Simple Harmonic Motion with Rotational Inertia

[Vanessa Le]

Homework Statement

One end of a light spring with force constant k = 100 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. the string changes from horizontal to vertical as it passes over a pulley of mass M in the shape of a solid disk of radius R = 2.00 cm. The
pulley is free to turn on a fixed, smooth axle. The vertical section of the string supports an object of mass m = 200 g. The string does not slip at its contact with the pulley. The object is pulled downward a small distance and released.

(a) What is the angular
frequency v of oscillation
of the object in terms of
the mass M?

(b)What
is the highest possible
value of the angular frequency
of oscillation of the object?

2. Homework Equations

w=(k/m)exp1/2

The Attempt at a Solution

I honestly do not know where to start... For a), wouldn't you simply use the w=(k/m)exp1/2 formula since the angular frequency only depends on the mass and the spring contsant?

 

[ehild]

Homework Statement

One end of a light spring with force constant k = 100 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. the string changes from horizontal to vertical as it passes over a pulley of mass M in the shape of a solid disk of radius R = 2.00 cm. The
pulley is free to turn on a fixed, smooth axle. The vertical section of the string supports an object of mass m = 200 g. The string does not slip at its contact with the pulley. The object is pulled downward a small distance and released.

(a) What is the angular
frequency v of oscillation
of the object in terms of
the mass M?

(b)What
is the highest possible
value of the angular frequency
of oscillation of the object?

2. Homework Equations [/B]

w=(k/m)exp1/2

The Attempt at a Solution

I honestly do not know where to start... For a), wouldn't you simply use the w=(k/m)exp1/2 formula since the angular frequency only depends on the mass and the spring contsant?

Do you think that the mass of the pulley does not affect the angular frequency?

 

[Vanessa Le]

Do you think that the mass of the pulley does not affect the angular frequency?

In the problem, it stated that the pulley had a mass M with Radius = 2.00cm so I am assuming the mass of the pulley does matter, which lead me to thinking that the mass used in the w=(k/m)exp1/2 equation is in fact m = mass of object + mass of pulley.

I tried finding the mass of the pulley using the moment of inertia formula before realizing that I'd actually need the pulley mass for that too..

 

[ehild]

In the problem, it stated that the pulley had a mass M with Radius = 2.00cm so I am assuming the mass of the pulley does matter, which lead me to thinking that the mass used in the w=(k/m)exp1/2 equation is in fact m = mass of object + mass of pulley.

I tried finding the mass of the pulley using the moment of inertia formula before realizing that I'd actually need the pulley mass for that too..

The mass of the pulley does matter. It is M which can have different values. Solve the problem in terms of M and k. Write the acceleration of m with the forces acting on it and the angular acceleration of M with the angular momenta of the forces acting on it. What are those forces?

 

[Vanessa Le]

What would I use to find the M mass of the pulley? I've tried moment of inertia and that doesn't work because you need the mass for I=MR^2.

 

[ehild]

What would I use to find the M mass of the pulley? I've tried moment of inertia and that doesn't work because you need the mass for I=MR^2.

You can not find M. It is arbitrary. Find the frequency in terms of M.

 

[ehild]

Draw the free-body diagram for m and M. What forces act on m, and at the rim of the disk? How is the acceleration of m related to these forces? How is the angular acceleration of the disk related to the torque of the forces acting at its rim?