The radius of curvature of the mirror is 0.30 m, the height of the image is 0.00960 m, and the image is inverted.
Given
Object height h₀ = 3.20 mm = 0.00320 m
Object distance u = -20.0 cm = -0.20 m (negative sign indicates object is placed in front of the mirror)
Image distance v = 60.0 cm = 0.60 m
Image height hᵢ = ?
Using mirror formula
1/f = 1/v - 1/u
where f is the focal length of the mirror.
Substituting the values, we get
1/f = 1/0.60 + 1/0.20
f = 0.15 m
The radius of curvature of the mirror is given by
R = 2f = 0.30 m
Using magnification formula
m = -v/u = hᵢ/h₀
where m is the magnification.
Substituting the values, we get:
hᵢ/h₀ = -v/u
hᵢ = -m*h₀
hᵢ = -(60.0/20.0)*0.00320
hᵢ = -0.00960 m
The negative sign indicates that the image is inverted.
To know more about radius of curvature:
https://brainly.com/question/15841157
#SPJ4
Four quartz samples of equal size and shape were placed in a stream. Which of the four quartz samples below has most likely been transported farthest in the stream?
I've attached the complete question.
Answer:
Option D
Explanation:
From the quartz images attached, we can see they now have different shapes, level of roughness and irregularity. However, the one that will have transported farthest will be option D which is the one that looks circular and has undergone the most abrasion from its body surface and size so far . This is because abrasion is a type of weathering were rocks and sediments wear out their surfaces by grinding out against each other.
The only option that looks to have undergone the most abrasion which means has transported the farthest is the sample in option D
A train travels for 120 seconds (s) at a speed of 50 meter per second (m/s). What was the distance (m) that it travelled?
Answer:
2
Explanation:
50 times 2
forces and motion until test for physical science eginuity credit recovery ????
Forces and motion are fundamental concepts in physics that help us understand the behavior of objects in motion. Forces can cause objects to accelerate, change direction, or stop moving altogether.
The three laws of motion proposed by Sir Isaac Newton provide a framework for understanding how forces affect motion. The first law states that an object at rest will stay at rest, and an object in motion will stay in motion, unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. The third law states that every action has an equal and opposite reaction. To test these concepts in physical science, experiments can be designed to measure the effects of forces on motion, such as the acceleration of objects on inclined planes, the motion of objects in free fall, or the forces involved in collisions.
Learn more about forces here
https://brainly.com/question/13191643
#SPJ1
The complete question is
Forces and motion until test for physical science eginuity credit recovery ?
An electron moves in a circular path with a speed of 1.26 ✕ 107 m/s in the presence of a uniform magnetic field with a magnitude of 1.90 mT. The electron's path is perpendicular to the field.
(a) What is the radius (in cm) of the circular path?
(b) How long (in s) does it take the electron to complete one revolution?
Answer:
Explanation:
To solve this problem, we can use the equation for the centripetal force experienced by a charged particle moving in a magnetic field:
F = (mv^2) / r
where:
F is the centripetal force,
m is the mass of the electron,
v is the velocity of the electron,
r is the radius of the circular path.
We also know that the centripetal force is provided by the magnetic force:
F = |q| * v * B
where:
|q| is the magnitude of the charge of the electron,
B is the magnitude of the magnetic field.
Setting the two equations equal to each other and solving for the radius (r), we have:
(mv^2) / r = |q| * v * B
Simplifying and rearranging for r:
r = (mv) / (|q| * B)
Given:
m = 9.11 x 10^-31 kg (mass of the electron)
v = 1.26 x 10^7 m/s (velocity of the electron)
|q| = 1.6 x 10^-19 C (charge of the electron)
B = 1.90 x 10^-3 T (magnetic field)
(a) Calculating the radius (r):
r = (9.11 x 10^-31 kg * 1.26 x 10^7 m/s) / (1.6 x 10^-19 C * 1.90 x 10^-3 T)
r ≈ 0.00296 m
Converting the radius to centimeters:
r = 0.00296 m * 100 cm/m
r ≈ 0.296 cm
The radius of the circular path is approximately 0.296 cm.
(b) To find the time it takes for the electron to complete one revolution, we can use the equation for the period (T) of circular motion:
T = 2πr / v
Given the radius (r) and velocity (v), we can calculate T:
T = (2π * 0.00296 m) / (1.26 x 10^7 m/s)
T ≈ 1.48 x 10^-7 s
The time it takes for the electron to complete one revolution is approximately 1.48 x 10^-7 s.
