Post a New Question

Physics - Center of Mass

posted by .

The density of a 5.0-m 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 center-of-mass coordinate.

  • Physics - Center of Mass -

    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 -

    Question: Shouldn't the 2404.2 be in grams and not Kg?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    The density of a 4.41-m 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 …
  2. Physics

    The density of a 4.41-m 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 …
  3. Physics

    The density of a 5.0-m 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 …
  4. Physics

    A long thin rod lies along the x-axis 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 …
  5. Physics

    A long thin rod lies along the x-axis 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 …
  6. Physics - please help!!..

    A long thin rod lies along the x-axis 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 …
  7. 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 …
  8. Physics

    A long thin rod lies along the x-axis 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 …
  9. 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 …
  10. 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 …

More Similar Questions

Post a New Question