Challenging physics problems uniform circular motion, centripetal force

[adeel]

challenging physics problems...uniform circular motion, centripetal force

here is the setup, we had a lab in class, in which a string was strung through a plastic tube. On on end, rubber stoppers were attached and in this case acted as a mass. On the other end, metal masses were hooked on to cause tension in the string. The apparatus was swung around and the time taken for 20 revolutions was recorded. One that was complete, we divided 20/time taken to get frequency. Throughout the experiment, the tension force (weight of metal masses), the mass (the rubber stoppers) and the radius of the string were altered. Once this has been completed, we are to create an equation incorporating frequency and its relationship to tension force, radius, and mass.

From my experiment, frequency is proportional to the square roots of 1/radius and 1/mass and is proportional to the square root of the tension force.

Also, the standard equation is tension = 4 x pi x pi (or pi squared) x mass x radius x frequency x frequency (frequency squared)

does anyone know how to derive a formula using the proportionality statements i came up with? Can anyone help me?

 

[sridhar_n]

Hi

According to what I understood of the problem this is how u proceed:

Let T = tension, m = mass of the cork, v = linear velocity of the cork, r = radius, f = frequency, w = ang.frequency; a=accln

then,

T - (mv²)/r = M*a
w = 2*π*f

Substitute this and find the value of T w.r.t f


Sridhar

 

[M98Ranger]

First, let's define the variables:

- F = tension force
- m = mass of rubber stoppers
- r = radius of string
- f = frequency

From your experiment, we can see that frequency is proportional to the square root of 1/radius and 1/mass. This can be written as:

f ∝ √(1/r) and f ∝ √(1/m)

To combine these proportions into one equation, we can use the proportionality constant k:

f = k√(1/r)√(1/m)

Now, let's look at the relationship between frequency and tension force. We can see that frequency is also proportional to the square root of the tension force:

f ∝ √F

Again, we can use a proportionality constant k to combine these proportions into one equation:

f = k√F

Combining this equation with the previous one, we get:

f = k√(1/r)√(1/m)√F

Simplifying this equation, we get:

f = k√(F/rm)

Finally, we can substitute the standard equation for tension (F = 4π²mrƒ²) into our equation:

f = k√(4π²mrƒ²/rm)

f = k√(4𲃲)

f = 2πkƒ

Therefore, the final equation incorporating frequency, tension force, radius, and mass is:

f = 2πkƒ = 2πk√(4π²mrƒ²/rm)