The direction of the force on the particle due to the magnetic field a charged particle is moving is perpendicular to the plane.
Glamorous fields ply forces on moving charges. This force is one of the most introductory known. The direction of the glamorous force on a moving charge is vertical to the aeroplane formed by v and B and follows right hand rule – 1( RHR- 1). The magnitude of the force is commensurable to q, v, B, and the sine of the angle between v andB.
still, or is zero, the glamorous force will be zero, If the flyspeck haste happens to be aligned resemblant to the glamorous field. This differs from the case of an electric field, where the flyspeck haste has no bearing, on any given moment, on the magnitude or direction of the electric force.
The angle dependence of the glamorous field also causes charged patches to move vertical to the glamorous field lines in a indirect or spiral fashion, while a flyspeck in an electric field will move in a straight line along an electric field line.
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2.16 for the circuit in fig. p2.16, assuming an ideal op amp, find the currents through all branches and the voltages at all nodes. since the current supplied by the op amp is greater than the current drawn from the input signal source, where does the additional current come from?
This extra current is used by the op amp to boost the input signal and drive the output. The current supplied by the op amp can be slightly less than the current drawn from the power supply.
What current does an op-amp consume?Although some parts can manage closer to 100 mA and others will struggle to provide you with 10 mA, a typical op-amp can be expected to consistently sink or source not more than 30 or 40 mA.
What does an op-power amp's supply look like?Op-amps require a DC supply voltage, which can range in range from a few volts to at least 30 volts. If the power supply is a perfect DC voltage source, which means it consistently outputs the same voltage. The only factors influencing the op-output amp's are its inputs.
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What happens when you change the amplitude of a mass on a spring?
By changing the amplitude of a mass on a spring the maximum displacement, velocity, potential energy, and kinetic energy of the system are all affected.
A mass on a spring changes its greatest displacement from its equilibrium position as its amplitude is changed. This has numerous effects on how the mass-spring system moves:
1. Changing the amplitude of a mass on a spring has no effect on the motion's period, which remains constant. The object's mass and the spring's spring constant are the only factors that affect the period.
2. Increases in the maximum velocity of the mass are correlated with increases in the amplitude of the mass on the spring. This is because the mass accelerates more when it is further away from its equilibrium position when it encounters a stronger force from the spring.
3. The system's maximum potential energy rises because a mass on a spring has potential energy that is proportional to its square of displacement from equilibrium. As a result, increasing the mass of the spring's amplitude likewise raises the system's maximum potential energy.
4. The system's maximal kinetic energy rises: The kinetic energy of the mass on the spring oscillates between zero and a maximum value as it moves back and forth. The maximal kinetic energy of the system grows as the mass of the spring's amplitude increases.
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What's the frequency of AC ( alternating current ) ?
The frequency of alternating current (AC) is the number of times the current changes direction per second. It is measured in hertz (Hz).
In most parts of the world, the frequency of alternating current (AC) is 50 Hz, meaning that the current changes direction 50 times per second. However, in some parts of the world, such as the United States and Canada, the frequency of AC is 60 Hz. This means that the current changes direction 60 times per second. It is important to note that the frequency of AC is determined by the power source, and cannot be changed by the user.
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a system containing 1 atm of an ideal gas is doubled in temperature and halved in volume. what is the new pressure?
The amount of moles of gas n=RT PV using the Ideal gas equation
P ′ = 2P new pressure
T ′ = 2T new temperature
V ′ =V/2 new volume
Hence, the number of moles of gas n ′ = (2P)/(V/2) / R(2T) (2P)(V/2) = n/2
When all other variables are held constant, pressure is directly proportional to force (F) and inversely proportional to area (A). As a result, when Area A is doubled, the pressure is cut in half. Area A is cut in half. The pressure P has been doubled. At STP (standard temperature, 273.15 K and pressure, 1 atm), the volume of 1.00mol of any gas is measured to be 22.414L. 1 atm equals 760 mm Hg. The Pascal, on the other hand, is the standard international unit for pressure. 1 atm Equals 101325 Pa. The English physicist Robert Boyle conducted a series of pressure tests and arrived at a general law—that the volume of a gas varies inversely with pressure—in 1662. PV stands for constant.
