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 mw, and moment of inertia I=kmwr2. Assume that the axles apply the same torque ? 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.

Part A

If there is no slipping, a frictional force must exist between the wheels and the ground. In what direction does the frictional force from the ground on the wheels act? Take the positive x direction to be to the right

Part B

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

Express your answer in terms of any given variables and f, the force of friction acting on eachwheel.

Part C

Use Newton's laws to find an expression for N, the normal force on each wheel.

Express your answer in terms of m and g, the magnitude of the acceleration due to gravity.

Part D

Now assume that the frictional force f is not at its maximum value. What is the relation between the torque ? applied to each wheel by the axles and the acceleration a of the car? Once you have the exact expression for the acceleration, make the approximation that the wheels are much lighter than the car as a whole.

Express your answer in terms of some or all of the variables m, r, ? and the magnitude of the acceleration due to gravity g.

The car shown in the figure has mass m(this includes the mass of the wheels). The wheels have radius r, mass mw, and moment of inertia I=kmwr2. Assume that the axles apply the same torque ? 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. Part A If there is no slipping, a frictional force must exist between the wheels and the ground. In what direction does the frictional force from the ground on the wheels act? Take the positive x direction to be to the right Part B Use Newton's laws to find an expression for the net external force acting on the car. Ignore air resistance. Express your answer in terms of any given variables and f, the force of friction acting on eachwheel.

Explanation / Answer

Part A

The frictional force acts in the positive x direction.

Part B

The vertical forces balance. The net force is in the horizontal direction: F total=4f where total = f is the friction force in each wheel.

Part C

Forces in the y direction: 4Nwheel -mg = 0 where Nwheel is the normal force on each wheel that we take to be equal since the weight is equally distributed.

Nwheel= mg/4

Part D

The torque force at each wheel is: ? = rf .

The linear acceleration is obtained from the sum of the forces 4f = ma

f = ? / r and

f = ma / 4 , then ( ma/4 / = ?/r )

and a= 4?/ mr

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