Answer:
Potential energy is converted into kinetic energy by a force. For example, when you pick up a rock, you work against gravity to give it some potential energy. And then when you drop it, the gravitational force causes the rock to accelerate towards the ground
Explanation:
Potential energy is transformed into kinetic energy through various natural processes. An example is a rollercoaster which at the peak has high potential energy due to its height, but as it descends and increases speed, the potential energy is transformed into kinetic energy. This phenomenon is guided by the Law of Conservation of Energy.
Explanation:In physics, potential energy is stored energy that an object has due to its position or state. Kinetic energy on the other hand, is the energy that an object possesses due to its motion. The transformation between these two forms of energy occurs continuously in the natural world.
For instance, think of a rollercoaster at the peak of a track. It has a high potential energy because of its height. As the rollercoaster starts to descend, the potential energy is transformed into kinetic energy as the rollercoaster increases speed (due to gravity). When it gets to the lowest point, all of its potential energy has been converted into kinetic energy. This cycle continues for the duration of the ride, with the rollercoaster's energy constantly being transformed between potential and kinetic.
This transformation between potential and kinetic energy is referred to as the Law of Conservation of Energy, which states that energy cannot be created or destroyed, it can only be transformed from one form to another.
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In an arcade game a 0.144 kg disk is shot across a frictionless horizontal surface by compressing it against a spring and releasing it. If the spring has a spring constant of 164 N/m and is compressed from its equilibrium position by 7 cm, find the speed with which the disk slides across the surface.
Answer:
The speed with which the disk slides across the surface is 2.36 m/s.
Explanation:
Given that,
Mass of the disk, m = 0.144 kg
Spring constant of the spring, k = 164 N/m
The spring is compressed from its equilibrium position by 7 cm or 0.07 m
We need to find the speed with which the disk slides across the surface. It is a case of conservation of energy in which the energy of the spring is gained by its kinetic energy. It is given by :
[tex]\dfrac{1}{2}kx^2=\dfrac{1}{2}mv^2[/tex]
v is speed of the disk.
[tex]kx^2=mv^2\\\\v=\sqrt{\dfrac{kx^2}{m}} \\\\v=\sqrt{\dfrac{164\times 0.07^2}{0.144}} \\\\v=2.36\ m/s[/tex]
So, the speed with which the disk slides across the surface is 2.36 m/s.
The fastest possible conduction velocity of action potentials is observed in ________.
A student wants to determine whether an unknown solid is an ionic compound. He puts some in water and finds that it does not dissolve. He says that this proves the solid is ionic. Which best evaluates the student's reasoning? (2 points) He is incorrect, because water can dissolve ionic solids. The test proves nothing, because water dissolves all solids. He is correct, because polar liquids cannot dissolve ionic solids. The test proves nothing, because it only shows that the solid is a compound.
Answer:
b
Explanation:
When a DVD is played, a laser light hits the surface of the disk and then returns to the detector. An illustration of DVD with an arrow pointing toward a spot on the disk labeled detector. Which wave phenomenon allows the DVD player to work? absorption interference reflection refraction
Answer:
Reflection
Explanation:
The wave phenomenon that allows the DVD player to work is REFLECTION.
Reflection is defined as the repropagation of incident light striking a plane surface.
The light ray striking the surface is incident ray while the repropagated light ray is the reflected ray. The DVD was able to play because the laser light that hits the surface of the disk was able to reflect back and returns to the detector. The detector senses the light and cause the DVD to play. If the laser light didn't reflect, assuming it was absorbed by the surface of the disk, the detector wouldn't have detected the light and the DVD wouldn't have played.
Answer:
C. Reflection
Explanation:
Edge 2020
If the light strikes the first mirror at an angle θ1, what is the reflected angle θ2? express your answer in terms of θ1.
Final answer:
The reflected angle θ2 is equal to the incident angle θ1 due to the Law of Reflection, and when light reflects off two perpendicular mirrors, the outgoing ray is parallel to the incoming ray.