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in the book example concerning the figure above, a force of 0.086 n from an external agent was required to keep the rod moving at a constant speed. suppose the light bulb in the figure is unscrewed from its socket. how much force would now be needed to keep the rod moving at a constant speed? justify your answer.
The correct answer is 0 N.
There will be no current in the rod and thus no magnetic force resisting the motion. Without any resistance, it will keep moving until acted on by an outside force according to Newton's first law.
What is motion?
Numerous physical systems, including objects, bodies, matter particles, matter fields, radiation, radiation fields, and radiation particles, as well as curvature and space-time, are affected by motion. One can also talk about how borders, shapes, and pictures move. A physical system's configuration or locations continuously changing in space is what is often meant by the term "motion." For instance, one can discuss the motion of a wave or a quantum particle, where the configuration is made up of the probabilities that the wave or particle would occupy particular places.To know more about motion, click the link given below:
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When should the power switch be in the off position? Check all that app
When reading about how to build the circuits, while building the circuits.
What is Power in off position?The power button is a round or square button that powers an electronic device on and off. Nearly all electronic devices have power buttons or power switches.
A hard power button is mechanical—you can feel a click when pressed and usually see a difference in depth when the switch is on versus when it's not. A soft power button, which is much more common, is electrical and appears the same when the device is on and off.
Some older devices have a power switch that accomplishes the same thing as a hard power button. A flip of the switch in one direction turns the device on, and a flip in the other turns it off.
Therefore, When reading about how to build the circuits, while building the circuits.
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a cube has a side of 5 cm. it has a mass of 250 grams. the density of the cube is a. 50 g/cm3 and will float in water b. 2.0 g/cm3 and will float in water c. 50 g/cm3 and will sink in water d. 2.0 g/cm3 and will sink in water
To determine: A cube's density and its ability to float on water. Explanation: Side: 5 cm. Volume is equal to (side)3 = 53 = 125 cm3. Cube weight is 250 g. Cube density = mass / volume = -250
What in physics is volume?
Describe volume. Describe volume. Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space filled within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
What distinguishes the terms volume and capacity?
Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold. Check the cylinder's volume here. The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
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how does an electromagnetic wave propagates?
the moon is decreasing in light between a full moon and a last quarter moon called___
The moon is decreasing in light between a full moon and a last quarter moon called waning.
Describe about moon?
Moon is the satellite of Earth and the only natural satellite of Earth. It is the fifth-largest natural satellite in the Solar System. It orbits around Earth in an elliptical path and takes 27.3 days to complete one revolution. It is made up of different types of rocks and dust and has no atmosphere. Its surface is covered with impact craters, mountains, valleys, and lava-filled plains. It also has frozen water at the poles. The moonlight is reflected sunlight and the light of the moon changes its shape throughout the month due to its changing position with respect to the Earth and the Sun. It is the Earth's only natural satellite and the most visible object in the night sky.
Therefore, The moon is decreasing in light between a full moon and a last quarter moon called waning.
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A photon with a frequency of 5.23 E14 Hz strikes a photoemissive surface whose work function is 1.75 eV. Planck's constant is 4.14 E−15 eV*s. Calculate the energy of the photon. Calculate the maximum kinetic energy of the ejected photoelectron. Calculate the threshhold frequency for the material
The energy of the photon will be 2.1652 Joules and the maximum kinetic energy of the ejected photoelectron from the atom will be 0.415 Joules. The threshold frequency will be same as the frequency of incident photon.
What is the energy of a photon?Photon energy is the energy which is carried by a single photon particle. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, it is inversely proportional to the wavelength of the photon. The higher the photon's frequency, the higher will be the energy.
Frequency = 5.23 × 10¹⁴ Hz
E = hf
h = 4.14 × 10⁻¹⁵
E = 4.14 × 10⁻¹⁵ × 5.23 × 10¹⁴
E = 21.652 × 10⁻¹
E = 2.1652 Joules
Maximum kinetic energy = hf - Ф
Ф is the work function
Max. KE = (4.14 × 10⁻¹⁵ × 5.23 × 10¹⁴) - 1.75
Max. KE = 2.165 - 1.75
Max. KE = 0.415 Joules
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suppose you charge a parallel plate capacitor with a dielectric between the plates using a battery and then remove the battery, isolating the capacitor and leaving it charged. you then remove the dielectric from between the plates. the potential difference between the plates will
If the dielectric is then removed, the capacitance of the capacitor decreases and the electric field between the plates increases.
When a parallel plate capacitor is charged with a dielectric between the plates using a battery, the charges on the plates are distributed in a way that results in a potential difference between the plates equal to the voltage of the battery. After the battery is removed and the capacitor is isolated, the charges on the plates remain fixed and the potential difference is maintained.
If the dielectric is then removed, there increase in electric field results in an increase in potential difference between the plates, and the amount of increase depends on the dielectric constant of the material used and the original capacitance of the capacitor.
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If you apply is 400 N pushing 20 - KG sled what is the acceleration ? solve the following problems
If you apply is 400 N pushing 20 - KG sled. The acceleration is 20 m/s².
What is acceleration?Acceleration is a vehicle's capacity to gain speed within a short time. The acceleration of an object is equal to the net force exerted on it divided by its mass, or a = F m, in accordance with Newton's second rule of motion.
When an item's mass and the net force acting on it are known, the acceleration of that object can be calculated using this equation for acceleration.
Acceleration = force/mass
Force = 400 N
Mass = 20 kg
400 / 20 = 20 m/s²
Therefore, the acceleration is 20 m/s².
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In the leading theory of solar system formation, the planets
a) were ejected from the sun following a close encounter with another star
b) formed from the same flattened, swirling gas cloud that formed the sun
c) are much younger than the sun
d) are much older than the sun
b) formed from the same flattened, swirling gas cloud that formed the sun in the solar system
What is the nebular hypothesis and how does it explain the formation of the solar system, including the differences in the composition of the inner and outer planets?
The leading theory of solar system formation is the nebular hypothesis, which proposes that the solar system formed from a rotating, flattened disk of gas and dust called the solar nebula. As gravity caused the cloud to collapse, it began to spin faster, and a central protostar formed at the center of the disk, which eventually became the Sun. As the disk cooled, solid particles began to stick together and form larger planetesimals, which eventually grew into the planets.
The planets that formed closest to the Sun, like Mercury, Venus, Earth, and Mars, are composed mostly of rock and metal, while the outer planets, like Jupiter, Saturn, Uranus, and Neptune, are composed mostly of hydrogen, helium, and other gases.
This is consistent with the idea that the inner planets formed from material that was close enough to the Sun to be solid at high temperatures, while the outer planets formed from material that remained gaseous even at low temperatures because they were farther from the Sun.
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a wave tank is 200 m long, 4.0 m wide, and 6.5 m deep. the tank is filled to a depth of 5 m with fresh water and a 0.75 m high, 4.5 sec period wave is generated. calculate the wave celerity, length, group velocity, and energy.
The wave celerity is approximately 4.4 m/s, the wavelength is approximately 16.2 meters, the group velocity is approximately 2.2 m/s, and the energy of the wave is approximately 187 joules
Wave celerity, c = √(gλ/2π)
where g is the acceleration due to gravity, λ is the wavelength.
Wavelength, λ = cT, where T is the period of the wave.
λ = cT = √(gλ/2π) × 4.5
Squaring both sides of the equation,
λ = (9.8 m/s^2 × 4.5^2)/(4π^2) ≈ 16.2 m
The wave celerity is,
c = √(gλ/2π) = √(9.8 m/s^2 × 16.2 m/(2π)) ≈ 4.4 m/s
Group velocity of the wave, v_g = c/2
v_g = 4.4 m/s / 2 = 2.2 m/s
Energy of the wave, E = (ρg/2)A^2ω^2, where ρ is the density of the water, g is the acceleration due to gravity, A is the amplitude, and ω is the angular frequency.
ω = 2π/T = 2π/4.5 ≈ 1.39 rad/s
Energy of the wave,
[tex]E = \dfrac{\rho g}{2} \times A^2\omega^2\\ = \dfrac{1000 \times 9.8}{2} \times (0.75)^2 (1.39)^2 \\=187 J[/tex]
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a spring mass system is driven from rest harmonically such that the displacement response exhibits a beat of period of 0.2 pi s. the period of oscillation is measured to be 0.02 pi s. calculate the natural frequency and the driving frequency of the system.
The system's natural frequency is 100rad/s.
The system's driving frequency is 10rad/s.
The natural frequency (ωn) of a system is the frequency at which the system will vibrate when the damping of the system is negligible and the system is disturbed from its equilibrium.The natural frequency of the system is given by the following equation:
[tex]\omega n[/tex] =[tex]\frac{2\pi}{T}[/tex]
where T is the period of oscillation.Hence, the system's inherent frequency is
[tex]\omega n = \frac{2\pi}{0.02\pi} \\= 100 rad/s[/tex]
The driving frequency (ωd) is the frequency at which an external force must be applied to the system in order to cause it to vibrate at the natural frequency of the system. The driving frequency of the system is given by the following equation:
[tex]\omega d = \frac{2\pi}{b}[/tex]
where Tb is the beat period. Therefore, the driving frequency of the system is
[tex]\omega d = \frac{2\pi}{0.2\pi} \\= 10 rad/s[/tex]
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ta student does an experiment to check the mass of a cart. the student sends a 1.0-kg cart with a spring attached at the front end into a collision with a cart of unknown mass. after the collision, the student notes that the 1.0-kg cart moves forward with reduced speed, and the unknown cart moves forward at a faster speed than the 1.0-kg cart. what does this experiment show about the mass of the unknown cart?
The experiment shows about the mass of the unknown cart is The unknown cart is less than 1 kg.
A change in velocity with respect to time is called acceleration. The speed of the cart and the amount of time it needs to accelerate down the plane are two crucial factors.
Keep in mind that the acceleration increases as the height of the slanted plane increases. This demonstrates how crucial it is to understand the inclined plane's height.
The necessity of the timer is based on the fact that we also need to know how long it takes the body to decelerate from the aircraft.
In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force.
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How does adding thermal energy to solid ice affect the molecules in the ice? Describe what happens to both their motion and spacing.
Once ice has been taken out of the freezer, its molecules start to travel more quickly when heat energy is supplied.
Motion and spacing Given that the ice is substantially colder than the air outside the freezer, heat energy will transfer from the air to the ice. The molecules' kinetic energy is increased by the heat input, which weakens the ice's structure. Hydrogen bonds that were keeping the ice together start to disintegrate when the ice warms up further, causing molecules to migrate more quickly. In time, the molecules will travel so swiftly that the ice will experience a phase shift and convert into water.For more information on heat energy kindly visit to
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a 41.0-kg child swings in a swing supported by two chains, each 2.90 m long. the tension in each chain at the lowest point is 352 n. (a) find the child's speed at the lowest point. m/s (b) find the force exerted by the seat on the child at the lowest point. (ignore the mass of the seat.)
The force exerted by the seat on the child at the lowest point is approximately 242 N.
(a) To find the child's speed at the lowest point, we can use conservation of energy. Assuming that the swing is released from rest at the highest point, we have:
Initial potential energy = mgh
Final kinetic energy = (1/2)mv^2
v is the speed of the child at the lowest point.
Since the height of the swing at the highest point is equal to the length of the chains, h = 2.9 m. We can solve for v by equating the two expressions for energy:
mgh = (1/2)mv^2
Solving for v, we get:
v = sqrt(2gh)
v = sqrt(2 × 9.81 m/s^2 × 2.9 m) ≈ 6.26 m/s
Therefore, the child's speed at the lowest point is approximately 6.26 m/s.
(b) At the lowest point, the child is moving in a circular path with a centripetal acceleration given by:
a = v^2/r
And,
T = mg + ma
Solving for a, we get:
a = (T - mg)/m
Substituting the given values, we get:
a = (352 N - 41.0 kg × 9.81 m/s^2)/(41.0 kg) ≈ 3.70 m/s^2
Substituting this value into the expression for centripetal acceleration, we get:
a = v^2/r
(3.70 m/s^2) = (6.26 m/s)^2/r
Solving for r, we get:
r = (6.26 m/s)^2/3.70 m/s^2 ≈ 10.6 m
Using Newton's second law, the force exerted by the seat is given by:
F = ma = m(v^2/r) = (41.0 kg)(6.26 m/s)^2/10.6 m ≈ 242 N
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A 5 kg box is attached to a spring that has an elastic coefficient of 110 N/m. The spring is compressed to a distance of 0. 65 meters. What is the velocity of the box after it is released from the spring?
The required velocity of the box after it is released from the spring is 5.35 m/s.
The mass of the box m is given as 5 kg.
Elastic coefficient k is given as 110 N/m.
Compression of the spring x is given as 0.65 m.
We know the expression for force as,
F = k x
where,
k is the elastic coefficient
x is the compression in spring
Entering the values we have,
F = k x = 110 × 0.65 = 71.5 N ----(1)
Force is nothing but the tension in the spring which is given by the expression,
F = T = 1/2 m v² = 1/2 (5)v² = 2.5 v² ----(2)
Equating (2) and (1), we have,
2.5 v² = 71.5
v² = 28.6
v = 5.35 m/s
Thus, the velocity of the box after it is released from the spring is 5.35 m/s.
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Inert gas is used in filament bulb why?
Answer:
When electric current passes through the tungsten filament, it gets heated up and starts to glow at a temperature around 2500 degree Celsius. If we do not fill any gas, at vacuum condition, the filament will evaporate due to high temperature. To protect the filament from damage, we are filling the bulb with inert gas.
Explanation:
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g a cheetah can accelerate from rest to a speed of 21.0 m/s in 6.75 s. what is its acceleration (in m/s2)? 3.11 correct: your answer is correct. m/s2
The acceleration of cheetah from rest to a speed of 21.0 m/s in 6.75 s is 3.1m/s2.
Given the speed of cheetah (v) = 21m/s
The time of acceleration from rest to given speed (t) = 6.75s
The acceleration of cheetah = am/s^2
We know that acceleration = speed of object/time of acceleration = v/t
Acceleration is the rate of change of velocity. It is the change in speed or direction of an object over a period of time. It is related to speed and time in that it is the rate at which the speed of an object changes over a given amount of time.
then a = 21/6.75 = 3.1m/s^2
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if the protons are both released from rest at the closer distance in part a, how fast are they moving when they reach their original separation? hint: the protons share the total available energy.
The total energy available is [tex]4.31 \times 10^-14 J.[/tex] Since the protons share this energy equally, each has[tex]2.155 \times 10^-14 J[/tex]. Using the formula for kinetic energy, [tex](1/2)mv^2 = 2.155 \times 10^-14 J[/tex] We find that each proton is moving at approximately [tex]1.68 \times 10^7 m/s.[/tex]
What are the properties of protons?To calculate the final velocity of the protons when they reach their original separation, we need to use the principle of conservation of energy.
The total energy of the system (protons) remains constant throughout the motion. When the protons are released, they have potential energy due to their separation, and as they move closer, this potential energy is converted into kinetic energy.
At their original separation, all the potential energy would have been converted into kinetic energy, which can be used to calculate the final velocity using the formula for kinetic energy (1/2mv^2).
Therefore, Since the protons share the total available energy, we can calculate the final velocity for each proton by dividing the total kinetic energy by the mass of each proton.
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what happens to most solar radiation when it reaches the surface of the earth?
When solar radiation reaches the surface of the Earth, a variety of processes can occur.
