The car shown in the figure has mass m (this includes the mass of the wheels). T

Question

The car shown in the figure has mass m (this includes the mass of the wheels). The wheels have radius r, mass m_w, and moment of inertia I=k*m_w*r^2. Assume that the axles apply the same torque t to all four wheels. For simplicity, also assume that the weight is distributed uniformly so that all the wheels experience the same normal reaction from the ground, and so the same frictional force.

a) Use Newton's laws to find an expression for the net external force acting on the car. Ignore air resistance.

Explanation / Answer

torque due to friction on car = 4fr = 4I = 4k(m/4)r^2(a/r) = kmar = kFr

since the weight of the car is on wheels. we can conside as if the there is no car and the mass of the wheel is m/4

F=4f/k

total force sum in vertical direction = 0

so 4N=m, N=m/4

t-fr=I=k(m/4)r^2(a/r)

t= r(mak/4 + f)

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