Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.60 m . The merry‑go‑round is spinning at 22.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.

final angular velocity: ________ rpm

why are systems with fixed restriction metering devices critical to charge

The pilot of an airplane executes a loop-the-loop maneuver in a vertical circle. The speed of the airplane is 250 mi/h, at the top of the loop and 450 mi/h at the bottom, and the radius of the circle is 1 150 ft. Note: His apparent weight is equal to the magnitude of the force exerted by the seat on his body.

(a) What is the pilot's apparent weight at the lowest point if his true weight is 160 lb?
lb

(b) What is the magnitude of his apparent weight at the highest point?
lb

(c) Describe how the pilot could experience weightlessness if both the radius and the speed can be varied.

A light source emits a photon during a time interval of 2.89 10-8 s. (a) Find the minimum uncertainty in the photon's energy. (b) Find the minimum frequency bandwidth of the light

An airplane’s propeller blades slow down to 2rev/s in 5s, making 200rev in the process. Assuming a constant acceleration, what was the blades’ angular speed before starting to slow down? Answer: 4680 rpm

Problem 6. In space, thermal equilibrium is achieved when incoming radiation (e.g. from the Sun) is balanced against outgoing radiation (e.g. from the surface of Earth). The equilibrium achieved is a dynamic one, because there is still a net flow of heat in and out of the system, and the Sun and Earth never reach the same temperature (thankfully) because much of the radiation leaves the system.

(a) The Sun provides a heat to the surface of Earth with an intensity (power per unit area) of about 1000 W/m2 . Compute the total power received. (Hint: The correct area to use is the cross-sectional area of the Earth, because that is the size of the ‘shadow’ of solar radiation that is absorbed.) (In reality, about 1400 W/m2 reaches Earth and about 30% is reflected.)

(b) Suppose the Earth is a perfect black-body absorber and emitter of radiation, and has a uniform surface temperature. (This is not a great assumption.) Find the equilibrium temperature T of the surface in Kelvin and in Celsius, where Earth radiates exactly as much power as it receives from the Sun. Is it anywhere close to Earth’s average surface temperature?

(c) In fact, Earth’s atmosphere is not transparent to the outgoing radiation, which makes the emissivity of Earth imperfect. The result is a delicate balance that preserves a life-friendly temperature. What emissivity e is required to achieve the current 15◦C average surface temperature? What emissivity e would cause the temperature to rise by 2◦C? This is a vastly oversimplified model of Earth’s climate. More accurate models include multiple coupled layers with independent temperatures and emissivities; these models can fairly accurately predict the surface temperature as a function of greenhouse gas emissions (which determine the emissivity of the atmosphere). The net effect of adding carbon dioxide to the atmosphere is to reduce the amount of infrared emission at a given temperature, lowering e and raising the temperature.

Problem 1. Calculate the average speed of nitrogen molecules (N2) in air at room temperature (∼ 300 K). Compare to the speed of sound, which is about 343 m/s at the same temperature. Speculate on why they might be similar.

Suppose that the dipole moment associated with an iron atom of an iron bar is 1.7 × 10^-23 J/T. Assume that all the atoms in the bar, which is 7.0 cm long and has a cross-sectional area of 1.1 cm², have their dipole moments aligned. (a) What is the dipole moment of the bar? (b) What torque must be exerted to hold this magnet perpendicular to an external field of 2.0 T? (The density of iron is 7.9 g/cm³ and its molar mass is 55.9 g/mol.)

Complete the following statement: The maximum speed at which a car can safely negotiate an unbanked curve depends on all of the following factors except

A) the diameter of the curve.

B) the acceleration due to gravity.

C) the coefficient of static friction between the road and the tires.

D) the coefficient of kinetic friction between the road and the tires.

E) the ratio of the static frictional force between the road and the tires and the normal force exerted on the car.

Please explain in detail.

Three point charges are placed on the x-y plane: a +40.0nC charge at the origin, a -40.0nC charge on the x axis at 10.0cm, and a +100.0nC charge at the point (10.0cm, 9.00cm).

(A) Find the total electric force on the +100.0nC charge due to the other two.

Please answer in this format: ( ? N)x + ( ? N)y

(B) What is the electric field at the location of the +100.0nC charge due to the presence of the other two charges?

Please answer in this format: ( ? N/C)x + ( ? N/C)y

1. What condition is necessary for a shock wave to be created? How are sonic booms (a kind of sound wave) and Cherenkov radiations (a kind of light wave) similar? How are they different?

2. Explain how "light shockwaves" are created, if light is the fastest-moving thing in the universe. As an example, describe how the blue glow in the nuclear reactor pulse is created.

In the inside of a TV set an electron is accerlerated by a potential difference of 20 kV in an evacuated tube. It is then passed through an uniform magnetic field of 100 mT which deflects it to the desired position on the screen.

1) Draw a diagram showing the path of the electron as it passes from the electron source to the screen.

2) After passing through the accelerating potential, what is the kinetic energy of the electron in eV? In joules?

3) What is the speed of the electron just before it enters the magnetic deflecting field?

4) What will be the radius of curvature of its path in the field?