A 4-wheel drive car of mass M = 2100 kg accelerates from rest to 100 km/h in 3.4

Question

A 4-wheel drive car of mass M = 2100 kg accelerates from rest to 100 km/h in 3.40 seconds, and we will assume that the acceleration is constant. In the following, ignore resistance from the air and the rolling friction of the wheels against the surface. The wheels are rolling without sliding, and they have a diameter of D = 50.0 cm. Each wheel has a mass of m= 18.0 kg, and has a moment of inertia around their centre of mass corresponding to a disc, I = 1/2 mR^2. The mass of the wheels is included in the total 2100 kg. The wheels are taken to be identical and carry the same amount of weight. The gravitational constant is q = 9.80 m/s^2. a) What is t he required torque t hat the engine has to provide for each wheel, to have this acceleration? Provide both the algebraic expression. and the numerical result.

Explanation / Answer

torque acting on the each wheel=I*ALPHA

I=1/2*18*0.25^2=0.5625 kg m^2

a=r*alpha

torque=rFsin90

F=mg

torque=mgr=I*a/r

acceleration a=(100/3.4)*5/18=8.17 m/s^2

torque=0.5625*8.17/0.25=18.38 N m

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