Centripetal Force and free body diagram

[KL90]

Homework Statement

a. Draw a free body diagram for mass M_b while in motion (fig. 2a). Identify the centripetal force. assume that the mass hangs vertically

b. Calculate the magnitude of the force exerted by the spring on mass M_b = 402g, moving in a circle of radius r=18cm (fig. 2a). The mass makes 20 revolutions in 12 seconds. Determine the mass m, suspended over the pulley (fig 2b), which stretch the spring by the same amount as during the rotation.

Homework Equations

The Attempt at a Solution

a. Mb would have 3 forces: F spring (F_sp), F centripetal force (F_c) and F gravity (F_g).
Fsp is point outwards to the right, Fc pointing inwards to the left, and Fg is pointing downwards.
I was wondering if it would have tension from the string supporting Mb?

b. Fsp=Fc = mv²/r = m(2[tex]\pi[/tex]f)²r
here, v = 2[tex]\pi[/tex]r/T = circumference/Period and frequency = 1/T

1) Fsp = 0.402kg x (2[tex]\pi[/tex] 20rev/12sec)² x 0.18m'
= 7.967 Nt
I'm not entirely sure if what i did is correct.

2) I'm not entirely sure how to calculate m after this point.

 

[turin]

a. Mb would have 3 forces: F spring (F_sp), F centripetal force (F_c) and F gravity (F_g).

I agree with the number of applied forces, but you are double-counting one of them, and you are neglecting another one.

Actually, if you want to count pseudo-forces (other than weight), then you can list four, and you have listed all but one of them.

Fsp is point outwards to the right, Fc pointing inwards to the left, ...

I think that you should reread the attachment.

I was wondering if it would have tension from the string supporting Mb?

Good thinking. Ask yourself: Is the mass in (instantaneous) translational equilibrium (in the rotating frame)? Should there be a force that counteracts the weight, and, if so, what supplies this force?

 

[tomcue]

I would need more information on the spring constant and the amount of stretch in order to determine the mass m. Additionally, the information provided does not specify whether the spring is ideal or not, so that may affect the calculation as well. It would be helpful to have more context or information to accurately determine m in this scenario.