Physics  Center of Mass
posted by Joe .
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 the centerofmass coordinate.

m=∫ρ•dx =∫(145+14.2x) •dx =
= ∫145•dx+∫14.2•x•dx =
=145•x + 14.2x²/2=
=145•5 + 14.2•25/2 =902.5 g.
Calculate the integral
∫ρ•x•dx =
=∫(145+14.2x) •x •dx =
= ∫145•x•dx+∫14.2•x²•dx =
=145•x²/2 + 14.2x³/3=
=145•25/2 + 14.2•125/3=2404.2 kg.
x(c/m/) =∫ρ•x•dx/∫ρ•dx =2404.2/902.5=2.66 m.
C.M. (2.66 m; 0) 
Question: Shouldn't the 2404.2 be in grams and not Kg?
Respond to this Question
Similar Questions

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
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 … 
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  please help!!..
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 …