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

AI Thread Summary
The discussion focuses on calculating the speed of a pivot-mounted rod and the spring constant of a spring it rests on. The rod, with a mass of 0.5 kg and a length of 0.55 m, is released from an angle of 63.0 degrees and moves through a horizontal position before stopping at 105.0 degrees. Participants emphasize using energy conservation principles, noting that only the center of mass height should be considered for gravitational potential energy. The kinetic energy equation includes both the center of mass and rotational components, while the spring constant can be derived from energy conservation at maximum compression. The conversation highlights the importance of understanding these concepts to solve the problem effectively.
zhenyazh
Messages
55
Reaction score
0
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
 

Attachments

  • Capture.JPG
    Capture.JPG
    6.2 KB · Views: 532
Physics news on Phys.org
Welcome to PF!

zhenyazh said:
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! :smile:

(have an omega: ω :wink:)

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. :smile:
 
thanks
can u help me out with the second part too? i just get confused with the equations
 
zhenyazh said:
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? :smile:​
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »

Similar threads

Question about springs and rotational/translational energy
Replies
4
Views
1K
Why can we move the spring with constant speed when we apply a force?
Replies
29
Views
2K
What Is the Frequency of Small Oscillations for a Pivoted Rod with Two Springs?
Replies
19
Views
2K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
1K
Calculating the spring force constant K
Replies
14
Views
2K
A block dropping onto a spring system
2
Replies
58
Views
2K
Pan suspended by a spring (Energy + SHM)
Replies
20
Views
3K
Calculate the spring constant k
Replies
2
Views
4K
A rocket on a spring, related to potential/kinetic energy
Replies
3
Views
2K
Body attached to a block by a spring, shaped like an inclined plane
Replies
1
Views
880

Hot Threads

Recent Insights

Back
Top