the wood block. The scale or sensor should read 0 N before any force is applied to the block. A force is applied, parallel with the tabletop, until the block moves forward at a constant velocity. When the block is moving at a constant velocity, the applied force and friction force are equivalent. Trials should be repeated until the measured force is consistent. The coefficient of friction can then be calculated using Equation 1 and the mass of the block.

Sample Data

Introductory Activity 

Analyze the Results Guided-Inquiry Design

Effect of Surface Area

The block from the Introductory Activity is turned onto one of its long edges. The spring scale or force sensor is attached to the eyebolt. The scale or sensor is pulled parallel to the surface of the tabletop.

1. Gradually increase the pulling force until the block moves forward. The maximum force measured before the block moves is the static friction force. The trial is repeated until the maximum force value is consistent. 
2. Apply a pulling force to the block until it moves at a constant velocity. When the velocity is constant, record the force. This corresponds to the sliding (kinetic) friction force. Repeat the trial until the force values are consistent.
   {13784_Data_Table_3}
   Conclusion: When comparing the data collected in the Introductory Activity to the data above, there is little to no difference between the force of friction of the wood block on its flat surface and the edge. This agrees with the general formula for calculating the force of friction: F_f = μN (Equation 1). Surface area is not a variable in the equation. Therefore, surface area does not have an effect on the force of friction.

Effect of Surface Type

The wood block and mirror assembly is used. The spring scale or force sensor is attached to the eyebolt. The scale or sensor is pulled parallel to the surface of the table. The wood side is pulled across the tabletop and a strip of sandpaper. Then the mirror is pulled across the tabletop and a strip of sandpaper.

1. Gradually increase the pulling force until the block moves forward. The maximum force measured before the block moves is the static friction force. The trial is repeated until the maximum force value is consistent.
2. Apply a pulling force to the block until it moves at a constant velocity. When the velocity is constant, record the force. This corresponds to the sliding (kinetic) friction force. Repeat the trial until the force values are consistent.
   {13784_Data_Table_4}
   {13784_Data_Table_5}
   Conclusion: When comparing the friction forces of the wood side and mirror side on both the tabletop and sandpaper surfaces, the forces were greater for the wood side. The assumption can be made that the mirror has a smoother surface that interacts less strongly with the tabletop and sandpaper surfaces. The wood has a rougher surface that interacts more strongly with the tabletop and sandpaper surfaces. The data can be generalized that smoother surfaces have smaller frictional forces when compared to rougher surfaces.

Effect of Adding Weight

The block from the Introductory Activity is laid flat on the tabletop. The spring scale or force sensor is attached to the eyebolt. The scale or sensor is pulled parallel to the surface of the tabletop. Masses are added in 100-g intervals up to 500 g.

1. Gradually increase a pulling force until the block moves forward. The maximum force measured before the block moves is the static friction force. The trial is repeated until the maximum force value is consistent.
2. Add a 100-g mass to the top of the block. Repeat step 1.
3. Add a total mass of 200-g through 500-g to the top of the block in separate trials. Repeat step 1 for each additional mass.
4. Apply a pulling force to the block until it moves at a constant velocity. When the velocity is constant, record the force. This corresponds to the sliding (kinetic) friction force. Repeat the trial until the force values are consistent.
5. Add a 100-g mass to the top of the block. Repeat step 4.
6. Add a total mass of 200-g through 500-g to the top of the block in separate trials. Step 4 is repeated for the individual masses.
7. Graph the data as “Frictional Force vs. Weight Added” for static friction and kinetic friction.
   {13784_Data_Figure_1}
   Conclusion: When additional mass is added to the wood block, the force of friction increases. This is true of both static and kinetic friction. These observations are consistent with the general formula for calculating the force of friction: F_f = μN (Equation 1). As mass is added to the block, the weight of the block increases, thereby increasing the normal force of the block. As the normal force increases, the friction force increases. The slopes of the trendlines are the coefficients of static and kinetic friction. The coefficients are the ratio of the frictional force to the normal force. The value of the coefficient of static friction is 0.23. The value of the coefficient of kinetic friction is 0.18.

