Assume a cup contains about 12 oz or 340 g of water at room temperature, about 20 degree C. The electric kettle draws energy from the wall outlet at a rate (Power) of 990W. Draw a single Energy-Interaction Diagram for the process of bringing the water to a rolling boil. Choose an appropriate physical system, as well as an initial and a final point in time and indicate all initial and final conditions on your timeline. Explicitly state any other assumptions you're making in words (incl. observations) and include an energy-conservation equation. Use your energy-conservation equation to calculate the amount of energy necessary to bring the water to a rolling boil. Then use what you know about the power of the electric kettle to calculate how long it will take to bring the water to a rolling boil (all water in liquid/gas mixed state).
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A metallic circular plate with radius r is fixed to a tabletop. An identical circular plate supported from above by a cable is fixed in place a distance dd above the first plate. Assume that dd is much smaller than r. The two plates are attached by wires to a battery that supplies voltage V.
1) What is the tension in the cable? Neglect the weight of the plate.
Express your answer in terms of the variables d, r, V, and constants ϵ0, pi.
F=
2)
The upper plate is slowly raised to a new height 2d. Determine the work done by the cable by integrating ∫d to 2d F(z)dz, where F(z) is the cable tension when the plates are separated by a distance z.
Express your answer in terms of the variables d, r, V, and constants ϵ0,pi.
W=
3) Compute the energy stored in the electric field before the top plate was raised.
Express your answer in terms of the variables d, r, V, and constants ϵ0, pi.
U=
4) Compute the energy stored in the electric field after the top plate was raised.
Express your answer in terms of the variables d, r, V, and constants ϵ0, pi.
U=
5)
is the work done by the cable equal to the change in the stored electrical energy? If not, why not?
| The work done in separating the plates is equal to energy change in the plates. |
| The work done in separating the plates is equal to the magnitude of the energy change in the plates. This does not mean that the work done is equal to the change in the energy stored in the plates. The work done on the plates is positive but the plates lose energy. The plates are connected to the battery, so the potential difference across them remains constant as they are separated. Therefore charge is forced off of the plates through the battery, which does work on the battery. |
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An airplane pilot wishes to fly to his destination 500 mi due west, but the wind is blowing at 23.1 mi/hr toward 14.1° north of west. The speed of the plane relative to the air is 166.5 mi/hr. At what angle (south of west) must the pilot orient the plane in order to fly to his destination directly?
If the pilot orients the plane at that angle, what will be the speed of the plane relative to the ground?
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Suppose the electron in a hydrogen atom is modeled as an
electron in a one-dimensional box of length equal to the Bohr
diameter, 2a0. What would be the ground-state
energy of this "atom"?
______________eV
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An object is formed by attaching a uniform, thin rod with a mass of mr = 7.25 kg and length L = 5.56 m to a uniform sphere with mass ms = 36.25 kg and radius R = 1.39 m. Note ms = 5mr and L = 4R.
1)What is the moment of inertia of the object about an axis at the left end of the rod?
3) What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere?
5) What is the moment of inertia of the object about an axis at the right edge of the sphere?
6)
Compare the three moments of inertia calculated above, from least to greatest (or equal)
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How many inhabitable planets are there in the universe? Two estimates are given by Drake's Equation and Seager's Equation. Do a little research on Drake's Equation and Seagar's Equation. Summarize what you've found. From a probability standpoint, particularly subjective probability, how do these equation hold up?
Comment and justify your comments particularly in the light of subjective probability.
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Find the total energy associated with the earths current rotation and compare this to the gain in the moons orbital energy. What fraction of the energy has been lost as heat?
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The magnetic field perpendicular to a circular wire loop 7.7 cmcm in diameter is changed from +0.44 TT to -0.27 TT in 150 msms , where + means the field points away from an observer and - toward the observer.
Calculate the induced emf.
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A car’s initial velocity is 50.0 km/h in the direction 60.0° north of east, and its final velocity is 70.0 km/h in the direction 40.0° south of east. If the time period for this journey is 30.0 minutes, what is the magnitude of the car’s average acceleration? Group of answer choices
186 km/h/h
240 km/h/h
92.8 km/h/h
3.94 km/h/h
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The figure shows a cut-away drawing of a thermos bottle (also known as a Dewar flask), which is a device designed specifically to slow down all forms of heat transfer. Explain the functions of the various parts, such as the vacuum, the silvering of the walls, the thin-walled long glass neck, the rubber support, the air layer, and the stopper.
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1) While a lawn mower moves forward 2 meters, a man pulls on the handle of the lawnmower with a force of 100 Newtons. The angle between the displacement of the lawn mower and the direction of the applied force is 135.6 degrees. How much work was done on the lawnmower by the man?
A) 200 Joules
B) - 200 Joules
C) zero
D) - 141 Joules
E) 141 Joules
2) If the lawn-mower had 300 Joules of kinetic energy before the man pulled on it, about how much kinetic energy does it have after the work done by the man? (Assume there are no energy losses to friction).
A) 440 Joules
B) 500 Joules
C) 300 Joules
D) negative kinetic energy
E) 160 Joules
3) A car changes its speed from 30 mph to 90 mph. How many times greater is its final kinetic energy compared to its initial kinetic energy?
A) eight times as much
B) four times as much
C) twice as much
D) three times as much
E) nine times as much
4) Assume that the car changes chemical potential energy (gasoline) into kinetic energy with the same efficiency at all speeds. How many times more gas will it take far the car to go from 30 to 90 mph, compared to going from zero to 30 mph?
A) twice as much
B) nine times as much
C) three times as much
D) six times as much
E) the same amount
F) eight times as much
5) The scalar product of two vectors is equal to ...(choose all correct responses).
A) the magnitude of the first vector times the magnitude of the
second vector times the cosine of the angle between the
vectors
B) the magnitude of one of the vectors multiplied by the component
of the other vector that is parallel to the first vector
C) a vector quantity
D) the product of a scalar and a vector
E) none of the other answers is correct
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The answer and solutions are not given. Solve everything from a through f.
An automobile takes 9.89 seconds to accelerate from rest to 60 miles per hour. a) Find the automobile's acceleration (assuming that is constant) and b) the distance traveled in reaching 60.0 miles per hours. Assuming that this acceleration remains constant over 0.25 miles, predict c) the time it takes to cover this distance and d) the car's velocity at the end. e) convert this velocity to miles per hour. f) sketch graphs of position, velocity, and acceleration versus time for this automobile.
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Four identical masses of 2.6 kg each are located at the corners
of a square with 1.2 m sides. What is the net force on any one of
the masses?
? ?? N toward ...............opposite corner
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A subway train starts from rest at a station and accelerates at a rate of 2.00 m/s2 for 14.0 s. It runs at constant speed for 66.0 s and slows down at a rate of 4.00 m/s2 until it stops at the next station. Find the total distance covered.
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Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 555 km above the earth’s surface, while that for satellite B is at a height of 778 km. Find the orbital speed for (a) satellite A and (b) satellite B.
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