find the center of mass

label Calculus
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

May 25th, 2015

According to given question

he plate has a constant density and thickness so the mass is evenly distributed. You only have to find the gravitational center of the figure. 

You see instantly that the figure is mirror-symmetric around the x-axis, so the gravitational centre must be on the y-axis. 

The y-coordinate of the gravity centre is difficult to calculate (using arccos) over the y-axis. But when we look at the surface of the figure you see 3 distinct areas. make (o,g) the gravitational point. and h the point where y = g = 2cos(h) . Then we integrate over the x-axis 
The integral from x = 0 to h must be equal to 1/2 (half the total area) - g.h 
1 - 2sin(h) = 1 - g.h or 2sin(h) = 1 + 2cos(h).h 
I can't see how to calculate this in an algebraic form. you can approach it by interpolation. 
f(h) = 2sin(h) - 1 - 2cos(h).h 
gives h = 1.202 g = 0,36

Answer

Hope This will help you

May 25th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
May 25th, 2015
...
May 25th, 2015
Jun 28th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer