B. Dynamics · Dynamics: Forces and Motion in a PlaneDynamics at Work: Technologies, Their Impacts, and Careers
B1.1 B1.2 A2.1 A2.2 A1.3 A1.7 A1.9About 75 minutes
Learning goals- I can analyse how a technological device applies the principles of linear or circular motion.
- I can assess the social and environmental impact of devices that use linear or circular motion.
- I can find, evaluate and cite reliable sources for a technology analysis.
- I can describe careers that use dynamics and the education they require, and the contributions of scientists and engineers, including Canadians.
Words to know
inertia reel (retractor)
The spring-loaded spool in a seat belt that lets the belt move freely in normal driving but locks in a sudden stop.
centrifuge
A machine that spins samples at high speed; the large centripetal acceleration separates substances by density.
runaway truck ramp
An uphill lane of deep gravel beside a steep downhill highway, where a truck with failed brakes can stop safely.
cost-benefit analysis
A comparison of the advantages and disadvantages (social, economic, environmental) of a technology.
credible source
A source that is current, relevant, written by qualified people, accurate (checked against other sources) and clear about its purpose.
Physics you can trust your life to
Pull your seat belt out slowly and it unrolls smoothly. Yank it, or brake hard, and it locks. Inside the retractor is a tiny dynamics lab: a pendulum that behaves exactly like the accelerometer in Inertial and Non-inertial Frames of Reference.
Many technologies are built on the ideas of this unit: forces in two dimensions, friction, inclined planes, pulleys and circular motion. In this lesson you will analyse several of them, weigh their effects on people and the environment, and meet some of the careers and people behind them.
Analysing a device: the seat-belt retractor (B1.1)
A seat-belt retractor usually has two locking systems:
- Vehicle-sensitive lock: a small pendulum (or a ball in a cup) hangs inside the retractor. When the car decelerates sharply, the pendulum keeps moving forward because of its inertia (in the car's frame, a fictitious force swings it forward). Its swing pushes a pawl into the teeth of the spool, locking the belt.
- Belt-sensitive lock: if the webbing is pulled out quickly, the spool spins fast, and a centrifugal clutch (weights that swing outward as the spool spins) engages the lock.
Using physics: the pendulum tilts by an angle θ where tan θ = a ÷ g. If the pawl engages when the pendulum tilts 15°, the belt locks at a deceleration of a = 9.8 tan 15° = 2.6 m/s², which is a firm brake but well below what a collision produces.
Worked exampleExample 1: A runaway truck ramp
On steep mountain highways, trucks whose brakes overheat can steer into an uphill gravel ramp. A truck enters a ramp inclined 10° upward at 20 m/s. The loose gravel gives an effective coefficient of resistance of 0.40. How long must the ramp be?
- Moving up the slope, both the down-slope component of gravity and the gravel's resistance slow the truck (as in Inclined Planes).
- a = g(sin θ + μ cos θ) = 9.8(sin 10° + 0.40 cos 10°) = 9.8(0.174 + 0.394) = 5.56 m/s² (deceleration).
- d = v² ÷ (2a) = 20² ÷ (2 × 5.56) = 36 m.
About 36 m, plus a safety margin. Engineers design ramps with an upward slope and deep, loose gravel because both increase the deceleration; the mass of the truck cancels.
Worked exampleExample 2: Spin cycles and the environment
A washing machine drum has a radius of 25 cm. Compare the centripetal acceleration at spin speeds of 800 rpm and 1200 rpm, and discuss one environmental trade-off.
- 800 rpm: f = 13.3 Hz; a = 4π²(0.25)(13.3)² = 1.75 × 10³ m/s², about 180g.
- 1200 rpm: f = 20 Hz; a = 4π²(0.25)(20)² = 3.95 × 10³ m/s², about 400g.
- Water in the clothes needs a large inward force to keep moving in the circle; at high spin rates the fabric cannot supply it, so the water leaves through the drum's holes along tangent lines.
About 180g versus 400g. A faster spin removes more water, so a clothes dryer needs less electricity afterward (or clothes dry faster on a line). The trade-offs: faster spinning means more vibration, noise, wear on bearings and more creasing, and the machine costs more. Hanging clothes to dry avoids the dryer's energy use altogether.
Assessing impacts (B1.2)
When you assess a technology, consider benefits and costs for people, society and the environment, and ask who gains and who pays.
- Seat belts and their retractors: they greatly reduce deaths and serious injuries in collisions, and wearing them is required by law in every province and territory. Concern: they work only if worn correctly; children need car seats and booster seats designed for their size.
- Medical and lab centrifuges: they separate blood into plasma and cells for transfusions and tests, and are used in research and water treatment. Concerns: energy use, cost, and the need for careful balancing and maintenance.
- Roller coasters and rides: recreation, tourism and jobs. Concerns: high forces on riders' bodies (which is why designers use clothoid loops and set height and health restrictions), energy use, noise and land use.
- Banked highways and runaway ramps: safer travel and fewer collisions. Concerns: construction cost, land and gravel use, and maintenance in winter.