Answers to Questions

Guided-Inquiry Discussion Questions

1. Explain, in your own words, the cause of friction between the surfaces of two touching objects.

   When two objects come into contact, surface irregularities interact. At the molecular and atomic scale, the ridges and projections can interlock causing the two objects to stick together. It requires a certain amount of force to overcome the attraction of the ridges and projections. This force is friction. A smoother surface will have less ridges and projections, thereby decreasing opportunities for surface interactions. A rougher surface will have more ridges and projections, thereby increasing opportunities for surface interactions.

2. Based on the equations provided in the Background for calculating the forces of static and kinetic friction, explain the mathematical relationship between the normal force, N, and friction force, F_f.

   The relationship between the normal force, N, and the friction force, F_f, is a direct relationship. As the normal force increases, the friction force also increases by a certain factor. That factor is the coefficient of friction, μ, between the two surfaces.

3. Expanding on your answer to the previous two questions, predict and explain how the following physical factors affect the force of friction.
   1. Large versus small surface areas of equal mass.

      Based on Equation 1 and the direct relationship between the normal force and friction force, surface area will not have an effect. Surface area is not a variable in Equation 1 and does not affect the weight (normal force) of an object.

   2. Large versus small masses of equal surface area.
   3. A large mass will exert a greater normal force than a small mass. The direct relationship between the normal force and friction force indicates that as the mass of an object increases, the friction force it experiences will also increase.
   4. Rough surface versus smooth surface of equal mass and surface area.

      The different surfaces affect the coefficient of friction, μ, between the two surfaces. A rougher surface will have a larger coefficient when compared to a smoother surface. With a larger coefficient, the rougher surface will result in greater friction between the two surfaces.

4. Examine the wood block and mirror assembly.
   1. Predict the relative coefficients of friction between the wood block on the tabletop and the mirror on the tabletop.

      The coefficient of friction between the mirror and tabletop will be less than the coefficient between the wood and tabletop. The mirror has a smoother surface and will require less applied force to overcome friction.

   2. Predict the relative coefficients of friction between the wood block on sandpaper and the mirror on sandpaper.

      The coefficient of friction between the mirror and sandpaper will be less than the coefficient between the wood and sandpaper. The mirror has a smoother surface and will require less applied force to overcome friction.

5. Examine the four graphs below of frictional force vs. normal force.
   1. Identify the graph displaying the correct relationship between the force of friction and the normal force.

      Graph III displays the correct relationship (direct). As the normal force increases, the friction force increases as well.

   2. For those graphs not selected, explain why they are incorrect.

      Graph I initially displays a direct relationship between the normal force and friction force. However, the plot levels off and the friction force remains constant with a greater normal force. This does not match the direct relationship.
      Graph II does not display a direct relationship between normal force and friction force. The plot appears more like a squared-function of normal force to friction force.
      Graph IV displays a direct relationship, but the plot starts above the (0,0) point. If the weight of an object is 0 N, then there would be no friction force.

Review Questions for AP^® Physics 1

1. A box of mass m₁ = 2.5 kg rests atop a box of mass m₂ = 3.0 kg. Box m₂ rests on a frictionless surface. Box m₁ is pulled by a 95 N force and slides with friction (μ_k = 0.33) across the top of box m₂. What is the acceleration of box m₂?
   {13784_Answers_Figure_1}
2. A cardboard box with a mass of 10.0 kg is at rest on a ramp with an angle of 25°.
   1. Determine the coefficient of static friction between the box and the ramp.
      {13784_Answers_Figure_2}
   2. A 68.0 N force is applied parallel to the ramp causing the box to move up the incline at a constant velocity. Calculate the coefficient of kinetic friction between the box and the ramp.
      {13784_Answers_Figure_3}
3. A box of mass m = 10.25 kg is at rest on a rough floor. The coefficient of static friction between the box and the floor is μ_s = 0.35. A rope is attached to the box and pulled at an upward angle of θ = 30° with a tension of T = 45 N. Does the box move? If so, what is its acceleration?
   {13784_Answers_Figure_4}
   The box moves with an acceleration of 1.14 m/s².

