A long thin rod lies along the xaxis from the origin to x=L, with L= 0.890 m. The mass per unit length, λ (in kg/m) varies according to the equation λ = λ0 (1+1.410x2). The value of λ0 is 0.700 kg/m and x is in meters.
1. Calculate the total mass of the rod.
*Here I got a correct answer: 8.549×101 kg
2. Calculate the xcoordinate of the center of mass of the rod.
??
3. Calculate the moment of inertia of the rod with respect to the yaxis.
???
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

dm = .7 (1+1.41 x^2) dx
m = .7 [ x + 1.41 x^3/3] 0 to .89
= .854935 etc yes check
cg = (integral x dm)/m
= .7[ x + 1.41 x^3] dx /m
= .7[x^2/2 + 1.41 x^4/4 ]/m 0 to .89
= .43205147/.854935
=.50536
I = integral x^2 dm
= integral x^2[ .7 (1+1.41 x^2) dx]
= .7 int [x^2 + 1.41 x^4 ] dx same limits
= .7 l [x^3/3 +1.41 x^5/5] at x = .89
= .274722 👍
 👎
 ℹ️
 🚩
Damon
Answer this Question
Related Questions

calculus
A point in the first quadrant lies on the parabola y = x^2. Express the coordinates of P as function of the angle of inclination of the line joining P to the origin

Physics
The magnitudes of the four displacement vectors shown in the drawing are A = 14.0 m, B = 11.0 m, C = 12.0 m, and D = 25.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the

physics
One mole of titanium (6 1023 atoms) has a mass of 48 grams, and its density is 4.54 grams per cubic centimeter, so the centertocenter distance between atoms is 2.60 1010 m. You have a long thin bar of titanium, 2.4 m long, with a square cross section,

calculus
A uniform thin sheet of metal is cut in the shape of a semicircle of radius R and lies in the xy plane with its center at the origin and diameter lying along the x axis. Find the position of the Center of Mass using polar coordinates.

Physics E&M
A Geiger counter detects radiation such as alpha particles by using the fact that the radiation ionizes the air along its path. A thin wire lies on the axis of a hollow metal cylinder and is insulated from it. View Figure A large potential difference is

math
an equation is being tested for symmetry with respect to the xaxis, the yaxis, and the origin. explain why, if two of these symmetries are present then remaining one must also be present.

Physics
An infinitely long line charge of uniform linear charge density λ = 3.00 µC/m lies parallel to the y axis at x = 2.00 m. A point charge of 4.70 µC is located at x = 1.50 m, y = 2.50 m. Find the electric field at x = 2.50 m, y = 2.00 m. I get 23.7

phys urgent!
A particle leaves the origin with a speed of 2.4 times 10^6 m/s at 38 degrees to the positive x axis. It moves in a uniform electric field directed along positive y axis. Find Ey such that the particle will cross the x axis at x = 1.5 cm if the particle is

Physics
Two charges are located on the positive xaxis of a coordinate system. Charge q1 = 2.00 × 10−9C, and it is 0.020 m from the origin. Charge q 2 = –3.00 × 10 −9 C, and it is 0.040 m from the origin. What is the electric force exerted by these two

physics
A sphere of mass M is supported by a string that passes over a pulley at the end of a horizontal rod of length L . The string makes an angle θ with the rod. The fundamental frequency of the standing waves in the portion of the string above the rod is f.

PHYSICS
The figure shows a ball with mass m = 0.405 kg attached to the end of a thin rod with length L = 0.516 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then

physics
In the figure, particle A moves along the line y = 29 m with a constant velocity of magnitude 3.5 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration of

physics
A commonly used method of fastening one part to another part is called "shrink fitting." A steel rod has a diameter of 2.0046 cm, and a flat plate contains a hole whose diameter is 2.0000 cm. The rod is cooled so that it just fits into the hole. When the

physics
A point charge Q = 400 nC and two unknown point charges, q1 and q2, are placed as shown. Point charge q1 is located 1.3 meters along the +xaxis, point charge q2 is located 0.7 meters down the yaxis, and point charge Q is located 2.0 meters from the

Physics
One mole of tungsten has a mass of 184 grams, and its density is 19.3 grams per cubic centimeter, so the centertocenter distance between atoms is 2.51×1010 m. You have a long thin bar of tungsten, 2.2 m long, with a square crosssection 0.16 cm on a

Trigonometry
If a point on the Cartesian plane lies at (4, 2), what is the angle made between the line containing the point and the origin, and the negative yaxis? a) 1.249 radians b) 0.463 radians c) 0.523 radians d) 1.047 radians

Algebra
For each equation, determine whether its graph is symmetric with respect to the axis, the axis, and the origin. 4y^4+24x^2=28 and y=1/x^2+5 Check all symmetries that apply xaxis,yaxis,origin or non of the above.

precap
a rectangle has one corner in quadrant I on the graph of y=25x^2, another at the origin, a third at the positive yaxis, and the fourth on the positive xaxis

Physics
A uniform disk with mass m = 9.42 kg and radius R = 1.31 m lies in the xy plane and centered at the origin. Three forces act in the +ydirection on the disk: 1) a force 315 N at the edge of the disk on the +xaxis, 2) a force 315 N at the edge of the disk

physics
The 4.00kg block in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended towards the rod and each have a length of 1.25. The length from the upper string and lower
Still need help?
You can ask a new question or browse existing questions.