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

In summary, a thin uniform rod with mass 0.5 kg and length 0.55 m is at rest on a compressed spring with a pivot at one end. It is released from an angle of 63.0o and moves through its horizontal position before stopping at an angle of 105.0o. Neglecting friction at the pivot, the task is to calculate the speed of the rod's center of mass at its horizontal position and the spring constant based on its length at two different positions. The first part can be solved using energy conservation, taking into account the potential energy of the center of mass and the kinetic energy of the rod. For the second part, also use energy conservation at maximum compression when the kinetic energy
  • #1
zhenyazh
56
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: 500
Physics news on Phys.org
  • #2
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:
 
  • #3
thanks
can u help me out with the second part too? i just get confused with the equations
 
  • #4
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:​
 

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

What is a rigid body?

A rigid body is an object that maintains its shape and size even when subjected to external forces. It does not deform or change its dimensions under the influence of forces.

What is energy in relation to rigid bodies?

Energy in relation to rigid bodies refers to the ability of a body to do work. It is the measure of the capacity of a rigid body to exert force and cause movement.

How does a spring affect the energy of a rigid body?

A spring can store and release energy, which can affect the energy of a rigid body. When a spring is compressed or stretched, it stores potential energy. When it is released, this potential energy is converted into kinetic energy, which can cause the rigid body to move.

Is the energy of a rigid body constant?

In an ideal scenario, the energy of a rigid body remains constant. This means that the total energy of the body, which includes kinetic energy and potential energy, does not change unless an external force is applied.

How does the energy of a rigid body change when it interacts with other bodies?

The energy of a rigid body can change when it interacts with other bodies through collisions or other forces. In such cases, energy can be transferred between the two bodies, resulting in changes in the energy of the rigid body.

Similar threads

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
1K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
597
Calculating the spring force constant K
Replies
14
Views
938
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
383
Rotation of Rigid Bodies: Rotating stick with disc on top
Replies
9
Views
2K
Find elastic energy in the compressed spring.
Replies
12
Views
2K

Hot Threads

Recent Insights

Back
Top