Maximum Kinetic Energy from a Physical Pendulum

[xoxomae]

Homework Statement

Determine the maximum kinetic energy of a uniform rod of mass 0.5Kg and length 0.75 that has an angular displacement of 5 degrees.

Homework Equations

y = rsin (x) where x is the angular displacement

The Attempt at a Solution

Using conservation of energy E_Total = E_Mech + E_POTENTIAL

Kinetic energy is at a maximum when all potential energy is converted to kinetic energy

Centre of mass of of physical pendulum is equal to L/2

Therefore max kinetic energy = mg (l/2) sin (x)
= 0.0163417 J

I just have no idea if this is right

 

[TSny]

1
Using conservation of energy E_Total = E_Mech + E_POTENTIAL

Did you mean to write E_Kinetic instead of E_Mech?

Kinetic energy is at a maximum when all potential energy is converted to kinetic energy

Centre of mass of of physical pendulum is equal to L/2

Therefore max kinetic energy = mg (l/2) sin (x)

Can you explain why you used a factor of sin(x) here? Be sure to draw a picture to help find the change in vertical height of the center of the rod.

 

[xoxomae]

I used a factor of sin (x) because the change in the y-axis * mg is equal to total potential energy
y = r sin (theta) when changing between polar and cartesian coordinates
Is this the wrong way to think about it?

 

[TSny]

First of all, I want to make sure I'm interpreting the question correctly. I assume from the title that you are dealing with a swinging physical pendulum. I am also assuming that the maximum angular displacement from equilibrium is 5 degrees. Is this correct?

 

[xoxomae]

Would I have to use cos (x) instead of sin (x)?

Umm yes that's the question :)

 

[TSny]

Would I have to use cos (x) instead of sin (x)?

It's not a matter of just replacing sin(x) by cos(x). Did you draw a picture?

 

[xoxomae]

Okay, so i drew a picture and realized that I made a mistake.

I got to
Change in x = l/2 * (1- cos(x))

 

[TSny]

Looks good. But you're using x for two different things!