C. Forces · ForcesNewton's Laws at Work: Analysing and Improving Technologies
C1.1 C3.3 C2.4About 70 minutes
Learning goals- I can analyse how a technology applies Newton's laws and friction.
- I can use calculations to compare the performance of technologies such as anti-lock brakes.
- I can propose a realistic improvement to a technology and explain it with physics.
- I can weigh the trade-offs of a design change.
Words to know
anti-lock braking system (ABS)
A system that rapidly releases and reapplies the brakes on a wheel that is about to lock, so the tire keeps rolling and the driver can still steer.
electronic stability control (ESC)
A system that senses when a car begins to skid sideways and brakes individual wheels to help keep it on the driver's intended path.
bearing
A part that lets one part turn or slide on another with little friction, often using small balls or rollers.
trade-off
A cost or disadvantage that comes with a benefit. Every design involves trade-offs.
jerk
The rate of change of acceleration (units m/s³). Roller-coaster designers pay attention to it for rider comfort.
Physics you can buy
Anti-lock brakes, running shoes, hockey sticks, roller coasters, skate bearings, snow tires: all of them were designed by people who used Newton's laws and the physics of friction. In this lesson you will take the engineer's point of view: how does this technology use forces, how well does it work, and how could it work better?
A method for analysing a technology
- Purpose: What is the technology supposed to do?
- Forces: Draw an FBD of the key object. Which forces matter? Friction (static or kinetic)? Normal force? Tension?
- Laws: Which of Newton's laws explains how it works (inertia, Fnet = ma, action-reaction)?
- Performance: What limits it? Use numbers where you can.
- Improve: Propose a change. Explain with physics why it would help.
- Trade-offs: cost, safety, energy use, environment, who can access it.
Case 1: Anti-lock brakes and stability control
When a driver slams on ordinary brakes, the wheels can lock: they stop turning and the tires skid. Then:
- only kinetic friction acts, and μk is less than the peak static value, so the car stops in a longer distance on most paved roads;
- a skidding front tire cannot push the car sideways, so the driver cannot steer around the hazard.
ABS senses when a wheel is about to lock and rapidly releases and reapplies that wheel's brake, many times per second. The tire keeps rolling, so the bottom of the tire is not sliding on the road: static friction acts, and steering still works. Electronic stability control goes further: it senses a sideways skid and brakes individual wheels to turn the car back onto its path.
ABS does not work miracles. On loose gravel or deep snow, a locked tire can pile up material in front of it, and ABS stopping distances can actually be longer. ABS mainly helps you keep steering.
Worked exampleExample 1: How much does ABS help on dry pavement?
A car is moving at 20 m/s (72 km/h) on dry concrete. Assume ABS keeps the tires near the peak static friction, μs = 1.0, while locked wheels give μk = 0.8. Compare the braking distances.
- On a level road, a = −μ g, and Δd = v₁² ÷ (2 μ g).
- ABS: Δd = 400 ÷ (2 × 1.0 × 9.8) = 400 ÷ 19.6 ≈ 20 m.
- Locked: Δd = 400 ÷ (2 × 0.8 × 9.8) = 400 ÷ 15.68 ≈ 26 m.
- Improvement ≈ 5 m (25.5 − 20.4), roughly a car length, plus the driver can still steer. (Real ABS cannot hold the tires exactly at the peak, so the real benefit is somewhat smaller.)
About 20 m with ABS versus 26 m skidding.
Case 2: Roller coasters
A launch coaster uses motors or magnets to push the train from rest to high speed in a couple of seconds. The rider's body has inertia: the train accelerates, and the seat back must push the rider forward. Riders feel pressed back into the seat. On a hill, the normal force from the seat changes, so riders feel heavier at the bottom of a dip and lighter at the top of a hump (like the elevator in the lesson on mass and weight). Designers use Newton's laws to keep the forces exciting but safe, and they design restraints (lap bars, shoulder harnesses) so that inertia cannot carry a rider out of the seat.
Worked exampleExample 2: A launch coaster
A launch coaster takes a 60 kg rider from rest to 100 km/h (27.8 m/s) in 2.0 s. Find the rider's acceleration and the horizontal force from the seat back. Compare it with the rider's weight.
