Question

If ρ(x,y) is the density of a wire (mass per unit length), then m=∫Cρ(x,y)ds is the...

If ρ(x,y) is the density of a wire (mass per unit length), then

m=∫Cρ(x,y)ds

is the mass of the wire. Find the mass of a wire having the shape of a semicircle x=1+cos(t),y=sin(t), where t is on the closed interval from 0 to π, if the density at a point P is directly proportional to the distance from the y−axis and the constant of proportionality is 3. Round in the tenths place.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A lamina with constant density ρ(x, y) = ρ occupies the given region. Find the moments...
A lamina with constant density ρ(x, y) = ρ occupies the given region. Find the moments of inertia Ix and Iy and the radii of gyration x and y. The region under the curve y = 4 sin(x) from x = 0 to x = π.
A rod with density δ(x)=2+sin(x) (in mass per unit length) lies on the x-axis between x=0...
A rod with density δ(x)=2+sin(x) (in mass per unit length) lies on the x-axis between x=0 and x=π/3. Find the center of mass of the rod.
(1). The mass density of a semicircular wire of radius a varies directly with the distance...
(1). The mass density of a semicircular wire of radius a varies directly with the distance from the diameter that joins the two endpoints of the wire. ​Find the mass equation 人(x,y) (2) Let say now the density varies directly as the cube of the distance from the line that divided the wire in half vertically. Fin the mass equation 人(x,y)
A rod with density δ(x)=4+sin(x) (in mass per unit length) lies on the x-axis between x=0...
A rod with density δ(x)=4+sin(x) (in mass per unit length) lies on the x-axis between x=0 and x=2π/3. Find the center of mass of the rod.
A. A uniform wire is made from material with an average mass density of ρ=3,044kg/m3, a...
A. A uniform wire is made from material with an average mass density of ρ=3,044kg/m3, a radius of 1.26 mm, and a length of 0.63m. The wire is held under a tension of 11.2 N. Transverse waves are sent down the wire. What is the speed of the waves through the wire in m/s? Assume 3 significant figures B. A mass on a spring is undergoing simple harmonic motion in the x-direction with an amplitude of 0.86 m and a...
1.) Let f ( x , y , z ) = x ^3 + y +...
1.) Let f ( x , y , z ) = x ^3 + y + z + sin ⁡ ( x + z ) + e^( x − y). Determine the line integral of f ( x , y , z ) with respect to arc length over the line segment from (1, 0, 1) to (2, -1, 0) 2.) Letf ( x , y , z ) = x ^3 * y ^2 + y ^3 * z^...
I have some integration questions for calc homework 1. Compute ds (the differential of arc length)...
I have some integration questions for calc homework 1. Compute ds (the differential of arc length) for f(x) = 2^x . 2. Compute the arc length of f(x) = 9x ^ 2/3 over the interval [0, 1]. 3. Find the surface area of the hollow shape obtained by rotating f(x) = sin(x) from x = 0 to x = π about the x-axis. Thanks for any help!
1. In an experiment to study standing waves, you use a string whose mass per length...
1. In an experiment to study standing waves, you use a string whose mass per length is µ = (1.8 ± 0.1) × 10−3kg/m. You look at the fundamental mode, whose frequency f is related to the length L and tension T of the string by the following equation L = 1 2f s T µ . You make a plot with L on the y-axis and √ T on the x-axis, and find that the best fitting line is...
1) A standing-wave pattern is observed in a thin wire with a length of 4.00 m....
1) A standing-wave pattern is observed in a thin wire with a length of 4.00 m. The wave function is y = 0.002 00 sin (πx) cos (100πt) where x and y are in meters and t is in seconds. (a) How many loops does this pattern exhibit? (b) What is the fundamental frequency of vibration of the wire?
A straight, cylindrical wire lying along the x axis has a length of 0.616 m and...
A straight, cylindrical wire lying along the x axis has a length of 0.616 m and a diameter of 0.6 mm. It is made of a material described by Ohm's law with a resistivity of ρ = 4.72 ✕ 10−8Ω· m. Assume a potential of 4.85 V is maintained at the left end of the wire at x = 0. Also assume V = 0 at x = 0.616 m. Find the current density (in A/m2) in the wire.