Answer:
The index of refraction of quartz for violet light is 1.47.
Explanation:
It is given that, a narrow beam of white light is incident on a sheet of quartz.
The beam disperses in the quartz, with red light at an angle, \(\theta_r=26.3^{\circ}\) wrt to the normal and violet light traveling at an angle of \(\theta_v=25.7^{\circ}\)
The index of refraction of quartz for red light is 1.45.
We need to find the index of refraction of quartz for violet light.
Using Snell's law of red light as follows :
\(\mu_a\sin\theta_i=\mu_r\sin\theta_r\)
Here,
\(\mu_a\) is the refractive index of air
\(\theta_i\) is the angle of incidence
We can find the value of angle of incidence as follows :
\(\sin\theta_i=\dfrac{\mu_r \sin\theta_r}{\mu_a}\\\\\sin\theta_i=\dfrac{1.45\times \sin(26.3)}{1}\\\\\theta_i=\sin^{-1}(0.642)\\\\\theta_i=39.79^{\circ}\)
Now again using Snell's law for violet light as follows :
\(\mu_a\sin\theta_i=\mu_v\sin\theta_v\\\\\mu_v=\dfrac{\mu_a\sin\theta_i}{\sin\theta_v}\\\\\mu_v=\dfrac{1\times \sin(39.79)}{\sin(25.7)}\\\\\mu_v=1.47\)
So, the index of refraction of quartz for violet light is 1.47.
i'd like you to explain this to me, I don't have a clue on how to do this
1. I would like you to then go into detail as to why this is an important discovery or application of this scientific principle.
2. Then I would like you to explain how this applies to what we have learned.
"discovery" - Spanish flu
scientific concept/principle - exponential growth
thank you!
Answer:
Explanation:
The Spanish flu pandemic of 1918, the deadliest in history, infected an estimated 500 million people worldwide about one-third of the planet’s population and killed an estimated 20 million to 50 million victims, including some 675,000 Americans. The 1918 flu was first observed in Europe, the United States and parts of Asia before swiftly spreading around the world. At the time, there were no effective drugs or vaccines to treat this killer flu strain. Citizens were ordered to wear masks, schools, theaters and businesses were shuttered and bodies piled up in makeshift morgues.
Does this sound familiar?
Its the same thing but with a different name called the Corona virus pandemic the same thing happened in 1918 and now it is happening again in 2020 , but in in 2020 there are far less people infected by the Corona virus as compared to the Spanish flu the numbers approximate around 70 million infected and deaths are around 2 million.
The rapid spread of Spanish flu in the fall of 1918 was at least partially to blame on public health officials unwilling to impose quarantines during wartime. The public health response to the crisis in the United States was further hampered by a severe nursing shortage as thousands of nurses had been deployed to military camps and the front lines. But one of the chief reasons that the Spanish flu claimed so many lives in 1918 was that science simply didn’t have the tools to develop a vaccine for the virus. Microscopes couldn’t even see something as incredibly small as a virus until the 1930s.
That is why the Spanish Flu claimed so many lives in 1918 and the Corona Virus didn't claim that many.
The Corona Virus patients with respect to Spanish Flu patients exponentially decreased because in 2020 we had the specific tools to fight the virus and since mankind was aware when the world engrossed into the pandemic 100 years before the new the risks that it could impose on the world , People started to Quarantine themselves, more nurses/doctors are available rather than in the era of the 19th century.
Mathematically we would say that the exponential growth would be:
\(y=ab^x\)
This is an exponential function, which means as you increase x , y increases exponentially, and where a is the initial value and b is the growth factor.
For example:
There are 100,000 cases of Coronavirus when the virus outbroke. If the number of cases doubles every week then how many cases would be there in 10 weeks?
So the solution would be
\(y=ab^x\\y=100000(2)^{10}\\y=102400000\)
Which means people infected with the virus would be approximate 102.5 million. But since this kind of pandemic already broke out in 1918 called the Spanish flu mankind was wise and controlled its growth factor (b) by Quarantining people , shutting down businesses, schools and implying them to work from home , closing off cafeteria's restaurants for dine in purposes and just allowing take away to reduce human contact, and since 1918 we have more doctors and nurses to treat the infected in 2020 we reduced the outbreak to 70 million in about 10 months other wise it could have been 100 million in just 2.5 months as we can see.
