A car of mass 1500 kg is able to deliver a total of 3200 Nm of torque to the dri

Question

A car of mass 1500 kg is able to deliver a total of 3200 Nm of torque to the drive wheels of the car.
(i) The radius of the tyres is 0.326 m. Assuming all the force is transferred to the road. What is the acceleration of the car in m/s2?
(ii) Assuming the car starts from a stationary position, what is the speed of the car (in km/hr) after it has accelerated for 10 seconds at the rate determined in (i)?

(b) The car described above is travelling at 200 km/hr, when the driver takes the car out of gear and slams on the brakes bringing the car to a halt. The 4 steel disk brake rotors on the car absorb all of the kinetic energy of the car in the form of heat, assuming no other losses such as tyres skidding.
(i) What is the kinetic energy of the car at 200 km/hr?
(ii) Given each disk rotor has a mass of 3.5 kg and the specific heat of a steel brake disk is 500 J/kg/K, what increase in temperature (in degrees C) will occur on each of the 4 disk rotors?

Explanation / Answer

= FR

=>F =/R = 3200/.326 = 9815.95N

i)F = Ma

=> a =9815.95/1500 =6.54m/s^2

ii) V= u +at

after 10 sec starting from rest

v = 10*6.54 = 65.4 m/sec = 6.54*3600/1000 =235.4km/h

b)

i)kinectic energy = .5Mv^2

v= 200km/hr = 200*1000/3600 = 55.56m/s

KE = .5*1500*55.56^2 = 2314815 J

ii) energy to each disk is 2314815/4 = 578703.75 J

Let rise in tempreature = T

T*m*s =578703.75

=> increase in tempreature of each disk = T = 578703.75/(3.5*500) =330.68oc

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