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Balanced versus Unbalanced Force and Friction

Lesson Plan

Balanced versus Unbalanced Force and Friction

Objectives

Students will explore the relationship between force and motion and friction. Specifically, they will learn:

  • motion is produced by unbalanced force.

  • in real-world situations, friction can be expected to oppose motion.

  • friction can be quantified or measured.

Essential Questions

  • What causes objects to move?

Vocabulary

  • Force: The cause of acceleration or the change in an object’s velocity.

  • Friction: The force that opposes movement when two surfaces touch one another.

  • Coefficient of Friction: The ratio of the force that maintains contact between an object and a surface and the frictional force that resists the motion of the object.

  • Acceleration: The rate of change of velocity of an object over time.

  • Inertia: The property of matter by which it retains its state of rest or its velocity along a straight line so long as it is not acted upon by an external force.

  • Momentum: A quantity that characterizes the motion of a body, equal to its mass multiplied by its velocity.

  • Velocity: Rate of change of position (speed) with a direction.

  • Terminal Velocity: The speed at which resistance (especially air resistance) balances acceleration (especially the acceleration of gravity). Commonly used to describe the highest speed reached by a falling object, when the forces of gravity and air resistance are in equilibrium and there is no acceleration.

  • Unbalanced Force: The situation where some forces acting on an object are greater than others so its speed and/or direction of motion are changed.

  • Balanced Force: The situation where the forces acting on an object cancel each other out so there are no changes in speed and/or direction of motion.

  • Gravity: The mutual force of attraction between particles of matter. On the surface of the Earth, it is the force that constantly accelerates objects toward the center of the Earth at a rate of 9.8 meters per second squared (9.8m/s2).

Duration

30 minutes/1 class period

Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

Materials

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Formative Assessment

  • View

    During the lesson, monitor students’ understanding of the following points, and adjust as necessary, to help students master targeted learning goals within the time frame:

    • An object whose speed is not increasing can still be experiencing acceleration, but the acceleration has been balanced by friction.

    • An object that is not moving at all may be experiencing acceleration, but the acceleration is being entirely balanced by another force.

    • The forces acting on an object are balanced when it is not speeding up, slowing down, or changing direction.

    • Braking is acceleration against the direction of movement, also called deceleration, and is often supplied by friction.

    • There are multiple kinds of frictions, and they can be measured.

    • The coefficient of friction is the ratio of the force needed to move an object across a particular surface to its mass.

    • Lower coefficients means less contact between the object and the surface.

    • Higher speeds mean longer braking distances.

    • Lower coefficients of friction mean longer braking distances.

Suggested Instructional Supports

  • View
    Active Engagement, Explicit Instruction
    W:

    Students will be given an understanding of the basics of motion and force, especially acceleration, balanced and unbalanced forces, and friction.

    H:

    Students’ experience with car travel will be used as a basis for understanding force and motion, and in the process they will be exposed to information that could save their lives someday, as they will calculate braking distances using real data.

    E:

    Students will be provided with the experience of calculating car braking distances for various speeds and driving conditions, using friction as a source of unbalanced force.

    R:

    Students will be asked to reflect on how friction and velocity, as expressed in road conditions, affects their daily experiences.

    E:

    Students will be able to express their understanding by charting and discussing the effect of speed and friction on car braking distances.

    T:

    The lesson plan is flexible and relates to different learning styles, as it involves hands-on material, class discussion, math practice, and reflections on the daily experience of the students.

    O:

    The lesson examines the forces that act on objects to produce and affect motion, and gives students the opportunity to scientifically examine the kinds of friction that are factors in their daily experience of road travel. Calculators are used to prevent the necessary math from being intimidating.

Instructional Procedures

  • View

    Call students’ attention to any stationary object in the room in common view, such as a book on a table. Then ask students to consider what the stationary object has in common with:

    • a car moving down the highway at a steady speed, in a straight line.

    • a skydiver who has leapt from an airplane and, a few seconds later, has reached terminal velocity, meaning he or she is falling at a steady speed.

    The answer is that all three are subject to balanced forces, although it would appear that their situations have nothing in common. Anything subject to balanced force is neither speeding up nor slowing down, nor is it changing direction.

    • The stationary object is being accelerated toward the center of the Earth (i.e., downward) at a rate of 9.81 meters per second squared (32.17 feet per second squared). But the strength of the surface it is sitting on opposes the acceleration. Therefore, the object is not falling. There being no other force acting on it, it is at rest—at least in the frame of reference of the classroom. (Someone in space would note that the object is on the surface of the rotating Earth, which is in turn orbiting the Sun, etc.)

    • The car is being accelerated forward by its engine, and that acceleration is opposed by the friction of the tires on the road, the air against the car body, and the friction of the parts in the engine itself. The end result is that the power of the engine, as applied by the driver, exactly balances the friction opposing the car, so that it moves at a steady speed.

    • The skydiver, like the stationary object, is being accelerated downward by gravity, but momentarily lacks the support of a solid surface to counter that acceleration. Like the car, the skydiver encounters friction, although in this case the friction is entirely provided by the air, in the form of wind resistance. The resistance increases with speed. In fact, it soon balances the acceleration of gravity, so that the skydiver is at terminal velocity. In a prone, face-down spread-eagle position, this is about 120 miles per hour. After the parachute opens, its increased wind resistance slows the skydiver to a new terminal velocity of about 12 miles per hour.