Explanation:
The Law of Reflection states that the angle of reflection (θ2) is equal to the angle of incidence (θ1). This means that when light strikes a mirror at an angle θ1, it reflects off the mirror at the same angle θ2 such that θ2 = θ1. When light reflects from two mirrors that meet at a right angle, the outgoing ray will be parallel to the incoming ray, according to the law of reflection, because the two consecutive reflections each change the direction of the ray by the same angle, effectively rotating the ray by a total of 180 degrees, which makes it parallel to the original direction of incidence.
In summary, if the light strikes the first mirror at an angle θ1, the reflected angle θ2 in terms of θ1 is simply θ2 = θ1.
what is an incident wave,and a normal
Answer:
An incident wave is a current or voltage wave that travels through a transmission line from the generating source towards the load. It becomes incident when it arrives at a discontinuity or another medium with different propagation characteristics. Wave normal. A unit vector which is perpendicular to an Equiphase surface of a wave, and has its positive direction on the same side of the surface as the direction of propagation.
Explanation:
Answer:
A current or voltage wave that is traveling through a transmission line in the direction from source to load.
Explanation:
Hope this helps!
A car approaches a pedestrian standing on the side of the road. The car is traveling at 24.2 m/s. The horn of the car emits a sound wave with a frequency of 482 Hz. What frequency is heard by the pedestrian
Final answer:
The frequency heard by the pedestrian as the car approaches, using the Doppler Effect, would be approximately 518 Hz.
Explanation:
To determine the frequency heard by the pedestrian as the car approaches, we use the Doppler Effect equation:
f' = f(v + v0)/(v - vs)
where:
f' is the frequency heard by the observer (pedestrian)
f is the frequency of the source (car horn's frequency)
v is the speed of sound
v0 is the speed of the observer (pedestrian, which is 0 m/s since they are standing)
vs is the speed of the source (car)
Given the car horn's frequency, f = 482 Hz, and the car's speed, vs = 24.2 m/s. Assuming the speed of sound on a standard day (approximately 343 m/s), the equation modifies to:
f' = 482(343 + 0)/(343 - 24.2)
We can now calculate:
f' = 482(343)/(318.8) ≈ 518 Hz
The frequency heard by the pedestrian would be approximately 518 Hz when the car is approaching.
What three changes in motion show that an object is accelerating?
Answer:
There are three ways an object can accelerate: a change in velocity, a change in direction, or a change in both velocity and direction.
Explanation:
The three changes in motion show that an object is accelerating are,
a = ∆v / ta = F / ma = w²rWhat are the changes happened in an object?An object is accelerating with the changes in motion are,
1. If the velocity is increasing.
From equation of motion
a = ∆v / t
So, if the velocity increases with time, the acceleration increases. But if it decreases with time, it decelerating.
2. Also, from newton second law,
F = ma
a = F / m
Where a = acceleration
F is force applied
m is the mass
So, if the force is increase and the mass is reduced, then the acceleration is increase.
3. Also, in Circular motion,
a = w²r
Where,
a is linear acceleration
w is angular speed
r is the radius.
So, when the angular speed is increased, then the linear acceleration is increased.
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The vapor pressure of any substance at its normal boiling point is
Answer: one atmosphere!
Explanation: The normal boiling point of a liquid is the temperature at which its vapor pressure is equal to one atmosphere (760 torr). I hope this answers your questionl.
The vapor pressure refers to the force created by a gas in the confined container that is in balance with a liquid or a solid at a particular temperature. The vapor pressure of any substance at its normal boiling point is 1 Atm.
What is Boiling Point?When a liquid reaches its boiling point, which occurs at a degree where the pressure that the environment and the liquid's vapor impose on it are equal, the liquid turns into its vapor without increasing the temperature.
Until the pressure imposed by the vapor reaches a specific amount known as the pressure of the fluid at that temp, a liquid partially evaporates into the air above it at any temperature.