Given that An electron moves in a circular path with a speed of 1.26 ✕ 10^7 m/s in the presence of a uniform magnetic field with a magnitude of 1.90 mT. The electron's path is perpendicular to the field. The task is to find the radius (in cm) of the circular path and how long (in s) it takes the electron to complete one revolution.
(a) To calculate the radius of the circular path, we need to use the formula that is used to find the radius of the circular motion under the influence of a magnetic field.
R = mv/qBR = (1.6 x 10^-19 C)(1.26 x 10^7 m/s)/(1.6 x 10^-19 C)(1.90 x 10^-3 T)R = 5.27 x 10^-2 mConverting meter into cm.R = 5.27 x 10^-2 m x 100 cm/mR = 5.27 cm(b) We can calculate the time taken by the electron to complete one revolution using the following formula for the time period.T = 2πm/qBTT = (2 x π x m)/(qB)T = (2 x π x 9.11 x 10^-31)/(1.6 x 10^-19 C)(1.90 x 10^-3 T)T = 2.10 x 10^-7 sThus, the time taken by the electron to complete one revolution is 2.10 x 10^-7 s.About MagnitudeThe seismic magnitude scale is used to describe the overall strength or "size" of an earthquake. It is distinguished from the seismic intensity scale which categorizes the intensity or severity of ground shaking caused by earthquakes at a specific location.
Learn More About Magnitude at https://brainly.com/question/30337362
#SPJ11
Mousa builds a bike ramp at 22 degrees that allows him to just barely jump his bike across a 5 m wide stream in the local neighborhood. Bilyan wants to replicate Mousa’s jump by building his own ramp, but at a different angle. At what angle should Bilyan construct his ramp?
A.
44 degrees
B.
11 degrees
C.
78 degrees
D.
68 degrees
Una pelota cae con una energía de 1 J y bota al llegar al suelo. Si tras el bote su energía es de 0,998 J, ¿podemos afirmar que la energía se ha destruido?
Answer:
The energy is not destroyed, the energy has been transformed into another kind of energy, in this case to heat with energy of 0,002 J
Explanation:
One of the fundamental principles of physics states that energy is neither created nor destroyed, it is only transformed.
In this case, when the ball with an energy of 1 J bounces on the ground, it loses an energy equivalent to 1-0.998 J = 0.002 J. This energy of 0.002 J is not destroyed in the process, but is transformed into another type of Energy. In this case, said energy has been converted to heat. A heat equivalent to 0.002 J of energy.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Translation to spanish
Uno de los principios fundamentales de la física afirma que la enegía no se crea ni se destruye, sólo se transforma.
En este caso, cuando la pelota con una energía de 1 J rebota en el suelo pierde una energía equivalente a 1-0,998 J = 0,002 J. Esta energía de 0,002 J no se destruye en el proceso, sino que se transforma en otro tipo de energía. En este caso dicha energía se ha convertido en calor. Un calor equivalente a 0,002 J de energía.
car moves a distance of 420 m. Each tire on the car has a diameter of 42 cm. Which shows how many revolutions each
tire makes as they move that distance?
Plzzzz help asap
Answer:
10 is the correct answer
Answer:
Total Distance: 420 meters
Diameter: 42 cm
Notice the units meters vs cm
420÷ 42 = 10 total revolutions
As we move from left to right across the periodic table, what is the general trend?
A) Atomic radii increase.
B) Electronegativity decreases.
C) Nuclear shielding increases.
D) Metallic character decreases.
As we move from left to right across the periodic table, the general trend is that the atomic radii decrease and the electronegativity increases while the metallic character decreases and the nuclear shielding remains constant. The option d is correct
The periodic table is an organized arrangement of elements that are ordered according to the periodic law, which is a basic principle of chemistry. This principle explains that the chemical and physical properties of elements are periodic or repeated based on their atomic structure. The table has been designed to demonstrate the relationship between the chemical and physical properties of elements. It comprises 118 elements in total and is arranged in order of atomic number. Elements have been classified into groups based on their chemical and physical properties. Each group is identified by the number of valence electrons the element has, which plays a significant role in determining the element's behavior.