References

AP^® Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014.

Introduction

In many force and motion problems, friction is often minimized or even ignored. In the real world, there are many practical applications that are used to increase or decrease friction, depending on the desired results. Discover the physical variables that affect the force of friction between two objects.

Concepts

• Kinetic friction
• Coefficient of friction
• Static friction
• Normal force

Background

Friction is created when any two surfaces are in contact with each other. The factors that influence friction include the surface finish (or smoothness), the cohesive and adhesive ability of molecules, and the force holding the surfaces together.

Surface finish is a major contributor to the frictional force. All surfaces, no matter how smooth, have irregularities. Even the smoothest object will still have irregularities at the atomic level because atoms and molecules never bond together to form completely flat surfaces. These irregularities cause a grinding action to occur when two surfaces move against each other. As a result, heat is generated (the moving objects lose energy) and particles are worn away from the materials. Smaller irregularities, or smoother surfaces, produce less frictional force to act against the direction of motion than larger irregularities.

Another contributor to friction is the cohesive and adhesive abilities of the atoms and molecules in the materials. Cohesion is the attraction of like atoms or molecules. When two plates of glass come in contact with each other (with no air pockets), the two pieces nearly “fasten” together. Glass is considered to have a very smooth surface, but it is very difficult to pull or slide the two pieces apart. This is an example of cohesion. Adhesion is the attraction of unlike atoms or molecules. Water droplets clinging to the side of a glass beaker is an example of adhesion. Cohesion and adhesion affect frictional force because, in order to move the object and maintain its motion at the macroscopic level, additional force is required to break the attraction between the surfaces at the atomic level.

The perpendicular force (or normal force) holding two surfaces together is a very important factor influencing the frictional force. The larger the force holding two surfaces together, from gravity or some other outside force, the larger the force of friction. In the case of an object sliding on a horizontal surface, the normal force equals the weight of the object. A mathematical equation for frictional force is as follows, where F_f is the force of friction, μ is the coefficient of friction (Greek letter mu), and N is the normal force.

The coefficient of friction is a unique property used to describe the relationship between the frictional properties of two surfaces in contact with one another and frictional force. This property is based on the first two factors that contribute to friction—the smoothness of the two surfaces and their adhesive or cohesive properties.

There are two different types of friction (and therefore different coefficients of friction). Static friction is the frictional force that initially prevents two surfaces from sliding past each other. Sliding (or kinetic) friction is the frictional force between two surfaces in contact that are moving past each other. Static friction is larger than sliding friction because when two surfaces are in contact with each other and at rest, the tiny irregularities of the two surfaces tend to interlock with each other. Also, the adhesive and cohesive properties can take effect. When the surfaces slide past each other, there is less of a tendency for the surface’s tiny grooves to interlock, and the cohesive or adhesive properties are less effective. Instead, the two surfaces just ride along the outer edges of “bumps” and there is less force acting against the motion. Static friction is the frictional force up to a certain limit. Once that limit is exceeded (by an applied force), the static friction will be overcome, the object will begin to move, and sliding friction will take over.

