The instantaneous electric power provided to the heater will be 1.32 kW.
Electric power can be defined as the rate by which an electric circuit transfers the electrical energy. An electric heater is drawing a constant current which is equal to 6 ampere with an applied voltage of 220 volts for a duration of 24 hours.
To calculate the instantaneous power supplied to the electric heater,
Power = Voltage × Current
P = V × I
P = 220 × 6
P = 1320 W
To convert it into kW, we divide the value by 10³
= 1320/10³ = 1.32 kW
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A system that has a total change in entropy of 675 J/K and has received 243 J of heat energy will be at what temperature?
The required temperature of the system which has a certain entropy change and receives heat energy is 273.36 °C.
Given that,
The change in entropy of the system = 675 J/K
Heat energy = 243 J
Temperature of the system = ?
The temperature of the system is calculated below.
ΔS = ΔH/T
where,
ΔH is the heat energy
ΔS is the change in entropy of the system
T = ΔH/ΔS = 243/675 = 0.36 K
By converting temperature in kelvin to temperature in degrees centigrade, we get,
T = 273 + 0.36 = 273.36 °C
Thus, temperature of the system which has a certain entropy change and receives heat energy is 273.36 °C.
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the electrical potential due to a dipole on its axis at a point p at a large distance x from the dipole is given by v
The electrical potential due to a dipole at a point P on its axis at a large distance x from the dipole is given by the formula: V = (p * x) / (4 * pi * epsilon_0 * x^2)
Where:
p is the dipole moment, a vector quantity that represents the magnitude and direction of the dipole. It is defined as the product of the magnitude of one of the charges (q) and the distance between the charges (d), p = q*d.x is the distance from the dipole to point P, it is a scalar quantity.epsilon_0 is the electric constant or vacuum permittivity, it is a scalar quantity that relates the electric flux density to the electric field strength. Its value is approximately 8.85 x 10^-12 C^2/Nm^2.The equation assumes that point P is located on the axis of the dipole (the line connecting the two charges) and that the distance x is much larger than the size of the dipole. This means that the dipole can be considered as a point source of electric potential and the field at point P is well approximated by the field of a point charge.It's important to note that the formula gives the potential at point P due to the dipole, however, the dipole itself also has an electric field which can be found by taking the gradient of the potential.Learn more about the electrical potential here:
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What is the relationship between torque and force lever arm length?
Torque is produced by multiplying the length of a lever arm by the force acting perpendicular to the lever arm. There are two conceivable orientations for the scalar quantity torque: clockwise and anticlockwise.
What is the result of the force times the lever arm?A torque is created when a force is applied perpendicular to a lever arm. The lever arm or moment arm is the length that extends perpendicularly from the pivot point, or the centre of rotation, to the point at which the force is applied. A torque is always defined with reference to a pivot point.
How can torque be multiplied?A torque multiplier multiplies the torque applied to the bolt with each gearing level. For instance, a 5:1 torque multiplier will result in an output.For example, a torque multiplier with a 5:1 ratio will result in an output at the shaft that is five times the torque, but the speed will only be one fifth of the original since no energy can be created.
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A block of substance has a width of 4.9 cm, a length of 5.1 cm, and height of 1.9 cm . Its mass is 0.54 kg. Calculate the density of the substance.
The 4.7 g/cm3 is the density of the substance.
What is density ?
How tightly something is packed can be used to gauge a material's density. Formally, it is defined as the mass per unit of volume. Formula for Density or Density Symbol: D D = m/V, where m is mass and V is volume, stands for density.
What is mass ?
The most basic characteristic of matter, it is one of the fundamental quantities in physics. As a way to gauge how much matter is there in a body, we might use the term mass. Kilograms are the SI unit of mass (kg).
density = mass of sample/ volume of sample
mass = 1.5 kg = 1500 g
volume = W*L*H
Vol = 3.2*17.1*5.8 cm3 = 317.376 cm3
Now,
D = mass/V = 1500/317.376
D = 4.726255 g/cm3
=4.7 g/cm3
Therefore, 4.7 g/cm3 is the density of the substance.
