Find the center of mass for the region bounded by y = x² and y = x + 2 with density p(x,y) = x.
- print Print
- list Cite
Expert Answers
calendarEducator since 2012
write1,281 answers
starTop subjects are Math and Science
To determine the bounded region, graph the given equations. (Please see attached figure.)
On the bounded region, draw a dot to represent its center of mass. To get its coordinates, we have to solve for its mass. Also, let's consider the bounded region as a thin plate.
The formula to compute its mass is:
`M = rho int_a^b f(x) - g(x)dx`
where ` rho ` represents the density, f(x) is the upper curve and g(x) is the lower curve.
The upper graph of the bounded region is y = x +2 and the lower curve is y=x^2. And bounded region starts at x=-1 and ends at x=2.
So, the mass of the plate is:
`M=x...
(The entire section contains 361 words.)
Already a member? Log in here. Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- `y=sqrt(x), y=0 , x=4` Find the x and y moments of inertia and center of mass for the...
- 1 Educator Answer
- Find the centroid of the region bounded by the graphs of `y=sqrt(r^2-x^2)` and `y=0`
- 1 Educator Answer
- Find the volume of the solid obtained by rotating the region bounded by the given curves about...
- 1 Educator Answer
- `y = x^2, y = 6x - 2x^2` Use the method of cylindrical shells to find the volume generated...
- 1 Educator Answer
- `y = e^(-x), y = 1, x = 2` Find the volume of the solid obtained by rotating the region...
- 1 Educator Answer