Experiment Overview

The purpose of this advanced inquiry lab activity is to identify the physical factors that affect the force of friction between two objects. The lab begins with an introductory activity to determine the coefficient of static and kinetic friction between a wood block and a tabletop. Students create and use free-body diagrams to analyze each situation. The procedure provides a model for the guided-inquiry activity, during which students design and carry out experiments to determine variables that influence frictional forces between surfaces. As optional extensions, the coefficient of friction for everyday objects may be found, or students may investigate how the force of friction is affected when an object is on an inclined plane

Materials

Prelab Questions

1. A box of mass m is dragged across a floor by a 50.0 N force, parallel to the floor. The box is accelerating at a rate of 3.00 m/s².
   1. Draw a free-body diagram of the box assuming the floor is frictionless.
   2. Calculate the mass m of the box.
2. The same box now encounters a rough surface and moves with a constant velocity.
   1. Draw a free-body diagram of the box, and identify the force opposing the motion.
   2. Determine the coefficient of friction between the box and the surface.
3. The same box is then pulled over an especially rough surface and comes to a stop. The pulling force is still applied and the box does not move.
   1. Draw a free-body diagram of the box, and identify the force opposing the motion.
   2. The applied pulling force is increased to 70.0 N. The box remains stationary. Determine the coefficient of friction between the box and the floor.
   3. The applied pulling force is steadily increased. Just before the box moves forward, the force is recorded to be 144.0 N. Determine the maximum coefficient of friction between the box and the surface.
4. The same box is being pulled by a force, F, at an angle, θ, above the horizontal, across a rough surface at a constant velocity.
   1. Draw a free-body diagram of the box.
   2. Identify the forces acting on the box in the x- and y-axes.
   3. Will the frictional force increase or decrease as θ is increased from 0° to 45°? Explain your reasoning.
5. Considering your answers to Prelab Questions 2, 3 and 4, and the provided materials, write a procedure for how you would determine the coefficient of kinetic (sliding) friction and the coefficient of static friction. Be sure to define the conditions of the system in your procedure.

Safety Precautions

The materials in this lab are considered nonhazardous. Please follow all laboratory safety guidelines.

Procedure

Introductory Activity

1. Place the wood block without the mirror flat on a tabletop.
2. Attach a Vernier force sensor or spring scale to the eyebolt.
3. Measure the static friction between the block and the tabletop. Perform an adequate number of trials to ensure the accuracy of the measurements. Record the results in a data table.
4. Measure the kinetic (sliding) friction between the block and the tabletop. Perform an adequate number of trials to ensure the accuracy of the measurements and record the results.

   Analyze the Results: Use the collected data to determine the values of the coefficients of kinetic and static friction between the wood block and tabletop.

Guided-Inquiry Design and Procedure

Form a working group with other students and discuss the following questions.

1. Explain, in your own words, the cause of friction between the surfaces of two touching objects.
2. Based on the equations provided in the Background for calculating the forces of static and kinetic friction, explain the mathematical relationship between the normal force, N, and friction force, F_f.
3. Expanding on your answer to the previous two questions, predict and explain how the following physical factors affect the force of friction.
   1. Large versus small surface areas of equal mass.
   2. Large versus small masses of equal surface area.
   3. Rough surface versus smooth surface of equal mass and surface area.
4. Examine the wood block and mirror assembly.
   1. Predict the relative coefficients of friction between the wood block on the tabletop and the mirror on the tabletop.
   2. Predict the relative coefficients of friction between the wood block on sandpaper and the mirror on sandpaper.
5. Examine the four following graphs of frictional force vs. normal force.
   {13784_Procedure_Figure_1}
   1. Identify the graph displaying the correct relationship between the force of friction and the normal force.
   2. For those graphs not selected, explain why they are incorrect.
6. Design a set of experiments to determine the effects of surface area, mass, and surface type on the forces of kinetic and static friction. Write a detailed, step-by-step procedure to determine the effect of each physical factor.
7. Review additional variables that may affect the reproducibility or accuracy of the experiment and how these variables will be controlled.
8. Carry out the experiment and record results in an appropriate data table.

Analyze the Results
Calculate the coefficients of static and kinetic friction for each variable tested: surface area, mass and surface type. Display collected data and calculated values in appropriate data tables. Present the mass added data in graphical form and perform appropriate analysis on the data set. Include a paragraph conculsion summarizing the data and analyses for each variable.

Student Worksheet PDF

13784_Student1.pdf