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Homework due 5-10-2013
1. A system consists of two blocks, each of mass M, connected
by a spring of force constant k. The system is initially shoved
against a wall so that the spring is compressed a distance D from
its original uncompressed length. The floor is frictionless. The
system is now released with no initial velocity.
a. Determine the maximum speed of the right-hand block.
b. Determine the speed of the center of mass of the system when the left-hand block is no
longer in contact with the wall
c. Determine the period of oscillation for the system when the left-hand block is no longer in
contact with the wall
2. A mass spectrometer, constructed as
shown in the diagram above, is to be
used for determining the mass of singly
ionized positively charged ions. There is
a uniform magnetic field B = 0.20 testa
perpendicular to the page in the shaded
region of the diagram. A potential
difference V = 1,500 volts is applied
across the parallel plates L and K,
which are separated by a distance d =
0.012 meter and which act as a velocity
a. In which direction, relative to the coordinate system shown above on the right, should the
magnetic field point in order for positive ions to move along the path shown by the dashed
line in the diagram above?
b. Should plate K have a positive or negative voltage polarity with respect to plate L ?
c. Calculate the magnitude of the electric field between the plates.
d. Calculate the speed of a particle that can pass between the parallel plates without being
e. Calculate the mass of a hypothetical singly charged ion that travels in a semicircle of radius
R = 0.50 meter.
f. A doubly ionized positive ion of the same mass and velocity as the singly charged ion
enters the mass spectrometer. What is the radius of its path?
3. In the circuit shown above, the battery
has been connected for a long time so that
the currents have steady values. Given
these conditions, calculate each of the
a The current in the 9-ohm resistor
b. The current in the 8-ohm resistor.
c. The potential difference across the 30-
Homework due 5-10-2013
microfarad capacitor.
d. The energy stored in the 30-microfarad capacitor.
At some instant, the connection at point P fails, and the current in the 9-ohm resistor becomes
e. Calculate the total amount of energy dissipated in the 8-ohm resistor after the connection fails
4. A slab of infinite length and infinite
width has a thickness d. Point P 1 is a point
inside the slab at x = a and point P2 is a
point inside the slab at x = -a. For parts (a)
and (b) consider the slab to be
nonconducting with uniform charge per unit volume ρ as shown.
a. Sketch vectors representing the electric field E
at points P1 and P2 on the following diagram.
b Use Gauss's law and symmetry arguments to
determine the magnitude of E at point Pl.
For parts (c) and (d),
consider the slab to be
conducting and uncharged
but with a uniform current
density J directed out of the
page as shown below,
a. Sketch vectors representing the magnetic field B
at points P1, and P2, on the following diagram.
d. Use Ampere's law and symmetry arguments to
determine the magnitude of B at point P1