The normalized wave function of an electron in a linear accelerator is ψ = (cos χ)e^ikx + (sin χ)e^–ikx, where χ (chi) is a parameter. (a) What is the probability that the electron will be found with a linear momentum (a) +kħ, (b) −kħ? (c) What form would the wave function have if it were 90% certain that the electron had linear momentum +kħ? (d) Evaluate the kinetic energy of the electron.

Bart and Nelson challenged each other to a bumper car game. Bart, whose car had a mass of 120 kg (with him in it), traveled west at a velocity of 9 m/s. Nelson and his car had a total mass of 150 kg traveled a velocity of 7 m/s east, heading towards Bart. The two had a head-on collision. Use the frame of reference in which the east is positive.

a) If Bart left the collision at a velocity of 7 m/s east, what velocity did Nelson leave with?

b) Determine the total kinetic energy for Bart and Nelson before the collision. Determine the total kinetic energy after the collision.

c) Instead of heading towards each other, Bart was going 9 m/s east following behind Nelson, whose velocity is still 7 m/s east. At what velocity would Bart travel at after the collision if Nelson left the collision with a velocity of 7 m/s east?

Show how the wave function of the even states of a particle in an infinite well extending from x=-L/2 to x=L/2 evolve in time. Details!

5) A solenoid passes through the x-y plane. A charge of +5 Coulombs with a mass of 5 x 10-7 kg moving at 5 m/s (in the x-y plane) is placed in the solenoid. Due to the magnetic field produced by the solenoid, the charge moves counter-clockwise in a circle at a frequency of 34 Hz. The charge is removed and a circular wire wound 3 times with a radius of 0.6 meters is placed in the solenoid. If the total magnetic field at the center of the circular is zero, what is the amount and direction of the current in the circular wire in amps? Indicate clockwise by a negative sign (negative answer) and don't enter a sign for counter-clockwise.

4. Ammeter: Explain how to setup a DMM to measure current in the circuit. Will it matter if the ammeter (DMM used to measure current) is before or after the resistor (on the side of the + or – terminal)?.

A rocket has an initial mass of 28500 kg, of which 20% is the payload (i.e., the mass of the rocket minus the fuel). It burns fuel at a rate of 195 kg/s and exhausts its gas at a relative speed of 1.5 km/s.

(a) Find the thrust of the rocket.
kN
(b) Find the time until burnout.
s
(c) Find its final speed assuming it moves upward near the surface of the earth where the gravitational field g is constant.
km/s

1.Answer the following questions

A) Describe how the molecules in a gas produce an emission spectrum. How is this useful in astronomy if we assume that the laws of physics are the same everywhere?

B) Why was the uniform expansion model adopted? How does this lead to a necessary differentiation between classical and cosmological redshift

After they completely run out of fuel, all stars leave behind one of three objects, which do not usually do any more nuclear fusion. What are these three objects? Give the name of each and quick description.

A flywheel in a motor is spinning at 540.0 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 36.0 s, and during this time the flywheel slows down uniformly due to friction in its axle bearings. During the time the power is off, the flywheel makes 230.0 complete revolutions.

1. At what rate is the flywheel spinning when the power comes back on?

2. How long after the beginning of the power failure would it have taken the flywheel to stop if the power had not come back on?

Express your answer in seconds.

3. How many revolutions would the wheel have made during this time?

5a) A 5-kg object travels at a constant velocity of 25 m/s east on a smooth, frictionless surface. An 8-kg object travels at a constant velocity of 55 m/s west on the same surface and then collides directly with the 5 kg-object. The two objects stick together. What is the velocity of the two-object system, just after they collide and stick together?

b) After a .20 kg street-hockey puck is hit, it has an initial velocity of 35 m/s and travels on a uniform, horizontal cement surface and uniformly slows to a stop in 6 seconds (due to the friction between the puck and the cement). What is the coefficient of kinetic friction between the puck and the cement surface?

c) A horizontal spring has a spring constant of 150 N/m. ; a 0.25 kg mass is placed at the spring's free end, on a level, horizontal, frictionless surface. The spring- mass system is compressed 12 cm, and then released from rest. What is the maximum speed, in meters per second, of the released mass?

A thin stick of length 80.0 cm and mass 120.0 g has two small spherical masses attached

to its opposite ends (treat them as point masses). One mass is 20.0 g and the other mass is

50.0 g. The stick rotates frictionlessly about a horizontal axis passing through its centre. If the

stick starts from rest in a horizontal position, what is the linear speed of the larger spherical

mass at the moment that it is passing through its lowest point?

please include any free body diagram if required

Biologists have studied the running ability of the northern quoll, a marsupial indigenous to Australia. In one set of experiments, they studied the maximum speed that quolls could run around a curved path without slipping. One quoll was running at 2.8 m/s around a curve with a radius of 1.6 mm when it started to slip.

What was the coefficient of static friction between the quoll's feet and the ground in this trial?

A cylinder with a piston contains 0.160 mol of nitrogen at 1.80×105 Pa and 310 K . The nitrogen may be treated as an ideal gas. The gas is first compressed isobarically to half its original volume. It then expands adiabatically back to its original volume, and finally it is heated isochorically to its original pressure.

a.) Find the work done by the gas during the adiabatic expansion.

b.) Find the heat added to the gas during the adiabatic expansion.

c.) Find the internal-energy change of the gas during the adiabatic expansion.

Suggest 6 ways to increase the brightness of the lamp when AC is used?