What Are the Solutions for Static Equilibrium Mass and Disk Rotation Angle?

[stonecoldgen]

Homework Statement

I need help with #2 and #5.

#2 just aks what is the mass of m1, in order for the system to be in static equilibrium

#5 aks what angle will the disk spin when pushed to go up that step. It also asks what is the minimum force needed in order for the disk to go up.

The Attempt at a Solution

I tried solving #2 just like i did with #1. They are giving me 2 sets of distances (in #1 just one) i also tried with the other set of distances and it didnt work. I even tried combinating the 2 sets of distances and not even that works.

For #5 tried combinating some formulas:

$\sum$F
_______________ = a/r = $\Delta$$\Theta$/$\Delta$t
$\sum$m

but all of those unkowns ''freak me out''



EDIT: and you can see that my teacher has an answer bank, i know that $\Theta$ is obviously 30, but i don't know how to get there

[Attachment removed as it contains personal information]

 

[anathema]

Dear student,

For problem #2, in order to find the mass of m1, you will need to use the equation for static equilibrium, which is ΣF = 0. This means that the sum of all the forces acting on the system must equal zero. You will need to set up an equation with the forces acting on m1, which include the weight of m1 and the tension in the string.

For problem #5, you will need to use the equation for rotational motion, which is Στ = Iα. This means that the sum of all the torques acting on the disk must equal the moment of inertia of the disk times the angular acceleration of the disk. To find the angle at which the disk will spin, you will need to solve for the angular displacement, θ, using the formula θ = ω0t + 1/2αt^2, where ω0 is the initial angular velocity and t is the time. To find the minimum force needed to push the disk up the step, you will need to use the equation F = ma, where m is the mass of the disk and a is the linear acceleration of the disk up the step.

I hope this helps you with your homework. Remember to always set up your equations correctly and use the correct units for all your values. Good luck!