When a liquid reaches its boiling point, vapor bubbles start to form within it and ascend to the surface as the temperature rises, increasing the evaporation rate.
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Which of the following is not an effect of climate change?
Rising sea levels
Coastal flooding
Increased glacial ice
Extreme weather
3. This diagram shows that Al can see the reflections of Ed and Fred in the
mirror. Which two students can both see the reflections of Cy, Di, Ed and
Fred? *
For
Answer:
Only Cy and Di could see the reflections.
Explanation:
Reflection is a property of light that makes it to travel through its initial path on hitting a plane surface. It is good to note that the angle of the incident ray to the surface is equal to the angle of reflection after hitting the surface. It can generally be classified into diffuse and specular.
A ray of light travels on a straight path, the images of the students are formed due to reflection of light at the plane surface. By ray constructions and observation, it would be observed that only Cy and Di could see the reflections of the four students. This is due to their positions with respect to the reflecting surface.
The air speed of a plane is defined as its velocity with respect to the surrounding air, or in other words how fast the plane would move in still air. The ground speed is the speed of the plane as measured from the ground. A Nimbus-4 glider is traveling at an air speed of 144 km/h. a) What is the glider’s ground speed if it is experiencing a 48 km/h headwind (wind coming from the front)?
Answer:
3
Explanation:
because
A football player weighing 110 kg and traveling at +6 m/s runs head on into another player who weighs 150 kg and is traveling at -4 m/s. In which direction will they travel after they collide (stuck together) and what would their combined velocity be?
This is an inelastic collision. The equation for an inelastic collision is: [tex]m_{1}v_{1}_{i} + m_{2}v_{2}_{i} = (m_{1} + m_{2})v_{f}[/tex]
(110)(6) + (150)(-4) = (110 + 150)(vf)
660 - 600 = 260vf
60 = 260vf
vf = 0.2308 m/s
They will travel in the positive direction, right, and their combined velocity will be 0.2308 m/s.
Hope this helps!! :)
What is the relationship between heavy objects and inertia
Answer:
Inertia is the measure of mass of a body which means that grater the mass grater will be the inertia.
The relationship between heavy objects and inertia is heavy objects have more inertia than lighter objects. The correct option is b.
The ability or propensity of an object to resist changes in motion is known as inertia. An object's mass is how much matter there is inside of it, and heavier objects have more mass than lighter ones.
The mass of an object has an impact on inertia. More mass means an object has more inertia, which makes it more resistant to changes in motion.
Both physical items and human minds exhibit inertia, which can support aversion to change and the preservation of habituated behaviours.
It is true that heavier items have more inertia than lighter ones in terms of their relative weights.
Thus, the correct option is b.
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Your question seems incomplete, the probable complete question is:
What is the relationship between heavy objects and inertia?
a. Heavy objects have less inertia than lighter objects.
b. Heavy objects have more inertia than lighter objects.
c. Heavy objects have the same amount of inertia as lighter objects.
d. The relationship between heavy objects and inertia is not defined.
What is the distinction between glass transition temperature and melting temperature?
Answer:
Glass transition temperature is a characteristic of soda lime glass and melting temperature is for a Borosilicate glass.
Explanation:
The glass transition is the change of an amorphous solid from soft and flexible to glass-like, i.e. hard and brittle. On the other hand, the melting temperature is the temperature at which the liquid - solid phase transition occurs in a crystalline substance.
You are in your car at rest when the traffic light turns green. You place your coffee cup on the horizontal dash and hit the gas. The coffee cup does not slide as you accelerate forward. The work done by friction on your coffee cup is
Answer:
[tex]\mu mgd[/tex]
Explanation:
In the situation described in the problem, there are 3 forces acting on the coffee cup:
- The weight of the cup, acting downward
- The normal force exerted by the horizontal dash on the cup, acting upward
- The force of friction, acting forward and "keeping" the cup travelling together with the car, without sliding backward
For the purpose of this problem, we ignore the weight and the normal force, since they cancel each other out.