- Counterweighted elevators: accessibility for people who use wheelchairs, older adults and anyone carrying loads; counterweights greatly reduce the energy needed. Concerns: electricity use and the materials in tall buildings.
Research skills: finding, evaluating and citing sources (A1.3, A1.7, A1.9)
For a technology report, look for: government agencies (Transport Canada, provincial ministries of transportation), engineering and scientific organizations, manufacturers' technical documents, university pages and textbooks.
Evaluate each source by asking:
- Current? When was it written or updated?
- Relevant? Does it answer your question at the right level?
- Authority? Who wrote it, and are they qualified?
- Accurate? Do other independent sources agree? Are numbers referenced?
- Purpose? Is it trying to inform, or to sell or persuade?
Record every source as you go, and cite it in a consistent style, for example APA: Author, A. A. (Year). Title of page. Site Name. URL
Careers that use dynamics (A2.1)
- Mechanical engineer: designs vehicles, machines, amusement rides and safety systems. A four-year university engineering degree; to practise as a Professional Engineer (P.Eng.) in Ontario, a licence from Professional Engineers Ontario.
- Civil or transportation engineer: designs roads, ramps, bridges and runaway truck ramps (bank angles, friction, stopping distances).
- Aerospace engineer: aircraft, drones and spacecraft, where banking, orbits and forces in turns are everyday work.
- Kinesiologist or biomechanist: applies forces and motion to the human body (sport performance, injury prevention, ergonomics). University degree in kinesiology or a related science.
- Collision reconstructionist: police officers and engineers who use friction, stopping distances and momentum to work out what happened in a crash.
- Elevating devices mechanic: a skilled trade (apprenticeship) that installs and maintains elevators, escalators and lifts.
- Physicist or physics teacher: research and education. Physics degrees lead to many fields, including data science and finance.
People behind the physics (A2.2)
- Galileo Galilei (1564 to 1642) used inclined planes to study accelerated motion and showed that projectile motion splits into horizontal and vertical parts.
- Isaac Newton (1643 to 1727) stated the three laws of motion and showed that the force keeping the Moon in its orbit is the same gravity that makes objects fall.
- Elsie MacGill (1905 to 1980) was the first woman in Canada to earn a degree in electrical engineering and is widely described as the world's first woman aircraft designer. During the Second World War she led the production of Hawker Hurricane fighters at the Canadian Car and Foundry plant in Fort William (now Thunder Bay), Ontario.
- Wilbur Franks (1901 to 1986), a University of Toronto medical researcher, invented a water-filled anti-g suit (the Franks Flying Suit) used by Allied pilots in the Second World War. It helped pilots stay conscious during tight turns and pull-outs, when the large centripetal accelerations you calculated in Vertical Circles drain blood from the brain.
- The Canadarm, the robotic arm built in Canada for NASA's Space Shuttle program (first flown in 1981), moved and caught satellites in orbit, where objects are weightless but still have all their inertia.
Just for funDuring the war, Elsie MacGill's work was celebrated in a comic book that called her the "Queen of the Hurricanes". Not many engineers get their own comic-book story.
Hands-on activityInvestigate your own seat belt, then analyse a device
Part 1 (in a parked car, engine off). Sit in the passenger seat. Pull the seat belt out slowly: it unrolls. Now give it a quick, sharp tug: it should lock (the belt-sensitive lock). Let it retract and repeat. Explain each result using circular motion (the spool spins fast when you yank) and inertia. Never test the vehicle-sensitive lock by braking hard on a road.
Part 2 (research). Choose one device that uses linear or circular motion: a seat-belt retractor, a centrifuge, a roller coaster, a washing machine, an elevator, a velodrome, a runaway truck ramp or a playground spinner.
- Explain how it works, using at least two physics ideas from this unit and one calculation with realistic numbers.
- List two social and two environmental impacts (positive and negative), and suggest one improvement.
- Use at least three sources. Evaluate each with the five questions in the lesson, and cite them in APA style.
- Name one career connected to the device and the education it requires.
Your turn
1A seat belt's pendulum sensor locks the belt when it swings 20° from the vertical. At what deceleration does it lock?
a = g tan 20° = 9.8 × 0.364 = 3.6 m/s².
2A lab centrifuge spins samples at 3000 rpm at a radius of 15 cm. Find the centripetal acceleration in m/s² and in g.
f = 50 Hz. a = 4π²(0.15)(50)² = 1.5 × 10⁴ m/s², about 1500g.
3A runaway truck ramp slopes up at 8° with an effective resistance coefficient of 0.45. What length stops a truck entering at 25 m/s?
a = 9.8(sin 8° + 0.45 cos 8°) = 9.8(0.139 + 0.446) = 5.73 m/s². d = 25² ÷ (2 × 5.73) = 55 m.
4Give one social benefit and one environmental trade-off of high-speed spin cycles in washing machines.
Social benefit: clothes come out drier, so they dry faster and save time. Environmental trade-off: less dryer electricity is needed afterward (a benefit), but faster spinning causes more vibration and wear, so parts may need replacing sooner (more materials and waste).
5Name three questions to ask when evaluating a website as a source.
