Physics · Grade 12 · Dynamics and Kinematics in Three Dimensions · Term 1

Friction and Drag Forces

Students will analyze the effects of friction and air resistance on motion, including terminal velocity.

• Ontario Curriculum Expectations
• HS.PS2.A.1
• HS.PS2.A.2

About This Topic

Friction and drag forces oppose motion between surfaces or objects moving through fluids. Students analyze static friction, which prevents initial motion, and kinetic friction, which acts during sliding. They explore drag forces, which increase with speed and depend on shape, size, and fluid density. A key focus is terminal velocity, the point where drag equals gravitational force, resulting in zero net force and constant speed. Calculations involve mass, cross-sectional area, drag coefficient, and equations like F_d = (1/2)ρv²C_d A.

In the Ontario Grade 12 Physics curriculum, this topic fits within the Dynamics and Kinematics in Three Dimensions unit. Students predict motion outcomes, draw free-body diagrams, and evaluate engineering strategies, such as tire treads to maximize friction or aerodynamic shapes to minimize drag. These skills connect to real applications in automotive design, aviation, and sports equipment, building quantitative reasoning and problem-solving abilities.

Active learning suits this topic well. Students test predictions through experiments, like measuring incline angles for sliding or comparing fall speeds of coffee filters. Such approaches reveal force balances visually, encourage iterative design, and solidify abstract concepts through direct measurement and peer discussion.

Key Questions

1. Analyze how friction and drag forces influence the motion of objects in various environments.
2. Predict the terminal velocity of an object given its mass, shape, and fluid density.
3. Evaluate strategies to minimize or maximize friction in engineering applications.

Learning Objectives

• Calculate the coefficient of kinetic friction given the mass of an object, the applied force, and the normal force.
• Analyze free-body diagrams to determine the net force acting on an object experiencing friction and/or drag.
• Predict the terminal velocity of a falling object by equating gravitational force and drag force.
• Evaluate the effectiveness of different tread patterns on tires for maximizing friction in various road conditions.
• Design a simple experiment to measure the drag coefficient of a common object.

Before You Start

Newton's Laws of Motion

Why: Students must understand the relationship between force, mass, and acceleration to analyze how friction and drag affect motion.

Free-Body Diagrams

Why: Students need to be able to represent all forces acting on an object to solve problems involving friction and drag.

Vectors and Vector Addition

Why: Understanding how to resolve and combine forces is essential for calculating net force when friction or drag is present.

Key Vocabulary

Static Friction	The force that opposes the initiation of motion between two surfaces in contact. It is variable and can prevent an object from starting to slide.
Kinetic Friction	The force that opposes motion between two surfaces that are sliding relative to each other. It is generally constant for a given pair of surfaces.
Drag Force	A resistive force exerted by a fluid (like air or water) on an object moving through it. It increases with the object's speed.
Terminal Velocity	The constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration.
Drag Coefficient	A dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment. It depends on the object's shape and surface texture.

Watch Out for These Misconceptions

Common Misconception

Friction always reduces speed.

What to Teach Instead

Static friction enables acceleration, like tires gripping road. Kinetic friction opposes sliding. Ramp experiments where students push blocks at threshold angles clarify roles, as groups debate and test force directions.

Common Misconception

All falling objects reach same terminal velocity.

What to Teach Instead

Terminal velocity depends on mass, shape, area. Coffee filter drops show lighter, larger area reaches lower speed. Pairs predict and measure, revising models through data comparison in class discussions.

Common Misconception

Drag force is constant.

What to Teach Instead

Drag increases with v or v². Fan cart runs with velocity-time graphs reveal deceleration, helping students plot and derive force laws collaboratively.

Active Learning Ideas

Incline Plane: Friction Coefficients

Provide wood blocks and inclines with varied surfaces (sandpaper, plastic, felt). Students raise the incline until sliding starts, measure angle, calculate μ_s = tanθ. Repeat for kinetic friction by timing slides from fixed height. Groups graph results and compare predictions.

45 min·Small Groups

Parachute Drop: Terminal Velocity

Students cut parachutes from plastic bags in different sizes, attach to same-mass objects. Drop from balcony or stairs, time to reach floor, video for velocity analysis. Calculate approximate terminal velocity from average speed, discuss shape effects.

35 min·Pairs

Fan Cart: Drag in Air

Use air tracks or fan carts with sails of varying area. Measure acceleration as function of distance, plot velocity vs time to estimate drag force. Predict changes by altering sail shape or adding mass.

50 min·Small Groups

Fluid Drag Comparison: Water vs Air

Drop spheres of same size but different densities into water tanks and air. Use slow-motion video to track velocities, identify terminal speeds. Compare drag forces qualitatively and quantitatively.

40 min·Pairs

Real-World Connections

• Automotive engineers use principles of friction to design tire treads that provide optimal grip on dry, wet, and icy roads, ensuring vehicle safety and performance.
• Aerospace engineers calculate drag forces and terminal velocity to design parachutes for safe landings of spacecraft and skydivers, ensuring a controlled descent.
• Sports equipment designers analyze friction and drag to create faster swimsuits, more aerodynamic cycling helmets, and skis that reduce resistance for competitive athletes.

Assessment Ideas

Quick Check

Present students with a scenario: 'A wooden block rests on a horizontal surface. A horizontal force of 10 N is applied, but the block does not move. The mass of the block is 5 kg.' Ask: 'What is the minimum possible coefficient of static friction? Draw the free-body diagram for the block.'

Exit Ticket

Provide students with a data set for a falling object (mass, cross-sectional area, drag coefficient). Ask them to calculate the object's terminal velocity and explain in one sentence why terminal velocity is reached.

Discussion Prompt

Pose the question: 'Imagine you are designing a new type of shoe for a marathon runner. How would you adjust the sole design to minimize friction with the track while maximizing grip during push-off? Explain your reasoning based on the concepts of static and kinetic friction.'

Frequently Asked Questions

How do you calculate terminal velocity in class?

Use F_net = mg - (1/2)ρv²C_d A = 0, so v_t = sqrt(2mg / ρC_d A). Provide values for skydiver or parachutist problems. Students solve step-by-step with vectors, then verify via simulation software or drop tests for validation.

What active learning strategies work for friction and drag?

Incorporate station rotations with inclines for friction, parachute builds for drag, and video analysis of falls. Students predict outcomes, collect data in lab notebooks, and present findings. This builds ownership, reveals misconceptions through peer review, and links math models to observations effectively.

How does this topic connect to engineering?

Students evaluate tire designs for grip (high friction), car spoilers for downforce (manage drag), or bike helmets for low drag. Case studies of Formula 1 aerodynamics prompt design challenges where groups prototype and test models, applying force balances to optimize performance.

What are common errors in free-body diagrams for drag?

Students omit drag or mislabel as friction. Guide with scaffolded diagrams, then peer review sessions. Experiments like falling objects force revisions as actual motions contradict incomplete diagrams, reinforcing complete force analysis.