One ring to rule them all. N identical beads (mass m) can move
along the ring...
One ring to rule them all. N identical beads (mass m) can move
along the ring of radius R. Each bead is connected
to the one behind it and to the one in front of it by a spring of
constant k. Find all normal
frequencies.
Consider a particle of mass m that can move in a one-dimensional
box of size L with the edges of the box at x=0 and x = L. The
potential is zero inside the box and infinite outside.
You may need the following integrals:
∫ 0 1 d y sin ( n π y ) 2 = 1 / 2 , for all
integer n
∫ 0 1 d y sin ( n π y ) 2 y = 1...
Evaluate the following integral using the Midpoint Rule M(n),
the Trapezoidal Rule T(n), and Simpson's Rule S(n) using
nequals4. Integral from 2 to 6 StartFraction dx Over x cubed plus x
plus 1 EndFraction Using the Midpoint Rule, M(4)equals
A mass of 1.1kg is attached to a spring and constrained to move
without friction along the x-axis. The mass is attached to a spring
of spring constant 80?? N m ; one end of the spring is attached to
a fixed point along the x-axis while the other is attached to the
mass. The equilibrium position of the mass is the origin. The mass
has a position as a function of time which can be expressed:
?(?)=?cos(??+?) x (...
The particle has a mass of 0.6 kg and is confined to move along
the smooth horizontal slot due to the rotation of the arm OA.
Assume the particle contacts only one side of the slot at any
instant. The arm has an angular acceleration of θ¨ = 3 rad/s2 when
θ˙ = 2 rad/s at θ = 30∘. (Figure 1) Part A Determine the magnitude
of the force of the rod on the particle when θ = 30∘. Express...
Two billiard balls with the same mass m move in the direction of
one another. Ball one travels in the positive x-direction with a
speed of V1i, and ball two travels in the negative x-direction with
a speed of V2i. The two balls collide elastically, and both balls
change direction after collision. If the initial speeds of the
balls were v1i=2.0m/s and v2i =1.0m/s, what would be the final
speed and direction of ball two, v2f, in m/s? Thank...
One particle whose mass is defined by m is moving along a
certain line in the region x>0 is subjected to a conservative
net force given by the following equation: F(x)= F₀x eˣ^²/²ᴸ^²
The constants F and L are both positive real quantities with
appropriate physical dimensions.
Find the formula for the corresponding U(x), with the given
assumption that the limₓ↠∞U(x)=0.
Secondly, we know that the particle is launched from an initial
location x₀>>>L towards x=0. (the >>> mean that...
A 1.005 m chain consists of small spherical beads, each with a
mass
of 1.00 g and a diameter of 5.00 mm, threaded on an elastic
strand
with negligible mass such that adjacent beads are separated by
a
center-to-center distance of 10.0 mm. There are beads at each
end
of the chain. The strand has a spring constant of 28.8 N/m.
The
chain is stretched horizontally on a frictionless tabletop to
a
length of 1.50 m, and the beads at...
Let's suppose we are pulling a box of mass m along a horizontal
floor. All sides of the box have the same type of surface (same
coefficient of friction between any side and the floor). In one
case, the contact surface is much larger (first picture) and in
another, it is much smaller. Will there be any difference in the
force of friction? Why?
A car of mass M and a small truck of mass 3M
are travelling along two roads perpendicular to each other as
shown.The car and the truck collide at the intersection at
O.
The speed of the truck just before collision is
VT =15.0m/s. Immediately after the
collision, the wreckage moves as a single mass with
Vf =12.0m/s as shown.
Using conservation of momentum:
[a] Find the value (in
degrees) of θ?
A car of mass M and a small...
The uniform line charge density extends over entire ring
λ=1.96E-6 C/m Mass of ring M=0.13 kg. Radius of ring R=0.67 m.
Radius of Magnetic field region, a=0.41 m. Magnetic field, B=1.61
T. The magnitude of the angular velocity of the wheel after the
field is suddenly switched off is w= radians/sec.? The moment of
inertia of a loop is MR2.