Question

The linear mass density of a thin rod is given by Lambda(l) =
2e^{-l} lb ft^-1, where l is a dimensionless variable
representing the length in meter. The total length of the rod is 2
m. What is the mass of the rod in the SI unit? Given: 1 ft 0.305 m,
1 lb 0.454 kg

Answer #1

A thin rod of length L has uniform linear mass density λ
(mass/length).
(a) Find the gravitational potential Φ(r) in the plane that
perpendicularly bisects the rod where r is the perpendicular
distance from the rod center. Assume the gravitational potential at
infinity is zero.
(b) Find an approximate form of your expression from part (a)
when r >> L.
(c) Find an approximate form of your expression from part (a)
when r<< L.

The linear density (lamda) of a thin rod varies with position x
as (lamda)=lamda0(x^3/L^3). The rod lies along the X axis. If M is
the mass of the rod and L is the total length, then,
a) Find lamda0 in terms of M and L
b)Find the position of the centre of mass
c)Find the moment of inertia around the centre of mass.
d) Now imagine the same thin rod is attached to a hinge that is
allowed to rotate....

A two meter long thin rod is composed of two different materials
(fused together). Metal 1 is 0.6 meter long and metal 2 is 1.4
meter long. Metal 1 linear mass density is 5g/cm and metal 2 linear
mass density is 4g/cm. Where is the center of mass located for this
two meter long rod?

A thin rod of length L is non-uniformly charged. The charge
density is described by the expression λ=cx, where c is a constant,
λ is the charge per length, and x is the coordinate such that x=0
is one end of the rod and x=L is the other. Find the total charge
on the rod and the electric potential at a field point just
touching the rod at the x=0 end.

Calculate the center of mass of a nonuniform rod of length L,
whose linear density
is p(x) = p0√x and the moment of inertia for this rod
when the axis of rotation is located
at the lighter end.

A long thin rod of mass M and length L is
situated along the y axis with one end at the origin. A
small spherical mass m1 is placed at the
location P, which is at a distance d from the origin.
If L = 2.00 ? 104 m, d = 18.0 ?
104 m,M = 14.0 ? 106 kg,and
m1 = 8.00 ? 106 kg,what is the value
of this potential energy?

A rod (length L, total charge +Q) with charge density lambda =
a(y+b), where a and b are constants, is positioned along the y-axis
such that the upper end is at the origin.
a. Determine the electrical field (magnitude and direction) at
point P, on the y-axis, distance b from the upper end of the
rod.
b. Set up an integral that would allow you to determine the
electrical potential at point P.
c. Determine constant a in terms of...

A rod (length L, total charge +Q) with charge density lambda =
a(y+b), where a and b are constants, is
positioned along the y-axis such that the upper end is at the
origin.
(a) Determine the electric field (magnitude and direction) at
point P, on the y-axis, distance b from the upper end of
the rod
(b) Set up, but do not integrate, an integral that would allow
you to determine the electric potential at point P.
(c) Extra credit:...

An object is formed by attaching a uniform, thin rod with a mass
of mr = 7.22 kg and length L = 5.52 m to a uniform
sphere with mass ms = 36.1 kg and radius R = 1.38 m.
Note ms = 5mr and L = 4R.
1)What is the moment of inertia of the object about an axis at
the left end of the rod?
2)If the object is fixed at the left end of the rod, what...

A
thin 1 m long uniform rod with a total mass of 750g is suspended
vertically at the upper end. The moment of inertia of the rod in
respect to the center of mass is mL*2/12 (where L is the total
lenght of the rod). A 9 g bullet is shot to the lower end of the
rod and embeds there. The bullet speed before impact is 580 m/s.
Calculate the amount of energy transfered to the heat during the...

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