- a = Δv ÷ Δt = 27.8 ÷ 2.0 ≈ 13.9 m/s².
- The seat back gives the only horizontal force (ignoring air), so F = ma = 60 × 13.9 ≈ 833 N forward.
- Weight = 60 × 9.8 = 588 N. Ratio 833 ÷ 588 ≈ 1.4: the seat pushes the rider forward with about 1.4 times her weight.
About 14 m/s² and 830 N, about 1.4 times her weight.
A 60 kg rider during a launch-coaster start. The seat back provides the whole horizontal net force: 833 N, about 1.4 times the rider's weight. (Air resistance on the rider is ignored.)Case 3: Sports equipment and bearings
- Golf clubs: the club head pushes the ball for well under a thousandth of a second. The ball's launch speed depends on the club head's speed and mass and on how the face and ball compress. Lighter shafts (graphite instead of steel) let players swing the head faster; a larger "sweet spot" makes off-centre hits less costly.
- Athletic shoes: the sole's tread and rubber compound set μs for pushing off (third law: push back on the ground, ground pushes you forward). Cushioned midsoles spread each landing over a longer time, so the stopping force on the foot is smaller (F = mΔv/Δt).
- Bearings and low-friction coatings: ball bearings in skateboard wheels, bicycle hubs and machines replace sliding friction with much smaller rolling friction. Less friction means less wasted energy, less heat and less wear. Some research coatings, such as "near-frictionless" carbon films, have extremely low coefficients of friction in lab tests.
Worked exampleExample 3: Proposing an improvement
A youth hockey team finds that its players slip when pushing off on their outdoor rink's rubber mats between the bench and the ice. Analyse the problem and propose an improvement.
- Purpose: players must walk on skates safely on the mats.
- Forces: to push off, a blade pushes back on the mat; the mat pushes forward (third law) through static friction. Max static friction = μs FN.
- Problem: wet, icy rubber has a low μs, so the blades slip when the horizontal push exceeds μs FN.
- Improvement: a textured, drainable mat (or one with grooves that hold blades), cleared of slush regularly, increases μs. The FN cannot easily change (it is the skater's weight), so μs is the variable to increase.
- Trade-offs: textured mats can dull blades (so choose a material made for skates), cost money, and need regular cleaning.
Increase μs with a textured, drained, skate-safe surface; consider blade wear and maintenance.
Just for funPhysics has an official name for a change in acceleration: jerk, measured in metres per second cubed. So a smooth roller coaster is, scientifically speaking, one designed to avoid being a jerk.
Hands-on activityAnalyse a technology at home
Choose one technology you can examine at home: running shoes or winter boots, a bicycle (brakes and bearings), a skateboard or scooter, a sled or toboggan, a hockey stick, or a car's braking features (look in the owner's manual for ABS and stability control).
- Describe its purpose and draw an FBD of the key object while it is working.
- Name the Newton's law(s) that explain how it works, and where friction helps or hurts.
- Measure something if you can: compare the grip of two shoes with a drag test (from the friction lessons), or time how long a spun bicycle wheel keeps turning.
- Propose one improvement and explain the physics behind it.
- List at least two trade-offs (cost, durability, safety, environmental impact).
What to look for: an FBD with labelled forces, a correct law, a specific (not vague) improvement, and honest trade-offs.
Your turn
1Explain why locked (skidding) wheels make a car harder to control.
A skidding tire is sliding, so only kinetic friction acts along the direction of sliding; the front tires can no longer produce the sideways static friction needed to steer, and kinetic friction is usually smaller, so stopping takes longer.
2Which type of friction does ABS try to keep using, and why?
Static friction, because the tires keep rolling without sliding. Peak static friction is usually larger than kinetic, and it allows steering.
3A launch coaster accelerates a 50 kg rider at 12 m/s². What force does the seat back exert on her?
F = ma = 50 × 12 = 600 N forward.
4Why do roller coasters need shoulder harnesses or lap bars? Use the first law.
When the train changes velocity suddenly (stops, drops, turns), the rider's inertia keeps her moving the old way. Restraints provide the force that changes her velocity along with the train.
5How do ball bearings reduce friction in a skateboard wheel?
