Section 1 of 6Force from Deceleration
A resultant force is needed to slow any moving object down.
Newton's second law
- The resultant force equals mass multiplied by acceleration, F = m × a, and a deceleration is a negative acceleration.
Estimating mass
- A small family car has a mass of roughly 1000 to 1500 kg, and a person about 70 kg.
Estimating deceleration
- Normal braking is about 2 to 3 m/s², while an emergency stop on a dry road is roughly 7 to 8 m/s².
Direction
- The decelerating force acts opposite to the direction of motion, so it is shown as negative in a calculation.
| Situation | Typical deceleration | Force on 1200 kg car |
|---|---|---|
| Gentle braking | 2 m/s² | 2400 N |
| Hard braking | 5 m/s² | 6000 N |
| Emergency stop, dry road | 8 m/s² | 9600 N |
Section 2 of 6Work Done by the Brakes
Braking transfers kinetic energy, and this gives a second way to estimate the force.
1
A moving car has kinetic energy equal to ½mv², which depends on the square of its speed.
2
The brakes apply a force over the braking distance, and work done equals force multiplied by distance.
3
To stop the car, the work done by the braking force must equal the kinetic energy it had.
4
Therefore F × d = ½mv², so a longer braking distance means a smaller average braking force.
5
The kinetic energy becomes thermal energy in the brakes, tyres and road, which is why brakes get hot.
Section 3 of 6Reducing Forces in Collisions
Reducing Forces in Collisions
Force and time
- For the same change in momentum, taking longer to stop reduces the average force on a person.
Crumple zones
- The front and rear of a car are designed to collapse, which lengthens the stopping time and absorbs energy.
Seat belts and air bags
- These spread the force over a larger area and stretch the stopping time, so injuries are reduced.
Cycle helmets
- The foam lining crushes during an impact, increasing the stopping time and lowering the force on the skull.
Section 4 of 6Making Sensible Estimates
Round numbers
- Use one significant figure and typical values, because the answer is only meant to give the right order of magnitude.
Check units
- Convert mass to kilograms and speed to metres per second before using any equation.
Cross-check
- Compare the answer with a familiar force, such as the weight of a car at about 12 000 N.
State assumptions
- Say that braking force is treated as constant, even though real forces vary during a stop.
Section 5 of 6Worked Example
Question
- A car of mass 1200 kg travelling at 20 m/s brakes to a stop in 40 m.
- Estimate the average braking force.
- Kinetic energy = ½ × 1200 × 20² = ½ × 1200 × 400 = 240 000 J.
- Work done by the brakes equals this energy, so F × 40 = 240 000.
- F = 240 000 ÷ 40 = 6000 N.
- Check with F = maa = 20² ÷ (2 × 40) = 5 m/s², and 1200 × 5 = 6000 N.
Answer The average braking force is about 6000 N.
Section 6 of 6Exam Checklist & Tips
8.1.5 – Key Points for the Exam
- Deceleration Acceleration that reduces the speed of an object, with the force acting opposite to the motion.
- Resultant force The single force that has the same effect as all the forces acting on an object.
- Kinetic energy The energy of a moving object, given by ½mv².
- Crumple zone A part of a vehicle that deforms in a crash to increase the time taken to stop.
- Order of magnitude An estimate that is correct to the nearest power of ten.
Common Mistakes
- Using speed in km/h or mph in equations instead of converting to m/s.
- Forgetting to square the speed when finding kinetic energy.
- Using the car mass in tonnes instead of kilograms.
- Thinking a longer stopping distance needs a bigger braking force; it needs a smaller one.