What is the magnitude of the acceleration of the center of mass

[noppawit]

A constant horizontal force F of magnitude 12 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 10 kg, its radius is 0.1 m, and the cylinder rolls smoothly on the horizontal surface.

(a) What is the magnitude of the acceleration of the center of mass of the cylinder? (The answer is 1.6m/s^2)

(b) What is the magnitude of the angular acceleration of the cylinder about the center of mass? (The answer is 16rad/s^2)

(c) In unit-vector notation, what is the frictional force acting on the cylinder? (The answer is (4.0N)i )

I tried with τ (Torque) = I*a (alpha)

(12 - f)(r) = $$\stackrel{Ia}{r}$$

12- f = $$\stackrel{0.05a}{0.1^2}$$
I have 2 unknowns. What shall I do?

The answers that I typed are the correct ones, I would like to know that solution.

Thank you very much.

 

[anantchowdhary]

Try using the fact that the cylinder rolls without slipping...so this means that the net velocity of the contact point with the ground is zero

 

[noppawit]

Yes? But how can I find the frictional force?
Which equation I have to use to start at this problem?

 

[anantchowdhary]

hmm..see form three eqns...one using the condition of rolling
and one using Newton's second law on the body
and then one using the torque equation...thus find the frictional force

 

[noppawit]

The force is acting on the edge of cylinder (not pass center of mass).

As I wrote, I used Torque = Moment of inertia x Alpha
(12N-friction force) = (0.5x10x0.1^2)(a/0.1)

Then, I don't know how to find 2 unknowns, as I have only 1 equation.

So, which equation I need for solving 2 unknowns.

 

[anantchowdhary]

no...write Newtons law for the WHOLE BODY...using Newtons law for a system of particles!