• If a block of mass m at speed v collides inelastically with a block of mass M at rest, what is the final velocity of each block? What fraction of the initial energy is lost?

• Two identical circular hockey pucks of radius r traveling towards each other at the same speed v collide elastically. Their centers are separated by a vertical distance d, which is less than r. After the collision, with what angle relative to the initial path of the pucks will each one travel along?

• Explain the physics of Newton’s Cradle.

1. Derive Laws of Black Body Radiation from Wien’s Law: u_ν = ν³F(ν/T)
   1. What is Stephen’s Law?
   2. Please Prove Stephen’s Law from Wien’s Law
   3. Please Prove Wien’s Displacement Law from Wien’s Law

19 - 3 -4

A heat engine operates between a reservoir at 29°C and one at 341°C.

What is the maximum efficiency possible for this engine?

heat engine operates in a Carnot cycle between 88.0°C and 345°C. It absorbs 21,200 J of energy per cycle from the hot reservoir. The duration of each cycle is 3.00 s.

(a) What is the mechanical power output of this engine?
kW

(b) How much energy does it expel in each cycle by heat?

The sound from a busy highway contains a 500 Hz Fourier component whose power at the highway is 1.5 ✕ 10⁻⁶ watt/m. (Ignore sound interactions with the ground).

(a)What are the sound intensity (in W/m²), the sound intensity level (in dB) and the loudness (in phon) of that Fourier component at a distance of 25 m from the highway?

intensity=?  W/m²

intensity level =? dB

loudness=?  phon

(b)What are the sound intensity (in W/m²), the sound intensity level (in dB) and the loudness (in phon) of that Fourier component at a distance of 50 m from the highway?

intensity=? W/m²

intensity level=? dB

loudness=? phon

A package of mass 50 kg sits on an airless asteroid of mass 1.25 x 10^13 kg and radius 1000 m. We want to launch the package straight up so that it reaches a maximum distance of 4000 m from the center of the asteroid, where it will be picked up by a waiting ship before it can fall back down. We have a powerful spring whose stiffness is 1000 N/m. How much must we compress the spring to release it with the energy needed to reach the required altitude?

A 8.50 kg mass is attached to the end of a hanging spring and stretches it 28.0 cm. It is then pulled down an additional 12.0 cm and then let go. What is the maximum acceleration of the mass? At what position does this occur? What is the position and velocity of the mass 0.63 s after release?

A balance and torque experiment is conducted with an UN-balanced ruler.

Length of the ruler: 1 m

Mass of the ruler: 149 g

The pivot is at the 32-cm mark.

A 77-g mass is located at the 24-cm mark of the ruler.

We want to balance the ruler by placing another mass at the 11-cm mark.

What should be magnitude of this additional mass?

A balance and torque experiment is conducted with an UN-balanced ruler.

Length of the ruler: 1 m

Mass of the ruler: 97 g

The pivot is at the 61-cm mark.

A 45-g mass is located at the 33-cm mark of the ruler.

We want to balance the ruler by placing a 207-g mass somewhere on the ruler.

At which mark on the ruler should we place the 207-g mass?

you have preparing your coffee in the morning. it comes out of the brewrt at a whopping 100c and you pour about 3kg of coffee. you then add in 1kg of cream at 15c to customize your taste and 1 ice cube with mass of 0.05kg at 0c. if we can assume both the cream and coffee behave like water, what will be the final temperature of your coffee mixture?

(let coffee= 1, cream=2, ice cube=3)

Question: calculate the final equilibrium temperature.

Define each of the following reaction mechanism, giving its distinguishing characteristics

a) direct reaction; b) compound nucleus reaction; c) pre-equilibrium reaction; d) heavy-ion reaction, e) Stripping reaction f)Resonance and in each case give an example of the nuclear reaction described.

A Car weighs 4900 N, and can accelerate from 0 to 72 km/hour in 5 seconds

What is the acceleration?

How large is the net force acting on the car?

When three soap bubbles touch, the larger is inflated by the smaller until they form a single bubble. (a) What is the gauge pressure inside a soap bubble with a 1.50-cm radius? (b) Inside a 2.50-cm-radius soap bubble? (c) Inside a 3.75-cm-radius soap bubble? (d) Inside the single bubble they form if no air is lost when they touch?

Consider the delta function potential well :V(x) = −αδ(x) (α > 0).

(a) What are the boundary conditions on the bound state wave function and its derivative at x = ±∞ and x = 0? Explain. Hint: You may find the property stated in Prob. 2 useful.

(b) Show that there is only one bound state.

(c) Find the energy E and wave function ψ(x) of the bound state.

(d) Find the transmission coefficient for scattering states, with energy E > 0 and incident form the left

Why is the emission frequency lower than the excitation? What happens to the difference in energy?

You are in Denver, which is 5,280 ft above sea level. Compare the acceleration due to gravity in Denver to that at sea level (h = 0). What are your Weight and your mass at each of these locations? Rearth = 6.371 x 10^6 m. Mearth = 5.9763 x 10^24 kg

a) list the given

b) List what you are trying to find

c) what equations will you use? List below

d) calculate the accelerations due to gravity for each location ( report your answer to 3 decimal places)

e) compare these accelerations (make a ration of the two to see the relationship)

f) calculate your mass (in kg) and your weight (in newtons) for both locations

John’s mass is 98.6 kg, and Barbara’s is 67.0 kg. He is standing on the x axis at xJ = +9.45 m, while she is standing on the x axis at xB = +4.39 m. They switch positions. How far and in which direction does their center of mass move as a result of the switch?