In the figure below, a constant horizontal force Fapp of magnitude 18 N is applied to a wheel of mass 12 kg and radius 0.50 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.50 m/s2. What is the friciotnal force on the wheel

(a.)

F applied - m(a) = Frictional force, remember negative component.
(b.)
Torque = Frictional force*(radius)

Inertia = Torque/alpha

alpha= Acom/Radius= A/R

To find the frictional force on the wheel, we can start by using Newton's second law of motion:

Fnet = m * a

Where Fnet is the net force acting on the wheel, m is the mass of the wheel, and a is the acceleration of the wheel's center of mass.

In this case, the net force acting on the wheel is the horizontal force Fapp minus the frictional force Ffriction. So we can rewrite the equation as:

Fapp - Ffriction = m * a

We know that the applied force Fapp is 18 N and the mass of the wheel m is 12 kg. And we are given that the acceleration a is 0.50 m/s^2. So we can substitute these values into the equation to solve for the frictional force Ffriction:

18 N - Ffriction = 12 kg * 0.50 m/s^2

Simplifying the equation, we have:

18 N - Ffriction = 6 N

Now we can isolate the frictional force Ffriction:

Ffriction = 18 N - 6 N

Ffriction = 12 N

Therefore, the frictional force on the wheel is 12 N.

To find the frictional force on the wheel, we can use the equation of motion for rolling motion. The equation is:

Fapp - Ffriction = mass * acceleration

In this case, the applied force is the horizontal force Fapp, the frictional force is Ffriction, the mass of the wheel is the mass, and the acceleration is the given magnitude of 0.50 m/s^2.

For rolling motion, the frictional force is given by:

Ffriction = rolling resistance coefficient * normal force

where the normal force is the force exerted by the surface on the wheel.

Since it is stated in the question that the wheel rolls smoothly, it means that the only force acting on it in the vertical direction is its weight. Therefore, the normal force is equal to the weight, which can be calculated as:

Normal force = mass * g

where g is the acceleration due to gravity.

To find the rolling resistance coefficient, we need to know the physical properties of the wheel and the surface on which it is rolling. Without this information, we cannot determine the exact value of the rolling resistance coefficient. However, we can assume a reasonable range of values for this coefficient based on typical situations.

Once we have the rolling resistance coefficient, we can substitute the values into the equation and solve for the frictional force.

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