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 long thin rod of length 2.0 m has a linear density λ(x) = Ax where...
A rod of length 1.00 m has linear density (mass per unit length) given by λ = (40.0 kg/m) + (80.0 kg/m2)x where x is the distance from one end. (a) What is its mass? (b) How far from the x = 0 end is its center of mass?
1. A thin rod of length L and total mass M has a linear mass density that varies with position as λ(x)-γ?, where x = 0 is located at the left end of the rod and γ has dimensions M/L3. ĮNote: requires calculus] (a) Find γ in terms of the total mass M and the length L. (b) Calculate the moment of inertia of this rod about an axis through its left end, oriented perpen dicular to the rod; expressed...
A thin, uniform rod has length L and the linear density a (i.e. total mass M=al). A point mass m is placed at distance x from one end of the rod, along the axis of the rod. Calculate the gravitational force of the rod on the point mass m. (Hint: element of the mass is dM = adx) -GmM/x? O-GmM/(L2-x2) -GmM/(x+.5L) -GmM/(x2+Lx)
A long thin solid rod lies along the positive x-axis. One end is at x = 1.50 m and the other at x = 3.60 m. The linear mass density is λ = ax3 + bx, where λ is measured in kg/m, and the constants have the following values: a = 1.80 kg/m4 and b = 2.40 kg/m2. 1. Determine the total mass of the rod. 2. Calculate the x-coordinate of the center of the mass for this rod.
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?
(a) A thin plastic rod of length L carries a uniform linear charge density, λ-20 trCm, along the x-axis, with its left edge at the coordinates (-3,0) and its right edge at (5, 0) m. All distances are measured in meters. Use integral methods to find the x-and y-components of the electric field vector due to the uniformly-charged charged rod at the point, P. with coordinates (0, -4) m. 4, (o, 4 p2212sp2018 tl.doex
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?
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 charge of uniform linear density 2.0 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 5.0 cm, outer radius 10 cm). The net charge on the shell is zero. (a) What is the magni- tude of the electric field 15 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell?
An insulating rod having linear charge density λ = 45.0 μC/m and linear mass density μ = 0.150 kg/m is released from rest in a uniform electric field E = 100 V/m directed perpendicular to the rod (a) Determine the speed of the rod after it has traveled 2.00 m. (b) What If? How does your answer to part (a) change if the electric field is not perpendicular to the rod? Explain. E E λ, μ