## 1111 The energy of motion and work done in braking Fig 111

A moving vehicle possesses kinetic energy whose value depends on the weight and speed of the vehicle. The engine provides this energy in order to accelerate the vehicle from a standstill to given speed, but this energy must be partially or totally dissipated when the vehicle is slowed down or brought to a standstill. Therefore it is the function of the brake to convert the kinetic energy possessed by the vehicle at any one time into heat energy by means of friction (Fig. 11.1).

The equation for kinetic energy, that is the energy of motion, may be given by

Uk = % mV2 where Uk = kinetic energy of vehicle (J) m = mass of vehicle (Kg) V = speed of vehicle (m/s)

The work done in bringing the vehicle to rest is given by where

Uw = Fs work done (J) average braking force (N) distance travelled (m)

When braking a moving vehicle to a standstill, the work done by the brake drums must equal the initial kinetic energy possessed by the vehicle so that

.'. Average brake force F

Fig. 11.1 Illustration of braking conditions

Example (Fig. 11.1) A car of mass 800 kg is travelling at 36 km/h. Determine the following:

a) the kinetic energy it possesses, b) the average braking force to bring it to rest in 20 metres.

800 x 102

b) Work done to stop car = change in vehicle's kinetic energy

20 2kN

2000 N

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