They replace sliding friction between the axle and wheel with rolling friction of small balls, which is much smaller.
6Name one trade-off of making a running shoe sole stickier (higher μs).
Any one: it may wear out faster, add weight, make it harder to pivot (more stress on knees and ankles), or cost more.
More practice: warm-up
Anti-lock braking system.
2Which law explains why you feel pushed back into the seat when a coaster launches?
The first law (inertia): your body resists the change in motion until the seat pushes it forward.
3What kind of friction lets a sprinter push off the track?
A cost or disadvantage that comes along with a benefit.
5Name one technology designed to reduce friction.
Any one: ball bearings, lubricants/oil, low-friction coatings (Teflon), wheels, waxed skis.
More practice: on your own
1A car at 25 m/s brakes on wet concrete. With ABS assume μ = 0.7; skidding μk = 0.5. Compare braking distances.
ABS: 625 ÷ (2 × 0.7 × 9.8) ≈ 46 m. Skidding: 625 ÷ (2 × 0.5 × 9.8) ≈ 64 m. ABS saves about 18 m and keeps steering.
2Why can ABS stopping distances be longer on loose gravel or deep snow?
A locked tire on loose material plows up a wedge of gravel or snow in front of it, which helps stop the car. ABS keeps the tire rolling over the material instead, so this extra resistance is lost.
3A 0.046 kg golf ball leaves the club at 70 m/s after a contact time of 0.00050 s. Find the average force on the ball.
a = 70 ÷ 0.00050 = 140 000 m/s². F = 0.046 × 140 000 ≈ 6.4 × 10³ N (6440 N).
4Explain how a cushioned midsole reduces the force on a runner's heel.
The heel must slow from its landing speed to zero (same Δv). A cushion makes this take longer (bigger Δt), so the acceleration Δv/Δt is smaller and so is the force F = ma.
5Propose one improvement to a children's plastic sled so it goes farther down a hill, and give one trade-off.
Example: smoother, waxed runners or a lower-friction plastic base reduce μk, so friction is smaller and the sled keeps more of its speed. Trade-off: it may go too fast to stop safely, so it needs a handle-brake or should only be used on gentle hills with clear run-outs.
Challenge
1A golf club manufacturer claims a new lighter shaft lets an average player swing the club head 5% faster. If the ball's launch speed is proportional to club-head speed, by what percent does the average force on the ball increase (same contact time)? Explain.
Launch speed increases by 5%, so Δv is 5% larger. With the same Δt, a = Δv/Δt is 5% larger, so F = ma increases by 5%.
2Evaluate this claim: "With ABS, I can drive just as fast in winter as in summer."
False. ABS keeps the wheels rolling, but it cannot create friction that the road does not provide. On ice, μ may be about one eighth of the dry value, so braking distance is about eight times longer at the same speed, with or without ABS. Drivers must slow down, leave more space, and use winter tires.
3A roller-coaster designer wants riders to feel 1.5 times their normal weight at the bottom of a dip (scale reading). If a rider's mass is 60 kg, what upward acceleration is needed there? (Treat it like the elevator problem.)
FN = 1.5mg = m(g + a), so a = 0.5g = 4.9 m/s² up. (For a 60 kg rider, FN = 882 N; the mass cancels in finding a.)
Quiz
1. ABS helps a driver mainly by:
2. A locked, skidding tire experiences:
3. Riders feel pushed back into their seats as a coaster launches because of:
4. A cushioned sole reduces the force on a foot because it:
5. Ball bearings reduce friction by:
6. Which is the best-supported improvement for a sled that slides too slowly?
Big idea: Analysing technologies that apply Newton's laws and proposing improvements (C1.1), with qualitative use of the laws (C3.3) and friction coefficients (C2.4).
How to help: If you drive, show your teen where the ABS and stability-control warning lights are on the dashboard and read the owner's manual section together. Discuss: "What does this actually change about the forces on the tires?"
Common difficulties:
- Vague proposals ("make it better"). Push for a specific change and a physics reason.
- Forgetting trade-offs: cost, wear, safety, energy, environment.
- Believing technology removes physical limits. ABS cannot add friction that the road does not provide.