Any three: Is it current? Is it relevant? Who is the author and are they qualified? Is it accurate (do other sources agree)? What is its purpose (to inform or to sell)?
6Which Canadian invented an anti-g suit for pilots, and which physics from this unit explains why pilots needed it?
Wilbur Franks (Franks Flying Suit). In tight turns and pull-outs, the large centripetal acceleration (as in vertical circles) increases a pilot's apparent weight and pulls blood away from the brain; the suit helped counter this.
More practice: warm-up
1What part of a seat-belt retractor acts like an accelerometer?
The pendulum (or ball) sensor.
2What does a centrifuge use to separate substances?
A large centripetal acceleration from fast spinning; denser parts move to the outside.
3What does P.Eng. stand for?
4Who first stated the three laws of motion?
5Why are runaway truck ramps built uphill?
So that the down-slope component of gravity helps slow the truck, along with the gravel's resistance.
More practice: on your own
1A human centrifuge used to train pilots has an arm 8.0 m long. What speed and rate (rpm) give a centripetal acceleration of 9g?
a = 9 × 9.8 = 88.2 m/s². v = √(ar) = √(88.2 × 8.0) = 27 m/s. f = v ÷ (2πr) = 26.6 ÷ 50.3 = 0.53 Hz ≈ 32 rpm.
2Explain why a seat-belt retractor needs both a vehicle-sensitive lock and a belt-sensitive lock.
The vehicle-sensitive lock works even if the belt is not being pulled (it senses the car's deceleration or tilt). The belt-sensitive lock catches a fast pull on the webbing, for example if the occupant is thrown forward before the car has decelerated much. Two independent systems make failure less likely.
3Describe one way the physics of banked curves (from Banked Curves) is used in the design of a velodrome, and one social impact of building one.
The steep banking lets the normal force supply the centripetal force at racing speeds (tan θ = v² ÷ rg), so cyclists can ride fast through tight turns. Social impacts: training and competition facilities for athletes, community programs and events; costs include construction and operating expenses.
4A source about seat belts is a car company's advertisement from 2009. Evaluate it as a source for a physics report.
It may be out of date and its purpose is to sell, so it could be biased or leave out limitations. Its authority for technical details may be good, but the claims should be checked against independent sources such as a government safety agency or an engineering text.
5Choose a career from this lesson and outline the education path to it.
Sample: Mechanical engineer: Grade 12 university-preparation physics, calculus and chemistry; a four-year accredited engineering degree; supervised work experience and a professional practice exam; a licence from Professional Engineers Ontario to use the title P.Eng. (Other careers with accurate paths are fine.)
Challenge
1An elevator car of 1000 kg is balanced by a 1000 kg counterweight and carries 300 kg of passengers up 30 m at a constant speed. Compare the gain in gravitational potential energy the motor must supply with and without the counterweight (use ΔEg = mgΔh from SPH3U).
Without: the motor lifts 1300 kg: ΔEg = 1300 × 9.8 × 30 = 3.8 × 10⁵ J. With: the car and counterweight balance, so the motor only supplies the passengers' energy: 300 × 9.8 × 30 = 8.8 × 10⁴ J, less than a quarter. (Friction and acceleration add a little in both cases.)
2Design improvement: propose one change to a playground merry-go-round that would make it safer, and use circular-motion physics to justify it.
Sample: limit the maximum rotation rate with a speed governor (a friction brake that engages above a set rpm). Since ac = 4π²rf², halving the maximum frequency quarters the force riders must hold on with, so children are much less likely to be thrown off. Other good answers: handholds closer to the centre (smaller r means a smaller required force), a smooth enclosed edge.
3Assess this claim: "Since seat belts lock during hard braking, they must be pushing passengers backward in a crash with a force that the car's engine provides."
The claim is wrong. In the ground frame, the passenger tends to keep moving forward (inertia) while the car decelerates. The locked belt exerts a backward force on the passenger (a tension force), which is what slows the passenger along with the car. The engine plays no part: the belt is anchored to the car's body, which is itself being slowed by the brakes or the collision.
Quiz
1. In a seat-belt retractor, the vehicle-sensitive lock is triggered by:
2. A centrifuge separates blood components because:
3. A runaway truck ramp stops trucks quickly mainly because:
4. Which question is most important when judging whether a source might be biased?
5. Elsie MacGill is known for:
6. Which career most directly uses friction coefficients and stopping distances to explain car crashes?
Big idea: Students analyse technologies built on linear and circular motion (B1.1), weigh their social and environmental impacts (B1.2), practise research and source evaluation (A1.3, A1.7, A1.9), and explore careers and the contributions of scientists and engineers, including Canadians Elsie MacGill and Wilbur Franks (A2.1, A2.2).
How to help: Do Part 1 of the activity together in your parked car. Then ask about your own work or friends' jobs: where do forces, friction or motion come up? Students are often surprised how many careers use physics.
Common difficulties:
- Describing what a device does without explaining the physics of how it works.
- Listing only benefits (or only costs) instead of weighing both.
- Using a source without checking who wrote it and why.
Safety: test the seat belt only in a parked car with the engine off.