The force of friction here pushes the cup forward, allowing it to move together with the dash and the car, without sliding. The magnitude of this force of friction is
[tex]F_f = \mu mg[/tex]
where
[tex]\mu[/tex] is the coefficient of static friction between the cup and the dash
m is the mass of the cup
g is the acceleration of gravity
Since the cup is moving forward together with the car, it means that it has a certain displacement [tex]d[/tex], and therefore the force of friction is performing work, equal to the product between force and displacement, so:
[tex]W=F_f \cdot d = \mu mg d[/tex]
what happens overtime to rocks that are stressed
Answer:
Stress is the force applied to an object. In geology, stress is the force per unit area that is placed on a rock. Four types of stresses act on materials.
A deeply buried rock is pushed down by the weight of all the material above it. Since the rock cannot move, it cannot deform. This is called confining stress.
Compression squeezes rocks together, causing rocks to fold or fracture (break) (Figure below). Compression is the most common stress at convergent plate boundaries.
Explanation:
Use the drop-down menus to complete the sentences describing the important ideas in Hess’s theory.
Hess expanded on Wegener’s theory of (blank).
possible answers: Pangaea landmass, continental drift, or conveyor belt.
Hess proposed the idea that (blank) are places where crust is created.
possibles answers: mid-ocean ridges, continents, or deep-ocean trenches
Answer:
Use the drop-down menus to complete the sentences describing the important ideas in Hess’s theory.
Hess expanded on Wegener’s theory of
Continental drift .
.
Hess proposed the idea that
mid-ocean ridges are places where crust is created.
Explanation:
Hess expanded on Wegener's theory of continental drift.
Hess proposed the idea that mid-ocean ridges are places where crust is created.
An ion source is producing 6Li ions, which have charge +e and mass 9.99 × 10-27 kg. The ions are accelerated by a potential difference of 9.2 kV and pass horizontally into a region in which there is a uniform vertical magnetic field of magnitude B = 0.99 T. Calculate the strength of the smallest electric field, to be set up over the same region, that will allow the 6Li ions to pass through undeflected.
Answer:
[tex]5.38\cdot 10^5 V/m[/tex]
Explanation:
At first, the 6Li ions are accelerated by the potential difference, so their gain in kinetic energy is equal to the change in electric potential energy; so we can write:
[tex]q\Delta V=\frac{1}{2}mv^2[/tex]
where
[tex]q=+e=+1.6\cdot 10^{-19}C[/tex] is the charge of one 6Li ion
[tex]\Delta V=9.2 kV=9200 V[/tex] is the potential difference through which they are accelerated
[tex]m=9.99\cdot 10^{-27}kg[/tex] is the mass of each ion
v is the final speed reached by the ions
Solving for v, we find:
[tex]v=\sqrt{\frac{2q\Delta V}{m}}=\sqrt{\frac{2(1.6\cdot 10^{-19})(9200)}{9.99\cdot 10^{-27}}}=5.43\cdot 10^5 m/s[/tex]
After that, the ions pass into a region with a uniform magnetic field of strength
[tex]B=0.99 T[/tex]
The magnetic field exerts a force perpendicular to the direction of motion of the ions, and this force is given by
[tex]F=qvB[/tex]
In order to make the ions passing through undeflected, there should be an electric force balancing this magnetic force. The electric force is given by
[tex]F=qE[/tex]
where E is the strength of the electric field.
Since the two forces must be balanced,
[tex]qE=qvB[/tex]
From which we get
[tex]E=vB[/tex]
So the strength of the electric field must be
[tex]E=(5.43\cdot 10^5)(0.99)=5.38\cdot 10^5 V/m[/tex]
What is the electrical force between q1 and q2? Recall that k = 8.99 × 109 N•meters squared over Coulombs squared.. 4.3 × 10 N 3.5 × 10 N –5.4 × 10 N –5.8 × 10 N?
Answer:
Explanation:
Incomplete question but for understanding.