    Force is action that causes an object to accelerate. In our examples, the force is provided by gravity (for the stationary object and the skydiver) and an internal combustion engine (for the car.)

    Force acting to accelerate an object is typically opposed by its inertia and friction.

    • Inertia is an object’s resistance to changes in velocity or direction, and it increases with the body’s mass. When an object is already moving with respect to the observer, its inertia is usually referred to as momentum, and measured as mass times velocity.

    • Friction is the force resisting the movement of two surfaces in contact with each other.

    Here on the surface of the Earth, gravity and friction tend to drown out all other considerations. For instance, Newton’s First Law of Motion basically states: An object at rest tends to remain at rest, and an object in motion tends to remain in motion, unless acted on by an unbalanced force.

    That sums up space travel. But here on Earth, objects are constantly pressed into contact with each other by the acceleration of gravity. That contact soon produces enough friction to stop any motion relative to the friction-producing surface. Dropped through the air, an object will soon reach terminal velocity, and a less-dense object (like a feather) will reach it faster than a denser one (like a stone.) Therefore, the ancients believed, for instance, that heavier objects fell faster than lighter objects, since they were not able to consider the question without air resistance.

    Basically, movement on the surface of the Earth involves using the constant application of force to overcome friction, as was the case with our example of the car moving down the highway. Steady acceleration against constant friction keeps it at a steady speed.

    Friction, therefore, dominates our lives, so that’s what we are going to examine in this lesson, especially the friction involved in stopping a car.

    We rarely can afford the room to just let a car roll to a stop—we have to apply force in the opposite direction of travel, resulting in deceleration rather than acceleration. The standard method involves braking, where the wheels roll slower than the car’s speed. For braking to actually result in deceleration for the car, and stop it in the desired road space, there must be sufficient friction between the rubber wheels and the pavement.

    As we are about to see, this cannot always be assumed.

    The amount of friction between two surfaces is called their coefficient of friction. It is the ratio between the force required to move an object and its mass. If the coefficient is 0.5 for a ten-pound object, that means it will take five pounds of force to move it. (The ratio can be higher than 1.0 if the surface is sticky.)

    Meanwhile, there are several types of friction. Kinetic friction is the sliding friction for an object that is already moving. It is the kind of friction that we have to worry about when stopping a car. Static friction is the friction of an object that is now at rest but which you are trying to get into motion.

    Kinetic friction for a given surface is usually lower than its static friction. That is why, if you are sliding a crate across the floor, it is easier to keep it moving after you do get it moving. Adding lubricant can reduce kinetic friction by about 99 percent, and rolling friction can be even less.

    There are many sources of friction and there is no way to calculate what the coefficient of friction for the interaction of any two surfaces is going to be. It has to be measured directly. As you might imagine, a lot of effort has gone into making such measurements, especially concerning tires and roads.

    Distribute copies of the Braking Distance worksheet (S-8-7-1_Braking Distance Worksheet and KEY.doc). Before proceeding, make the following points about the worksheet:

    • The first five coefficients of friction are from various sources of automotive safety information. The other three are there for comparison.

    • The braking distance formula is credited to the American Association of State Highway and Transportation Officials, and assumes a flat road and a vehicle whose brakes are properly designed, and is not over-loaded or moving at an excessive speed.

    • Many factors are involved in braking and this formula cannot be expected to precisely predict braking distances for specific situations. But it can serve as a basis for comparison.

    Divide the class into teams according to the number of calculating devices. (If there is only one calculating device, have students take turns using it to produce results.)

    As indicated by the instructions on the worksheet, each team should use one coefficient of friction to calculate braking distances for the three different speeds on the chart. Each student should enter the results on his/her own sheet.

    For best results, see that one team uses the optimal coefficient of friction for the road (0.8) and that another team uses the coefficient for icy road conditions (0.15). Other teams should use intermediate coefficients.

    Once students are done calculating, lead them in a discussion of their results. Note these points if no one else brings them up (S-8-7-1_Braking Distance Worksheet and KEY.doc).

    The students can then be asked to discuss any personal experience they have had involving differing road conditions leading to differing braking distances.

    Extension:

    • The exercise refers to braking distance, not stopping distance. The latter is the complete distance it would take to stop, counting the braking distance plus the delay that will take place before the driver begins using the brakes. It can be assumed that the driver will take at least three-fourths of a second to decide that there is a problem, and another three-fourths to begin using the brakes. So have students add the distance traveled in 1.5 seconds at the original velocity to the previously calculated braking distances.

      The Pennsylvania School Bus Driver Training Manual, Unit F, page 12 (at www.dmv.state.pa.us/pdotforms/schoolbus_manual/unit_f.pdf ) contains a chart of both braking and stopping distances. It can be computed that the braking distances all assume the same coefficient of friction. Using the formula on the Braking Distance Worksheet (S-8-7-1_Braking Distance Worksheet and KEY.doc), have students calculate what that coefficient of friction was, and discuss the assumptions that the manual-writer must have made. (The braking distances are consistent with a coefficient of friction of 0.67. According to the data on the worksheet, this assumes the use of moderately worn tires. The manual also assumes a total reaction time, over and above braking time, of one second. This assumes an alert, professorial driver.)

    • For students performing above and beyond the standards, have them convert the formula for braking distance into metric units. This will emphasize unit conversion and provide additional practice with the concepts imbedded in the formula.

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DRAFT 11/19/2010
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