As we move from left to right across the periodic table, the trend is that the atomic radii decrease due to the increased nuclear charge that attracts the electrons more strongly to the nucleus. This decreases the size of the atom. Additionally, the electronegativity increases because the effective nuclear charge, which is the net charge an electron feels from the nucleus, increases. The metallic character of the element decreases as we move from left to right because the elements lose their metallic character and become non-metallic. Finally, nuclear shielding remains constant because it remains the same across a period. The option d is correct
To know more about periodic table visit:
https://brainly.com/question/28747247
#SPJ11
1. A 500.0 g metal block absorbs 5.875 × 103 J of heat to raise its temperature by 50.0 K. What is the substance? Show your work.
Specific Heats of Selected Substances
Substance
C [J/(kg·K)]
Water (ice)
2,060
Iron
450
Aluminum
897
Gold
130
Copper
385
Silver
235
Ammonia (liquid)
4,700
Water (liquid)
4,180
Water (steam)
2,020
Lead
128
The name of the substance is silver based on the specific heat capacity value.
What is the specific heat capacity of the substance?The specific heat capacity of the substance is calculated by applying the following formula for heat capacity.
Q = mcΔθ
where;
m is the mass of the substancec is the specific heat capacity of the substanceΔθ is the change in temperaturec = Q / mΔθ
The specific heat capacity of the substance is calculated as;
c = (5875 J ) / ( 500 g x 50 )
c = 0.235 J/kgK
The substance that has the same specific heat capacity calculated above is silver.
Learn more about specific heat capacity here: https://brainly.com/question/16559442
#SPJ1
When does a rational function attain a horizontal asymptote and when does it attain a vertical asymptote? Use limits in your conclusion
A rational function attains a horizontal asymptote when the degree of the numerator is less than or equal to the degree of the denominator.
Let's consider a rational function f(x) with numerator N(x) and denominator D(x). If the degree of N(x) is less than the degree of D(x), then the horizontal asymptote is y = 0. This is because as x approaches infinity or negative infinity, the higher degree terms in the denominator will dominate, causing the function to approach zero. If the degree of N(x) is equal to the degree of D(x), then the horizontal asymptote is determined by the ratio of the leading coefficients of the numerator and denominator. Let's say the leading coefficient of N(x) is a and the leading coefficient of D(x) is b. In this case, the horizontal asymptote is y = a/b. As x approaches infinity or negative infinity, the ratio of the leading coefficients determines the value that the function approaches. A rational function attains a vertical asymptote when the denominator becomes zero at certain values of x. To determine the vertical asymptote, we find the values of x that make the denominator zero and take the limit of the function as x approaches those values. If there is a factor (x - c) in the denominator, where c is a constant, then x = c is a vertical asymptote. As x approaches the value c, the function approaches positive or negative infinity, depending on the signs of the coefficients of the terms in the numerator.
Learn more about rational function here : brainly.com/question/27914791
#SPJ11
1.You are traveling from point A to B on the following route:
From A, move 12 km to the East, and 15 km to the West, ( here is point B). If this takes 45 min, find the average velocity based on km/h
V = 4 km/h to the west
V = 36 km/h to the west
V = 4 km/h to the east
V = 36 km/h to the east
2.Two objects with different mass ( m1 = 0.2 kg, m2 = 0.1 kg) from the same height and with no initial velocity release at the same time( no air resistance), which one will reach the ground first?
m1
m2
They will reach at the same time
3.A car ( m= 1500 kg) is moving with 72 km/h ( = 20 m/s)
How much force is required to stop this car in 5 seconds.
F = - 6000 N
F = 6000 N
F = - 150,000 N
F = 150,000 N
4.You are traveling from point A to B on the following route:
From A, move 20 km to the East, 10 km to the North and finally 20 km to the West, ( here is the point B). a) find the total displacement
b) find the total distance traveled
a) total displacement = 10 km to the west
b) total distance = 50 km
a) total displacement = 10 km to the North
b) total distance = 50 km
a) total displacement = 50 km to the North
b) total distance = 10 km
a) total displacement = 10 km to the South
b) total distance = 50 km
V = 4 km/h to the west.
Based on the given information, the total distance traveled is 12 km to the East and 15 km to the West, which cancels each other out. Therefore, the net displacement is 0 km, indicating that the starting point and ending point are the same. The total time taken to travel this distance is 45 minutes.
To calculate the average velocity, we need to convert the time from minutes to hours. Since there are 60 minutes in an hour, 45 minutes is equal to 45/60 = 0.75 hours.
Average velocity is defined as displacement divided by time. In this case, the displacement is 0 km and the time is 0.75 hours. Therefore, the average velocity is 0 km/0.75 hours = 0 km/h.
The negative sign indicates that the velocity is in the westward direction. Thus, the average velocity is 0 km/h to the west.In conclusion, the average velocity based on the given scenario is 0 km/h to the west. This means that there is no net displacement over time, indicating that the object returns to its starting point.
The calculation of average velocity helps us understand the overall motion and direction of an object, providing valuable information about its movement.Velocity is a vector quantity that takes into account both magnitude (speed) and direction. In this case, the average velocity of 0 km/h indicates that there is no net displacement over time.
It suggests that the object returns to its initial position after traveling to the east and then to the west. Understanding the concept of velocity and its relationship to displacement and time can provide insights into the motion of objects and how they change their positions.
Learn more about information
brainly.com/question/33276597
#SPJ11
Height of tallest wave possible
a particle moving along the x axis has a position given by where 22 m/s, 3.8 m/s3 and is measured in seconds. what is the magnitude of the acceleration of the particle at the instant when its velocity is zero? please give your answer in units of m/s2.
Answer:
Therefore, the magnitude of the acceleration of the particle at the instant when its velocity is zero is approximately 18.258 m/s².
Explanation:
To find the magnitude of acceleration at the instant when velocity is zero, we need to differentiate the given velocity equation with respect to time (t) to obtain the acceleration equation.
Given:
Velocity equation: v(t) = 22 - 3.8t^2
Differentiating the velocity equation with respect to time, we get:
a(t) = d(v(t))/dt = -2 * 3.8t
To find the magnitude of acceleration at the instant when velocity is zero, we need to solve for t when v(t) = 0.
0 = 22 - 3.8t^2
3.8t^2 = 22
t^2 = 22/3.8
t^2 ≈ 5.789
Taking the square root of both sides, we find:
t ≈ √(5.789)
t ≈ 2.403
Now we can substitute this value of t into the acceleration equation to find the magnitude of acceleration at that instant:
a(t) = -2 * 3.8 * 2.403
a(t) ≈ -18.258
Therefore, the magnitude of the acceleration of the particle at the instant when its velocity is zero is approximately 18.258 m/s².
Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 2.10×10^6 N
, one at an angle 17.0 ∘
west of north, and the other at an angle 17.0 ∘
east of north, as they pull the tanker a distance 0.630 km
toward the north. What is the total work done by the two tugboats on the supertanker?
Express your answer in joules, to three significant figures.
To pull the tanker 0.630 km total work to be done is 1.871 × 10⁹ Joule.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
Resultant force acting on the tugboat = √2 × 2.10 × 10⁶ N.
To pull the tanker 0.630 km, that is, 630 m, work done = force × displacement
= √2 × 2.10 × 10⁶ N × 630 m
= 1871004543.01 Joule.
= 1.871 × 10⁹ Joule.
Learn more about force here:
https://brainly.com/question/13191643
#SPJ1
1. A spring is stretched 0. 2 m from equilibrium. The force constant (k) of the
spring is 2500 N/m. What is the potential energy of the spring?
The energy can either be decreased or increased it all depends on the velocity of the stream
za stack emitting 80 g/s of no has an effective stack height of 100 m. the windspeed is 4 m/s at 10 m, and it is a clear summer day with the sun nearly overhead. estimate the ground-level no concentration
The ground-level no concentration 57.2 micro gram per cubic meter.
Calculation:-
C ( 2, 0.1, 0) = 80/π × 5.65 × 289.9 × 233.6 × exp ( -100²/2 × 289.9 ²) × exp ( -100²/2× 255.6²)
=
57.2 micro gram per cubic meter.
Wind speed affects climate forecasting, aviation and maritime operations, creation projects, increase and metabolism price of many plant species, and has limitless other implications. be aware that wind course is normally nearly parallel to isobars (and not perpendicular, as one might assume), due to Earth's rotation.
The concentration in air of a pollutant to which a human being is normally exposed, i.e. between the ground and a height of some 2 meters above it.
Learn more about windspeed here :-
https://brainly.com/question/29801913
#SPJ4
two cars in opposite directions were going at 50 mph before a collision. they had a head on inelastic collision, i.e., the two cars stuck together afterward. the mass of car 1 is 1,000 kg, and car 2 is 4,000 kg. find the common speed in mph of the combined piece right after the collision. what direction did the cars move afterward?
The common speed in mph of the combined piece right after the collision was 30 mph. The cars move towards the lighter car.
An inelastic collision is a collision in which there is no internet loss in kinetic energy within the gadget because of the collision. each momentum and kinetic electricity are conserved portions in elastic collisions.
Calculation:-
50 mph = (50 × 0.477)
= 22.35
Applying the law of conservation of momentum.
we get the:-
m₁u₁ + m₂u₂ = (m₁ + m₂)V
V = m₁u₁ + m₂u₂/(m₁ + m₂)
= 4000 × 22.35 + 1000 × (-22.35) / 4000 +1000
V = 13.41 m/s
= 13.41/0.447
= 30 mph
Hence, the common speed of the car is 30mpH.
An inelastic collision is a come between two bodies in which the full kinetic energy of the two bodies remains equal. In an ideal, perfectly elastic collision, there may be no internet conversion of kinetic strength into other kinds which includes heat, noise, or capacity electricity.
Elastic collisions arise whilst both the momentum and kinetic energy are conserved, just like how billiard balls bounce off each different and move at the same speeds as earlier. Inelastic collisions appear whilst simplest the momentum is conserved but not the kinetic power.
Learn more about collision here:-https://brainly.com/question/7694106
#SPJ4
two objects with momentum values of 50.0kgm/s and -75.0kgm/s collide elastically. after the collision the first object has a momentum of -40.0kgm/s, what is the momentum of the second?
In an elastic collision, both momentum and kinetic energy are conserved. Let's denote the momentum of the first object before the collision as p1, the momentum of the second object before the collision as p2, the momentum of the first object after the collision as p1', and the momentum of the second object after the collision as p2'.
Given:
p1 = 50.0 k gm/s (momentum of the first object before the collision)
p1' = -40.0 k gm/s (momentum of the first object after the collision)
We need to find p2 (momentum of the second object after the collision).
Since momentum is conserved, we can write the equation:
p1 + p2 = p1' + p2'
Substituting the given values:
50.0 k gm/s + p2 = -40.0 k gm/s + p2'
To find p2', we need to determine p2 by rearranging the equation:
p2' = 50.0 k gm/s + p2 - (-40.0 k gm/s)
Simplifying the equation:
p2' = 50.0 k gm/s + p2 + 40.0 k gm/s
p2' = p2 + 90.0 k gm/s
Therefore, the momentum of the second object after the collision is p2 + 90.0 k gm/s.
.
learn more about elastic collision here:
https://brainly.com/question/24616147
#SPJ11
A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at 40∘C at a rate of 850m3/min and leaves the turbine at 650∘C. Assuming a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent, determine
(a) the net power output,
(b) the back work ratio, and
(c) the thermal efficiency.
Use constant specific heats with
cv=0.821kJ/kg?
K,cp=1.108kJ/kg?
K, and k=1.35.
Answer:
a) 6498.84 kW
b) 0.51
c) 0.379
Explanation:
See the attached picture below for the solution
Given-
Temperature at state 1 \(T_{1}\) is 40 degree cel. This is equal to the 313 K.
Temperature at state 1 \(T_{2}\) is 650 degree cel. This is equal to the 923 K.
To know the mass flow rate use the idol gas equation. Idol gas equation for a substance can be given as,
\(PV=nRT\)
Rewrite this equation for \(n\),
\(n=\dfrac{PV}{RT}\)
Put the value of known variable from the question,
\(n=\dfrac{100\times\dfrac{850}{60} }{0.287\times 313}\)
\(n=15.77\)
Thus the value of n is 15.77 kg/sec.
Temperature at state 2 is,
In Bryon cycle we know that the processes 1-2 and 3-4 are isotropic. Hence,
\(T_{2} =T_{1}\left (1+ \dfrac{r_{p}^{\dfrac{\gamma-1}{\gamma}-1} }{c_{v} } \right )\)
\(T_{2} =313\left (1+ \dfrac{16^{\dfrac{1.35-1}{1.35}-1} }{0.821 } \right )\)
\(T_{2} =700\)
Temperature at state 3 is,
\(T_{3} =\dfrac{T_4}{1+c_p(r_p^{\dfrac{\gamma-1}{\gamma}-1}-1)}\)
Put the value in above equation we get,
\(T_3=1682\)
Net power output is,\(W=mc_p(T_i{n}-T_{out})\)
\(W=mc_p(T_3-T_2-T_4+T_{1})\)
\(W=15.77\times1.109(1682-700-923+313)\)
\(W=65\)
Thus the net power output is 70 watt.
The back work ratio,
\(r_b=\dfrac{T_2-T_1}{T_3-T_4}\)
\(r_b=\dfrac{700-313}{1682-923}\)
\(r_b=0.51\)
Hence the back work ratio is 0.51.
The thermal efficiency-\(\eta=\dfrac{W}{Q_{in}}\)
\(\eta=\dfrac{65}{mc_p(T_3-T_2)}\)
\(\eta=0.379\)
Hence, for the given problem the net power output is 70 watt,the back work ration is 0.51, and the thermal efficiency is 0.379.
For more about the Brayton cycle, follow the link below-
https://brainly.com/question/24696911
which explanation of the solar system best fits the observations of the planets and how they orbit the sun?responses
The heliocentric model of the solar system best fits the observations of the planets and their orbits around the Sun, and is widely accepted as the most accurate scientific explanation of our solar system.
The most widely accepted scientific explanation of the solar system is the heliocentric model, which was first proposed by the Polish astronomer Nicolaus Copernicus in the 16th century. This model states that the Sun is at the center of the solar system and the planets orbit around it.
The heliocentric model fits the observations of the planets and their orbits around the Sun better than the previous geocentric model, which placed the Earth at the center of the universe with the planets, including the Sun, orbiting around it. The heliocentric model explains the observations of the planets' retrograde motion, where planets appear to move backward in the sky at certain times, which was difficult to explain in the geocentric model.
The heliocentric model is supported by a wealth of evidence, including observations of the planets and their orbits, as well as the laws of motion and gravity discovered by Sir Isaac Newton. The model has also been refined over time to account for new observations and discoveries, such as the existence of asteroids and comets.
To know more about solar system.
https://brainly.com/question/18365761
#SPJ4
what is electromagnetic spectrum
Answer:
range of wavelength and frequencies is the answer
Explanation:
the defintion is:
the range of wavelengths or frequencies over which electromagnetic radiation extends.
and also
It is the most complete range of all types of radiation that has both electric & magnetic fields and travels in waves.
Making electromagnetic spectrum a electromagnetic spectrum
Range of wavelength and frequencies being the answer
In which medium does light travel faster: one with a critical angle of 27.0° or one with a critical angle of 32.0°? Explain. (For both cases, air is the second medium.)
Answer:
Among those two medium, light would travel faster in the one with a reflection angle of \(32^{\circ}\) (when light enters from the air.)
Explanation:
Let \(v_{1}\) denote the speed of light in the first medium. Let \(v_{\text{air}}\) denote the speed of light in the air. Assume that the light entered the boundary at an angle of \(\theta_{1}\) to the normal and exited with an angle of \(\theta_{\text{air}}\). By Snell's Law, the sine of \(\theta_{1}\!\) and \(\theta_{\text{air}}\!\) would be proportional to the speed of light in the corresponding medium. In other words:
\(\displaystyle \frac{v_{1}}{v_{\text{air}}} = \frac{\sin(\theta_{1})}{\sin(\theta_{\text{air}})}\).
When light enters a boundary at the critical angle \(\theta_{c}\), total internal reflection would happen. It would appear as if the angle of refraction is now \(90^{\circ}\). (in this case, \(\theta_{\text{air}} = 90^{\circ}\).)
Substitute this value into the Snell's Law equation:
\(\begin{aligned}\frac{v_{1}}{v_{\text{air}}} &= \frac{\sin(\theta_{1})}{\sin(\theta_{\text{air}})} \\ &= \frac{\sin(\theta_{c})}{\sin(90^{\circ})} \\ &= \sin(\theta_{c})\end{aligned}\).
Rearrange to obtain an expression for the speed of light in the first medium:
\(v_{1} = v_{\text{air}} \cdot \sin(\theta_{1})\).
The speed of light in a medium (with the speed of light slower than that in the air) would be proportional to the critical angle at the boundary between this medium and the air.
For \(0 < \theta < 90^{\circ}\), \(\sin(\theta)\) is monotonically increasing with respect to \(\theta\). In other words, for \(\!\theta\) in that range, the value of \(\sin(\theta)\!\) increases as the value of \(\theta\!\) increases.
Therefore, compared to the medium in this question with \(\theta_{c} = 27^{\circ}\), the medium with the larger critical angle \(\theta_{c} = 32^{\circ}\) would have a larger \(\sin(\theta_{c})\). such that light would travel faster in that medium.
.An electron moves at 2.40 ×10^6 m/s through a region in which there is a magnetic field of unspecified direction and magnitude 7.90 ×10^−2T.
A. What is the largest possible magnitude of the acceleration of the electron due to the magnetic field?
B. What is the smallest possible magnitude of the acceleration of the electron due to the magnetic field?
C. If the actual acceleration of the electron is one-fourth of the largest magnitude in part A, what is the angle between the electron velocity and the magnetic field?
A. The largest possible magnitude of the acceleration of the electron due to the magnetic field is 1.89 × 10⁶ m/s².
B. The smallest possible magnitude of the acceleration is 0 m/s².
C. If the actual acceleration is one-fourth of the largest magnitude, the angle between the electron velocity and the magnetic field is 60 degrees.
When an electron moves through a magnetic field, it experiences a force known as the magnetic force. The magnitude of this force can be calculated using the formula F = qvBsinθ, where F is the force, q is the charge of the electron, v is its velocity, B is the magnetic field magnitude, and θ is the angle between the velocity and the magnetic field.
A. To find the largest possible magnitude of acceleration, we need to consider the maximum value of sinθ, which is 1. Therefore, the maximum acceleration occurs when the electron's velocity is perpendicular to the magnetic field. Using the given values, we can calculate the largest acceleration as F/m = (qvBsinθ)/m = (1.6 × 10⁻¹⁹ C)(2.40 × 10⁶ m/s)(7.90 × 10^−2T)/9.11 × 10⁻³¹ kg ≈ 1.89 × 10⁶ m/s².
B. The smallest possible magnitude of acceleration occurs when the angle θ between the velocity and the magnetic field is 0 degrees, causing sinθ to be 0. In this case, the magnetic force is zero, resulting in no acceleration.
C. If the actual acceleration is one-fourth of the largest magnitude, it would be 1.89 × 10⁶ m/s² divided by 4, which is approximately 4.73 × 10⁵ m/s². To find the angle θ, we rearrange the formula as sinθ = (a/m)/(qvB) and substitute the known values, sinθ = (4.73 × 10⁵ m/s²)/(1.6 × 10^-19 C)(2.40 × 10⁶ m/s)(7.90 × 10^−2T) ≈ 0.156. Taking the inverse sine of 0.156, we find that the angle θ is approximately 60 degrees.
Learn more about magnetic field
brainly.com/question/14848188
#SPJ11
A very light rope is wrapped around a wheel of radius r and does not slip. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 20 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 3 seconds. What is the mass of the wheel?.
The mass of the wheel is 400/3s² divided by the square of the radius.
What is mass?Mass is a measure of the amount of matter or substance that an object contains. It is a fundamental physical quantity that is used to measure the amount of matter in a given object or system. It is measured in kilograms (kg) or grams (g). Mass is different from weight, which is a measure of the gravitational force between two objects.
At the start, all the energy is potential energy:
\(PE_{initial\) = mgh + Iω²/2
At the end, all the energy is kinetic energy:
\(KE_{final\) = mv²/2 + Iω²/2
Since the system is released from rest, we know that the initial angular velocity ω is 0, and the final velocity v is 10m/3s.
Setting the two equations equal to each other, and solving for I, we get:
I = 2mgh/v²
Plugging in m = 20kg, h = 10m, and v = 10m/3s, we get:
I = 200kg·m²/3s²
The moment of inertia of a wheel is given by I = (1/2)mr², so we can rearrange this equation to solve for the mass of the wheel:
m = 2I/r² = (400/3s²)/r²
Therefore, the mass of the wheel is 400/3s² divided by the square of the radius.
To learn more about mass
https://brainly.com/question/86444
#SPJ4
i’ll give a brainliest
Answer:
hey buddy
Explanation:
Answer:
The net force of the box is 40 Newtons.
Explanation:
There are 50 N of rightward force on the box.
There are 10 N of friction acting upon the box.
50-10=40 N
a rigid rod of length and mass has small point like masses and attached as shown. here 0.08 kg, 0.6 m. the rod is spinning in a horizontal plane about a vertical axis passing through the smaller mass . the linear speed of mass is 2.5 m/s. find the angular momentum of the rod and masses system with respect to the point on the fixed axis that intersects with the rod.
The angular momentum of the rod and masses system is 2.5 ms.
Angular momentum is the rotational analog of linear momentum. it is an essential bodily quantity due to the fact it is a conserved amount—the entire angular momentum of a closed device remains constant. Angular momentum has both a route and a value, and both are conserved.
Angular momentum is defined as The property of any rotating item given via second of inertia instances angular velocity. it's far the property of a rotating frame given with the aid of the made of the instant of inertia and the angular pace of the rotating item.
Calculation:-
The moment of inertia of the system about the basics is,
I e mos + (2m) [2 = me+ 2m22 3
= 7(0-0819) 0.6m) 2
= 0.0672 LG. ma ✓
= 2.5 ms
Learn more about angular momentum here:-https://brainly.com/question/4126751
#SPJ4
In water quality, the symbol "mg/L" is equivalent to:
a. Micrograms per liter
b. Parts per million
c. Parts per billion
d. Mostly good levels
The symbol "mg/L" in water quality represents milligrams per liter, which is a unit of measurement commonly used to express the concentration of substances in water. Option a is right choice.
The symbol "mg/L" in water quality refers to milligrams per liter, which is a unit of measurement commonly used to express the concentration of substances in water.
This unit represents the number of milligrams of a particular substance that are present in one liter of water.
In the context of water quality, the concentration of various substances is typically measured in parts per million (ppm) or parts per billion (ppb). For example, the concentration of dissolved oxygen in water is typically expressed in milligrams per liter (mg/L), which is equivalent to ppm.
Micrograms per liter (µg/L) is another unit of measurement that is commonly used to express the concentration of substances in water.
However, this unit is typically used for substances that are present in very low concentrations, such as certain pollutants or toxins. In some cases, concentrations may be expressed in parts per trillion (ppt), which is equivalent to µg/L.
Option a is right choice.
For similar question on water quality
https://brainly.com/question/8920269
#SPJ11
Assume each mark on the scale represented 1 g. Estimate how much a sheet of paper would mass. A sheet of paper is 28 cm by 21.7 cm.
Answer:
607.6g
Explanation:
Assume each mark on the scale represented 1 g. That is 1 cm = 1g
To estimate how much a sheet of paper would mass a sheet of paper is 28 cm by 21.7 cm, first calculate the area.
Area = 28 × 21.7 = 607.6 cm^2
Mass = 607.6 × 1g = 607.6 g
Therefore, the estimation will be 607.6g
A 2-kg ball rolls down the hill. By the time it is at the bottom,
the ball's Kinetic Energy is 25 J. What is its velocity at the
bottom of the hill?
Answer:
v = 5 [m/s]
Explanation:
Kinetic energy is related to speed, that is, whenever we have kinetic energy we will have a body with speed moving. This can be calculated using the following equation.
\(E_{k}=\frac{1}{2}*m*v^{2}\\\)
where:
m = mass = 2 [kg]
v = velocity [m/s]
Ek = kinetic energy = 25 [J]
Now replacing:
\(25 = \frac{1}{2}*2*v^{2} \\v=\sqrt{25} \\v = 5 [m/s]\)
the eccentricity aspect of the astronomical theory refers to
In astronomy, the eccentricity aspect of the astronomical theory refers to the shape of an object's orbit around another object. Specifically, it measures how much an orbit deviates from a perfect circle.
The eccentricity of an orbit is defined as the ratio of the distance between the two foci of the ellipse that describes the orbit to the length of the major axis of the ellipse. An orbit with an eccentricity of 0 is a perfect circle, while an orbit with an eccentricity of 1 is a parabola, and an orbit with an eccentricity greater than 1 is a hyperbola. In the context of the Solar System, the eccentricity of a planet's orbit determines how close it comes to the Sun at its closest approach (perihelion) and how far away it gets at its furthest point (aphelion).
For example, the eccentricity of Earth's orbit is about 0.0167, which means that its distance from the Sun varies by about 3.1 million miles (5 million kilometers) between perihelion and aphelion. The eccentricity of an orbit can have important effects on the object that is orbiting. For example, objects with highly eccentric orbits may experience significant changes in temperature or gravitational forces as they move closer to or further away from the object they are orbiting.
This can have important consequences for the object's physical and chemical processes, and may even contribute to the development of life in some cases.
For such more questions on Eccentricity
https://brainly.com/question/29484069
#SPJ4