I am having trouble with the last portion of this question. If someone can help me, I would sincerely appreciate it.

A bicycle wheel has a radius R = 32.0 cm and a mass M = 1.82 kg which you may assume to be concentrated on the outside radius. A resistive force f = 147 N (due to the ground) is applied to the rim of the tire. A force F is applied to the sprocket at radius r such that the wheel has an angular acceleration of a = 4.50 rad/s^2. The tire does not slip.

a) If the sprocket radius is 4.53 cm, what is the force F (N)?

(mr^2)(4.5) = (r)(F)- (147)(.32)
(1.82)(.32^2)(4.5) = (.0453)(F)-(147)(.32)
= 1056.9

b) If the sprocket radius is 2.88 cm, what is the force F(N)?

(1.82)(.32^2)(4.5) = (.0288)(F)-(147)(.32) = 1662.45

c) What is the combined mass of the bicycle and rider (kg)?
I am not sure how to do this last part

To solve the last part of the question and find the combined mass of the bicycle and rider, we need to use the concept of torque and angular acceleration.

The formula for torque is given by:

Torque = Force x Radius

In this case, the torque due to the applied force F on the sprocket is equal to the torque due to the resistive force f applied to the rim of the tire.

So, we can write the equation for torque as:

(Torque due to F) = (Torque due to f)

(F)(r) = (f)(R)

We already know the values of r (sprocket radius = 2.88 cm = 0.0288 m), f (resistive force = 147 N), and R (wheel radius = 32.0 cm = 0.32 m) for part b).

Substituting these values into the equation, we have:

(F)(0.0288) = (147)(0.32)

Now we can solve for F:

F = (147)(0.32) / 0.0288

F ≈ 1635.42 N

So, the force applied to the sprocket (F) required to achieve the given angular acceleration with a sprocket radius of 2.88 cm is approximately 1635.42 N.

To find the combined mass of the bicycle and rider, we need to use Newton's second law, which states that the sum of all forces on an object is equal to the mass of the object multiplied by its acceleration.

The net force acting on the bicycle and rider can be calculated by subtracting the resistive force (f) from the force applied to the sprocket (F).

Net Force = F - f

We can rearrange the equation to solve for the mass (M):

Net Force = M x acceleration

M = Net Force / acceleration

Substituting the known values, we have:

M = (F - f) / a

M = (1635.42 - 147) / (4.50)

M ≈ 337.53 kg

Therefore, the combined mass of the bicycle and rider is approximately 337.53 kg.