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A weight of 10 N hangs motionless from a spring. The spring is stretched 0.286 m from its original length. What is the force constant for the spring?
a-2.8 N/m
b-22 N/m
c-35 N/m
d-43 N/m
Answer:
C. -35N/m
Explanation:
Using Hooke's Law, we know that the elastic constant of a spring can be found with this formula:
[tex]F=-kx[/tex]
where:
[tex]F[/tex] is the force ( in Newtons)
[tex]k[/tex] is the constant ( in Newtons per meter)
[tex]x[/tex] is the extension ( in meters)
thus, by rearranging the formula we can get:
[tex]k=-\frac{F}{x}[/tex]
[tex]k = -\frac{10}{0.286}[/tex]
[tex]k=-34.96503N/m[/tex]
Rounding off the answer, we get -35N/m
1. When the current I is positive, the capacitor charge Q isdecreasing.
2. When the current I is positive, the measured VOLTAGE IN 2 willbe negative.
3. When the capacitor charge Q is positive, the measured VOLTAGE IN1 is positive.
4. The capacitor charge Q exponentially decays to zero when the RELAY is thrown to position N.O.
5. The transient currents that flow in this experiment decay exponentially to zero
1. The capacitor charge Q is decreasing while the current I is positive is false
2. If the measured voltage in 2 is negative when the current I is positive, it is false.
3. When the measured VOLTAGE IN1 is positive, the capacitor charge Q is positive, which is True.
4. When the RELAY is thrown to the position N.O is False, the capacitor charge Q rapidly decays to zero.
5. This experiment's transient currents flow exponentially decrease to zero, which is false
A capacitor is a type of electric device that can charge and store electrical energy when a voltage is applied to its terminals.
Formulas link the applied voltage to the capacitor's charge Q and currents I.
The final formula shows that while the current is positive, the capacitor's voltage is positive (increasing) and the
Q=CV
I=dQ/dt=C(dQ/dt)
The charge is rising.
As a result, the question's assertion is false.
As the currect is flowing from VOLTAGE IN 2 to VOLTAGE IN 1 it will be positive.
As a result, the question's assertion is false.
The measured VOLTAGE IN1 is positive when the capacitor charge Q is positive.
As a result, the question's assertion is True.
The position of the relay is the N.O. position which stands for "normally opened", i.e. no current can flow through it.
As a result, the question's assertion is false.
The following formula provides the transient current flow in this experiment:
[tex]i=i_0e^{\frac{-t}{RC}}[/tex]
As a result, the question's assertion is false.
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Note: The diagram of the question is added bellow,
In an 11v11 adult game, I see a defender challenge for the ball. The defender misses the ball and with their momentum they accidentally but careelessly trip the opponent. The ball rolls over the touchline. What is the restart
For the Direct free kick, the game restarted.
What does a soccer direct free kick entail?There are two different kinds of free kicks used in soccer: direct and indirect.The term "direct free kick" refers to a kick that can be used as a direct strike.Indirect free kicks require a second touch before the ball can be used as a shot at goal.
A direct penalty kick is what?If a player attacks an opponent in a way that the referee deems to be irresponsible, reckless, or employing excessive force, the referee will award a direct free kick.jumps, kicks, or makes an attempt to kick.
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A small cart on a 5.0-m long air track moves with a speed of 0.75 m/s. Bumpers at either end of the track cause the cart to reverse direction and maintain the same speed. Find the period and frequency of this motion.
The frequency of the cart's motion for a distance of 10.0 meters is 0.075 Hz (Hertz), which means the cart completes 0.0775 round trips per second.
1) Period (T):
The period (T) is the time taken for one complete round trip. The cart travels from one end to the other and back in one round trip.
T = (distance/speed)
T = (10.0 / 0.75 )
T = 13.33 seconds
So, the period of the cart's motion for a distance of 10.0 meters is approximately 13.33 seconds.
2) Frequency (f):
The frequency (f) is the number of complete round trips per unit time. It is the reciprocal of the period.
f = 1 / T
f = 1 / 13.33
f = 0.075 Hz
So, the frequency of the cart's motion for a distance of 10.0 meters is approximately 0.075 Hz (Hertz), which means the cart completes approximately 0.0775 round trips per second.
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hi, can someone explain each paragraph or rephrase each paragraphs for my reporting sana , thanks !
X-rays Ultraviolet rays are followed immediately by X-rays. Although they have a shorter wavelength than the UV, they are more energetic.
An X-ray tube is used to create X-rays. When quickly traveling electrons strike a metal object, they are released. Wilhelm Conrad Roentgen made the X-ray discovery in 1895.
The flesh can be penetrated by long wavelength X-rays, but not the bones. They assist doctors in viewing the inside of the body through X-ray imagery. They are helpful in identifying malignancies and bone fractures.
Even metals can be penetrated by short wavelength X-rays. They are applied in industry to check for flaws in welded joints.
All X-rays pose a risk because they have the potential to harm the body's healthy, functioning cells.
This is why exposure to X-rays on a regular basis should be avoided. Body tissues can be harmed by excessive X-ray exposure, which can also lead to cancer.
How are X-Rays created?To create images of the body, its organs, and other internal structures for diagnostic purposes, X-rays use external radiation. A "negative" type image is created when X-rays penetrate human structures and land on specially treated plates (similar to camera film) or digital media (the more solid a structure is, the whiter it appears on the film).
Different bodily components permit various amounts of the X-ray beams to pass through when the body is exposed to X-rays. The majority of the X-ray energy can pass through soft tissues in the body, including blood, skin, fat, and muscle, making them look dark gray on film or digital media. Few X-rays can penetrate dense soft tissue like a bone or a tumor.
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true/false
It is possible to view the Moon in first-quarter phase the day after a total lunar eclipse.
False. The Moon will typically appear in a crescent phase the day after a total lunar eclipse.
What is lunar eclipse?
A lunar eclipse is an astronomical event that occurs when the Moon passes directly behind the Earth into its umbra (shadow). During a lunar eclipse, the Earth blocks the light from the Sun from reaching the Moon.
The Moon, in turn, takes on a reddish hue as the Earth's shadow covers it. A lunar eclipse can only occur at Full Moon, when the Sun and Moon are in exact alignment with Earth in the middle. The Moon will usually appear larger than usual during a lunar eclipse, due to the reddish hue it takes on.
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What magnitude point charge (in C) creates a 16,000 N/C electric field at a distance of 0. 260 m?
C
How large (in N/C) is the field at 15. 0 m?
The magnitude of the point charge is 12.03 × 10⁻¹² C and the electric field at 15.0m is 4.63 × 10⁻² N/C.
A point charge creates a 16,000 N/C electric field at a distance equal to 0.260 m.
E = 16,000 N/C
r = 0.260 m
k = 8.99 × 10⁹
To calculate the point charge,
E = kq/r²
16000 = 8.99 × 10⁹ × q / (0.26)²
q = 16000 × 0.0676 / 8.99 × 10⁹
q = 10816 / 8.99 × 10⁹
q = 12.03 × 10⁻¹² C
When r= 15.0 m
E = kq/r²
E = 8.99 × 10⁹ × 12.03 × 10⁻¹² / (15)²
E = 0.4630 × 10⁻³
E = 4.63 × 10⁻² N/C
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600 Joules of work is used to lift a box from the ground to a height of six meters. How much work would have been done if a lever
would have been used with an effort arm of 12 meters and a load arm of 6 meters? (1 point)
O 100 J
0 72 J
O 50 J
O 600 J
Accounting for things like how many team members should be assigned to a task, how many resources are required, how many hours tasks will take and more.
Why is it necessary for the effort arm to be longer than the load arm?When the effort arm is longer than the load arm, there is a significant mechanical advantage.The lever is made up of two “arms”: The load arm (also known as the output arm) is the portion of the lever that is directly attached to the load. The effort arm (or applied force arm) is the section of the lever to which the effort, or input force, is applied.
A= W P = 1 , Where W represents the load and P represents the effort. So, if we utilize one fixed pulley to raise the weight, the effort required will be 50 k g w t in one direction.
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What causes the tectonic plates to move?
Answer:
The heat from the radioactive processes within the planets inferior causes the plates to move sometimes away from each other. This movement is called the tectonic shift
What is the position of the particle at time t 0?
The position of the particle is zero because the velocity is zero for the particle. The velocity of the particle at t=0 is zero because the particle is in rest position and did not moving at any of the instance or travelling at an uniform speed through out the whole journey or yet did not start from the source point.
