### Summary

In the culminating activity of the unit, students explore and apply their knowledge of forces, friction, acceleration and gravity in a two-part experiment. First, student groups measure the average acceleration of a textbook pulled along a table by varying weights (with optional extensions, such as with the addition of a pulley or an inclined plane). Then, with a simple modification to the same experimental setup, teams test different surfaces for the effects of friction, graphing and analyzing their results. Students also consider the real-world applications for high- and low-friction surfaces for different situations and purposes, seeing how forces play a role in engineering design and material choices.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### Engineering Connection

Engineers apply their understanding of gravitational force, friction and acceleration to a variety of design problems. These concepts are key to understanding how friction can impact the movement of objects. Similarly, the understanding how a force applied to an object affects its acceleration help students to understand how forces are important in explaining the movement of objects in everyday situations.

Engineers must consider how forces play a role in their designed systems in order to predict and fine tune the movement of objects involved. For example, when engineering a rocket, engineers determine how much force must be applied by the engine in order to accelerate the rocket and overcome gravitational force.

### Pre-Req Knowledge

Conduct this activity after presenting the three lessons in the What Are Newton's Laws? unit so that students are familiar with the concepts associated Newton's laws of motion, forces, acceleration and weight.

### Learning Objectives

After this activity, students should be able to:

- Explain the impact of friction on the movement of an object.
- Compare acceleration of an object acted on by varying amounts of force.

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###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### NGSS: Next Generation Science Standards - Science

- Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- Compare, contrast, and classify collected information in order to identify patterns. (Grades 3 - 5) Details... View more aligned curriculum... Do you agree with this alignment?

###### California - Science

- Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

Each group needs:

- table or desk
- string, a bit more than 2 meters
- measuring tape, at least 1 meter long
- stopwatch
- textbook that weighs 0.5-0.75 kg (~1-1.7 lbs)
- ~60 cm (~24 in) length of one material; choose from wax paper, plastic wrap, baking parchment paper, aluminum foil (or any other provided by the teacher)
- tape
- plastic soda bottle with cap, 12 oz. (≈ 355 ml), with a small hole pierced in the cap
- room temperature water and sink/drain
- graduated cylinder, to measure water
- tool to pierce hole in cap for string
- graph paper
- Sliding Textbooks Worksheet, one per student
- scale, to weigh the water bottle (class can share a scale, or obtain water bottle weights in advance)
- (optional) calculator
- (optional) pulley with table clamps (see the Activity Extensions section)

### Introduction/Motivation

Newton's second law of motion states that an object's acceleration is dependent on the strength of the unbalanced force acting on it, and the mass of the object. How do we write this mathematically? (Expect students to be able to provide the equation. Write it on the classroom board.) That's right, we write this as F=*m*a, where "F" is the strength of the force acting on the object, "*m*" is the mass of the object and "a" is acceleration. How could we rearrange this equation to be able to use it to calculate acceleration if we know the force acting on the object and the mass of the object? (Listen for student ideas.) That's right, we rearrange it to a=F/*m*.

Many different types of forces can act directly on objects. What are some types of these "contact" forces? (Expect students to know this from previous lessons in the unit.) Examples of contact forces include applied force, spring force, drag force, frictional force and normal force. Other forces act indirectly. What are some examples of those? (Again, expect students to know this.) Some examples are magnetic, electric and gravitational forces.

In real-world situations, usually multiple forces act on objects at the same time. For example, a box sitting on the ground is acted on by a gravitational force downward and a normal force upwards. These forces balance so the box does not accelerate. When an object accelerates forward on the ground that usually indicates that two forces are acting on it. First, an applied force exists, which is a force applied with the intention of moving the object forward. Second, a frictional force exists—from the object's contact with the ground. The resulting acceleration of the object depends on how much greater the applied force is in comparison to the frictional force, as well as the object's mass.

In our everyday lives an analysis of the forces at play in any situation can explain how the objects move and function. For example, the acceleration of an airplane, cruise ship or snowmobile can be explained by the forces applied by the engine, gravity and drag. The acceleration of an electric bicycle can be explained by applied force exerted by the motor through the wheels, friction force and drag force. When designing objects that shoot something (projectiles), like satellite and weather balloon launches, cannons, tranquillizer guns or delicate medicine delivery devices, the amount of force being applied to the object being shot can be adjusted to fine tune the object's acceleration, and thus how far it goes, which, as you can imagine, is often quite important to get precisely correct.

