## Forces & Braking

The **stopping distance** of a vehicle is the sum of the distance the vehicle travels during the driver’s reaction time (thinking distance) and the distance it travels under the braking force (braking distance). For a given braking force the greater the speed of the vehicle, the greater the stopping distance.

**total stopping distance = thinking distance + braking distance**

## Thinking Distance

The thinking distance is the distance a car travels while the driver reacts to needing to brake

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**Reaction times **vary from person to person. Typical values range from 0.2 s to 0.9 s.

A driver’s reaction time can be affected by tiredness, drugs and alcohol. Distractions may also affect a driver’s ability to react.

## Braking Distance

The braking distance is the distance the car travels whilst the brakes are applied

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The** braking distance** of a vehicle can be affected by adverse road and weather conditions and poor condition of the vehicle.

Adverse road conditions include wet or icy conditions. Poor condition of the vehicle is limited to the vehicle’s brakes or tyres.

A force is applied to the brakes of a vehicle, **work done** by the friction force between the brakes and the wheel reduces the kinetic energy of the vehicle and the temperature of the brakes increases.

The greater the speed of a vehicle the greater the **braking force** needed to stop the vehicle in a certain distance.

The greater the braking force the greater the deceleration of the vehicle. Large decelerations may lead to brakes overheating and/or loss of control.

You can estimate the forces involved in the deceleration of road vehicles in typical situations on a public road.

**Step 1**: Calculate the Acceleration of the car as it stops

**final velocity² – initial velocity² = 2 × acceleration × distance**

0^{2} – 13.4^{2} = 2 x acceleration x 23

179.56 = 46 x acceleration

acceleration = 179.56 / 46

acceleration = 3.9 m/s^{2}

**Step 2**: Calculate the Force needed to stop

**force = mass x acceleration**

force = 1150 x 3.9

The force needed to stop the car is **4485 Newtons**

## Momentum (unit: kgm/s)

Momentum is a quantity that every moving object has. Momentum is a vector quantity. A stationary object has** zero momentum.**

Momentum is defined by the equation:

**momentum = mass × velocity**

**Question**: A skater travels with a velocity of 3.2 m/s and has a momentum of 200 kg m/s

Calculate the mass of the skater

**momentum = mass × velocity**

200 = mass x 3.2

mass = 200 / 3.2

The mass of the skater is **62.5 kg**

In a closed system, the total momentum before an event is equal to the total momentum after the event. This is called **conservation of momentum.**

**total momentum before event = total momentum after event**

The conservation of momentum can be used to solve problems about collisions and explosions.

**Question**: A skater ( A)travels with a velocity of 3.2 m/s and has a momentum of 200 kg m/s

The skater bumps into another skater (B) who is stationary. The skaters move off together in a straight line.

Explain what happens to the velocity of each of the skaters. (3 marks)

- (total) momentum before (collision) = (total) momentum after (collision)
- momentum of skater A decreases and momentum of skater B increases
- velocity of skater A decreases and velocity of Skater B increases

**Question:** A skateboarder stands still on a skateboard.

The mass of a skateboard is 1.8 kg and the mass of the skateboarder is 42 kg.

Calculate the velocity at which the skateboard moves backwards if the skateboarder jumps forwards at a velocity of 0.3 m / s.

**total momentum before event = total momentum after event**

momentum before event = (mass of skateboarder x velocity of skate boarder) + (mass of skateboard x velocity of skate board)

momentum before event = (42 x 0) + (1.8 x 0) = **0 kgs/s**

Momentum before event = Momentum after event = (momentum of skater + momentum of skateboard)

0 = (mass of skateboarder x velocity of skate boarder) + (mass of skateboard x velocity of skate board)

0 = (42 x 0.3) + (1.8 x velocity of skateboard)

-12.6 = 1.8 x velocity of skate board

velocity of skate board = -12.6 / 1.8

velocity of skateboard = -7 m/s

The velocity of the skate board is **7m/s in the opposite direction to the skateboarder**

## Changes in Momentum (Triple Physics Only)

When a force acts on an object that is moving, or able to move, a **change in momentum** occurs.

Force equals the rate of change of momentum.

** force = change in momentum/time taken**

**Question: ** A braking force of 12N acts on a car for 1 minute. Calculate the change in momentum of the car.

** force = change in momentum/time taken**

12 = change in momentum / 60

change in momentum = 12 x 60

The change in momentum is **720 kgm/s**

Many **safety features** use this concept to keep us safe, for example: air bags, seat belts, gymnasium crash mats, cycle helmets and cushioned surfaces for playgrounds.

The safety features all:

- increase the time taken for the change of momentum to happen
- which decreases the rate of change of momentum
- which reduces the force acting

**Question**: Since 1965, all cars manufactured for use in the UK must have seat belts.

It is safer for a car driver to be wearing a seat belt, compared with not wearing a seat belt, if the car is involved in a collision.

Explain why.

- the seat belt stretches
- so driver takes a longer time to slow down and stop (than a driver hitting a hard surface / windscreen / steering wheel)
- for the (same) change of momentum
- a smaller force is exerted (so driver less likely to have serious injury than driver without seat belt)