Velocity is the rate of change of velocity. At any point on a trajectory, the magnitude of the velocity is given by the rate of change of velocity in both magnitude and direction. Velocity of the body that we can consider is the increasing value of the velocity of any object at a constant rate and that of we can calculate. Hence by the primary information that we have we can formerly consider that the velocity which is acting on the particle at t=0 is zero because the particle is in rest position and did not moving at any of the instance or travelling at an uniform speed through out the whole journey or yet did not start from the source point and the position of the particle is zero because the velocity is zero for the particle.
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Define the following
a. Friction:
b.Sliding friction:
c.Static friction
d.Rolling friction
e.Air resistance
f. Terminal velocity
g.Gravity
h.Weight
i. Centripetal force:
j.Momentum
These are just personal definitions of the following. They aren't official ones that may come from your textbook, but they are still accurate.
a. Friction is a force that acts against forces in contact with an object.
b. Sliding Friction is a force that acts against the forces making an object slide (e.g. the y component of the object's weight force if it's on an incline)
c. Static Friction is a force that acts on an object that is still/not moving.
d. Rolling Friction is the force making an object roll.
e. Air resistance is a frictional force that acts to slow down a falling object.
f. Terminal velocity is the maximum an object can reach while in free fall due to air resistance.
g. Gravity is a mutual attractive force in between two objects.
h. Weight is the mass of an object multiplied by the gravitational force (usually 9.81 for objects on earth). Weight is a force acting against the normal force keeping objects from phasing through each other.
i. Centripetal force is a force that acts on an object that is turning. This force pulls the object to the outside of the turning track.
j. Momentum is defined by mv (mass times velocity). Momentum is not a force, it is the idea that the motion of an object can depend on its mass and velocity.
I would check official dictionaries, just to make sure these definitions align with your textbook's.
The sound that reaches the ears after bouncing off a wall or a floor is called _____.
(a) direct sound
(b) indirect sound
(c) virtual sound
(d) harmonics.
The correct option is B, the sound that reaches the ears after bouncing off a wall or a floor is called indirect sound.
Indirect sound is a type of sound that is not heard directly by the listener. Instead, it is heard through reflections of the original sound off of nearby surfaces. This sound is more muffled, as the reflections tend to lose some of the original sound's energy as it is reflected from wall to wall. Indirect sound is often used in recording studios and concert halls, as it can create a more natural or realistic sounding environment.
This is due to the fact that in real life, the sound is rarely heard directly by the listener, but rather bounces off of nearby surfaces. By using indirect sound, a more natural sound can be created for the listener. Indirect sound is also used in sound reinforcement systems, as it can help distribute sound more evenly throughout a space. This can help to create a more uniform sound.
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ANALOGY: Natural pressure is to artesian wells as mechanical pressure is to ___________________
Water flows naturally under pressure from an artesian well without the need for pumping.
What causes pressure in an artesian well?A well that can bring water to the surface without a pump is known as an artesian well. This happens when the aquifer's positive pressure is high enough to force the water to the surface. This positive pressure is brought on by the confinement of an artesian aquifer between impermeable rocks or clay.
Free-flowing spring water that springs from underground wells is known as artesian water. Water in artesian wells rises to the surface naturally owing to pressure, unlike conventional wells that require a pump.
When water seeps into a porous rock material, such as limestone, sand, or gravel, artesian wells are created. Simply doing this wouldn't cause water to rise. But when a thick rock layer surrounds the porous earth.
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A sports car of mass m has the same kinetic energy as an SUV with a mass 3m as each is driven along the same road. Which vehicle, if either, has the largest momentum and what is the difference in their momenta, if any? Express your result as a percentage.
a. The car has about 42% greater momentum than the SUV.
b. The car has about 33% greater momentum than the SUV.
c. The SUV has about 73% greater momentum than the car.
d. Since their kinetic energies are the same, their momenta are the same. The difference is zero percent.
e. The SUV has about 66% greater momentum than the car
Option (a) is correct- The car has about 42% greater momentum than the SUV.
What is momentum ?
As a measure of an object's kinetic energy, momentum is easily defined. Simply put, momentum is the result of mass times velocity. full response Simply said, momentum is concerned with the quantity of motion. The conserved quantity is another definition for it.
