10) A solid disk with a c of 1/2, mass of 2 kg, and radius of 1.4 meters lies on a horizontally (so the normal force and weight can be ignored). A force of 9 Newtons is applied 0.37 meters directly to the right of center in the +x direction, a force of 25 Newtons is applied 0.80 meters directly below of center in the +x direction, and a force of 9 Newtons is applied at the edge of the disk directly above the center in the +x direction. Again, ignoring the weight and normal force, if the disk starts from rest, what is the angular velocity of the disk after these forces are applied for 3 seconds, in rad/s? If clockwise, include a negative sign.

Coefficient of drag (flat plate, NASA) = C(d) = 1.28

Weight = W = 4451 lbs

Gravitation constant = g = 32.2 ft/sec^2

Area = A = 197.5"" long x 78.2"" wide x (1 ft^2/ 14 in^2)

Vehicle falls flat, wheels 1st, straight down, at constant acceleration with no aerodynamic drag until terminal velocity

Horsepower needed to accelerate is AVERAGE - not peak

100% driveline efficiency

A hydrogen-rich gas stream contains 1.0 mole % carbon monoxide. It is desired to use a microporous ceramic membrane for separating carbon monoxide (CO) from hydrogen gas at a pressure of 1 atm and a temperature of 400C. The average pore diameter of the membrane is 15 nm and the void fraction is 0.30.

a) Estimate the molecular diffusivity of CO in a mixture with H2

b) Determine the Knudsen diffusion coefficient and the effective diffusion coefficient for CO in the membrane

In the “race” of conceptual problem 5 (and similar to what we did in lab), the uniform cylinder, uniform sphere, and cylindrical hoop race down a 2 meter long ramp tilted 10^o to the horizontal. Each object has the same mass (10.0 kg) and radius (10.0 cm). Assume no slippage between the ramp and object and the coefficient of friction = 0.5. Calculate the following: (a) the final velocity of each (b) the center of mass acceleration of each object, (c), the time required for each object to race down the ramp, (d) the frictional force acting on each object. Fill in the table below with the numerical values (but make sure you show how you obtained the necessary relationships!).

A wheel turns through 2.1 revolutions while accelerating from rest at 16 rpm/s.

What is its final angular speed?

How long does it take?

The rearview mirror of a car is a convex mirror (R = -15 m). Consider the image formed by a car that is 10 m from the mirror.

1. A convex mirror means that the mirror has a _positive/ negative_ radius of curvature. So, the center of curvature and

   focal length are located on the _same/ opposite_ side of the mirror as the incident and reflected (outgoing) light.

2. For a mirror, the focal length is equal to __________ of the radius of curvature.

3. What is the image distance?

4. What is the image magnification?

5. The sign of the image distance is ___________________, so the image is _real/ virtual_ and is formed on the _same/ opposite_ mirror side as the object. The sign of the magnification is __________________, so the image is _upright/ inverted_. The magnification is _less than/ equal to/ greater than_ 1, so the image size is ______________________ than the object size.

A bullet is fired horizontally at a stationary 7.0 kg target. The target sits on a frictionless horizontal

surface and is connected to a spring on the backside of the target. The spring has a spring constant

of 5000 N/m. The 11.0 g bullet is traveling horizontally at 675 m/s the moment before it strikes

the target. After 1 ms, the bullet is embedded into the target and begins to oscillate. Ignore air

resistance.

(a) Determine the speed of the block immediately after the collision.

(b) Find the period and amplitude of the resulting simple harmonic motion.

(c) On separate graphs, plot the position vs. time, velocity vs. time, and acceleration vs. time for the system starting when the bullet is fully embedded into the target. Be sure to clearly label

your axes and the scale of each graph.

(d) On a single graph, plot the potential energy, kinetic energy, and total mechanical energy as a function of time for the system starting when the bullet is fully embedded into the target. Be sure to clearly label your axes and the scale of your graph.

3. (a) What is “photon bunching”? Draw a simple diagram.

(b) Explain which histories interfere and why assuming that the photons are indistinguishable.

(c) What is the final conclusion? What do the photons do?

9) A flywheel initially rotating at 1200 rpm stops in 4.00 min when only friction acts. If an additional torque of 300 N-m is applied, it stops in 1.00 min. (a) What is the rotational inertia of the wheel? (b) What is the frictional torque?

(b) The plane is parallel to the xy-plane. 

 (c) The plane contains the y-axis, and its normal makes an angle of 30.0° with the x-axis.

1. (a) Explain the “one-time pad” method for sending secret messages. In particular, explain the nature and the role of the secret key.

(b) Why is it impossible for anyone without the secret key to read the encrypted message?

During high-intensity exercise such as sprinting or lifting a very heavy weight, energy is provided to cells by the phosphogen system (or ATP-PC system), which only works for a few seconds. If the diffusion constant of ATP is 3 ×10⁻¹⁰ m² s^-1, how far could this molecule diffuse in 5 seconds? (not 5.477E-5 m)

Driven RC circuit in parallel. A capacitor C is connected in parallel to a resistor R and an AC source providing a voltage v(t) = V sin(ωt).

(a) Make a phasor diagram at time t showing all relevant based on Kirchhoff’s rules.

(b) Find the impedance of this circuit and make a plot of Z vs. ω.

(c) What are the small and large frequency behaviors of the peak capacitor and resistor currents?

(d) What is the phase difference between the total current and the input voltage? (e) (5pts.) Write an expression for i(t), the total current thought the circuit, if V = 120 V, C = 47 µF, R = 230 Ω, and f = 440 Hz