We want to find the electrical force between two charges, then you can use the coulombs law which states that the force of attraction or repulsion between two charges is directly proportional to the product of the two charges and inversely proportional to the square of their distance apart,
So,
F = kq1•q2 / r²
Where k is a constant and it is given as
K = 8.99 × 10^9 Nm²/C²
q1 and q2 are the charges and in this question it is not given, so the question is incomplete. Let assume that,
q1 = - 1.609 × 10^-19 C electron
q2 = 1.609 × 10^-19 C proton
Since unlike charges attract, then it is force of attraction
Also, r is the distance apart and it is not given, let assume the distance between the two charges is 2 × 10^-5m
Then,
F = kq1•q2 / r²
F = 8.99 × 10^9 × 1.609 × 10^-19 × 1.609 × 10^-19 / (2 × 10^-5)²
F = 5.82 × 10^-19 N
Answer:
c –5.4 × 1010 N on edge
Explanation:
. The density of ice is 917 kg/m3, and the latent heat of fusion of water is 3.35 x 105 J/kg. The driver of the van turns on the rear-window defroster, which operates at 12 V and 29 A. The defroster directly heats an area of 0.56 m2 of the rear window. What is the maximum thickness of ice above this area that the defroster can melt in 3.8 minutes?
Answer:
[tex]s = 1.472\,m[/tex]
Explanation:
The heat require to melt the ice formed in the rear window is:
[tex]Q = m_{ice}\cdot L_{f}[/tex]
[tex]Q = \rho_{ice}\cdot V_{ice}\cdot L_{f}[/tex]
[tex]Q = \rho_{ice}\cdot A_{w}\cdot s \cdot L_{f}[/tex]
The heat transfer rate given by the defroster is:
[tex]\dot Q = \epsilon\cdot i[/tex]
But:
[tex]\epsilon \cdot i \cdot \Delta t = \rho_{ice}\cdot A_{w}\cdot s \cdot L_{f}[/tex]
The maximum thickness of ice that can be melt is:
[tex]s = \frac{\epsilon \cdot i \cdot \Delta t}{\rho_{ice}\cdot A_{w}\cdot L_{f}}[/tex]
[tex]s = \frac{(12\,V)\cdot (29\,A)\cdot (3.8\,min)\cdot (\frac{60\,s}{1\,min} )}{(917\,\frac{kg}{m^{3}} )\cdot (0.56\,m^{2})\cdot (105\,\frac{J}{kg} )}[/tex]
[tex]s = 1.472\,m[/tex]
Answer:
Max thickness; h = 4.61 x 10^(-4) m
Explanation:
We are given;
Current; I = 29A
Voltage; V = 12 V
Time; t = 3.8 minutes = 228 seconds
Density;ρ = 917 kg/m³
latent heat of fusion of water; L = 3.35 x 10^(5) J/kg
Area; A = 0.56 m²
We know that volume = Area x Height.
Thus, V = Ah and h = V/A
We also know that density is given by;
ρ = mass/volume = m/V
Amd V = m/ρ
Thus, h can be written as;
h = (m/ρ)/A - - - - - (eq1)
Now, we know that;
The specific latent heat (L) of a material is a measure of the heat energy (Q) per mass (m) released or absorbed during a phase change.
It is defined through the formula
Q = mL
Thus, m = Q/L
So, putting Q/L for m in eq 1,we have; h = (Q/Lρ)/A = Q/LρA
Now, power(P) is; Q/t where Q is energy dissipated and t is time.
