Object 1 is held at rest at the top of a rough inclined plane of length ? = 1.5 ? and angle ? = 25∘. When it is released, it moves with an acceleration of 2 ? down the plane. a) Find the coefficient of kinetic friction ?? of the inclined plane. (??) b) Find the speed of Object 1 when it reaches the bottom of the plane. (??) At the bottom of the inclined plane, Object 1 arrives at a smooth (frictionless) horizontal surface where it hits Object 2 of three times mass of Object 1 (?2 = 3?1). c) Assuming an elastic collision, find the speeds of Objects 1 and 2 just after the collision

Rewrite the following vectors in terms of their magnitude and angle (counterclockwise from the +x direction).

(a) A displacement vector with an x component of +9.1 m and a y component of -9.5 m.

(b) A velocity vector with an x component of -98 m/s and a y component of +38 m/s.

(c) A force vector with a magnitude of 54 lb that is in the third quadrant with an x component whose magnitude is 33 lb.

Two identical objects, A and B, are thermally and mechanically isolated from the rest of the world. Their initial temperatures are TA > TB. Each object has heat capacity C (the same for both objects) which is independent of temperature.
(a) Suppose the objects are placed in thermal contact and allowed to come to thermal equilibrium. What is their final temperature? How much entropy is created in this process? How much work is done on the outside world in this process?

(b) Instead, suppose objects A (temperature TA) and B (temperature TB < TA) are used as the high and low temperature heat reservoirs of a heat engine. The engine extracts energy from object A (lowering its temperature), does work on the outside world, and dumps waste heat to object B (raising its temperature). When the temperatures of A and B are the same, the heat engine is in the same state as it started and the process is finished. Suppose this heat engine is the most efficient heat engine possible. In other words, it performs the maximum work possible. What is the final temperature of the objects? How much entropy is created in this process? How much work is done on the outside world in this process?

1. Water flows through a 3 inch diameter pipe at a velocity of 10 ft/s. Find the a) volume flow rate in cfs(cubic feet per second) and gpm(gallons per minute) b) mass flow rate in slug/second.

a toy rocket is fired fired at rest vertically upwards and accelerates at a constant rate. At the instant the engine cuts out, the rocket has risen to 52 m and acquired a velocity of 80 m/s. The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground with negligible air resistance. The speed of the rocket upon impact on the ground is closest to

A magnesium ion (Mg⁺) moves in the xy-plane with a speed of 2.80 ✕ 10³ m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 2.75 ✕ 10⁻⁵ T, find the magnitude of the magnetic force acting on the ion and the magnitude of the ion's acceleration.

(a)

the magnitude (in N) of the magnetic force acting on the ion

_______ N

(b)

the magnitude (in m/s²) of the ion's acceleration

_______ m/s²

Anthony carelessly rolls his toy car off a 78.0-cm-high table. The car strikes the floor at a horizontal distance of 98.0 cm from the edge of the table.

(a) What was the velocity with which the car left the table? (Enter the magnitude.) m/s

(b) What was the angle of the car's velocity with respect to the floor just before the impact? ° below the horizontal

In this week's lecture #3, Walter Lewin lit a fluorescent bulb by holding it near a Van de Graaff generator, charged to 300,000 V. Suppose that the spherical conductor of the Van de Graaff has a diameter of 68.69 cm, that the bulb is 100.56 cm in length, and Prof. Lewin is holding the near end of the bulb 32.23 cm from the surface of the Van der Graaff. What is the potential difference (V) between the two ends of the bulb?

On neutron-capture induced fission, 235 92U typically splits into two new “fission product” 92 nuclei with masses in the ratio 1:1.4. These are born with the same proton to neutron ratio as the original uranium, so they have too many neutrons to be stable at their mass number and are highly radioactive. Energy is released in two stages: first an intermediate or prompt release leading to radioactive fission products in their ground state; and then a much slower release via the beta and gamma decays of the fission product nuclei, which continue until they become stable. Use the semi-empirical mass equation to estimate the magnitudes of the energy released per fission in each of the two stages. You may take the final Z/A ratios from appropriate known stable nuclei. Furthermore, as this is an estimate, you may ignore the incoming and outgoing neutrons, and drop the pairing term from the SEMF formula.

Please note that the problem as stated here is a simplification: In reality, the 235 92 U nucleus splits into a variety of daughter pairs, most commonly with approximately the above mass ratio, and in some rare instances even into three daughters.

I am supposed to answer these conceptual questions with this lab simulator, but I can never get the simulator to work https://phet.colorado.edu/en/simulation/legacy/energy-skate-park

Help please?

Energy State Park Lab Handout

Click on the “Energy State Park Simulation” link to perform simulations in the setup satisfying the given conditions.

Upon opening the simulation, the skate should be alternating between the walls of the skate park with no friction added and with Earth’s gravity. Click on the Show Pie Chart under the Energy Graphs section.

1. With no friction, will his motion every stop?

2. What principle can be applied to this situation?

3. What type of forces are applied here? (Conservative/Non-conservative)

4. What happens to the skater’s potential energy has he falls down a wall to the valley? What about when he moves up a wall from the valley?

5. What happens to the skater’s kinetic energy has he falls down a wall to the valley? What about when he moves up a wall from the valley?

6. Will any kinetic energy be transformed into thermal energy? If so , why? If not, why?

7. Where does the skater have the maximum potential energy?

8. Where does the skater have the maximum kinetic energy?

Now change the coefficient of friction to half way between None and Lots.

1. Are there any non-conservative forces in this simulation? If so what force?

2. With friction, will the skater ever stop?

3. Would thermal energy be created with this situation?

Conceptual Questions:

1. What is the formula for kinetic energy?

2. What is the formula for gravitational potential energy?

3. If the 75 kg skater reaches a maximum height of 5 feet, what is his maximum gravitational potential energy? (Hint: remember to convert to meters).

4. Is gravitational potential energy a conservative or non-conservative force? Is friction force a conservative or non-conservation force?

Inflation

(a) Why is it puzzling that the observed CMB temperature is almost exactly the same on opposite sides of the sky? How would this result be explained in cosmology theories that do not include inflation?

(b) How does inflation answer the puzzle from part (a)? What other properties of the homogeneous universe does inflation explain?

Write the fundamental postulates of magnetostatic in free space in differential form.

By making use of the expressions you have written,

a)Write the basic propositions of magnetostatic in integral form by showing step by step.

b)Discuss whether the magnetostatic field vector is solenoidal or irrotational. If the magnetic flux vector is not irrotational, in which case is it irrotational?

2. Temperature and Illumination

Alone in your dim, unheated room, you light a single candle rather than curse the darkness. Depressed with the situation, you walk directly away from the candle, sighing. The temperature (in degrees Fahrenheit) and illumination (in % of one candle power) decrease as your distance (in feet) from the candle increases. In fact, you have tables showing this information. (tables are in the text).

You are cold when the temperature is below 40◦. You are in the dark when the illumination is at most 50% of one candle power.

1. (a) TwographsareshowninFigures2.70and2.71.Oneistemperatureasafunctionofdistance and one is illumination as a function of distance. Which is which? Explain.

   Figure 2.70 Figure 2.71

2. (b) What is the average rate at which the temperature is changing when the illumination drops from 75% to 56%?

3. (c) You can still read your watch when the illumination is about 65%. Can you still read your watch at 3.5 feet? Explain.

4. (d) Suppose you know that at 6 feet the instantaneous rate of change of the temperature is −4.5◦F/ft and the instantaneous rate of change of illumination is −3% candle power/ft. Estimate the temperature and the illumination at 7 feet.

5. (e) Are you in the dark before you are cold, or vice versa?

For the TE10 and TE11 modes of a rectangular waveguide, derive expressions for the surface current density and the surface charge density.