Answer:
They hit the ground at the same time
Explanation:
Mass doesn't matter in free fall. As long as they were released with the same velocity and the same height, they'll hit the ground at the same time
Erma built the simple motor shown below with a battery, a permanent magnet, a copper coil of wire, and an iron bar. When the motor is turned on, the iron bar and coil spin in a circle The motor transforms _______ energy into _______ energy. Question 27 options: mechanical; chemical electrical; mechanical mechanical; electrical thermal; electrical
Answer:
electrical to mechanical
Explanation:
A sample of gas, initially with a volume of 1.0 L, undergoes a thermodynamic cycle. Find the work done by the gas on its environment during each stage of the cycle described below. (Enter your answers in J.)
Answer:
(a) W₁ = 3293.06 J = 3.293 KJ
(b) W₂ = 0 J
(c) W₃ = - 506.625 J = - 0.506 KJ
(d) W₄ = 0 J
(e) W = 2786.435 J = 2.786 KJ
Explanation:
The complete question has following parts:
(a) First gas expands from a volume of 1 L to 6 L at a constant pressure of 6.5 atm
(b) Second, the gas is cooled at constant volume until the pressure falls to 1 atm
(c) Third, the gas is compressed at a constant pressure of 1 atm from a volume of 6 L to 1 L.
(d) Finally the gas is heated until its pressure from 1 atm to 6.5 atm at constant volume
(e) what is the net work?
ANSWERS:
(a)
The work done by a gas at constant pressure is given as follows:
W = PΔV
where,
W = Work done by the gas
P = Constant Pressure of the Gas
ΔV = Change in Volume of The gas
Therefore, for the first step:
P = P₁ = (6.5 atm)(1.01325 x 10⁵ Pa/1 atm) = 6.58613 x 10⁵ Pa
ΔV = ΔV₁ = 6 L - 1 L = (5 L)(0.001 m³/1 L) = 5 x 10⁻³ m³
W = W₁
Therefore,
W₁ = (6.58613 x 10⁵ Pa)(5 x 10⁻³ m³)
W₁ = 3293.06 J = 3.293 KJ
(b)
The work done at a constant volume by a gas is always zero due to no change in volume:
W₂ = P₂ΔV₂
W₂ = P₂(0)
W₂ = 0 J
(c)
For the third step:
P = P₃ = (1 atm) = 1.01325 x 10⁵ Pa
ΔV = ΔV₃ = 1 L - 6 L = (- 5 L)(0.001 m³/1 L) = - 5 x 10⁻³ m³
W = W₃
Therefore,
W₃ = (1.01325 x 10⁵ Pa)(-5 x 10⁻³ m³)
W₃ = - 506.625 J = - 0.506 KJ
(d)
The work done at a constant volume by a gas is always zero due to no change in volume:
W₄ = P₄ΔV₄
W₄ = P₄(0)
W₄ = 0 J
(e)
Hence, the net work is given as follows:
W = W₁ + W₂ + W₃ + W₄
W = 3293.06 J + 0 J + (- 506.625 J) + 0 J
W = 2786.435 J = 2.786 KJ
You are designing a flywheel. It is to start from rest and then rotate with a constant angular acceleration of 0.200 rev/s^2. The design specifications call for it to have a rotational kinetic energy of 330 J after it has turned through 30.0 revolutions.
What should be the moment of inertia of the flywheel about its rotation axis?
Express your answer with the appropriate units.
Answer: 1.14 kg*m/s
Explanation:
The first person explained everything right, they just forgot to convert the angular acceleration to rads/sec^2 from revs/sec^2. Once that is converted, your answer should come out right.
Another small thing, the answer there has an extra unnecessary step. It tells you to find the square root of w^2 to find w but that is unnecessary since the final equation asked for w^2. Hope this helps! :)
The moment of inertia I of the flywheel about its rotation axis is
[tex]1.39Kgm^2[/tex]Given
Angular displacement,
[tex]\theta = 30rev \\\\\theta = (30) * 2\pi rad \\\\\theta = 188.495rad[/tex]
Therefore, Final angular velocity (w) will be:
[tex]w^2 = 2\alpha\theta\\\\w^2 = 2 * (0.200 * 2\pi) * (188.49)\\\\w^2 = 473.73\\\\w = 21.76 rad/s[/tex]
Therefore,
moment of inertia
[tex]I = 2 * K / w^2[/tex]
[tex]I = 2 * 330 / 473.73[/tex]
[tex]I = 1.39kgm^2[/tex]
For more information on moment of inertia
https://brainly.com/question/19557854?referrer=searchResults
Temporary Wind Turbines-
Answer:
lol what
Explanation:
You are explaining to friends why astronauts feel weightless orbiting in the space shuttle, and they respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn't so by calculating how much weaker gravity is 200 above the Earth's surface.
Delta G/G = ? %
Answer:
The gravity is 87.4% as strong as at the Earth’s surface.
Explanation:
Hope this helped!
Which temperature is warmer than the freezing point of water?
O A. OK
O B. 33K
O C. 1°C
O D.O°F
Answer:
C 1 degree
Explanation:
The current theory of the structure of the Earth, called plate tectonics, tells us that the continents are in constant motion.
Assume that the North American continent can be represented by a slab of rock 4450 km on a side and 31 km deep and that the rock has an average mass density of 2620 kg/m3.
The continent is moving at the rate of about 1 cm/year.
What is the mass of the continent? Answer in units of kg.
(part 2 of 3)
What is the kinetic energy of the continent? Answer in units of J.
(part 3 of 3)
A jogger (of mass 77 kg) has the same kinetic energy as that of the continent.
What would his speed be? Answer in units of m/s.
Answer:
1) The mass of the continent is approximately [tex]1.608\times 10^{21}[/tex] kilograms.
2) The kinetic energy of the continent is approximately [tex]8.04\times 10^{16}[/tex] joules.
3) The speed of the 77 kg-jogger would be approximately [tex]45.698\times 10^{6}[/tex] meters per second.
Explanation:
1) The mass of the North American continent can be estimated by using the following formula under the assumption that rock has an uniform density:
[tex]m = \rho \cdot L^{2}\cdot h[/tex] (1)
Where:
[tex]m[/tex] - Mass of the continent, measured in kilograms.
[tex]\rho[/tex] - Average density of the rock, measured in kilograms per cubic meter.
[tex]L[/tex] - Side of the continent, measured in meters.
[tex]h[/tex] - Depth of the continent, measured in meters.
If we know that [tex]\rho = 2620\,\frac{kg}{m^{3}}[/tex], [tex]L = 4.450\times 10^{6}\,m[/tex] and [tex]h = 31\times 10^{3}\,m[/tex], then the mass of the continent is:
[tex]m = \left(2620\,\frac{kg}{m^{3}} \right)\cdot (4.450\times 10^{6}\,m)^{2}\cdot (31\times 10^{3}\,m)[/tex]
[tex]m = 1.608\times 10^{21}\,kg[/tex]
The mass of the continent is approximately [tex]1.608\times 10^{21}[/tex] kilograms.
2) By assuming that continent can be represented as a particle, we define its kinetic energy as:
[tex]K = \frac{1}{2}\cdot m \cdot v^{2}[/tex] (2)
Where:
[tex]K[/tex] - Translational kinetic energy, measured in joules.
[tex]v[/tex] - Motion rate of the continent, measured in meters per second.
If we know that [tex]m = 1.608\times 10^{21}\,kg[/tex] and [tex]v = 1\times 10^{-2}\,\frac{m}{s}[/tex], then the kinetic energy of the continent is:
[tex]K = \frac{1}{2}\cdot (1.608\times 10^{21}\,kg)\cdot \left(1\times 10^{-2}\,\frac{m}{s} \right)^{2}[/tex]
[tex]K = 8.04\times 10^{16}\,J[/tex]
The kinetic energy of the continent is approximately [tex]8.04\times 10^{16}[/tex] joules.
3) The speed of the jogger is derived from the definition of translational kinetic energy:
[tex]v = \sqrt{\frac{2\cdot K}{m} }[/tex]
If we know that [tex]K = 8.04\times 10^{16}\,J[/tex] and [tex]m = 77\,kg[/tex], then the expected speed of the jogger is:
[tex]v = \sqrt{\frac{2\cdot (8.04\times 10^{16}\,J)}{77\,kg} }[/tex]
[tex]v\approx 45.698\times 10^{6}\,\frac{m}{s}[/tex]
The speed of the 77 kg-jogger would be approximately [tex]45.698\times 10^{6}[/tex] meters per second.
it is the question 12 part okay
Answer:
Yeah it's ok I think. Also, I can't see the answer you gave so maybe updating the question would be nice.
1) 1000 kg car takes travels on a circular track having radius 100 m with speed 10 m/s. What is the magnitude of the centripetal force acting on the car? *
1 point
1 N
100 N
1000 N
10000 N
2) 1000 kg car takes travels on a circular track having radius 100 m with speed 10 m/s. What is the magnitude of the acceleration of the car? *
1 point
0.1 m/s^2
1 m/s^2
10 m/s^2
100 m/s^2
Answer:
(1) 1000 N (2) 1 m/s²
Explanation:
(1) Given that,
The mass of a car, m = 1000 kg
Radius of a circular track, r = 100 m
Speed of the car, v = 10 m/s
We need to find the magnitude of the centripetal force acting on the car. The magnitude of the centripetal force is given by :
[tex]F=\dfrac{mv^2}{r}\\\\F=\dfrac{1000\times (10)^2}{100}\\\\F=1000\ N[/tex]
So, the correct option is (c) i.e. 1000 N
(2).The mass of a car, m = 1000 kg
Radius of a circular track, r = 100 m
Speed of the car, v = 10 m/s
We need to find the magnitude of the centripetal acceleration of the car. The magnitude of the centripetal acceleration is given by :
[tex]a=\dfrac{v^2}{r}\\\\a=\dfrac{(10)^2}{100}\\\\a=1\ m/s^2[/tex]
So, the correct option is (b) i.e. [tex]1\ m/s^2[/tex]
The electron dot diagram shows the arrangement of dots without identifying the element.
? with 2 dots above and 1 dot each right, below, left.
Which element’s symbol could replace the question mark in the diagram?
boron (B)
neon (Ne)
rubidium (Rb)
arsenic (As)
Answer:
Arsenic (As)
Explanation:
Arsenic is the only answer choice that has five valence electrons like the electron dot structure shows.
Answer:
Arsenic (As)
Explanation:
A ball is launched from a 300m cliff and lands 380m away from the cliff in 9 seconds. Calculate the initual speed and the angle of the ball when it was launched.
Answer:
Explanation:
Given
Maximum height H = 300m
Range (horizontal distance) = 380m
Required
Initial speed U and the angle of the ball when it was launched.
Range = U√2H/g
380 = U√2(300)/9.8
380 = U√600/9.8
380 = 7.8246U
U = 380/7.8246
U = 48.57m/s
The initial speed is 48.57m/s
b) Using the formula for calculating time of flight;
T = 2Usin theta/g
9 = 2(48.57)sin theta/9.8
9*9.8 = 97.14sin theta
88.2 = 97.14sin theta
88.2/97.14 = sin theta
sin theta = 0.9079
theta = sin^-1(0.9079)
theta = 65.23°
hence the angle when the ball was launched is 65.23°
An oscilloscope is set on a TIME/DIV setting of 50 ms. There are 10 divisions on the time scale. A sinewave on the oscilloscope display has exactly three full cycles of the sine wave that fit on the 10 divisions. What is the frequency of the wave?
Answer:
f= 6 Hz
Explanation:
Since the TIME/DIV setting is set to 50 ms, and there 10 divisions on the time scale, that means that full scale display is 500 msec.If a sinewave has exactly three full cycles of the sine wave that fit on the 10 div, this means that one cycle is just one-third of the 10 div value, as follows:[tex]T = \frac{500 msec}{3} = 166.7 msec (1)[/tex]
Since the frequency of a wave is just the number of cycles per unit time, can be written as follows:F = 1/T = 1/(166.7 msec) = 6 HzA rollercoaster moves from the bottom of a hill and approaches the top of the hill. If friction between the wheels and the track is ignored, which statement describes the components of the total energy?
*answer choices pic attached*
{If anyone has the answers to the Energy Flows Quick Check or others please let me know}.
Answer:
The kinetic energy remains same and gravitational potential energy increases.
Explanation:
KINETIC ENERGY:
As, we know that the kinetic energy depends upon the speed of the object. Hence, the kinetic energy is given as:
K.E = (1/2)mv²
where,
m = mass
v = speed
K.E = Kinetic Energy
Since, the friction is ignored, therefore the speed of roller coaster will remain same.
Therefore, its Kinetic Energy will also remain same.
POTENTIAL ENERGY:
The potetial energy od a body depends upon its height, as follows:
P.E = mgh
where,
P.E = potential Energy
m = mass
g = acceleration due to gravity
h = height
As, the roller coaster moves up hill its height increases.
Therefore, its potential energy will also increase.
hence, the correct option is:
The kinetic energy remains same and gravitational potential energy increases.
Explain what it means when we say a substance is magnetic.
Discuss the relationship between electric and magnetic fields.
Which types of wires (cooper, aluminum, or string) are ferromagnetic metals?
Answer: See the explanation.
Explanation:
When we say a substance is magnetic it means the atoms are lined in a way that created a magnetic field that goes from one side to the other
These are essentially two aspects of the same thing, because a changing electric field creates a magnetic field, and a changing magnetic field creates an electric field. This is the relationship.
Answer: Copper isn't ferromagnetic,
Aluminum isn't ferromagnetic,
String does have a ferromagnetic property
Why is the metric system used globally, but we use the US customary units?
Answer:
The biggest reasons the U.S. hasn't adopted the metric system are simply time and money. When the Industrial Revolution began in the country, expensive manufacturing plants became a main source of American jobs and consumer products.
Explanation:
someone help please
waves disturb ____, but do not transmit it.
a. energy
b. matter
c. sound
d. none of the above
Answer:
b. matter
Explanation:
Waves disturb matter but do not transmit it.
Waves are disturbances that transmit energy from one point to another. Although they cause disturbances, they do not transfer the matters in the medium.
Energy is propagated by a wave. When for example, sound waves are produced, the disturbance is propagated via particle - particle interaction But after the wave train moves, the particles remain.An object moves in along the x-axis with an acceleration given by: a = 5t (m/s2). The position of the object at t=0.0 is 6 m, and its velocity at t=0.0 s is 4 m/s. Calculate the position at t=5 s.
Answer:
The position of the object at [tex]t = 5\,s[/tex] is 130.167 meters.
Explanation:
Let [tex]a(t) = 5\cdot t\,\left[\frac{m}{s^{2}} \right][/tex] the acceleration experimented by the object along the x-axis. We obtain the equation for the position of the object by integrating in acceleration formula twice:
Velocity
[tex]v(t) = \int {a(t)} \, dt[/tex] (1)
[tex]v(t) = 5\int {t} \, dt[/tex]
[tex]v(t) = \frac{5}{2}\cdot t^{2}+v_{o}[/tex] (2)
Where [tex]v_{o}[/tex] is the initial velocity of the object, measured in meters per second.
Position
[tex]s(t) = \int {v(t)} \, dt[/tex] (3)
[tex]s(t) = \frac{5}{2}\int {t^{2}} \, dt+v_{o}\int \, dt[/tex]
[tex]s(t) = \frac{5}{6}\cdot t^{3}+v_{o}\cdot t + s_{o}[/tex] (4)
Where [tex]s_{o}[/tex] is the initial position of the object, measured in meters per second.
If we know that [tex]s_{o} = 6\,m[/tex], [tex]v_{o} = 4\,\frac{m}{s}[/tex] and [tex]t = 5\,s[/tex], then the position of the object is:
[tex]s(5) = \frac{5}{6}\cdot (5)^{3}+\left(4\right)\cdot (5)+6[/tex]
[tex]s(5) = 130.167\,m[/tex]
The position of the object at [tex]t = 5\,s[/tex] is 130.167 meters.
what happens to the strength of an electromagnet when the voltage in the coils of the solenoid is decreased
Answer:
Make sure you look at the wording!
Explanation:
if the last word is increased, the answer is increased
if the last word is decreased, the answer is it decreases!
If the total mechanical energy of the block spring system is 512 J, what is the amplitude for this oscillation?
Answer:
A = 2.26 m
Explanation:
Given that,
The total mechanical energy of the block spring system is 512 J
Let the spring constant, k = 200 N/m
We need to find the amplitude for this oscillation. The mechanical energy of the spring mass system is given by :
[tex]E=\dfrac{1}{2}kA^2[/tex]
k is spring constant
[tex]A=\sqrt{\dfrac{2E}{k}} \\\\A=\sqrt{\dfrac{2\times 512}{200}} \\A=2.26\ m[/tex]
So, the amplitude of the oscillation is 2.26 m
10- The coefficient of volumetric expansion for gold is 4.20 x 10°/C°. The density of gold is
19 300 kg/m at 0.0 °C. What is the density of gold at 1050 °C?
(a) 20 200 kg/m
(b) 19 000 kg/m
(c) 18 500 kg/m
(d) 19 300 kg/m
(e) 18 800 kg/m
Answer:
ρ = 19215 kg / m³ , the answer the correct is D
Explanation:
All materials are sold when heated, in first approximation
ΔV = β V₀ (T -T₀)
for this case
ΔV = 4.20 10⁻⁶ Vo (1050 - 0)
ΔV = 4.41 10⁻³ Vo m³
V-Vo = 4.41 10⁻³ Vo
V = 1.00441 Vo
density is defined by
ρ = m / V
a T = 0ºc
ρ₀ = m / Vo
aT= 1050ºC
ρ = m / V
ρ = m / (1,00441 Vo)
ρ = 1 / 1.00441 m/Vo
ρ = 0.9956 ρ₀
ρ = 0.9956 19300
ρ = 19215 kg / m³
when checking the answers the correct one is D
If Earth’s Moon were replaced with a typical neutron star, what would the angular diameter of the neutron star be as seen from Earth?
Answer:
[tex]0.00005202\ \text{rad}=0.003^{\circ}[/tex]
Explanation:
d = Diameter of typical neutron star = 20 km = 20000 m
D = Distance between Earth and Moon = [tex]384.4\times 10^6\ \text{m}[/tex]
Here, [tex]D>>d[/tex] so we use small angle approximation
[tex]\delta=\dfrac{d}{D}\\\Rightarrow \delta=\dfrac{20000}{384.4\times 10^6}\\\Rightarrow \delta=0.00005202\ \text{rad}=\dfrac{0.00005202\times 180}{\pi}=0.003^{\circ}[/tex]
The angular diameter of the neutron star would be [tex]0.00005202\ \text{rad}=0.003^{\circ}[/tex] from Earth.
A current-carrying wire passes through a region of space that has a uniform magnetic field of 0.96 T. If the wire has a length of 2.7 m and a mass of 0.79 kg, determine the minimum current needed to levitate the wire.
Answer:
I = 2.99 A
Explanation:
magnetic field, B = 0.96 T, length of wire, l = 2.7 m, mass of wire, m = 0.79 kg.
Since it is expected that the wire would vibrate or move in the magnetic field, from Newton's second law of motion;
F = mg
where F is the force on the wire, m is the mass of the wire and g is the acceleration due to gravity.
But,
F = BIL
⇒ BIL = mg
0.96 x I x 2.7 = 0.79 x 9.8
2.592I = 7.742
I = [tex]\frac{7.742}{2.592}[/tex]
= 2.9869
I = 2.99 A
The required minimum current is 2.99 A.
200. Un automóvil se desplaza
hacia la izquierda con
velocidad constante v,
en el momento en que se
deja caer un saco de lastre
desde un globo en reposo.
El vector que representa
la velocidad del saco vista
desde el automóvil en ese
instante en que se suelta es
HELP THIS IS DUE IN 5 MINUTES!!!!!!!!!!!! WILL GIVE BRAINLIEST
what is the definition of total velocity?
Answer:
Image result for total velocity definition
The average speed of an object is defined as the distance traveled divided by the time elapsed.
Explanation:
Sitting in a parked bu s, you suddenly look up at a bus moving alongside and it appears that you are moving. Why is this? How about with both buses moving in opposite directions?
Answer:
Explained below
Explanation:
When one sits in a parked bus, and another bus is moving alongside, it means the other bus is moving relative to you. However, this makes the brain register in such a way that it's feels the bus you are in is the one moving.
In the second case where both buses are moving in opposite directions, the brain will register it in such a way that it seems the bus in which you are at is moving at a far higher speed than the speed in which it is actually moving.
This is because the relative velocity of the other vehicle is higher and it is therefore what makes your brain think your bus is moving at a faster speed.
When the palmaris longus muscle in the forearm is flexed, the wrist moves back and forth. If the muscle generates a force of 39.5 N39.5 N and it is acting with an effective lever arm of 2.75 cm2.75 cm, what is the torque that the muscle produces on the wrist?
Answer:
Explanation:
Torque is expressed according to the formula;
Torque = Force × radius
Given
Force = 39.5N
Radius = 2.75cm
Convert radius to metres
100cm ,= 1m
2.75cm = (2.75/100)
2.75cm = 0.0275m
Find the torque
Torque = 39.5×0.0275
Torque = 1.08625Nm
Hence the torque is 1.08625Nm
A cyclist is riding his bike up a mountain trail. When he starts up the trail, he is going 8 m/s. As the trail gets steeper, he slows to 3 m/s in 1 minute. What is the cyclist’s acceleration?
Answer:
[tex]\boxed {\boxed {\sf a\approx -0.08 \ m/s^2}}[/tex]
Explanation:
Acceleration can be found by dividing the change in velocity by the time.
[tex]a=\frac{v_f-v_i}{t}[/tex]
The final velocity is 3 meters per second. The initial velocity is 8 meters per second.
We need to convert the time to seconds.
t= 1 minute 60 seconds = 1 minute t=60 secondsSo, we know that:
[tex]v_f=3 \ m/s \\v_i= 8 \ m/s\\t= 60 \ s[/tex]
Substitute the values into the formula.
[tex]a=\frac{3 \ m/s - 8 \ m/s}{60 \ s}[/tex]
Solve the numerator.
3 m/s - 8 m/s = -5 m/s[tex]a=\frac{-5 \ m/s}{60 \ s}[/tex]
Divide.
[tex]a=-0.0833333333 \ m/s/s[/tex]
Let's round to the nearest hundredth.
The 3 in the thousandth place tells us to leave the 8 in the hundredth place.
[tex]a\approx -0.08 \ m/s^2[/tex]
The cyclist's acceleration is about [tex]\boxed {-0.08 m/s^2}[/tex]
A baseball player exerts a force of 100 N on a ball for a distance of 0.5 mas he throws it. If the ball has a mass of 0.15 kg, what is its velocity as it leaves his hand?
Answer:
25.82 m/s
Explanation:
We are given;
Force exerted by baseball player; F = 100 N
Distance covered by ball; d = 0.5 m
Mass of ball; m = 0.15 kg
Now, to get the velocity at which the ball leaves his hand, we will equate the work done to the kinetic energy.
We should note that work done is a measure of the energy exerted by the baseball player.
Thus;
F × d = ½mv²
100 × 0.5 = ½ × 0.15 × v²
v² = (2 × 100 × 0.5)/0.15
v² = 666.67
v = √666.67
v = 25.82 m/s
This question involves the concepts of the law of conservation of energy and kinetic energy.
The baseball leaves the hand with a velocity of "25.82 m/s".
From the law of conservation of energy the work done on the ball must be equal to the kinetic energy of the ball:
[tex]W=K.E\\\\Fd=\frac{1}{2}mv^2\\\\v=\sqrt{\frac{2Fd}{m}}\\\\v=\sqrt{\frac{2(100\ N)(0.5\ m)}{0.15\ kg}}[/tex]
where,
F = force applied = 100 N
d = displacement of ball = 0.5 m
m = mass of ball = 0.15 kg
v = 25.82 m/s
Learn more about the law of conservation of energy here:
brainly.com/question/20971995?referrer=searchResults
The attached picture explains the law of conservation of energy.
Please answer my question
Answer:
Answer is (b) Mercury, venus and Mars.
Explanation:
i think b is correct!!
;-) :-) :-) :-)
Light from two lasers is incident on an opaque barrier with a single slit of width 4.0 x 10-5 m. One laser emits light of wavelength 4.0 x 10-7 m and the other is 6.0 x 10-7 m. A screen to view the light intensity pattern is 2.0 m behind the barrier. What is the distance from the center of the pattern to the nearest completely dark spot (dark for both colors)?
Answer:
y = 6 10⁻² m
Explanation:
This is a diffraction exercise which is described by the expression
a sin θ = m λ
we can use trigonometry to find the distance from the inside of the screen to the dark point (y)
tan θ = y / L
angles are very small in diffraction experiments, so we can approximate
tan θ = sin θ /cos θ = sin θ
sin θ = y / L
substituting
a (y / L) = m λ
Let's find the points where the intensity becomes zero
y = m L λ / a
λ₁ = 4.0 10⁻⁷ m
m = 1
y = 1 2.0 4.0 10⁻⁷/ 4.0 10⁻⁵
y = 2 10⁻² m
m = 2
y = 4 10⁻² m
λ₂ = 6.0 10⁻⁷ m
m = 1
y = 1 2.0 6.0 10⁻⁷ / 4.0 10⁻⁵
y = 3 10⁻² m
m = 2
y = 6 10⁻² m
if we want a point where the two colors are dark, we set the two expressions equal
y₁ = y₂
m₁ L λ₁ / a = m₂ L λ₂ / a
m₁/m₂ = λ₂/λ₁
m₁ / m₂ = 6 10⁻⁷ / 4 10⁻⁷
m₁ / m₂ = 1.5
since the quantities m must be integers, the smallest relation that the relation fulfills is
m₁ = 3
m₂ = 2
the distance for this destructive interference is
y = 3 2 4.0 10⁻⁷ / 4.0 10⁻⁵
y = 6 10⁻² m
this is the first point where the minimum of the two wavelengths coincide