Some of the energy is reflected back into space by clouds, snow, ice, and other reflective surfaces. Some of the energy is absorbed by the atmosphere, where it can be scattered, reflected, or absorbed by gases and particles. The remaining solar radiation that reaches the surface of the Earth can be absorbed by the ground, plants, and other materials, where it is converted into heat. This process is responsible for warming the Earth's surface and is a critical component of the Earth's climate system.
Solar radiation is a combination of different types of electromagnetic waves, including visible light, ultraviolet (UV) radiation, and infrared (IR) radiation. When solar radiation reaches the Earth's atmosphere, a portion of it is reflected back into space by the atmosphere itself, clouds, and other reflective surfaces.
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for a system in thermal contact with a heat reservoir at a fixed temperature t, fixedvolume v , and fixed number of particles n, what is the probability of finding thesystem in a particular microstate?
A system has an equal chance of being in any microstate that corresponds to its current macrostate. Equilibrium is defined as an isolated system that meets the postulate of equal a priori probabilities.
The probability of discovering a system in a specific microstate is simply one divided by the total number of microstates.
The thermodynamic probability (denoted by W) is equal to the number of microstates that realise a given macrostate, so W = 1.
To put it simply, the microcanonical ensemble is defined as assigning an equal probability to every microstate whose energy falls within a range centred on E. The probability of all other microstates is set to zero.
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What is the pH of a solution containing 11.7 g of NaCl for every 200 mL of solution?
A. 1.0x10
B. 9.0
C. 10
D. 7.0
The pH of the solution cannot be determined from the information given.
NaCl is a salt and, when dissolved in water, it dissociates into its constituent ions, Na+ and Cl-. Neither of these ions affect the pH of the solution since they are neither acidic nor basic. Therefore, the pH of a solution containing NaCl depends on any other acidic or basic substances that may be present in the solution.
To calculate the pH of a solution, we need to know the concentration of H+ ions in the solution. This information is not provided in the question. Therefore, we cannot calculate the pH of the solution using the given information.
In conclusion, the answer is not A, B, C, or D. The pH of the solution cannot be determined without additional information.
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which person below developed a system for predicting planetary positions that remained in use for some 1500 years?
Ptolemy. Ptolemy was a Greek astronomer who developed the Ptolemaic system of astronomy.
What is astronomer?Astronomer is an individual who studies the universe and its components such as stars, planets, galaxies, and other celestial bodies. They use observational data, mathematical models, and theoretical principles to understand the physical properties, evolution and origin of the universe. Astronomers often work in teams, and employ a variety of techniques to observe and analyze the data they collect. Astronomers may use ground-based telescopes, spacecraft, or other instruments to observe the universe and the objects within it.
This system used a combination of observational data and mathematical calculations to accurately predict the positions of the planets. This system was used for around 1500 years, until the invention of the telescope in the 17th century.
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(ii) has the particle moved to a position where the electric potential is higher than before, unchanged, lower than before, or unpredictable?
The particle has moved to a position where the electric potential is lower than before.
Electric potential is a scalar quantity that represents the amount of electric potential energy per unit charge at a particular point in space. In the given scenario, as the particle has moved towards the negatively charged object, the distance between the particle and the object decreases. As a result, the electric potential energy between the two objects decreases, which in turn reduces the electric potential at the position of the particle. Therefore, the particle has moved to a position of lower electric potential than before. This can be visualized by the electric potential lines, which are closer together near the negatively charged object, indicating a higher electric field strength and lower electric potential in that region.
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A current of 0.33 A is following through a circuit .If the potential difference across two points of wire is 5V ,Claculate the resistance
Answer:
The value of resistance is
[tex]15.15ohm[/tex]
Explanation:
Greetings!!!
Given values:-current(I)= 0.33A
potential difference(V)= 5V
Required values:-resistance (R)= ?
Solution:-Firstly, recall the ohm's law
V= RISubstitute known variables into the equation
(5)= R(0.33)Solve for Resistance
R= 15.15 ΩIf you have any questions tag me on comments
Hope it helps!!!
Answer:
15 Ω.