In this activity, we will first explore how the acceleration of a textbook on a table changes with different amounts of applied force. The applied force will come from a weighted bottle hanging off the table. By changing the weight, we can change the applied force. In the second part of the activity, we will explore how different frictional forces from different surfaces affect the acceleration of the textbook.

### Vocabulary/Definitions

acceleration: The amount of change in an object's velocity.

force: A push, pull or twist of an object.

friction: The force resisting the relative motion of solid surfaces or fluid layers.

### Procedure

Background & Overview

Newton's second law of motion helps to explain the movement of all objects—those associated with the engineering world as well as everyday life. This physical law can be used to describe the acceleration of an object based on total force applied and the mass of the object. The equation is commonly written as F=*m*a. Simply put, the more force applied to an object, the faster it accelerates.

The experiments students conduct in this activity demonstrate Newton's second law of motion using a textbook as the object. The activity helps students explore how a change in force applied to an object changes its rate of acceleration. In addition, students explore how friction can affect this motion.

For the experimental setup (see Figure 1), a textbook is placed on a table with a string connecting the book to a weighted soda bottle that hangs off the table edge.

- In Experiment 1, water is added to the bottle, causing the book to move closer to the table edge. Varying the amount of water in the bottle changes the amount of force applied to the book. This can be observed through a calculation of acceleration based on the time it takes the book to move a given distance.
- In Experiment 2, students add some material to the tabletop setup as a "runway," with the intent to reduce the friction imposed on the system. They test and measure to see how a change in surface, and thus a change in friction, affects the acceleration of the book.
- For both experiments, expect students to see a trend of increasing acceleration with increasing weight.
- See the Activity Extensions section for activity variations that involve pulleys, inclined planes and an open-ended "sliding race competition." Using a pulley to modify the setup results in an increase in the acceleration, compared to the non-pulley system.

Before the Activity

- Preparing the activity takes some time, and it is best prepared in advance.
- Gather materials and make copies of the Sliding Textbooks Worksheet.
- Experiment to find the right textbook and water volume(s) to get the intended effect (see the Sliding Textbooks Worksheet Answer Key for example times).
- Decide whether or not to have students involved in preparing the experimental setups; gaining their help during breaks/lunch, or making it part of the experiment procedures makes preparations much easier. Refer to Figure 1 and/or the Sliding Textbooks Experimental Setup Visual Aid for the main experimental setup (with no pulley; both versions also on the worksheet). Follow these steps to prepare an experimental setup for each group (steps also provided on the worksheet).

- Measure 60 cm from the table edge, and place the textbook spine at the 60 cm mark.
- Loop the string around the spine of the book.
- Tie the two ends of the string together just above the bottle cap.
- Pierce a small hole in the middle of the bottle cap, just large enough to thread the string through.
- Thread the string through the top of the bottle cap, and tie a knot to secure it.

With the Students—Experiment 1

- Divide the class into groups of three students each. Have groups assemble at the experimental setups. Hand out the worksheets.
- Direct students to follow the worksheets to guide them in conducting the two-part experimental activity. Help groups set up their experiments correctly and get started. It may help to do the first run as a class. It also helps to either verbally explain or have students read the protocol in advance (individually or as a class).
- In each of the following replications of the experiment, do the following:

- Fill the bottle with the indicated volume of water (125 ml, 150 ml, 175 ml, 200 ml).
- Then screw the cap onto the water bottle, holding the bottle (do not let the bottle hang yet).
- Start the stopwatch at the moment the water bottle is released.
- Stop the watch when the spine of the textbook reaches the 10 cm mark.
- Record the time on the worksheet, along with your observations.

- Time each run (at every volume of water)
*three times*. - Once the activity is underway, circulate around the room to observe and keep students on task. Ask questions to test for comprehension, such as: Why is the textbook (not) sliding? What forces are acting on it? What is the result of unbalanced forces acting upon the textbook?