What is mass?
Measurement of inertia, a fundamental characteristic of all matter. The resistance a body of matter offers to a change in its speed or location as a result of the application of a force is what it is in essence.
Therefore, Option (a) is correct- The car has about 42% greater momentum than the SUV.
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Which of the following conditions should be met to make a process perfectly reversible?
Check all that apply.
(1) Any mechanical interactions taking place in the process should be frictionless.
(2) Any thermal interactions taking place in the process should occur across infinitesimal temperature or pressure gradients.
(3) The system should not be close to equilibrium.
1) Any mechanical interactions taking place in the process should be frictionless, to make a process perfectly reversible
What is mechanical interactions?
Mechanical interactions are physical forces that are used to affect the behavior of objects and materials. This can include contact forces such as friction, tension, and compression, as well as non-contact forces such as gravity, magnetism, and electric fields
Mechanical interactions can be used to cause objects to move, change shape, or experience a change in energy. These interactions can also be used to create, store, or transfer energy. Mechanical interactions are studied by engineers and scientists in multiple disciplines, and are used in many different applications, including the design of machinery, medical devices, and consumer products.
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Air conditioners not only cool air, but dry it as well. Suppose that a room in a home measures 5. 0m×9. 0m×2. 4m.
If the outdoor temperature is 30 ∘C and the vapor pressure of water in the air is 85 % of the vapor pressure of water at this temperature, what mass of water must be removed from the air each time the volume of air in the room is cycled through the air conditioner? The vapor pressure for water at 30 ∘C is 31. 8 torr
The volume of air in the room. The volume of the room is given by the product of its length, width, and height= 18.015 g/mol.
Calculation-Volume of air = 5.0 m × 9.0 m × 2.4 m = 108 m^3
Next, we need to find the number of moles of water vapor present in the air at 85% of the vapor pressure of water at 30°C.
The vapor pressure for water at 30°C is 31.8 torr. At 85% of this value, the vapor pressure of water in the air is:
Vapor pressure in air = 0.85 x 31.8 torr = 27.03 torr
We can use the Ideal Gas Law, PV = nRT, to find the number of moles of water vapor present in the air.
P = 27.03 torr
V = 108 m^3
R = 8.314 J/mol·K (The universal gas constant)
T = 303 K (Temperature in kelvins)
n = (PV) / (RT)
Find the mass of water that needs to be removed from the air each time the volume of air in the room is cycled through the air conditioner.mass of water = n * M(H2O)
Where M(H2O) is the molar mass of water which is 18.015 g/mol. It is important to note that this calculation assumes that air behaves as an ideal gas and that the temperature and pressure remain constant throughout the room. In reality, the temperature and pressure may vary throughout the room and the process of removing water vapor from the air can also affect the temperature and pressure.
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Is the torque the product of force and lever arm?
Lever arm length and force applied perpendicular to a lever arm are multiplied to create torque. A scalar quantity called torque has two possible directions: clockwise and counterclockwise.
What is the force times the lever arm's product?A force applied perpendicular to a lever arm produces a torque, which is the result. The distance that runs perpendicularly from the pivot point, or the center of rotation, to the location where the force is delivered, is known as the lever arm or moment arm. A pivot point is always used to define a torque.
How do you multiply torque?Each gearing stage of a torque multiplier amplifies the torque applied to the bolt. For instance, a torque multiplier with a 5:1 ratio will produce an output at the shaft that is five times the torque, but because no energy can be produced, the speed will only be one fifth of the original.
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a potential difference of 12 volts causes 2.0 x 10^ 20 electrons to pass a point in a wire in 1 minute calculate
1) the amount of the charge that passes the point in 1 minute ,given that the charge of each electron is 1.6 x10^-19
coulomb
2)electric current in the wire
3)resistance of the wire
Answer:
Q = N e total charge passing point
Q = 2.0E20 * 1.6E-19 coul = 32 coulombs
2) I = Q / t = 32 C / 60 s = .53 amps
3) R = V / i = 12 volts / .53 amps = 23 ohms
suggest how the thermal conductivity of a metal depends on its temperature
Answer:
With an increase in temperature, the electrical conductivity of a pure metal decreases. This implies that the thermal conductivity of the pure metal shows little variance with an increase in temperature. However, a sharp decrease is observed when temperatures approach 0K
at the top of a pole vault, an athelete actually can do work pushing on the pole before releasing it. suppose the pushing force that the pole ecerts back on the athelete is given by F(x)=(1.5*10^2N/m)x-(1.9*10^2N/m^2)x2 acting over a distance of 0.20m. how much work is done on the athelete?
2.49 Joules have been performed on the athlete, in accordance with the provided statement.
What in science is a force?In science, the word "force" has a concrete meaning. At this point, referring to a force as a push or simply a yank is perfectly appropriate. An constituent does not "have in it" or "contain" a factor. A force is felt by one entity coming from another. The idea of a force encompasses both living and non-living entities.
You must incorporate the work expression because it is a vital part of Fdx.
Gained is
W = integral of ( 150x - 190 x 2 ) dx
= 75 x2 - 63.333 x3
So now...
work done = 75 *0.202 - 63.333 *0.203 = 2.49Joules
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A coin placed 0.30 m away from the center of a rotating, horizontal turntable just begins to slip when its translational speed is 0.50 m/s. What is the coefficient of static friction between the coin and the turntable
According to the given statement The coefficient of static friction was found to be about 0.0850.
What is static friction ?Static friction is a force that prevents an item from moving. The friction encountered when persons attempt to move a stationary object on a surface without actually causing any relative motion between the body and the surface on which it is located.
The graph below depicts the turntable's constant maximum speed and the centripetal acceleration of the coin.
(a) The centripetal acceleration is caused by static friction.
(b) Using the diagram below,
mai^=fi^+nj^+mg(−j^)
Fy=0nmg, thus n=mg, and Fr=mrv2=f=n=mg
Then, \sμ=rgv²=(30.0cm)(980cm/s2)(50.0cm/s)²
=0.0850
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The complete question is -
A coin placed 30.0cm from the center of a rotating, horizontal turntable slips when its speed is 50.0cm/s. (a) What force causes the centripetal acceleration when the coin is stationary relative to the turntable? (b) What is the coefficient of static friction between coin and turntable?
Select the correct answer. a thermodynamic system undergoes a process in which its internal energy decreases by 500 joules. at the same time, 220 joules of work is done on the system. what is the amount of heat transferred to or from the system?
a. 280 joules
b. 720 joules
c. -280 joules
d. -720 joules
e. 0 joules
The amount of heat transferred to or from the system is −720 J. The first law of thermodynamics states that U = Q + W
Where U is the change in the system's internal energy and W is the work performed on it. From the given, we obtain: U = 500 J W = 220 J.
Thus, = Δ − = −500 − 220 = −720 J
Which procedure results in a decrease in internal energy?A process is referred to as adiabatic if there is no heat exchange. This process must be adiabatic because the system's internal energy drops and it is an ideal gas.
Does the adiabatic process cause a decrease in internal energy?As a result, in adiabatic operations, the temperature of the gas rises as its volume decreases. This is due to the temperature shift being fueled by the gas's increased effort.
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Answer: D.
-720 joules
Explanation: plato :)
The direction of the velocity of the planet is _______________________ (alwaysThe direction of the velocity of the planet is _______________________ (always, seldom, never) perpendicular to the net force acting upon the planet., seldom, never) perpendicular to the net force acting upon the planet.
According to the satellites' orbits and the speed at which they move, it either happens frequently or always.
As we begin to examine satellite orbits, we find that a circular orbit places the satellite always perpendicular to the object's net force and speed.
The orbit is stretched, just like in elliptical orbits. This informs us that the orbit has four points. As a result, the satellite rarely faces the satellite's net force in a perpendicular direction.
Rarely and always for elliptical orbits. According to the satellites' orbits and the speed at which they move, it either happens frequently or always.
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Turn your head _______ and right and glance over your shoulder to view what cannot be seen in the side-view mirrors. back down left up Submit answer
Turn your head left and right and glance over your shoulder to view what cannot be seen in the side-view mirrors.
What is mirror ?
An item that reflects an image is a mirror or looking glass. When focused through the lens of the eye or a camera, light that reflects off a mirror will reveal a picture of whatever is in front of it. Mirrors reflect light at an equal but opposite angle, which changes the direction of the image.
What is direction?
Direction can refer to a thing's course, the route one must take to get there in particular, the direction something is beginning to take shape, or the direction you are facing. Going straight instead than left is an example of direction.
Therefore, Turn your head left and right and glance over your shoulder to view what cannot be seen in the side-view mirrors.
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a skier of mass m starts from rest at the top of a solid sphere of radius r and slides down its frictionless surface. (a) aat what angle will the skier leave the sphere? (b) if friction were present, would the skier fl off at a freater or lesser angle?
A skier of mass m starts from rest at the top of a solid sphere of radius r and slides down its frictionless surface.
The net force on the skier in the radial direction must be equal to the centripetal force in order to sustain circular motion.
[tex]$F_{\mathrm{radial}}=\frac{m v^2}{r}$[/tex]where [tex]v[/tex] denotes the skier's tangential instantaneous speed. Gravity and the normal force are the two forces at work on the skier. While the gravitational force is constantly radially outward, the normal force is always dependent on the angle [tex]\theta[/tex]. Therefore, the net force in the radial direction is, if the skier is at an angle of [tex]\theta[/tex] down the sphere.
[tex]$F_{\text {radial }}=m g \cos \theta-N$[/tex]
where N is the normal force's magnitude. When these two equations are combined, we get,
[tex]$\frac{m v^2}{r}=m g \cos \theta-N$[/tex]
Using the principle of energy conservation, we now substitute v with values we already know. The loss of potential energy equals the increase in kinetic energy, which on a sphere is written as,
[tex]$\frac{1}{2} m v^2=m g r(1-\cos \theta)$[/tex]
As the skier begins at rest, there is no kinetic energy at the top of the sphere. After removing [tex]v^2[/tex], we are left with the equation,
[tex]$2 m g(1-\cos \theta)=m g \cos \theta-N$[/tex]
Quantifying the situation when the skier exits the sphere is the last aspect of the issue. We can see that when theta equals 0, we get N = mg, which means that the normal force acting on the skier precisely balances the force of gravity. N decreases as the skier descends the sphere's surface, balancing the equation until it equals zero at a certain angle. This occurs precisely when,
[tex]$2 m g(1-\cos \theta)=m g \cos \theta$[/tex]
The skier is no longer in contact with the sphere when the normal force acting on the skier is zero, as the sphere no longer exerts any force on the skier. This is assumed to be the prerequisite for the skier to leave the ground.
After calculating [tex]\theta[/tex], we have,
[tex]$2 m g=3 m g \cos \theta$[/tex]
[tex]$\Longrightarrow \theta=\cos ^{-1}(2 / 3) \approx 48.19^{\circ}$[/tex]
First, we can note that this response is unaffected by the physical parameters m, r, and g. No matter how heavy he is, how huge the sphere is, or how powerful gravity is, the skier will exit the sphere at the same angle.
However, we will discover from dimensional analysis that this independence is actually not all that remarkable. Consider the units of the variables we've provided,
[tex]$[m]=$ kilograms,$\quad[r]=$ meters,$\quad[g]=$ meters $\cdot$ seconds $^{-2}$[/tex]
Any algebraic statement containing m, r, and g cannot be transformed into a dimensionless quantity. As a result, we draw the conclusion that the solution to our problem cannot depend on these values as an angle is a dimensionless quantity.
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A car goes into a skid and comes to a gradual stop, accelerating at a constant rate to do so. At the midpoint of the skid, how much of its kinetic energy has the car lost (as a percentage, give % as the units)?
The percentage of the lost kinetic energy of the car, at the midpoint of the skid, is 50%.
In physics, work is the measurement of the energy used to move objects. When you are walking, you're using energy to move your body so the work done would be greater than zero.
According to work-energy theorem, work is equal to force times displacement (W = F · x).
A type of energy is kinetic energy, which is the energy of a moving object. If an object is at rest, its kinetic energy is zero. Kinetic energy is equal to one half of a mass times velocity squared (KE = 0.5 · m · v²).
When a car goes into a skid and comes to a gradual stop, at the midpoint of the skid the car has spend 50% its kinetic energy. This is simply because the velocity of the car at the midpoint of the skid is half the velocity of the car when the car starts going into a skid, assuming constant acceleration.
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