So guys stay indoors just go out if you REALLY need something, avoid meeting others , wear masks and gloves :)
If you put a 15 kg mass at 2 meters where on the other side do you have to put the
20 kg mass to balance the lever?
0.25 meters
0.5 meters
0.75 meters
1 meter
1.25 meter
1.5 meter
1.75 meter
2 meter
To balance the lever, the 20kg mass will be positioned at 1.5m
What is equilibrium?When all the forces that act upon an object are balanced, the object is said to be in a state of equilibrium. The forces are considered to be balanced if the rightward forces are balanced by the leftward forces and the upward forces are balanced by the downward forces. This however does not necessarily mean that all the forces are equal to each other.
The product of mass and distance of right hand side should be equal to the product of mass and distance of the left hand side.
m1 x d1 = m2 x d2
where m1 = 15kg
d1 = 2m
m2 = 20kg
m1 x d1 = m2 x d2
Therefore;
d2 = (m1 x d1 )/m2
d2 = (15 x 2)/20
d2 = 30/20
d2 = 1.5m
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what's the density of a block of gold with a mass of 170g and a volume of 9 cm3
The density of gold can also be used in various scientific and industrial applications, such as in the manufacturing of electronic components and medical implants.
The density of a material is defined as its mass per unit volume. In this case, we have a block of gold with a mass of 170g and a volume of 9 cm^3. To find the density, we can simply divide the mass by the volume:
Density = Mass / Volume
Density = 170g / 9 cm^3
Density = 18.89 g/cm^3
Therefore, the density of the gold block is 18.89 g/cm^3. This means that for every cubic centimeter of the block, there is a mass of 18.89 grams. Gold is a dense material, and its high density is one of the reasons why it is valued in jewelry and other decorative items.
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Why do we consider eyes, ears, and fingers as physical sensor
Answer:
because
Explanation:
because we need eye to see if you don't have eyes how you regnise some one
if you have ears how can you know who's voice is who's
if don't have fingers how can you know what your are holding this is why they are called physical sensors
Answer:
because they stimulate our brain and the sensor of human body detect stimuli.
Explanation:
You are designing an airplane propeller that is to turn at 2400 rpm (Fig. 9.13a). The forward airspeed of the plane is to be 75.0 m/s 75.0 m/s, and the speed of the propeller tips through the air must not exceed 270 m/s 270 m/s. (This is about 80% of the speed of sound in air. If the propeller tips moved faster, they would produce a lot of noise.) What is the maximum possible propeller radius?
Answer:
r = 1.07 m
Explanation:
The maximum radius of the propeller that can be allowed is given by the following formula:
\(v = r\omega\\\\r = \frac{v}{\omega}\)
where,
r = maximum possible radius of the propeller = ?
v = maximum possible linear speed of the propeller = 270 m/s
ω = angular speed of the propeller = (2400 rpm)(2π rad/1 rev)(1 min/60 s)
ω = 251.33 rad/s
Therefore,
\(r = \frac{270\ m/s}{251.33\ rad/s}\)
r = 1.07 m
Please PLEASE HELP ASAP
A student placed four objects on a plastic tray: a rock, an eraser, a wood block, and an ice cube. The student slowly lifts the tray and measures the height at which each object begins to slide in order to compare the friction of each object. The table above shows the results. In a separate experiment the student used the same objects and tray, but glued a piece of gritty sandpaper to the tray. What results would be expected? A) The items would slide faster at the same heights. B) The items would start to slide when the tray is not lifted as high. C) The items would not slide at all, no matter how high the tray is raised. D) The tray would need to be raised higher before the items start to slide.
Answer:
D) The tray would need to be raised higher before the items start to slide.
Explanation:
The tray would need to be raised higher due to the gritty sandpaper causing it to have more grip or fraction between the two surfaces. In the first experiment it would have a smooth surface to slide across but in the second experiment it would have a rougher surface to slide across.
Example: It would be like taking two different kinds of shoes like tennis shoes and football cleets. Then seeing which one has more traction when going up a hill.
Hope this helps!!
Let to the right be the positive direction.
A 25.8 g marble sliding to the right at 21.0
cm/s overtakes and collides with a 12.4 g
marble moving in the same direction at 13.8
cm/s. After the collision, the 12.4 g marble
moves to the right at 23.9 cm/s.
Find the velocity of the 25.8 g marble after
the collision.
Answer in units of cm/s. Answer in units
of cm/s.
The final velocity of the 25.8 g marble after the collision is 16.15 cm/s.
What is the velocity of the 25.8 g marble after the collision?
The velocity of the 25.8 g marble after the collision is calculated as follows;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is the mass of 25.8 g marblem₂ is the mass of 12.4 g marbleu is their initial speedsv is their final speedsThe final velocity of the 25.8 g marble after the collision is calculated as;
( 25.8 x 21 ) + ( 12.4 x 13.8 ) = ( 12.4 x 23.9 ) + ( 25.8v )
712.92 = 296.36 + 25.8v
25.8v = 416.56
v = 416.56 / 25.8
v = 16.15 cm/s
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An object is dropped from a high building. It reaches the ground in two seconds.
a) Find the distance travelled by the object.
b) Find the speed of the object, when it hits the ground.
Answer:
a: 19.6 meters b: 9.8meters per second
Explanation:
speed and object falls is 9.8 meters per second. 9.8 meter times 2 is 19.8 meters.
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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Given an electron and a proton aligned horizontally like this: - + and separated by a distance of 33 nm. In which direction will the electron accelerate?
Since the electron and proton are charged particles, they will experience a force due to their mutual Coulombic attraction. The direction of the force on each particle will be opposite to the direction of the other particle.
Since the electron is negatively charged and the proton is positively charged, the force on the electron will be in the direction of the proton (to the right), and the force on the proton will be in the direction of the electron (to the left).
Since the electron has a much smaller mass than the proton, it will experience a larger acceleration in response to the force. This means that the electron will accelerate to the right, in the direction of the proton.
If a pendulum's length is 2.00 m and ag = 9.80 m/s, how many complete oscillations does the pendulum make in 5.00 min?
Answer:
Number of oscillation = 106 oscillations
Explanation:
Given the following data;
Length = 2 mAcceleration due to gravity, g = 9.8 m/s²Time = 5 minutesTo find how many complete oscillations the pendulum makes in 5.00 min;
First of all, we would determine the period of oscillation of the pendulum using the following formula;
\( T = 2 \pi \sqrt{\frac{l}{g}} \)
Where;
T is the period.l is the length of the pendulum.g is acceleration due to gravity.Substituting into the formula, we have;
\( T = 2 * 3.142 \sqrt{\frac{2}{9.8}} \)
\( T = 6.284 \sqrt{0.2041} \)
\( T = 6.284 * 0.4518 \)
Period, T = 2.84 seconds
Next, we would determine the number of complete oscillation in 5 minutes;
We would have to convert the time in minutes to seconds.
Conversion:
1 minutes = 60 seconds
5 minutes = X seconds
Cross-multiplying, we have;
X = 5 * 60 = 300 seconds
Mathematically, the number of oscillation of a pendulum is given by the formula;
\( Number \; of \; oscillation = \frac {Time}{Period} \)
Substituting into the formula, we have;
\( Number \; of \; oscillation = \frac {300}{2.84} \)
Number of oscillation = 105.63 ≈ 106 oscillations
Number of oscillation = 106 oscillations
Electric field lines are used to represent the vector electric field around point charges and charged objects. Which of the following statements are true about electric field lines. Select ALL that apply.
Select all that apply
A. Electric field lines cannot cross.
B. Lines of electric field only originate from positive charges.
C. Field lines point in the direction of the force the electric field creates on an electron.
D. The strength of the electric field is greater in regions where the field lines are closer together.
E. In an electric-field-line drawing with many point charges, the number of field lines originating or terminating on each charge is proportional to the charge. That is, bigger charges have proportionally more field lines. F. The true strength of an electric field at any point can be determined from an electric field representation.
Electric field lines are a powerful tool to understand and visualize electric fields. They help to represent the direction and magnitude of the electric field at various points around a charged object.
The following statements are true about electric field lines:
A. Electric field lines cannot cross: This is because at the point where two field lines cross, there would be two directions for the electric field, which is impossible. Hence, the lines do not cross, and this is one of the fundamental characteristics of electric field lines.
B. Lines of electric field only originate from positive charges: Electric field lines originate from positive charges and terminate at negative charges. This is because positive charges repel positive charges and attract negative charges. Therefore, the electric field lines originating from a positive charge terminate at a negative charge.
C. Field lines point in the direction of the force the electric field creates on an electron: Electric field lines point in the direction of the force that would be experienced by a positive charge placed at any point in the field. Electrons, being negatively charged, would experience a force in the opposite direction to the electric field.
D. The strength of the electric field is greater in regions where the field lines are closer together: The density of field lines indicates the strength of the electric field. The closer the lines are, the stronger the field at that point.
E. In an electric-field-line drawing with many point charges, the number of field lines originating or terminating on each charge is proportional to the charge. That is, bigger charges have proportionally more field lines: The number of field lines originating or terminating on each charge is directly proportional to the magnitude of the charge.
F. The true strength of an electric field at any point can be determined from an electric field representation: The strength of the electric field at a point can be determined by the density of electric field lines at that point. However, the actual strength of the field would require quantitative measurements using instruments such as a voltmeter or an electrometer.
In conclusion, electric field lines are an essential tool in understanding the behavior of electric fields. They provide a visual representation of the electric field, its direction, and its strength at various points in space.
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Explain the procedures used and data recorded to identify a crystalline mineral based on its properties.
Answer:
By examining its external shape, color, hardness, etc.
Explanation:
how atoms are in one mole of patassuim
Answer:
There are 6.022 × 10²³ atoms of potassium in every mole of potassium.
A radio technician measures the frequency of an AM radio transmitter. The frequency is . What is the frequency in megahertz? Write your answer as a decimal.
Complete Question
A radio technician measures the frequency of an AM radio transmitter. The frequency is 14603 kHz . What is the frequency in megahertz? Write your answer as a decimal.
Answer:
The value is \(x = 14.6 \ MHz\)
Explanation:
From the question we are told that
The frequency is \(f = 14603 \ kHz = 14603 *1000 = 14603000 \ Hz\)
Generally
\(1 Hz \to 1.0 *10^{-6} \ MHz\)
\(14603000 \ Hz \to x MHz\)
=> \(x = \frac{14603000 * 1.0*10^{-6}}{1 }\)
=> \(x = 14.6 \ MHz\)
A moon orbits an isolated planet in deep space. Which of the following forces that the planet exerts on the moon can be considered as negligible?
A. The electric force
B. The force due to gravity
C. Both the electric force and the force due to gravity
D. Neither the electric force nor the force due to gravity
Answer:
A
Explanation:
electric force
The electrostatic force between the moon and the planet can be neglected. Hence, option (A) is correct.
The given problem is based on the comparison between the gravitational force and electrostatic force. Consider the two bodies as moon and a planet such that the force exerted between the moon and the planet is given as,
\(F_{g}=\dfrac{G\times M \times m}{r^{2}}\) ..................................................(1)
Here, G is the gravitational constant, M is the mass of moon, m is the mass of planet and r is the distance between the moon and the planet.
And the electrostatic force is the force between the two charged entities on moon and the planet. So, it is given as,
\(F_{e}=\dfrac{k \times Q \times q}{r^{2}}\) ....................................................(2)
Here, k is the Coulomb's constant, Q is the charge entity at moon and q is the charged entity on planet.
The forces obtained in equation (1) and (2) depends on the masses and charges, which clearly signifies that the masses have more numerical value than charges, hence the electrostatic force will leave much lesser influence than gravitational force. So, it can be neglected.
Thus, we conclude that the electrostatic force between the moon and the planet can be neglected. Hence, option (A) is correct.
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I need help lol .........
Answer:
a
Explanation:
A person walks 5 meters to the east, then turns and walks 7 meters south.
What is their total displacement?
Answer:
8.6 meters to south east
Explanation:
Displacement is change in position or a distance between initial position to final position.
Since a person walks to east and then to the south, it forms a right triangle path. We can use Pythagoras Theorem to help finding the displacement:
\(\displaystyle{\vec s = \sqrt{s_x^2 + s_y^2}}\)
Where \(\displaystyle{\vec s}\) is displacement, \(\displaystyle{s_x}\) is horizontal distance (east) and \(\displaystyle{s_y}\) is vertical distance (south). Therefore:
\(\displaystyle{\vec s = \sqrt{5^2 + 7^2}}\\\\\displaystyle{\vec s = \sqrt{25+49}}\\\\\displaystyle{\vec s = \sqrt{74}}\\\\\displaystyle{\vec s = 8.6 \ \, \sf{meters \ \, to \ \, south \ \, east}}\)
Therefore, the displacement is 8.6 meters to south east.
(The attachment is added for visual reference on displacement and direction.)
The is a pulley system as shown in the diagram. Mass one has a magnitude of 5.11 kg, and mass two has a magnitude of 3.01 kg. If the static frictional force has a magnitude of 31.833N. and the system is stationary, then determine Theta and the normal force.
if someone can answer quickly it's very much appreciated.
Maybe b normal focrec N??
Tom applied 10 000J of heat energy to four (4) metals A, B, C and D. All the metals were of the same mass and were initially at the same temperature. After heating the metals the temperature change was noted as shown in the table below. Metal 9 A.25 B.35 C.10 D.15 Which of these four (4) metals has the highest heat capacity?
The metal with the highest heat capacity between metals A.25 B.35 C.10 and D.15 is metal A.
How to determine heat capacity?Heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius. Metal A has a heat capacity of 400 J/kg°C, which means that it takes 400 joules of heat to raise the temperature of one kilogram of metal A by one degree Celsius.
Metal B has a heat capacity of 285.7 J/kg°C, metal C has a heat capacity of 1000 J/kg°C, and metal D has a heat capacity of 666.7 J/kg°C. Therefore, metal A has the highest heat capacity of the four metals.
Metal A's high heat capacity means that it can absorb a lot of heat without its temperature changing very much. This makes metal A a good material for things like heat sinks and thermal insulation.
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A jump ball in the center of the court is used to start a game
Question 1 options:
True
False
Question 2 (1 point)
Saved
A personal foul is a player that delays the game, has unsportsmanlike conduct, illegal entry or has excessive timeouts
Question 2 options:
True
False
Question 3 (1 point)
Saved
A offended player is awarded 2 free throws if the foul occurred while attempting to make a basket and the basket was missed
Question 3 options:
True
False
Question 4 (1 point)
A basketball game is played with 5 players from one team against 5 players from another team
Question 4 options:
True
False
Question 5 (1 point)
The height of the basket is:
Question 5 options:
9 ft.
11 ft.
10 ft.
8 ft. 6 in.
If a body travelled a distance 's' in 't'.
What is the distance travelled in 't'
Answer: Distance traveled in time t is s
Explanation: Self Explanatory
Which of the following is a hypothesis?
A. The thickness of transparent glass affects how much light passes through.
B. Light may pass through a transparent sheet of glass.
C. A transparent sheet of glass has some effect on light.
D. Light will travel slowly through glass.
The hypothesis is, the thickness of transparent glass affects how much light passes through. Option A is correct.
A hypothesis is a proposed explanation or prediction for a phenomenon or observation that is based on limited evidence and subject to testing and validation through further investigation. It is an essential part of the scientific method, which involves developing a research question, making observations, and forming a hypothesis to explain the observed phenomenon.
The hypothesis should be testable, falsifiable, and based on evidence and reasoning. Testing the hypothesis involves designing experiments and collecting data, which can either support or refute the hypothesis. If the hypothesis is supported by the data, it may be further developed into a scientific theory, which is a widely accepted explanation of a natural phenomenon that has been extensively tested and validated. Option A is correct.
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Discuss the consequences of poor health and safety when using non-ionising and ionising radiation technologies and the prevention and safety measures employed.
Poor health and safety practices when using non-ionizing and ionizing radiation technologies can have significant consequences. Here are some potential consequences and the prevention and safety measures employed to mitigate them.
Consequences of poor health and safety:
Non-Ionizing Radiation:
Thermal Effects: Prolonged exposure to high levels of non-ionizing radiation, such as from radiofrequency waves (RF) or microwaves, can lead to thermal effects, including tissue heating and burns.Ionizing Radiation:
Acute Radiation Syndrome (ARS): High doses of ionizing radiation, such as those experienced during a nuclear accident or radiation therapy accidents, can lead to ARS, which includes symptoms like nausea, vomiting, fatigue, and potentially fatal damage to vital organs.Prevention and safety measures:
Non-Ionizing Radiation:
Time, Distance, and Shielding: Minimize exposure time to non-ionizing radiation sources, maintain a safe distance from the source, and use shielding materials (e.g., lead aprons, and protective barriers) to reduce exposure.Compliance with Guidelines: Follow national and international guidelines and regulations regarding safe exposure limits for different types of non-ionizing radiation sources. For example, adherence to specific absorption rate (SAR) limits for mobile devices.Ionizing Radiation:
Risk Assessment and Minimization: Conduct thorough risk assessments to identify potential hazards, establish safety protocols, and minimize radiation exposure through engineering controls and administrative measures.Personal Protective Equipment (PPE): Use appropriate PPE, such as lead aprons, gloves, and goggles, to protect against direct radiation exposure.Training and Education: Provide comprehensive training and education to workers who handle ionizing radiation sources to ensure they are aware of the risks, safety protocols, and proper handling procedures.Monitoring and Dosimetry: Regularly monitor radiation levels in the workplace and ensure that employees wear dosimeters to measure their radiation exposure.Regulatory Compliance: Adhere to applicable regulations and standards, such as those set by radiation protection agencies and authorities, to ensure compliance with safety measures and limits on radiation exposure.know more about ionizing radiation here:
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Suppose you drop a superball of massMand a marble of mass m(both treated as point masses) from a heighthwith the marble just on top of the superball. A superbowl has essentially elastic collisions with hard objects. Thesuperball hits the floor, rebounds and then collides with the marble. How highdoes the marble go if all the motion is vertical
Answer:
h '= [ ( \frac{ M-m}{M +m } )+ 2 (\frac{M}{M+m})]² h
Explanation:
Let's analyze this problem, first the two bodies travel together, second the superball bounces, third it collides with the marble and fourth the marble rises to a height h ’
let's start by finding the velocity of the two bodies just before the collision, let's use the concepts of energy
starting point. Starting point
Em₀ = U = m g h
final point. Just before the crash
Em_f = K = ½ m v²
as there is no friction the mechanical energy is conserved
Em₀ = Em_f
mg h = ½ m v²
v = √2gh
this speed is the same for the two bodies.
Second point. The superball collides with the ground, this process is very fast, so we will assume that the marble has not collided, let's use the concept of conservation of moment
initial instant. Just when the superball starts contacting the ground
p₀ = M v
this velocity is negative because it points down
final instant. Just as the superball comes up from the floor
p_f = M v '
the other body does not move
p₀ = p_f
- m v = M v '
v ’= -v
Therefore, the speed of the asuperbola is the same speed with which it arrived, but in the opposite direction, that is, upwards.
Let's use the subscript 1 for the marble and the subscript 2 for the superball
Third part. The superball and the marble collide
the system is formed by the two bodies, so that the forces during the collision are internal and the moment is conserved
initial instant. Moment of shock
p₀ = M \(v_{1'}\)+ m v_2
final instant. When the marble shoots out.
P_f = Mv_{1f'}+ m v_{2f}
p₀ = p_
M v_{1'}+ m v_2 = M v_{1f'} + m v_{2f}
M (v_{1'} - v_{1f'}) = -m (v_2 - v_{2f})
in this expression we look for the exit velocity of the marble (v2f), as they indicate that the collision is elastic the kinetic nerve is also conserved
K₀ = K_f
½ M v_{1'}² + m v₂² = M v_{1f'}² + ½ m v_{2f}²
M (v_{1'}² - v_{1f'}²) = - m (v₂² - v_{2f}²)
Let's set the relation (a + b) (a-b) = a² - b²
M (v_{1'} + v_{1f'}) (v_{1'} - v_{1f'}) = -m (v₂ + v_{2f}) (v₂ - v_{2f})
let's write our two equations
M ( v_{1'} - v_{1f'}) = -m (v₂ - v_{2f}) (1)
M (v_{1'} + v_{1f'}) (v_{1'} - v_{1f'}) = -m (v₂ + v_{2f}) (v₂ - v_{2f})
if we divide these two expressions
(v_{1'}+ v_{1f'}) = (v₂ + v_{2f} )
we substitute this result in equation 1 and solve
v_{1f'}= (v₂ + v_{2f}) - v_{1'}
M (v_{1'} - [(v₂ + v_{2f}) - v_{1'}] = -m (v₂ - v_{2f})
-M v₂ - M v_{2f1'} + 2M v_{1'} = m v₂ - m v_{2f}
-M v_{2f} -m v_{2f} = m v₂ -M v₂ + 2M v_{1'}
v_{2f} (M + m) = - v₂ (M-m) + 2 M v_{1'}
v_{2f} = - \(( \frac{ M-m}{M +m } )\)) v₂ + 2 \((\frac{M}{M+m})\) v_{1'}
now we can substitute the velocity values found in the first two parts
\(v_{2f}\) = - ( \frac{ M-m}{M +m } ) √2gh + 2(\frac{M}{M+m}) √2gh
we simplify
v_{2f} = [( \frac{ M-m}{M +m } ) + 2 (\frac{M}{M+m})] \(\sqrt{2gh}\)
let's call the quantity in brackets that only depends on the masses
A = ( \frac{ M-m}{M +m } )+ 2 (\frac{M}{M+m})]
v_{2f}= A \sqrt{2gh}
in general, the marble is much lighter than the superball, so its speed is much higher than the speed of the superball
finally with the conservation of energy we find the height that the marble reaches
Starting point
Emo = K = ½ mv_{2f}²
Final point
Emf = U = m g h'
Em₀ = Em_f
½ m v_{2f}² = m g h ’
h ’= ½ v_{2f}² / g
h ’= ½ (A \sqrt{2gh})² / g
h ’= A² h
h '= [ ( \frac{ M-m}{M +m } )+ 2 (\frac{M}{M+m})]² h
An ecosystem with one dominant type of plant growing in it is a healthy, stable ecosystem. True or false?
Which system regulates involuntary muscles and internal organs?
parasympathetic system
somatic system
autonomic system
sympathetic system
C, the autonomic system :)
The Sun radiates energy at a rate of about 4×1026W. At what rate is the mass decreasing?
4.44×\(10^{9}\) kg/s is the rate at which the sun mass is decreasing.
The Sun radiates energy through a process called nuclear fusion, where hydrogen atoms combine to form helium, releasing a tremendous amount of energy in the process. According to Einstein's mass-energy equivalence principle (E=mc²), this energy release corresponds to a decrease in mass.
To calculate the rate at which the Sun's mass is decreasing, we can use the formula ΔE = Δmc², where ΔE is the change in energy, Δm is the change in mass, and c is the speed of light.
Given that the Sun radiates energy at a rate of 4×10^26 W, we can substitute this value into the equation as ΔE and solve for Δm.
ΔE = 4×10^26 W
c = 3×10^8 m/s (speed of light)
Using the equation ΔE = Δmc² and rearranging it, we get Δm = ΔE / c².
Substituting the values, we have:
Δm = (4×10^26 W) / (3×10^8 m/s)²
Evaluating this expression, we find that the rate at which the Sun's mass is decreasing is approximately 4.44×10^9 kg/s.
This calculation demonstrates that the Sun's mass is gradually decreasing as it continuously radiates energy into space, primarily through the process of nuclear fusion in its core.
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50 POINTS ANSWER CORRECTLY 4. Identify what elements are made in a Super Red Giant as it starts to die?
The super red giant star is the aging star and it is a dying star in the final stage of stellar evolution. From the burst of the super red giant star, magnesium is formed from the core of the red giant star.
The super red giant star has a larger mass and produces greater gravitational pressure. The giant red star is in the final stage of dying and the core of the red star has heavier elements like nitrogen, carbon, etc.
In the core of stars, nuclear fusion takes place. Nuclear fusion is the process of two lighter nuclei fusing or joining together to form a heavier nucleus.
The hydrogen fuses to form helium and helium fuses together to form carbon atoms. Carbon atoms fuse together to form oxygen atoms and it forms heavier elements like magnesium and iron.
Hence, from the burst of a super red giant star, heavier elements like magnesium, iron, carbon, and helium ions are formed.
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In Figure (a), both batteries have em - 1.20 V and the external resistance R is a variable resistor. Figure (6) gives the electric potentials V between the terminals of each battery as functions of
Curve 1 corresponds to battery 1, and curve 2 corresponds to battery 2. The horizontal scale is set by R, -0.500 . What is the internal resistance of (a) battery 1 and (b) battery 2?
0.60
V(V)
0
-0.350
(
R(0)
(6)
Answer:
i know da way ese'
Explanation: