Answer:
10,920 meters
Explanation:
distance = speed × time
which is, d = 21 × 520
Answer:
10920
Explanation:
distance traveled= 21 (speed) ×520 (time)
=10920
The anomalous expansion characteristics of liquid water are crucial to many biological systems. Rather than an approximately constant value for the coefficient of volume expansion, the value for water changes drastically, as illustrated in the figure.
Below what temperature T
does water shrink when heated?
If the temperature of water at 30 ∘C
is raised by 1 ∘C
, the water will expand. At approximately what initial temperature T
will water expand by twice as much when raised by 1 ∘C
?
(A) The water will shrink when is heated above 4°C. (B).water at an initial temperature of 33.3°C will be expand by twice as much when it is raised by 1°C compared to water at 30°C.
The anomalous expansion of water refers to the fact that its volume increases upon cooling from 4°C to 0°C, and then contracts upon further cooling to 0°C, and continues to contract upon further cooling. Similarly, when water is heated, its volume first contracts until it reaches 4°C, and then expands upon further heating.
To determine at what temperature water shrinks when heated, we need to find the point at which the coefficient of volume expansion, β, becomes negative. The coefficient of volume expansion is defined as the fractional change in volume per degree Celsius change in temperature, i.e.,
β = (1/V) (dV/dT)
where V is the volume of the water and dV/dT is the rate of change of volume with respect to temperature.
At temperatures below 4°C, the coefficient of volume expansion is positive, indicating that water expands upon heating. However, at temperatures above 4°C, the coefficient of volume expansion becomes negative, indicating that water contracts upon heating.
Therefore, water will shrink when heated above 4°C.
To determine the initial temperature at which water will expand by twice as much when raised by 1°C, we can use the formula for the coefficient of volume expansion:
β = (1/V) (dV/dT)
We want to find the initial temperature T such that
(dV/dT)T = 2 (dV/dT)30
where (dV/dT)T is the rate of change of volume with respect to temperature at temperature T, and (dV/dT)30 is the rate of change of volume with respect to temperature at 30°C.
Using the coefficient of volume expansion for water, we have
β = 3α
where α is the coefficient of linear expansion, which is approximately constant for small temperature changes. Therefore, we can write
(dV/dT) = V × 3α
Substituting this into the equation above and simplifying, we get
T = 30 + 10/3 = 33.3°C
Therefore, water at an initial temperature of 33.3°C will expand by twice as much when raised by 1°C compared to water at 30°C.
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Two atoms of the same element only differ because one of the atoms has more electrons, making it an ion. Which statement is true? They have the same A-number and the same Z-number. They have the same A-number but different Z-number. They have a different A-number but the same Z-number. They have different A-numbers and different Z-numbers.
The correct answer is Option B. The statement "they have the same A-number but different Z-number" is true .
Atoms of the same element only differ because one of the atoms has more electrons, making it an ion.
This difference does not affect the mass of the atom, which is determined by the sum of its protons and neutrons, represented by the atomic mass or A-number.
The number of protons in an atom is called the atomic number or Z-number.
The Z-number of an element is unique to it. All the atoms of a given element have the same number of protons.
Thus, for example, all carbon atoms have six protons, making the Z-number of carbon 6.
However, different isotopes of an element can have different numbers of neutrons.
This means that they have a different atomic mass or A-number.
Therefore, they have the same A-number but different Z-number.
Therefore the correct Option is B.
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Points A (-9,2), B (2,-9), and C (-9,-9) are placed in three different quadrants of a Cartesian coordinate system. Convert each set of Cartesian coordinates to polar coordinates. The angle should be reported as a positive angle, in degrees, from the positive x-axis. (0° < θ < 360°)
Answer:
answer
Explanation:
can anyone write for me all the equation of linear motion
All the equations of motion are as follows, Displacement (s) equation, Final velocity (v) equation, Average velocity (v_avg) equation, Displacement (s) equation with average velocity, and Displacement (s) equation.
Equations of MotionIn terms of its motion as a function of time, equations of motion define how a physical system behaves. In more detail, the equations of motion define how a physical system behaves as a collection of mathematical functions expressed in terms of dynamic variables.
s = ut + (1/2)at^2v = u + atv_avg = (u + v) / 2s = v_avg * ts = (u + v) / 2 * tv^2 = u^2 + 2asIn conclusion, equations of motion define how a physical system behaves in terms of how its motion changes over time.
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Which of these is another name for Newton's
first law?
A. the law of action-reaction
B. the law of force and acceleration
C. the law of gravity
D. the law of inertia
The velocity time graph of an object mass 50 g is shown in figure study graph and answer
1)calculate force acting on object in time interval 0-3 seconds
2)calculate the force acting on the object in the time interval 6-10 seconds
3)Is there any time interval in which no force acts on object.Justify
1) The force acting on the object during the time interval 0-3 seconds is 1/3 N.
2) The force acting on the object during the time interval 6-10 seconds is -0.5 N.
3) There is no time interval in which no force acts on the object.
(i) Force acting on the object in time interval 0-3 seconds. Force acting on the object is equal to the product of its mass and acceleration, i.e.,F = ma.
In the given velocity-time graph, the acceleration of the object can be determined by determining the slope of the velocity-time graph from 0 to 3 seconds.
Slope = (change in velocity) / (change in time)= (20-0) / (3-0) = 20/3 m/s^2
Acceleration, a = slope= 20/3 m/s^2
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × 20/3= 1/3 N.
Therefore, the force acting on the object during the time interval 0-3 seconds is 1/3 N.
(ii) Force acting on the object in time interval 6-10 seconds. Similar to the first question, the force acting on the object in time interval 6-10 seconds can be determined by determining the acceleration of the object during this time interval.
The slope of the velocity-time graph from 6 seconds to 10 seconds can be determined as follows:
Slope = (change in velocity) / (change in time)= (-20-20) / (10-6) = -40/4= -10 m/s^2 (negative sign indicates that the object is decelerating)
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × (-10)= -0.5 N.
Therefore, the force acting on the object during the time interval 6-10 seconds is -0.5 N.
(iii) Time interval in which no force acts on the object. There is no time interval in which no force acts on the object. This is because, as per Newton's first law of motion, an object will continue to remain in a state of rest or uniform motion along a straight line unless acted upon by an external unbalanced force.In other words, if the object is moving with a constant velocity, there must be a force acting on the object to maintain its motion.
Therefore, there is no time interval in which no force acts on the object.
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If you know the answer tell me ASAP
In order to measure the potential difference across one of the bulbs in the circuit, the voltmeter must be connected in parallel with it. So, option D.
When two points in a circuit have different electric potentials, a voltmeter is a tool or instrument that measures their potential difference.
We are aware that a voltmeter is a tool that measures the same potential drop in all configurations that are in parallel.
The potential difference between two points in a circuit is thus always measured by connecting a voltmeter in parallel across the conductor's ends.
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Hello question for JungKookLuver and jguzman577. What’s my favorite color don’t answer! Or you get reported!
Answer: Green!
Explanation: ThankYou bro
I need help with the following question:
USING THE FOLLOWING CONVERSION FACTOR:
Conversions Longitude:
1 degree= 52.505 miles
1 minute= 4620.5 feet
Conversions for Latitude:
1 degree= 69.005 miles
1 minute= 6072.5 feet
How Do I convert these coordinates into feet?
The length of side A (40° 51.485' N, 74° 12.080' W & 40° 51.485' N, 74° 11.883' W) = ------------- ft
The length of side B (40° 51.485' N, 74° 12.080' W & 40° 51.800' N, 74° 11.883' W) = ----------- ft
The length of the side A is 1,13,25,866.44 ft N, 2,70,34,989.4 ft W
The length of the side B is 1,13,25,866.44 ft N, 2,70,34,989.4 ft W
Length is the measurement of anything from end to end.
Conversions Longitude:
Longitude is the angular distance of a location east or west of the meridian in Greenwich, England, or west of the standard meridian of a celestial object.
1 degree= 52.505 miles
1 minute= 4620.5 feet
Conversions for Latitude:
Latitude is the angular distance of a location north or south of the Earth's equator.
1 degree= 69.005 miles
1 minute= 6072.5 feet
Also 1 mile = 5280 feet
The length of side A (40° 51.485' N, 74° 12.080' W)
40° 51.485' N = 40 * 52.505 * 5280 + 51.485 * 4620.5
40° 51.485' N = 1,10,88,000 + 2,37,866.44
40° 51.485' N = 1,13,25,866.44 feet.
74° 12.080' W = 74 * 69.005 * 5280 + 12.080 * 6072.5
74° 12.080' W = 2,69,61,633.6 + 73,355.8
74° 12.080' W = 2,70,34,989.4 feet
The length of side B (40° 51.485' N, 74° 12.080' W)
40° 51.485' N = 1,13,25,866.44 feet.
74° 12.080' W = 2,70,34,989.4 feet.
Side A = Side B = 1,13,25,866.44 ft N, 2,70,34,989.4 ft W.
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In a local park, a pine cone falls off a tree branch (starting at rest) and falls to the ground. We will model the pine cone hitting the ground as if it is a mass going onto a spring (with the ground being a spring). The pine cone has a mass of 0.116 kg, and starts at a height of 7.90 m above the ground. The pine cone compresses the spring (ground) by 0.0148 m, briefly coming to rest at the bottom of its motion. (It then bounces, which is not part of the time period that we'll cover in this problem.) Assume that the pine cone, the Earth and the spring (ground) are a system, and that no net work is done by external forces to the system or by non-conservative forces. Note: these are the assumptions necessary to assume that mechanical energy is conserved. Label the initial time point as the start of the pine cone's drop, and the final time point as the moment when the pine cone is at rest with the spring as compressed as it will get.
1. What is the change in gravitational potential energy from the initial time point to the final time point? Hint: don't forget that the pine cone actually goes slightly below the height of most of the ground. Joules
2. What is the spring constant of the spring? N/m
3. Now, let's look at the time point when the pine cone is 4.24 meters above the ground. You can do this by assuming that this new time point becomes the final time point, and the spring is no longer in the problem. What is the magnitude of the pine cone's velocity at this time point? m/s
Answer:
1)) ΔU = -8.96 J, 2) k = 8.18 10⁴ N / m, 3) v = 8.47 m / s
Explanation:
For this exercise we will use conservation of energy.
Starting point. Point where the pineapple comes out
Em₀ = U = m g h
where the reference frame is placed on the ground
Final point. Point where pineapple stops
Em_f = K_e + U = ½ k y² + m g y
1) the change in gravitational potential energy is
ΔU = U_f - U₀
ΔU = m g y - m g h
ΔU = mg (y-h)
let's calculate
ΔU = 0.116 9.8 (0.0148 - 7.9)
ΔU = -8.96 J
The negative sign indicates that the energy decreases
2) let's use energy conservation
Em₀ = Em_f
mg h = ½ k y² + mg y
k = mg (h-y) \(\frac{2}{y^2}\)
let's calculate
k = 0.116 9.8 (7.9 - 0.0148) \(\frac{2}{0.0148^2}\)
k = 8.18 10⁴ N / m
3) we use the same starting point and as the end point we use this height (y₂ = 4.24 m)
Em_{f2} = K + U = ½ m v² + mg y₂
energy is conserved
Em₀ = Em_{f2}
mgh = ½ m v² + m g y₂
v =\(\sqrt{ 2g(h-y_2)}\)
let's calculate
v = \(\sqrt{ 2 \ 9.8 \ (7.9-4.24)}\)
v = 8.47 m / s
a place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. when kicked, the ball leaves the ground with a speed of 23.9 m/s at an angle of 51.5 degrees to the horizontal. (a) by how much does the ball clear or fall short of clearing the crossbar?
(b) does the ball approach the crossbar while still rising or while falling?
Explanation:
Let's calculate the components of the football's velocity:
\(v_{0x} = (23.9\:\text{m/s})\cos{51.5°} = 14.9\:\text{m/s}\)
\(v_{0y} = (23.9\:\text{m/s})\sin{51.5°} = 18.7\:\text{m/s}\)
a) The time it takes for the football to travel 36.0 m horizontally is
\(t = \dfrac{x}{v_{0x}} = \dfrac{36.0\:\text{m}}{14.9\:\text{m/s}} = 2.4\:\text{s}\)
During this time, the y-displacement of the football is
\(y = v_{0x}t - \frac{1}{2}gt^2\)
\(\:\:\:\:= (18.7\:\text{m/s})(2.4\:\text{s}) - \frac{1}{2}(9.8\:\text{m/s}^2)(2.4\:\text{s})^2\)
\(\:\:\:\:= 16.7\:\text{m}\)
This means that the football cleared the crossbar by 16.7 m - 3.05 m = 13.7 m
b) To determine whether the football was rising or falling while clearing the crossbar, let's look at the y-component of its velocity after 2.4 s:
\(v_y = v_{0y} - gt = 18.7\:\text{m/s} - (9.8\:\text{m/s}^2)(2.4\:\text{s})\)
\(\:\:\:\:\:\:= -4.82\:\text{s}\)
Since its sign is negative, this means that the football was already on its way down.
Two hockey players are about to collide on the ice. One player has a mass of
70 kg and is traveling at 1.4 m/s north. The other has a mass of 75 kg and is
traveling at 1.0 m/s south. The system consists of the two hockey players.
According to the law of conservation of momentum, what is the total
momentum of the system after they collide? Assume the collision is an
elastic collision.
A. 173 kg.m/s south
B. 23 kg-m/s north
C. 23 kg.m/s south
D. 173 kg.m/s north
Answer:
B. 23 kg*m/s north
Explanation:
p_1 = p_2
(m*v)_1 + (m*v)_2 = (m*v)_1' + (m*v)_2'
(70kg*1.4m/s)+(75kg*-1.0m/s) = p_2
(98kg*m/s)+(-75kg*m/s) = 23kg*m/s north
B. 23 kg*m/s north
Two hockey players are about to collide on the ice, so the total momentum of the system when they collide is 23 kg m/s. Hence, option B is correct.
What is momentum?The result of a particle's mass and velocity is momentum. It has both magnitude and direction because momentum is a vector quantity. According to Isaac Newton's second law of motion, the force pushing a particle has an equal and opposite effect on the temporal rate at which its momentum changes.
\(Momentum (p)= Mass(m)*Velocity(v)\)
The given values according to the question is :
p₁ = p₂
(m × v)₁+ (m × v)₂ = (m × v)₁' + (m × v)₂'
(70 kg × 1.4 m/s) + (75 kg) × (-1.0 m/s) = p₂
(98 kg m/s) + (- 75 kg m/s) = 23 kg m/s North
Therefore, the total momentum after collision is 23 kg m/s North.
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How is the acceleration of a falling object calculated
Answer:
F=w=ma OR by using equations of motions vf=vi-at : a=vf-vi/t eq 1 s=vit+1/2at squre eq 2 2as=vf squre - vi squre eq 3
Explanation:
where m is the mass of falling body , f is the weight is the force acting down ward , vf is the final velocity, vi is the inetial velocity , t is the time and s is the distance covered by a body.
If you push a heavy box at rest, you must exert some force before it begins to move. Once its moving, you don’t have to as much force. Which of Newton’s three laws explains this?
Answer:
momentum does
Explanation:
Nitroball is similar to volleyball with no more than 3 touches per side?
Group of answer choices
True
False
Answer:
True!
Explanation:
Need help!
List 5 interesting facts from the the states of matter.
When a falling meteoroid is at a distance above the Earth's surface of 3.40 times the Earth's radius, what is its acceleration due to the Earth's gravitation
Answer:
g = 0.85 m\(s^{-2}\)
Explanation:
g = \(\frac{GM}{h^{2} }\)
were; g is the acceleration due to Earth's gravity, G is Newton's gravitation constant (6.674 x \(10^{-11}\) N\(m^{2}\)\(kg^{-2}\)), M is the mass of the earth (5.972 x \(10^{24}\) kg), and h is the distance of meteoroid to the earth.
h = 3.40 x R
= 3.40 x 6371 km
h = 21661.4 km
= 21661400 m
Thus,
g = \(\frac{6.674*10^{-11}*5.972*10^{24} }{(21661400)^{2} }\)
= \(\frac{3.9857 *10^{14} }{4.6922*10^{14} }\)
= 0.84944
g = 0.85 m\(s^{-2}\)
The acceleration due to the Earth's gravitation is 0.85 m\(s^{-2}\).
As water is cooled, its density increases until it reaches about
O A. 25° C
B. -2° C
O c. 4°C
O D.O°C
Answer:
4 degrees C
Explanation:
this is just a 'known'
give an example of natural(non man made) combination structures
Naturally occurring or organic substances and molecules such as cell membranes are combination structures.
What are combination structures?Combination structures are substances which result from the combination of two or more different substances.
What are some natural combination structures?Natural combination structures are found everywhere in the natural world.
Examples of combination structures are organic compounds and molecules including:
Cell membranes composed of lipids, proteins and carbohydrates.Therefore, organic substances and molecules such as cell membranes are combination structures.
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What force acts on a projectile in the horizontal direction?
The force that acts on a projectile in the horizontal direction is Gravitational force.
A projectile is an object upon which the only force is gravity. Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity.
Due to the absence of horizontal forces, a projectile remains in motion with a constant horizontal velocity. Horizontal forces are not required to keep a projectile moving horizontally. Hence, The only force acting upon a projectile is gravity.
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VERY EASY QUESTION FOR HIGH SCHOOL STUDENTS:
Which of the following frequencies would you expect a young person to be able to hear? 500 Hz, 6000 Hz, 25000 Hz, 15 Hz, 15000 Hz
Answer:
Explanation: 6000z
How is an interference pattern formed by a diffraction grating different from the pattern formed by a double slit
Answer:
Evaluate the following numerical expressions.
6 + 3 • 4 =
18
(6 + 3) ÷ (4 – 5) =
Explanation:
Evaluate the following numerical expressions.
6 + 3 • 4 =
18
(6 + 3) ÷ (4 – 5) =
In a DC generator, the generated emf is directly proportional to the
In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.
This relationship is described by the equation for the generated emf in a DC generator:
Emf = Φ * N * A * Z / 60
Where:
Emf is the generated electromotive force (in volts),
Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),
N is the number of turns in the armature winding,
A is the effective area of the armature coil (in square meters),
Z is the total number of armature conductors, and
60 is a constant representing the conversion from seconds to minutes.
From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.
The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.
The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.
Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.
By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.
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a lightweight rope is wrapped around a 100 lb drum, passes over a frictionless pulley, and is attached to a weight w (see below). the coefficient of friction between the drum and the surfaces is 0.50. determine the maximum amount of weight that can be supported by this arrangement.
The forces that are present when there is physical contact are referred to as the contact force and the forces that are present when there is no physical contact as the field force or non-contact force.
On the hanging weight since it is the constant speed we can assume that object is in equilibrium and
Tension = m*g
Where m = mass and g = acceleration due to gravity
On the drum since it is also moving with constant angular speed net torque on it will be zero.
τ - TR =0
Where τ = torque, T= tension and R= Radius of drum = 0.5 m
Replacing the expression for Tension of the rope in above equation:
τ(torque) = mgR
Solving for m using R = 0.5m, g = 10 m/ s2 and τ = 358 N.m
m = = 179 kg
Therefore the mass is -179 kg of the torque produced by the rope.
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What is the ratio P1/P2P1/P2 of their power dissipations if the same current passes through each resistor
This question is incomplete, the complete question is;
Resistors 1 and 2 are connected to identical batteries, resistor 1 dissipates 4.0 times more power than resistor 2
What is the ratio P1/P2of their power dissipations if the same current passes through each resistor
Answer:
the ratio P₁/P₂ of their power dissipations is 0.25
Explanation:
Given the data in the question;
\(P_{i}\) = \(I^{2} . R_i\) --------------let this be equation 1
\(P_{i}\) = \(\frac{V^{2} }{R_i}\) -----------------let this be equation 2
P₁ = V²/R₁
P₁ = 4P₂
so
P₁ = V²/R₁ = 4( V²/R² )
now, form the above equation;
R₁ = R₂/4
using equation 1, we get;
P₁ = \(I^{2} . R_1\)
P₂ = \(I^{2} . R_2\)
Hence;
P₁ = \(I^{2}\)( R₂/4)
P₁ = \(I^{2}\) × ( R₂/4)
P₁ = (1/4) P₂ or 0.25
Therefore; the ratio P₁/P₂ of their power dissipations is 0.25
You are riding on a carousel that is rotating at a constant 24 rpm. It has an inside radius of 4 ftand outside radius of 12 ft. You begin to run from the inside to the outside along a radius. Your peak velocity with respect to the carousel is 6 mph and occurs at a radius of 8 ft.What are your maximum Coriolis acceleration magnitude and its directionwith respect to the carousel
Answer:
magnitude of the Coriolis acceleration is 44.235 ft/s² and the direction of the acceleration is along the axis of transmission
Explanation:
Given the data in the question;
Speed of carousel N = 24 rpm
From the diagram below, selected path direction defines the Axis of slip.
Hence, The Coriolis is acting along the axis of transmission
Now, we determine the angular speed ω of the carousel.
ω = 2πN / 60
we substitute in the value of N
ω = (2π × 24) / 60
ω = 2.5133 rad/s
Next, we convert the given velocity from mph to ft/s
we know that; 1 mph = 1.4667 ft/s
so
\(V_{slip\) = 6 mph = ( 6 × 1.4667 ) = 8.8002 ft/s
Now, we determine the magnitude of the Coriolis acceleration
\(a_c\) = 2( \(V_{slip\) × ω )
we substitute
\(a_c\) = 2( 8.8002 ft/s × 2.5133 rad/s )
\(a_c\) = 44.235 ft/s²
Hence, magnitude of the Coriolis acceleration is 44.235 ft/s² and the direction of the acceleration is along the axis of transmission
Which statement is true about the SI System?
A-Uses different base units than the English measurement system.
B-Is used in scientific
measurement.
C-Includes the meter as its base unit for length.
D-All of the above.
Answer:
maybe the answer is in is D part
I need help with (c) please
The frequency of light with a wavelength of 655 nm is 4.58 x 1014 Hz, the frequency of light with a wavelength of 515 nm is 5.83 x 1014 Hz, and the frequency of light with a wavelength of 475 nm is 6.32 x 1014 Hz. The frequency of light can be calculated using the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.
The visible spectrum of electromagnetic radiation has a range of wavelengths that varies from the longest (red) to the shortest (violet) that our eyes can detect. The frequencies of light with wavelengths of 655 nm, 515 nm, and 475 nm can be calculated using the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.(a) For light with a wavelength of 655 nm, the frequency can be calculated as: c = λν ==> ν = c/λ where c = 3.00 x 108 m/s (speed of light in a vacuum)λ = 655 nm = 6.55 x 10-7 m. Therefore, ν = (3.00 x 108 m/s) / (6.55 x 10-7 m) = 4.58 x 1014 Hz(b) For light with a wavelength of 515 nm, the frequency can be calculated as: c = λν ==> ν = c/λ where c = 3.00 x 108 m/s (speed of light in a vacuum)λ = 515 nm = 5.15 x 10-7 m. Therefore, ν = (3.00 x 108 m/s) / (5.15 x 10-7 m) = 5.83 x 1014 Hz(c) For light with a wavelength of 475 nm, the frequency can be calculated as: c = λν ==> ν = c/λ where c = 3.00 x 108 m/s (speed of light in a vacuum)λ = 475 nm = 4.75 x 10-7 m. Therefore, ν = (3.00 x 108 m/s) / (4.75 x 10-7 m) = 6.32 x 1014 Hz.For more questions on frequency
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Three forces act on a flange as shown below. Determine the magnitude of the unknown force F (in lb) such that the net force acting on the flange is a minimum.
Answer:
The unknown force will be 18.116 lb.
Explanation:
Given that,
Three forces act on a flange as shown in figure.
The net force acting on the flange is a minimum.
\(\dfrac{dF_{net}}{df}=0\)
We need to calculate the unknown force
Using formula of net force
\(\vec{F_{net}}=\vec{F_{x}}+\vec{F_{y}}\)
Put the value into the formula
\(\vec{F_{net}}=(F\cos45+70\cos30-40)\hat{i}+(70\sin30-F\sin45)\hat{j}\)
\(\vec{F_{net}}=(F\cos45+70\times\dfrac{\sqrt{3}}{2})\hat{i}+(70\times\dfrac{1}{2}-F\sin45)\hat{j}\)
The magnitude of net force,
\(F_{net}=\sqrt{F_{x}^2+F_{y}^2}\)
\(F_{net}=\sqrt{(F\times\dfrac{1}{\sqrt{2}}+60.62)^2+(35-F\times\dfrac{1}{\sqrt{2}})^2}\)
\(F_{net}=\sqrt{F^2+(60.62)^2+121.24\times\dfrac{F}{\sqrt{2}}+(35)^2-70\times\dfrac{F}{\sqrt{2}}}\)
\(F_{net}=\sqrt{F^2+4899.78+36.232F}\)
On differentiating w.r.to F
\((\dfrac{dF_{net}}{dF})^2=2F+36.232\)
\(0=2F+36.232\)
\(F=-\dfrac{36.232}{2}\)
\(F=-18.116\ lb\)
Negative sign shows the direction of force which is downward.
Hence, The unknown force will be 18.116 lb.
Following are the solution to the given question:
Calculating the Net force on flange:
\(\overrightarrow{F_{net}} = ( F \cos 45^{\circ} + 70 \cos 30^{\circ} -40 ) \hat{i}+(70 \sin 30^{\circ} - F \sin 45^{\circ} )\hat{y} \\\\ \overrightarrow{F_{net}} = ( F \cos 45^{\circ} + 20.62 ) \hat{i}+(35 -F\sin 45^{\circ})\hat{y} \\\\ \)
Calculating the magnitude:
\(= \sqrt{f_{X}^2 +f_{y}^{2}}\\\\ = \sqt{( F \cos 45^{\circ} + 20.62 )^2+(35 -F\sin 45^{\circ})^2} \\\\ = \sqt{( F^2+20.62^2+ 35^2+ 41.24 F \cos 45^{\circ} -70 F\sin 45^{\circ})}\\\\ = \sqt{( F^2+20.33F +1650.1844)} \\\\\)
Differentiate the value
\(\to \frac{F_{net}}{df}=0 \)
\(\to 2F-20.33=0\\\\ \to 2F=20.33\\\\ \to F=\frac{20.33}{2}\\\\ \to F= 10.165\ lb \)
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brainly.com/question/15323099
How much charge is passing through a
circuit providing electricity for a 120 V light
bulb if it uses 300 J of energy?
6.25 coulombs of charge is passing through a circuit providing electricity for a 120 V light bulb if it uses 300 J of energy.
What is charge ?
When placed in an electromagnetic field, the physical property of matter known as electric charge causes matter to feel a force. A positive or negative electric charge can exist. (commonly carried by protons and electrons respectively, by convention). Like charges repel one another, while unlike charges draw one another. A neutral substance is one that does not have any net charge. Classical electrodynamics refers to early understanding of how charged substances interact, and it is still accurate for problems that do not require consideration of quantum effects.
Electric charge is a conserved characteristic; the net charge of an isolated system, which is the sum of positive and negative charges, cannot change. Subatomic particles carry electric energy. Negative charge in ordinary substance.
Calculate the amount of time that the energy is used.
\(\frac{300 J}{120 V}\)= 2.5 seconds
Calculate the current running through the circuit.
Current = Power / Voltage = \(\frac{300W}{120V}\)= 2.5 Amps.
Calculate the charge passing through the circuit.
Charge = Current x Time
= 2.5 Amps x 2.5 seconds
= 6.25 Coulombs of charge.
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