With the Students—Experiment 2

- Remind students that for Experiment 2, they will explore the effect of different surfaces on the amount of friction exerted on the textbook with the intent to
**reduce the friction**imposed on the system. Tell the students: Your engineering challenge is to determine which material will make the best "runway" so your book can accelerate the fastest. - As a class, brainstorm some real-world situations in which smoother or rougher surfaces may be preferred. What are the best types of surfaces for use in various situations? Write student ideas on the board. In some situations, such as a bowling alley lane, it is beneficial if the material has a low friction surface. In other situations, such as the soles of your shoes, you want materials that provide traction so you do not slip and slide. Other sports examples include curling and tennis; for example, fuzzy tennis balls help rackets create more spin to the balls and high-tech clothing fabrics reduce water and air resistance in competition sports. In most situations, engineers aim for a balance. For example, in designing a highway, some friction between the road material and wheels is essential to enable vehicle tire grip and braking, yet we want the road surface to be smooth enough not to impede overall fuel economy.
- Inform groups of the material options: wax paper, plastic wrap, baking parchment paper and aluminum foil. Then let student groups confer to choose a material and predict (on the worksheet) how they think it will affect the acceleration of the book.
- Direct the groups to tape the chosen surface material to the tabletop to create a smooth textbook "runway"—the area in the path of the textbook movement.
- Use the same book, string and plastic bottle used in Experiment 1.
- Use the same procedures as in Experiment 1, recording on the worksheet the time measurements and observations with the new surface.

Calculations

- Calculate and record the distance from the 60 cm mark to the 10 cm mark. This is distance,
*d*. - Average the times for each trial (A, B, C, D in Experiment 1, and E, F, G and H in Experiment 2). Record the average times in the table on the worksheet.
- Next, use these average times, together with the distance traveled, to calculate the average acceleration using the equation:
*a = 2d/t*, where^{2}*d*is distance and*t*is time.

Results, Analysis and Conclusion

- Weigh the empty water bottle. Knowing that 1 ml of water ≈ 1 gram (at 4 °Celsius, the equation is exact), calculate the mass of the bottle filled with water at each volume of water.
- Answer the worksheet page 4 analysis questions, which are also provided in the Assessment section along with their answers.
- After the activity, debrief students on what they learned about (static and dynamic) friction, acceleration due to gravity, and the relationship between mass and volume of water (concepts of density).
- Conclude by assigning students the final quiz, covering the entire unit, as described in the Assessment section.

### Attachments

### Assessment

Pre-Activity Assessment

*Experiment Design:* Prior to the activity, and after the What Is Newton's Third Law? lesson, introduce the concept/challenge of this activity: To investigate the effects of friction and applied force using a textbook sliding across a table. Inform them of the available materials for the experiment and have them each develop an experimental plan to test how applied force or friction force affects the acceleration of the book.

Activity Embedded Assessment

*Questions: *Throughout the activity, ask students questions to test their understanding of what is happening during the experiment. For example:

- What forces are acting on the textbook?
- How does the applied force change as water is added to the bottle?
- How can you tell if a friction force is present? Can you tell if it is smaller or larger than the applied force?

Post-Activity Assessment

*Worksheet:* Have students use the Sliding Textbooks Worksheet as a guide to the experimental procedures and answer the page 4 questions (also provided below), which are also suitable as class discussion questions. Review their observations, measurements, calculations, results, graphs and answers to gauge their comprehension of the concepts.

