(1 point) A rod has length 5 meters. At a distance x meters from its left...
A non-uniform rod of length 0.5m is placed along the x-axis at a distance.2m from the origin. The mass per unit length 2 varies according to the expression λ = 5 + 2x2, measured in units of kg/m, where x is measured in meters from the origin. Set up but do not solve an integral that will allow you to find the gravitational force exerted by the rod on a 0.1 kg mass placed at the origin (Hint: An element...
A long thin rod of length 2.0 m has a linear density λ(x) = Ax where x is the distance from the left end of the rod and A=3.0 kg/m. What is the mass (in kg) of the rod ?
A thin rod extends from x-o to x= 13.0 cm. It has a cross-sectional area A= 6.00 cm2, and its density increases uniformly in the positive x-direction from 2.50 g/cm3 at one endpoint to 18.5 g/cm3 at the other. (a) The density as a function of distance for the rod is given by p-B+ cx, where B and C are constants. What are the values of B (in g/cm3) and C (in g/cm4)? C1.2319/cm (b) Finding the total mass of...
HW 5.7. A rod of length 20.0 cm has linear density (mass per unit length) given by 1 = 40.0 + 10.0 x, where x is the distance from one end, measured in meters, and is in grams/meter. (a) What is the mass of the rod? (b) How far from the x = 0 end is its center of mass?
A thin rod extends from x 0 to x = 15.0 cm. It has a cross-sectional area A-e 6.00 cm, a increases uniformly in the positive x-direction from 2.00 g/cm3 at one endpoint to 19.5 g/cm3 at the other The density as a function of distance for the rod is given by B+ Cx, where B and Care constants. (a) What are the values of B (in g/cm3) and C (in g/cm) g/cm3 Finding the total mass of the rod...
A rod of Length L lies along the x axis with its left end at the origin. It has a nonuniform charge density lambda = alpha x, where alpha is a positive constant. Calculate the electric potential at point B, which lies on the perpendicular bisector of the rod a distance b above the x-axis. (Use the following as necessary: alpha, k_, L, b, and d.) v = A wire having a uniform linear charge density lambda is bent into...
20. A thin rod of mass M and length L gravitationally interacts with a point mass m that is a perpendicular distance a away from its left end (see the figure). The rod is non-uniform, and its linear density (mass per unit length) increases with the distance from its left end according to 2(x) = 2Mx/L?, where x is the horizontal coordinate along the rod (so that x = 0 is at its left end and x=L is at its...
A rod of length 30.0 cm has linear density (mass per length) given by: d = 50.0 20.0 x where x is the distance from one end, measured in meters and A is in kg/meter. (a) What is the mass of the rod? (b) How far from the x-0 end is its center of mass?
Consider a rod that is not uniformly charged, but rather has a charge density that increases linearly from right to left over the length of the rod: 2q λ(x) = x. L2 This means that a point charge at position x has a charge dq-λ (x)dx. The rod and its coordinate system are shown below. The total length of the rod is L. Answer the following in terms of q, L, d, and fundamental constants. λ dx correspond to? Evaluate...
The charge per unit length on the thin rod of length L shown below is λ what is the electric field at the point P, distance a away from the right end of the rod? 1. Define a segment of charge: 2. Express the charge of one segment: 3. Express the E field of that one segment. 4. Integral each of the components of that field: