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.

A father (weight W = 858 N) and his daughter (weight W = 372 N) are spending the day at the lake. They are each sitting on a beach ball that is just submerged beneath the water (see the figure). Ignoring the weight of the air in each ball, and the volumes of their legs that are under the water, find (a) the radius of father's ball and (b) the radius of daughter's ball

A hot-air balloon stays aloft because hot air at atmospheric pressure is less dense than cool air at the same pressure. The volume of a balloon is V = 1000.0 m3,

and the surrounding air has a temperature T0 which is 10.0 degrees C. The density of air at 10.0 degrees C and atmospheric pressure is p0=1.23 kg m-3.

a. What must the temperature T of the air in the balloon be for it to lift a total load of M plus the mass of the hot air? Express your answer only in terms of the variables defined above and any needed physical constants.

b. If this happens when T = 80.2◦C, what is the mass M in kilograms?

c. What is the density of the air inside the balloon in kgm−3?

An amusement park ride consists of a cylindrical chamber of radius R that can rotate. The riders stand along the wall and the chamber begins to rotate. Once the chamber is rotating fast enough (at a constant speed), the floor of the ride drops away and the riders remain "stuck" to the wall. The coefficients of friction between the rider and the wall are us and uk. 1. Draw a free body diagram of a rider of mass m after the floor has fallen away. 2. Is the rider on the wall accelerating? If so, in what direction? Should our FBD be balanced? 3. Write Newton's second law in the vertical direction. 4. Write Newton's second law in the horizontal direction. 5. If the ride takes a time T to go through one full revolution, what is the speed of the rider on the wall of the ride? 6. Assume that the ride is spinning just fast enough to keep the rider on the wall. Using the equations found in questions #3 and #4, calculate the minimum velocity to keep the rider suspended. 7. You get on the ride and notice another rider beside you who has twice your mass. If the ride is going just fast enough to keep you suspended, will the person beside you have a problem on the ride? 8. After a rider gets sick on the ride, the operator hoses down the walls of the ride, which reduces the coefficient of friction by half. What happens to the minimum velocity required for the rider to remain suspended?

A uniform solid ball of m=4.0 kg and radius r rolls smoothly down a ramp. The ball starts from rest. The ball descends a vertical height of 6.0 m to reach the bottom of the ramp. What is its speed at the bottom?