Physics
posted by James .
The density of a 5.0m long rod can be described by the linear density function λ(x) = 140 g/m + 14.8x g/m2. One end of the rod is positioned at x = 0 and the other at x = 5 m.
(a) Determine the total mass of the rod.
(b) Determine the centerofmass coordinate.
I found the total mass of the rod to be 885 g, how does one find the center of mass coordinate in the xdirection given this information?
Thank you in advance.

m=∫ρ•dx =∫(140+14.8x) •dx =
= ∫140•dx+∫14.8•x•dx =
=140•x + 14.8x²/2=
=140•5 + 14.8•25/2 =885 g.
Calculate the integral
∫ρ•x•dx =
=∫(140+14.8x) •x •dx =
= ∫140•x•dx+∫14.8•x²•dx =
=140•x²/2 + 14.8x³/3=
=140•25/2 + 14.8•125/3=2367 kg.
x(c/m/) =∫ρ•x•dx/∫ρ•dx =2367/885=2.67 m.
C.M. (2.67 m; 0)
Respond to this Question
Similar Questions

Physics
One cm of a 10cmlong rod is made of metal, and the rest is wood. The metal has a density of 5000 kg/m3 and the wood has a density of 500 kg/m3. When the rod is set into pure water, the metal part points downward. How much of the … 
Physics
The density of a 4.41m long rod can be described by the linear density function λ(x) = 111 g/m + 12.3x g/m2. One end of the rod is positioned at x = 0 and the other at x = 4.41 m. found total mass of rod to be: 609 grams need … 
Physics
The density of a 4.41m long rod can be described by the linear density function λ(x) = 111 g/m + 12.3x g/m2. One end of the rod is positioned at x = 0 and the other at x = 4.41 m. found total mass of rod to be: 609 grams need … 
Physics  Center of Mass
The density of a 5.0m long rod can be described by the linear density function λ(x) = 145 g/m + 14.2x g/m2. One end of the rod is positioned at x = 0 and the other at x = 5 m. a) Determine the total mass of the rod. b) Determine … 
Physics
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 … 
Physics
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 … 
physics
A rod with a length L = 0.385 m and a nonuniform linear mass density rests along the y axis with one end at the origin. If the linear mass density of the rod is given by λ = (5.00 ✕ 10−2 kg/m) + (1.50 ✕ 10−2 … 
Physics
A long thin rod lies along the xaxis from the origin to x=L, with L= 0.750 m. The mass per unit length, λ (in kg/m) varies according to the equation λ = λ0 (1+1.410x3). The value of λ0 is 0.600 kg/m and x is in … 
physics
A rod of length L has a varying density along its length that satisfies: λ(x) =((x^2/L^2)+1)λo where x = 0 is one end of the rod (which has density λo), and x = L is the other end (which has density 2λo). a. Find … 
Calculus
Let the length of a rod be 10 meters and the linear density of the rod ρ(x) be written in the form ρ(x) = ax + b with x = 0 representing the left end of the rod and x = 10 representing the right end of the rod. If the density of …