It is desired to take advantage of the current of a river coming upstream for an electric power generation project. The point where the turbine-generator will be installed is 50 meters below the upstream level. The upstream speed is 9 m / s and the downstream speed is 2 m / s. There will be a mass flow of water of 1500 kg / s. Calculate an estimate for the generation of electrical power produced if you have a turbine with an efficiency of 0.93 and an electric generator with an efficiency of 0.95.

A projectile launched from ground level lands 2.44 s later on a level field 40.0 m away from the launch point. How many degrees is the projectile above the horizontal?

In the Olympic shotput event, an athlete throws the shot with an initial speed of 13.0 m/s at a 44.0 ∘angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground.

How far does the shot travel?

Express your answer with the appropriate units.

5- how are the resistor currents related to the circuit current?

6- How are the resistor currents and resistances related?

7- how are the currents in the wires related to the currents in the resistors ?

8- what can you conclude about Currents in a series circuit? Is the circuit current the same as it was in the parallels circuit?why?

NASA has launched a mission to a newly discovered object, spherical in shape.

A satellite is given a gravitationally driven circular orbit around the object. The altitude of the satellite in its orbit is equal to the radius of the object, and it takes 19.4 × 103 ??? for the satellite to complete one orbit.

At the same time, a rover lands on the surface of the object. NASA engineers notice one of the support arms on it is broken and is swinging like a pendulum. The arm is 1.50 ? long and the period of its swing is 7.30 ???.

What is the radius (in km) and mass (in kg) of this newly discovered object?

What is the magnitude of the electric field at a point midway between a −7.7μC and a +6.2μC charge 10cm apart? Assume no other charges are nearby.

What is the direction of the electric field?

Provide a schematic diagram of the main parts of a nuclear spectroscopy set up and describe their functions. What are characteristics of the Si detectors which mostly affect the energy resolution of the spectroscopy set up?

A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length ?? where ? is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +?.

Part B

Find the direction of the electric field in terms of ?and the distance r from the axis of the tube forr<a.

Find the direction of the electric field in terms of  and the distance  from the axis of the tube for .

Part D

Find the direction of the electric field in terms of ?and the distance r from the axis of the tube for a<r<b.

Find the direction of the electric field in terms of  and the distance  from the axis of the tube for .

Part G

What is the charge per unit length on the inner surface of the tube?

Express your answer in terms of the given quantities and appropriate constants.

Part H

What is the charge per unit length on the outer surface of the tube?

Express your answer in terms of the given quantities and appropriate constants.

PLEASE SHOW ALL WORK! Thanks!

Consider a phase maneuver starting at Earth and ending up at the L5 point, using 1 revolution.a) Describe the phasing orbit in terms of semi-major axis, period, and distance from the sun at aphelion and perihelion.b) Calculate the ∆v’s required to enter the orbit from Earth and exit the orbit at L5.c) Looking at the symmetry of the situation, you should conclude that going to L4 and back takes just as much time and fuel as going to L5 and back. Can you think of a reason why L5 is preferred?

A ball of mass 0.5 kg makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.450 its original speed. The mass of the second ball in kg

A homogeneous three-dimensional solid has a heat capacity at constant volume CV that depends on temperature T. Neglecting differences in the transverse and longitudinal waves in the solid, there are 3N vibrational modes, where N is the number of atoms in the solid. Here, the solid has N = 3.01 x 1023 atoms which occupy a total volume V = 18.0 cm3 . There are two transverse shear waves and one longitudinal wave; all waves have the same speed of sound cs. The Debye temperature for this solid is θD = 120.0 K.

(a) In the high-temperature limit T >> θD, write an expression for CV. Evaluate this expression using the parameters at T = 750. K.

(b) In the low-temperature limit, T << θD, write an expression for CV based on the Debye model. Evaluate this expression using the parameters at temperature T = 10.0 K.

(c) In the Debye model, how does the density of states for the sound waves scale with frequency? Using parameters given previously, numerically evaluate the Debye frequency νD corresponding to the upper cutoff in the density of states.

(d) In the Debye model, the Debye frequency νD is related to cs by the density of states and knowing that the total number of modes is 3N and the volume is V. Using your knowledge of the density of states in the Debye model, write an expression to estimate cs. Numerically evaluate this expression. Your answer will be scored based on the scaling of the expression, not based on numerical prefactors.

A capacitor consists of two concentric spherical shells. The outer radius of the inner shell is a = 0.1 m and the inner radius of the outer shell is b = 0.2 m. a. What is the capacitance, C, of this capacitor? b. Suppose the maximum possible electric field at the outer surface of the inner shell before the air starts to ionize E max(r=a) = 3.0*10^6 V/m . What is the maximum possible charge on the inner capacitor? c. What is the maximum amount of energy stored in this capacitor? d. When E (r=a) = 3.0*10^6 V/m, what is the potential difference between the shells?

a. If the intensity of sound from a jet engine is 10 W/m 2 at a distance of 30 m, how far away from the jet do you have to be for the intensity to be 0.1 W/m 2 ?

b. Suppose that you hear a clap of thunder 5 s after seeing the lightning stroke. If the speed of sound in the air is 343 m/s and the speed of light in air is 3 × 10 8 m/s, how far are you from the lightning strike?

c. How long is the time gap between ultrasound reflections from the front and back of the heart, assuming the heart to be modeled as a cube of edge length 15 cm?

Luke Skywalker is flying his X-wing at 840 m/s down the Death Star trench.
Darth Vader is 320 meters behind him, going 740 m/s.
Luke's ship is going as fast as it can, so its speed isn't changing. Darth Vader's ship is gaining speed at a rate of 20.6 m/s². When Darth Vader gets to within 145 m, he will be close enough to lock on with his targetting system and blow up Luke's ship.

(a) How much time does Luke have to use the Force and launch his torpedoes at the Death Star already?
seconds.


(b) What is the furthest Luke's ship ever gets ahead of the TIE fighter?
m ahead.
_{Pro-tip: for as long as Luke's speed is faster than Vader's, the distance between them continues to increase and hasn't yet reached its maximum value.}

In my physics class, we are going over the Doppler Effect. We were given four different equations for two different scenarios:

- When the observer is stationary but the source is moving

- When the observer is moving but the source is stationary

I was given a problem where both the observer AND the source are moving at some velocity. The source is emitting a given frequency while traveling at a given velocity. The observer is OBSERVING that frequency at a given frequency provided in the problem, but their velocity is unknown. Seeing as the source is traveling at a CONSTANT velocity, can I treat it as though the source, relative to the observer, is stationary, and it is only the observer that is moving? I was thinking of using the receding observer equation of: f_- = (1 - v₀/v)*f_s , where v₀ is the speed of the observer and v is the velocity of sound in air, 343 m/s. Would this be correct? Or can I not treat the source as stationary even though it is moving at a constant velocity?

Thank you in advance! Please comment if you need clarification.