Work done on a Planar Lamina

So today I decided to find the work done by lifting a planar lamina to $y = h$. I first found the work done by lifting a circle to $y = h$. To my surprise, the total work done is $M\cdot g\cdot h$. I tried this for other shapes. I also got $M\cdot g\cdot h$. This compelled me to find the work done by lifting a generic 2D object to $y = h$. To my surprise again, the expression was simple to compute. These are my results. Enjoy!

Proof:

#Mechanics

Easy Math Editor

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Comments

Noice

Krishna Karthik - 2 months, 3 weeks ago

Thanks, it turns out this is extendable to a body of n dimensions.

S. P. - 2 months, 3 weeks ago

Cool! But since work is change in PE, each tiny component of the lamina is displace by the same height. Sum over masses will give mgh.

I realised it’s just what u did lol.

Rohan Joshi - 2 months, 3 weeks ago

Good catch!

S. P. - 2 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$