Calculate CM Speed of Rod on Compressed Spring

[Sumbhajee]

Homework Statement

A thin uniform rod has mass M = 0.31 kg and length L= 0.45 m. It has a pivot at one end and is at rest on a compressed spring as shown in (A). The rod is released from an angle θ1= 57o, and moves through its horizontal position at (B) and up to (C) where it stops with θ2 = 107o, and then falls back down. Friction at the pivot is negligible. Calculate the speed of the CM at (B).

http://schubert.tmcc.edu/res/msu/physicslib/msuphysicslib/21_Rot3_AngMom_Roll/graphics/prob32a_RodOnSpring.gif

Homework Equations

The Attempt at a Solution

Not sure where to start on this one. Thank you for your time and any help provided.

 

[rl.bhat]

Where is the figure? Problem is not clear without that.

 

[tomcue]

As a scientist, my first step in solving this problem would be to identify and list all the relevant equations and principles that can be applied to this situation. These may include conservation of energy, conservation of angular momentum, and the equations for rotational and translational motion.

Next, I would carefully read and analyze the given information and diagram to understand the scenario and determine what information is needed to solve the problem.

Based on the given information, it seems that the initial potential energy stored in the compressed spring is converted into kinetic energy as the rod moves from position A to position B. Therefore, the equation for conservation of energy, E = K + U, can be used to solve for the speed of the CM at position B.

To apply this equation, we first need to calculate the potential energy stored in the compressed spring at position A. This can be done using the equation for spring potential energy, U = 1/2kx^2, where k is the spring constant and x is the compression distance.

We can then calculate the kinetic energy of the rod at position B using the equation for rotational kinetic energy, K = 1/2Iω^2, where I is the moment of inertia and ω is the angular velocity.

Once we have the values for K and U, we can solve for the speed of the CM using the equation E = K + U and then rearranging for v (the speed of the CM).

It is also important to consider the conservation of angular momentum in this problem, as the rod is pivoting at one end. However, since the problem states that friction at the pivot is negligible, we can assume that there is no external torque acting on the system, and therefore angular momentum is conserved.

In summary, to solve for the speed of the CM at position B, we can use the equations for conservation of energy and rotational kinetic energy, along with the principles of conservation of angular momentum.