- When you put more mass (water) into the soda bottle, what happens to the average acceleration (does it get faster or slower)? Why? (Answer: It gets faster as a result of a greater force, which is the result of a larger mass working on the textbook [times the vector component of acceleration due to gravity, and minus the coefficient of dynamic friction].)
- On graph paper, plot the points from the first experiment (without the runway) and connect them as a line. Do the points lie perfectly in a line? Why or why not? (Answer: Since acceleration is the product of the [net] force times the mass, assuming the friction of the table surface is constant, that is, if the table is of uniform "smoothness" [which is a big assumption!], then the graph of the points
*should*approximate a straight line. This is unlikely to be the case in practice, however. But expect the trend to be clear. Give credit for any thoughtful answer discussing the "why" question that shows the use of relevant vocabulary and concepts.) - What difference do you see between Experiment 1 (the table and book) and Experiment 2 (with the added "runway" material)? Did the textbook accelerate faster or slower with the new surface? Why? (Answer: If the new surface is smoother than the table surface [as is typically the case], then the volume of water needed to overcome the static coefficient of friction is smaller, and the book accelerates faster, in Experiment 2. This is because the frictional force is smaller, and so the net force acting as the product of gravity and the mass of the water plus bottle [minus the frictional force] is greater.)
- For what types of situations might you want a smooth material? (Example answers: Smooth surfaces are useful for highways and have a big impact on the fuel economy of cars and trucks—but highways must not be made
*too*smooth because we also want tires to be able to grip the road! In mechanical devices, such as car motor pistons or lock mechanisms, lubricants are used to reduce friction. If the extension with pulleys was done, discuss the design of pulleys. In rope and pulley applications, you do not want much friction.) - For what types of situations might you want a rough material? (Example answers: Staying with the example of automobiles, brakes rely on friction to catch and quickly stop car wheels. Materials like Velcro, as well as soft natural or synthetic rubber types and other polymers, are often used for shoe soles, car tires and sports gloves [such as for mountain climbing and racket sports].)

*Unit Quiz: *After the activity, administer the *Newton's Laws Final Quiz* as an assessment that covers the entire unit. The quiz is provided as an attachment to the associated lesson, What Is Newton's Third Law? The quiz requires students to draw (conceptual) free-body diagram vectors (arrows) of force, velocity and acceleration.

### Activity Extensions

**Pulleys:** Have students add a pulley with table clamps to the experimental setup to examine the effect of looping the string through a pulley. How does this impact the coefficient of static/dynamic friction?

For teachers: Pulleys with table clamps are fairly inexpensive. Adding a pulley reduces the coefficient of static and dynamic friction; thus, making the textbooks slide "sooner" (that is, with less mass) and faster at a given mass. Encourage students to brainstorm examples of machines that use pulleys to reduce friction, apply forces and provide leverage.

Pulleys are a fundamental device that were developed and used as long ago as Ancient Greece (for example, by Hero of Alexandria) to provide mechanical advantage. They are often used as parts of belts and chain drives, in block and tackle setups, in rope and pulley systems, and in many other machines.

Expect students to recognize the value of pulleys in providing mechanical advantage and overcoming friction. Real-world design and engineering examples are ubiquitous.

**Inclined Planes: **Prop up the tables to make inclined planes. Have students make hypotheses and test the effects of friction and the magnitude of the force applied by the water bottles. If students have been introduced to trigonometry, forces can be decomposed quantitatively.

For teachers: Like pulleys, inclined planes are among the six classical simple machines that can provide mechanical advantage. Invite students to experiment with changing the incline angles and recording the effects on the coefficient of static friction. A vivid real-life example is parking cars on the steepest streets of San Francisco, where after rainfalls (or an earthquake!), if the streets were only a bit steeper, static frictional forces would be overcome, and the cars would slide much like the textbooks in this activity!

**Sliding Race Competition: **Challenge groups to re-run the friction testing portion of the activity (Experiment 2) as a class competition on another day by inviting students bring their own "runway" materials to compete to achieve the fastest "slide" of the textbook. Give teams 20 minutes to design and prepare a surface for testing. Then time two trials per team, applying 125 ml of water each time, and taking the faster of the two runs. The teacher serves as the official arbiter of any disputes on rules and also times the competition runs for all teams. Expect the winning design to be a smooth sliding surface with a "clean" execution—that means a smart choice of "runway" material that is taped carefully to the table without no folds or creases.

### Activity Scaling

Depending the level of your students, after all groups have completed collecting data for Experiments 1 and 2, you may want to do the calculations together as a class at the end of the period in a guided, participatory, step-by-step way.

### Contributors

Jacob Teter, Liz Anthony, Scott Strobel### Copyright

© 2014 by Regents of the University of Colorado; original © 2013 University of California Davis### Supporting Program

RESOURCE GK-12 Program, College of Engineering, University of California Davis### Acknowledgements

The contents of this digital library curriculum were developed by the Renewable Energy Systems Opportunity for Unified Research Collaboration and Education (RESOURCE) project in the College of Engineering under National Science Foundation GK-12 grant no. DGE 0948021. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: April 12, 2018

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