Explanation:
The resistance of a circuit can be calculated using Ohm's law, which states that the potential difference (V) across a conductor between two points is directly proportional to the current (I) flowing through it, given by the equation V = IR.
To find the resistance, we can rearrange the equation to R = V/I, where R is the resistance. Substituting the values we have, we get:
R = 5V / 0.33A = 15 Ω
So, the resistance of the circuit is 15 Ω.
a thermometer is taken from a room where the temperature is 72o f to the outside where the temperature is 32o f. after 2 minutes, the thermometer reads 48o f. how many minutes does the thermometer have to be outside for it to read 36o f?
A thermometer is taken from a room where the temperature is 72° F to the outside where the temperature is 32° F. 1.26 minutes does the thermometer have to be outside for it to read 36° F.
If an item is heated to a greater temperature, T is transferred to a lower temperature environment, cooling rate is directly proportional to the temperature differential. By separating the variables, rewrite the equation. In the derived equation, substitute 0 for t and 72 for T.
If an item is heated to a greater temperature,
T is transferred to a lower temperature environment, T then the cooling rate.
By Newton's Law of Cooling
[tex]T(t) = T_{s} + Ce^{tr}[/tex]
Here, the ambient temperature, [tex]T_{s} = 32^{\circ} F[/tex]
The temperature to the outdoor, T(0) = 72°F
Use the equation [tex]T(t) = T_{s} + Ce^{tr}[/tex] to obtain that,
[tex]T(0) = T_{s} + Ce^{k - 0}[/tex]
72 = 32 + C
C = 40
So, [tex]T(t) = 32 + 40 e^{kt}[/tex]
After half minute, the temperature reads 48°F,
so, T(1/2) = 48
Then,
[tex]T(1/2) = 32 + 40e^{k \times \frac{1}{2}}[/tex]
[tex]48 = 32 + 40e^{\frac{k}{2}}[/tex]
[tex]40e^{\frac{k}{2}} = 16[/tex]
[tex]e^{\frac{k}{2}} = \frac{16}{40}[/tex]
[tex]e^{\frac{k}{2} = \frac{2}{5}[/tex]
[tex]\frac{k}{2} = \ln \left(\frac{2}{5} \right )[/tex]
k = 2 ln (2/5)
Therefore,
[tex]T(t) = 32 + 40e^{2 \ln \left(\frac{2}{5} \right) t}[/tex]
[tex]T (t) = 32 + 40 \left[ e^{\ln (\frac{2}{5} ) \right ]^{2t}[/tex]
[tex]T (t) = 32 + 40 \left(\frac{2}{5} \right)^{2t}[/tex]
Now find the time t when T(t) = 36
[tex]32 + 40 (\frac{2}{5})^{2t} = 36[/tex]
[tex]40 (\frac{2}{5})^{2t} = 4[/tex]
[tex](\frac{2}{5})^{2t} = \frac{4}{40}[/tex]
[tex]2t\ \ln (\frac{2}{5}) = \ln (\frac{1}{10})[/tex]
[tex]t = \frac{\ln (\frac{1}{10})}{2 \ln (\frac{2}{5})}[/tex]
[tex]t = \frac{-2.30}{2 \times (-0.91)}[/tex]
t = -2.30/-1.82
t = 1.26 min
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What interesting features where developed before 1920 on old electric vehicles????
The record for the fastest vehicle until about 1900 belonged to an electric vehicle.Interest in electric vehicles is sparked by gas shortages.
Features The use of battery electric vehicles as private motor vehicles fell dramatically over the world in the 20th century due to their high cost, slow top speed, and limited range when compared to vehicles powered by internal combustion engines.Think about the late 1960s and early 1970s. Rising interest in reducing the United States' reliance on foreign oil and locating domestic fuel sources was sparked by rising oil costs and gasoline shortages, which peaked with the Arab Oil Embargo in 1973.The popularity of electric vehicles. Electric cars are quiet, simple to drive, and don't release noxious emissions, thus they quickly gain favor with urban people in comparison to the gas- and steam-powered automobiles of the time.For more information on electric vehicles kindly visit
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