How Do You Calculate the Speed and Spring Constant of a Pivot-Mounted Rod?

[zhenyazh]

hi, i'll be glad to get some help with that.
thanks

A thin uniform rod has mass M = 0.5 kg and length L= 0.55 m. It has a pivot at one end and is at rest on a compressed spring as shown in (A) in the attached image. The rod is released from an angle θ1= 63.0o, and moves through its horizontal position at (B) and up to (C) where it stops with θ2 = 105.0o, and then falls back down. Friction at the pivot is negligible. Calculate the speed of the CM at (B).
The spring in (A) has a length of 0.11 m and at (B) a length of 0.14 m. Calculate the spring constant k.

I will combine that two mandatory fields as i don't understand the first of them.
In general i see that the first question is an energy conservation question.
i can use the second and third state to find the speed.
so i write an equation where the potential energy of state c equals the kinetic energy of state b, in case i choose the zero line to where the rod is parallel to the ground.
what i don't know is how to treat the potential energy. i know that the kinetic one
consists of the c.m part and the 0.5Iw^2 part but what about mgh, different parts of the rod are in different hights?

thanks
and sorry if i wasn't totally formal, i just didn't know how to

 

[tiny-tim]

Welcome to PF!

In general i see that the first question is an energy conservation question.
…
what i don't know is how to treat the potential energy. i know that the kinetic one
consists of the c.m part and the 0.5Iw^2 part but what about mgh, different parts of the rod are in different hights?

Hi zhenyazh! Welcome to PF!

(have an omega: ω )

Yes, it's an energy conservation question.

For the gravitational PE, only the position of the centre of mass matters, so in mgh use h as the height of the centre of mass.

 

[zhenyazh]

thanks
can u help me out with the second part too? i just get confused with the equations

 

[tiny-tim]

thanks
can u help me out with the second part too? i just get confused with the equations

You mean "The spring in (A) has a length of 0.11 m and at (B) a length of 0.14 m. Calculate the spring constant k." ?

Again, use conservation of energy …

at maximum compression, the KE of the rod is zero.

What do you get? ​