Collisions
What is conserved in an elastic collision? What about an inelastic collision?
Momentum and internal energy is conserved in an elastic collision. Momentum is conserved in an inelastic collision, but not internal energy.
How is angular momentum defined?
L = I*w
Explain what energy quantization means.
Energy comes in minimal quantities or packets rather than continuous values.
In as simple terms as possible, what does the Second Law of Thermodynamics say?
You can't win. Entropy will always increase.
A meteor is approaching the edge of a satellite (similar to the one we did in class) with a velocity of 400 m/s and smashes through one of the solar panels. The meteor has a mass of 5000 kg. It goes through the 5 meter long solar panel, remaining at its angle of 35 degrees from the horizontal axis and leaves with a velocity of 325 m/s. The satellite has a mass of 7000 kg, an inner radius of 2 meters and is initially moving with an angular speed of 0.2 rad/s clockwise and a translational speed of 3 m/s to the right. What is the translational velocity and angular speed that the satellite will have after the collision?
v2,f = <47.14, 31.14, 0> m/s
w2 = 192.19 rad/s
Assuming an elastic collision, if a vehicle with a mass of 1500 kg with a speed of 2.3 m/s collides with a vehicle of mass 300 kg at rest, what will the speed of the second vehicle be after the collision?
11.5 m/s
What is the angular momentum of a sphere of mass 10 kg and radius of 0.2 meters spinning at 2.4 rad/s?
L 0.384 kgm2/s
Rank the energy level spacing size of rotational, electronic, and vibrational energies in descending order.
Electronic > Vibrational > Rotational
How many ways are there to flip 13 heads with 25 coin flips?
5200300
How is temperature related to energy? Explain graphically.
The inverse of the temperature is the slope of the graph where entropy is plotted against internal energy.
Imagine a cart with a mass of 20 kg is moving at 4.3 m/s and hits a cart with a mass of 100 kg. If the carts stick together after the collision, what velocity will they be moving with?
0.717 m/s
What is the angular momentum of a thin disk with a mass of 5 kg and a radius of 0.7 meters that is spinning at a speed of 8.9 rad/s?
L = 5.47 kgm2/s
What energy is required for a hydrogen atom to jump from its first electronic energy level to is third electronic energy level?
E = 12.09 eV
Explain/draw where the multiplicity formula for quantum oscillators: (q+N-1)!/q!(N-1)! is derived from the combination formula: N!/q!(N-1)!
Similar to listing heads and tails, you can list the quanta and the barriers of the oscillators and use the same combination formula for it. (See answer sheet)
True or false. The intersect of the entropy graphs against internal energy of two objects is where the system will tend towards.
False. The intersect is not necessarily where total entropy is maximum. It is maximized when total multiplicity is maximized.
A cart with a mass of 200 kg is moving with a speed of 3.4 m/s towards another cart with a mass of 45 kg at rest. If the second cart is moving at 3 m/s after the collision, what speed is the first cart moving at after the collision? What was the change in internal energy?
v1,f = 2.73 m/s
Change in internal energy = 208.81 J
Let's say a thin rod of 20 kg and a length of 0.5 m is spinning about its center at a speed of 3.5 rad/s. If I were able to increase its length to 0.7 m during its motion, what would its new speed be?
wf = 1.785 rad/s
What would the vibrational energy of a quantum harmonic oscillator be if its ground state energy is 1.3x10-33 J, it has a spring constant of 0.2 N/m, it has a mass of 0.05 kg, and it is at its sixth energy level?
E6 = 2.57x10-33 J
For a box with 15 slots, how many ways can I distribute 5 balls into the box? What is the entropy of this system?
S = 1.29x10-22 J/K
With an entropy versus internal energy graph of a two-object system, where does the system reach equilibrium. Why?
When the slopes are equal and opposite because that is when the temperatures are equal. That is why it is called thermal equilibrium.
Imagine that a clay ball of mass 10 kg is rolled on the ground with a velocity of <2, 1.5, 0> m/s. A second clay ball of mass 12.3 kg is also rolled towards the first ball with a velocity of <-3, 1.9, 0> m/s. Assuming the clay balls stick together, what will the final velocity be of the clay balls? What will the change in internal energy be?
vf = <-0.76, 1.72, 0>
Change in internal energy = 69.44 J
Two disks are next to each other so that when one moves, it can transfer its energy to the other so that it can begin moving. The first disk has a mass of 50 kg and a radius of 0.9 m and is initially spinning at 1.3 rad/s. If the second disk of mass 35 kg and radius 0.8 m initially starts at rest, but begins spinning due to the other disk, how fast is it moving when the first disk reaches 1 rad/s.
w2,f = 0.543 rad/s
True or false. A system has to be rise through every energy level to get to a desired higher energy level. Explain.
False. A system can jump from a lower energy level to a higher energy level without having to pass through each energy level between them, but it must obtain the exact energy needed to jump to that level.
I have two boxes, one with 30 slots and another with 20 slots. If I have 5 balls to randomly put into these boxes, without doing any math, what would the most likely state of the system be?
3 balls in box one and 2 balls in box 2.
How would you find the probability of a macrostate to occur?
Multiplicity of that macrostate divided by the total multiplicity of the entire system.