Homework due 5-1-2013
In the circuit illustrated above, switch S is initially open and the battery has been connected for a long
time.
(a) What is the steady-state current through the ammeter?
(b) Calculate the charge on the 10 µF capacitor.
(c) Calculate the energy stored in the 5.0 µF capacitor.
The switch is now closed, and the circuit comes to a new steady state.
(d) Calculate the steady-state current through the battery.
(e) Calculate the final charge on the 5.0 µF capacitor.
(f) Calculate the energy dissipated as heat in the 40 Ω resistor in one minute once the circuit has
reached steady state.
A horizontal force F is applied to a small block of
mass ml to make It slide along the top of a larger
block of mass m., and length l. The coefficient of
friction between the blocks is µ. The larger block
slides without friction along a horizontal surface. The blocks start from rest with the small
block at one end of the larger block, as shown
a. On the diagrams below draw all of the forces acting on each block. Identify each force.
b. Find the acceleration of each block a1, and a2, relative to the horizontal surface.
c. In terms of l, a1, and a2, find the time t needed for the small block to slide off the end
of the larger block.
d. Find an expression for the energy dissipated as heat because of the friction between the
two blocks.
Homework due 5-1-2013
A ball of mass m is attached by two strings to a vertical rod, as shown
above. The entire system rotates at constant angular velocity ω about the
axis of the rod.
a. Assuming ω is large enough to keep both strings taut, find the
force each string exerts on the ball in terms of m, g, R, and θ.
b. Find the minimum angular velocity, ωmin for which the lower
string barely remains taut
The horizontal uniform rod shown
above has length 0.60 m and mass
2.0 kg. The left end of the rod is
attached to a vertical support by a
frictionless hinge that allows the rod
to swing up or down. The right end
of the rod is supported by a cord
that makes an angle of 30o with the
rod. A spring scale of negligible
mass measures the tension in the
cord.0.50 kg block is also attached to
the right end of the rod.
(a) On the diagram below, draw and label vectors to
represent all the forces acting on the rod. Show each
force vector originating at its point of application.
(b)
Calculate the reading on the spring scale.
(c)
The rotational inertia of a rod about its center is ML2/12, where M is the mass of the
rod and L is its length. Calculate the rotational inertia of the rod block system about the hinge.
(d)
If the cord that supports the rod is cut near the end of the rod, calculate the initial
angular acceleration of the rod- block system about the hinge.