Thus, P = Q/t and thus, Q = Pt
Thus, h = Pt/LρA - - - - (eq2)
We also know that Power = IV
Thus, power = 29 x 12 = 348 W
Thus, plugging in the relevant values into eq(2),we have;
h = (348 x 228)/(3.35 x 10^(5) x 917 x 0.56)
h = 79344/(1720.292 x 10^(5))
h = 4.61 x 10^(-4) m
This diagram shows that Al can see the reflections of Ed and Fred in the mirror. Which two students can both see the reflections of Cy, Di, Ed and Fred? *
Answer:
Cy and Di
Explanation:
We cannot tell exactly where the right end of the mirror is, but if we assume it is short of allowing Ed and Fred to see each other, we have the following:
Cy can see Cy and everyone to the right
Fred can see Di and everyone to the left
The only two that can see all of Cy, Di, Ed, and Fred are Cy and Di.
_____
If the mirror extends far enough to the right for Ed to see Fred, then all of Cy, Di, and Ed can see the four folks of interest.
Answer:
Cy and Di
Explanation:
The U.S. Navy has long proposed the construction of extremely low frequency (ELF waves) communications systems; such waves could penetrate the oceans to reach distant submarines. Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves of frequency 71 Hz.
Answer:
The length of the antenna would be L = 1056 km
Explanation:
Given:-
- The frequency of ELF, f = 71 Hz
- The speed of EM wave, c = 3.00 *10^8 m/s
Find:-
Calculate the length of a quarter-wavelength antenna for a transmitter generating ELF waves
Solution:-
- We will first determine the wavelength (λ) of the ELF waves with frequency (f) generated by the transmitter. The relationship that holds true for all types of EM waves is:
λ = c / f
λ = (3.00*10^8 m/s) / ( 71 Hz )
λ = 4225352.11267 m
- The antenna of the transmitter is to be designed such that its length (L) is 1/4-wavelength of ELF generated. So:
L = 0.25*λ
L = 0.25*4225352.11267
L = 1056 km
using a cathode ray tube , what did Thomson confirm
Answer:
Its b
Explanation:
If ur on edgenuity!!
The roller coaster from problem #1 then tops a second hill at 15.0 m/s, how high is the second hill?
Problem #1: A roller coaster glides from rest from the top of an 80.0 meter hill. What is the speed of the roller coaster at the bottom of the hill?
To find the height of the second hill, we can use the conservation of mechanical energy principle.
Explanation:To find the height of the second hill, we can use the conservation of mechanical energy principle. At the top of the second hill, the roller coaster has a kinetic energy and a gravitational potential energy. The total mechanical energy at the top of the hill is equal to the total mechanical energy at the bottom of the first hill. We can set up the equation:
mgh + 0.5mv^2 = mgh2
where m is the mass of the roller coaster, g is the acceleration due to gravity, h is the height of the first hill, v is the speed at the bottom of the hill, and h2 is the height of the second hill. Substituting the given values into the equation will give us the height of the second hill.
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Final answer:
When a roller coaster tops the second hill at 15.0 m/s, the height of the hill can be calculated by rearranging the conservation of energy equation. By setting the kinetic energy equal to the potential energy, we can solve for the height of the hill.
Explanation:
The question relates to the conservation of energy in physics, specifically within the context of a roller coaster. We are looking to find how high the second hill is, knowing that the roller coaster tops it at 15.0 m/s.
First, let's solve problem #1 as reference: A roller coaster starting from rest on an 80.0 meter hill without friction will convert its potential energy entirely into kinetic energy at the bottom. The formula to calculate the final speed (v) at the bottom is given by v = √(2gh), where g is the acceleration due to gravity (9.8 m/s²) and h is the height. Substituting the given values, we find the final speed at the bottom of the first hill.
For the second part, the roller coaster tops the second hill at 15.0 m/s, which is the kinetic energy at that point. To find the height of the second hill, we'll set that kinetic energy equal to the potential energy at the top of the hill.
The formula rearranged to solve for the height (h) is h = v₂ / (2g). When we input the speed and acceleration due to gravity, we can determine the height of the second hill.
g What is the magnetic potential energy stored in a cylindrical volume of height hcylinhcylin = 50 mmmm and radius RcylinRcylin = 24 mmmm that symmetrically surrounds an infinitely long wire that has radius RwireRwire = 2.1 mmmm and carries current III = 4.9 AA ? The volume in which the energy should be calculated does not contain the wire.
Answer:
[tex]2.9\cdot 10^{-7} J[/tex]
Explanation:
The energy density associated to a magnetic field is:
[tex]u=\frac{B^2}{2\mu_0}[/tex] (1)
where
B is the strength of the magnetic field
[tex]\mu_0[/tex] is the vacuum permeability
The magnetic field produced by a current-carrying wire is
[tex]B=\frac{\mu_0 I}{2\pi r}[/tex]
where
I is the current in the wire
r is the distance from the wire at which the field is calculated
Substituting into (1),
[tex]u=\frac{\mu_0 I^2}{8\pi^2 r^2}[/tex] (2)
Since this is the energy density, the total energy stored in a certain element of volume [tex]dV[/tex] will be
[tex]U=u\cdot dV=\frac{\mu_0I^2}{8\pi^2 r^2}dV[/tex] (3)
Here the field strength changes as we move farther from the wire radially, so we can write dV as
[tex]dV=2\pi h r dr[/tex]
where
h is the height of the cylinder
r is the distance from the wire
So eq(3) becomes:
[tex]dU=\frac{\mu_0I^2}{8\pi^2 r^2} \cdot 2 \pi h r dr = \frac{\mu_0 I^2 h}{4\pi}\frac{1}{r}dr[/tex]
Now we have to integrate this expression to find the total energy stored in the cylindrical volume. We have:
h = 50 mm = 0.050 m is the height of the cylinder
I = 4.9 A is the current in the wire
[tex]b=2.1 mm = 0.0021 m[/tex] is the internal radius of the cylinder (the radius of the wire)
[tex]a=24 mm=0.024 m[/tex] is the external radius of the cylinder
So,
[tex]U=\int\limits^a_b {dU} =\frac{\mu_0 I^2 h}{4\pi} \int\limits^{0.024}_{0.0021} \frac{1}{r}dr = \frac{\mu_0 I^2 h}{4\pi} [ln(a)-ln(b)]=\\=\frac{(4\pi \cdot 10^{-7})(4.9)^2(0.050)}{4\pi}[ln(0.024)-ln(0.0021)]=2.9\cdot 10^{-7} J[/tex]
Two resistances, R1 and R2, are connected in series across a 9-V battery. The current increases by 0.450 A when R2 is removed, leaving R1 connected across the battery. However, the current increases by just 0.225 A when R1 is removed, leaving R2 connected across the battery. a) Find R1 b) Find R2
Answer:
a. R1 = 0.162 Ω
b. R2 = 0.340 Ω
Explanation:
Since the resistors R1 and R2 are connected in series, the current flowing through them when the 9 V battery is applied is 9/R1 + R2.
When the current increases by 0.450 A wen only R1 is in the circuit, the current is
9/R1 + R2 + 0.450 A = 9/R1 (1)
When the current increases by 0.225 A when only R2 is in the circuit, the current is
9/R1 + R2 + 0.225 A = 9/R2 (2)
equation (1) - (2) equals
9(1/R1 - 1/R2) = 0.450 A - 0.225
9(1/R1 - 1/R2) = 0.125
(1/R1 - 1/R2) = 0.125 A/9 = 0.0138
1/R1 = 0.0138 + 1/R2
R1 = R2/(1 + 0.0138R2) (3)
From (1)
9/R1 - 9/R1 + R2 = 0.450 A
9R2/[R1(R1 + R2)] = 0.450 A
R2/[R1(R1 + R2)] = 0.450 A/9 = 0.5
R2/[R1(R1 + R2)] = 0.5 (4)
From (3) R2/R1 = (1 + 0.0138R2) and from (4) R2/R1 = 0.5(R1 + R2). So,
(1 + 0.0138R2) = 0.5(R1 + R2)
0.5R1 + 0.5R2 = 1 + 0.0138R2
0.5R1 = 1 + 0.0138R2 - 0.5R2
0.5R1 = 1 - 0.4862R2 (5)
Substituting (3) into (5) we have
0.5R2/(1 + 0.0138R2) = 1 - 0.4862R2
R2 = (1 + 0.0138R2)(1 - 0.4862R2)
R2 = 1 - 0.4724R2 - 0.0067R2²
Collecting like terms, we have
0.0067R2² + 0.4724R2 + R2 - 1 = 0
0.0067R2² + 1.4724R2 - 1 = 0
Using the quadratic formula,
[tex]R_{2} = \frac{-1.4724 +/-\sqrt{(1.4724)^{2} - 4 X 0.0067 X -1} }{2 X 0.0067} \\= \frac{-1.4724 +/-\sqrt{2.1680 + 0.0268} }{0.0268}\\= \frac{-1.4724 +/-\sqrt{2.1948} }{0.0268}\\= \frac{-1.4724 +/- 1.4815 }{0.0268}\\= \frac{-1.4724 + 1.4815 }{0.0268} or \frac{-1.4724 - 1.4815 }{0.0268}\\= \frac{0.0091 }{0.0268} or \frac{-2.9539}{0.0268}\\= 0.340 or -110.22[/tex]
We choose the positive answer.
So R2 = 0.340 Ω
From (5)
R1 = 0.5 - 0.9931R2
= 0.5 - 0.9931 × 0.340
= 0.5 - 0.338
= 0.162 Ω
a. R1 = 0.162 Ω
b. R2 = 0.340 Ω
What other theory does the author compare to the Big Bang to?
Answer:
The two Russian authors based their exposition on what they called the Friedmann theory of a singular beginning of the universe, referring throughout to the “theory of the hot universe” as an alternative to the hot Big Bang theory.
Calculate the angular momentum of a 2 kg cylinder pulley with radius 0.1 m that rotates at a constant angular speed of 2 rad/s.
Answer:
The angular momentum of cylinder pulley is [tex]0.02 \ kg\ m^2\ rad /s\\[/tex] .
Explanation:
Given :
Mass of pulley , m = 2 kg .
Radius of pulley , R = 0.1 m .
Angular velocity of pulley , [tex]\omega=2\ rad/s[/tex] .
We need to find the angular momentum
We know , angular momentum of a rigid body is given by :
[tex]L=I\omega[/tex] ......( 1 )
Here , I is the angular momentum of cylindrical pulley and is given by :
[tex]I=\dfrac{MR^2}{2}\\\\I=\dfrac{2\times 0.1^2}{2}\\\\I=0.01\ kg \ m^2[/tex]
Putting value of I and [tex]\omega[/tex] in equation 1 .
We get :
[tex]L=0.01\times 2\ kg\ m^2\ rad /s\\\\L=0.02 \ kg\ m^2\ rad /s\\[/tex]
Therefore , the angular momentum of cylinder pulley is [tex]0.02 \ kg\ m^2\ rad /s\\[/tex] .
The angular momentum of the cylinder pulley can be determined by first calculating the moment of inertia using the mass and the radius of the pulley, and then substituting the obtained values and the given angular velocity into the formula for angular momentum. The calculated angular momentum for this cylinder pulley is 0.02 kg.m²/s.
The angular momentum of a rotating object, such as a cylinder pulley, is calculated by the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The moment of inertia of a cylinder is I = 0.5mr², where m is the mass and r is the radius of the cylinder.
First, we calculate the moment of inertia for our cylinder pulley: I = 0.5 x 2 kg x (0.1 m)² = 0.01 kg.m². Now, we can determine the angular momentum: L = 0.01 kg.m² x 2 rad/s = 0.02 kg.m²/s.
Therefore, the angular momentum of a 2 kg cylinder pulley with radius 0.1 m rotating at a constant angular speed of 2 rad/s is 0.02 kg.m²/s.
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My reaction time was 0.7268 seconds the first time and 0.3883 the second time. What was yours
Answer:
0.32493
Explanation: