A piece of wood of density 400kg/m³ lump of aluminium is tied to a lump of aluminium of mass 0.01kg and density of 270kg/m³ . the arrangement has a mean density of 100kg/m³and just float in water. Determine the just float in volume of the piece of wood
The just float in volume of the piece of wood is 0.008 cubic meters.
Just float calculationLet's denote the volume of the piece of wood as V_wood, and the volume of the lump of aluminum as V_aluminum.
We can start by using the information given to write two equations:
Equation 1: (density of wood) * V_wood + (density of aluminum) * V_aluminum = (mean density) * (V_wood + V_aluminum)
Substituting the given values, we get:
400 * V_wood + 270 * V_aluminum = 100 * (V_wood + V_aluminum)
Simplifying and rearranging, we get:
300 * V_wood = 70 * V_aluminum
Equation 2: The total mass of the arrangement is the sum of the masses of the wood and aluminum:
(density of wood) * V_wood + (density of aluminum) * V_aluminum = (total mass)
Substituting the given values, we get:
400 * V_wood + 270 * V_aluminum = 0.01
Now we can use Equation 1 to eliminate V_aluminum from Equation 2:
300 * V_wood = 70 * V_aluminum
V_aluminum = (300/70) * V_wood
Substituting this into Equation 2, we get:
400 * V_wood + 270 * [(300/70) * V_wood] = 0.01
Simplifying and solving for V_wood, we get:
V_wood = 0.008 m^3
Therefore, the just float in volume of the piece of wood is 0.008 cubic meters.
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A hydraulic system has two pistons. Input force on one piston is 15.8 lb and the other piston can lift a weight of 93 lb. What is the mechanical advantage?
Answer:
The mechanical advantage of a hydraulic system is given by the ratio of the output force to the input force. In this case, the input force is 15.8 lb and the output force is 93 lb.
So, the mechanical advantage of the hydraulic system is:
MA = Output force / Input force
MA = 93 lb / 15.8 lb
MA = 5.89
Therefore, the mechanical advantage of the hydraulic system is 5.89. This means that the system can lift a weight that is almost 6 times greater than the input force applied to the other piston.
Two equal charges repel one another with a force of 4.0 x 10^4 N when they are 10 cm apart. (Coulomb's constant is k=9.0 x 10 9 Nm^2/C^2). If they are moved until the separation is 5 cm, calculate the force. Is it an attractive or a repulsive force?
The new force of repulsion, given that their new separating distance is 5 cm, is 16×10⁴ N
How do i determine the new force?We know that Coulomb's law is written as shown below:
F = Kq₁q₂ / r²
Cross multiply
Fr² = Kq₁q₂
Kq₁q₂ => constant
F₁r₁² = F₂r₂²
Where
F₁ and F₂ are the initial and new forcer₁ and r₂ are the initial and new distance apartNow, we can shall obtain the new force between the two charge, given that their distance is 5 cm apart. This is shown below:
Initial force of repulsion (F₁) = 4.0×10⁴ NInitial distance apart (r₁) = 10 cmNew distance apart (r₂) = 5 cmNew force of repulsion (F₂) =?F₁r₁² = F₂r₂²
4.0×10⁴ × 10² = F₂ × 5²
4000000 = F₂ × 25
Divide both side by 25
F₂ = 4000000 / 25
F₂ = 16×10⁴ N
Thus, the new force of repulsion is 16×10⁴ N
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What is Ceres?
The largest asteroid identified to date.
The asteroid closest in orbit to the Earth.
The comet that passes near Earth most often.
The meteor that probably killed the dinosaurs.
The Ceres is (a).The largest asteroid identified to date is correct option.
With a diameter of around 590 miles (940 km), Ceres is the biggest asteroid between Mars and Jupiter. It is regarded as a minor planet, like Pluto, and was found in 1801 by Giuseppe Piazzi. Ceres is made of rock and ice, and due to its low density, it is likely that it contains a substantial amount of water ice inside.
The NASA Dawn spacecraft visited Ceres in 2015 and orbited the dwarf planet for more than three years, gathering useful information and taking stunning pictures of it.
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A bubble of air has a diameter of 1 mm when it is 0.5 m under the surface of water ( coefficient of surface tension 0.073 N/m). Find the gauge pressure inside the bubble.
The gauge pressure inside the bubble. is -101310.4 Pa.
The negative sign shows that the pressure inside the bubble is lower than the atmospheric pressure. Hence, the bubble will rise to the surface of the water.
How do we calculate?We apply Laplace's law to find the absolute pressure inside the bubble:
ΔP = 2γ/r
where ΔP is the pressure difference across the curved surface of the bubble, γ is the coefficient of surface tension of water, and r is the radius of curvature of the bubble.
r = 0.5 mm = 0.0005 m
Substituting the given values, we have:
ΔP = 2 × 0.073 N/m ÷ 0.0005 m
ΔP = 14.6 × 10^(-3) Pa
The atmospheric pressure at sea level is approximately 101325 Pa. Therefore, the gauge pressure inside the bubble is:
P_gauge = ΔP - P_atm
P_gauge = 14.6 × 10^(-3) Pa - 101325 Pa
P_gauge = -101310.4 Pa
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Find the ratio of the coulomb electric force Fe to the gravitational force Fg between two electrons in vacuum.
A soft drink (mostly water) flows in a pipe at a beverage plant with a mass flow rate that would fill 220 0.355-L cans per minute. At point 2 in the pipe, the gauge pressure is 152 kPa and the cross-sectional area is 8.00 cm2. At point 1, 1.35 m above point 2, the cross-sectional area is 2.00 cm2.
Find the gauge pressure at point 1.
Express your answer in kilopascals
The gauge pressure at point 1 = 145.2 kPa.
What is Bernoulli's equation?The equation states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid is constant along a streamline, in the absence of external forces like friction or viscosity.
The principle of continuity of mass flow rate and Bernoulli's equation, which connects pressure, velocity, and height of a fluid in a flow, can be used to solve this issue.
With the provided data, we can first determine the soft drink's mass flow rate:
mass flow rate =[tex](220 cans/min) x (0.355 L/can) x (1 kg/L) x (1 min/60 s)[/tex] = [tex]1.235 kg/s[/tex]
Then, we may compare the soft drink's velocities at positions 1 and 2 using the principle of continuity:
[tex]A1 v1 = A2 v2[/tex]
where A1 and A2 are the pipe's cross-sectional areas at points 1 and 2, respectively, and v1 and v2 are the soft drink's velocities at those same locations. When we solve for v1, we get:
[tex]v1 = (A2/A1) v2 = (8.00 cm^2)/(2.00 cm^2) v2 = 4 v2[/tex]
Now, we can link the pressures, velocities, and heights of the soft drink at points 1 and 2 using the Bernoulli's equation:
P1 + (1/2)ρv1²+ ρgh1 = P2 + (1/2)ρv2²+ ρgh2
where P1 and P2 are the gauge pressures at points 1 and 2, respectively; ρ is the soft drink's density; g is gravity's acceleration; and h1 and h2 are the heights of the respective points 1 and 2 above a reference level.
As the soft drink contains primarily water, we may calculate its density using the formula: = 1000 kg/m3. Moreover, we can decide to set the reference level at point 2, making h2 = 0.When the supplied values and the velocity relation are substituted, we obtain:
[tex]P1 + (1/2)(1000 kg/m^3)(16 v2^2) + (1000 kg/m^3)(9.81 m/s^2)(1.35 m)[/tex] =[tex]152 kPa + (1/2)(1000 kg/m^3)(v2^2)[/tex]
By condensing and figuring out P1, we get at:
[tex]P1 = 152 kPa + (1/2)(1000 kg/m^3)(15 v2^2) - (1000 kg/m^3)(9.81 m/s^2)(1.35 m)[/tex] = [tex]152 kPa + 6.75 v2^2 - 13.33 kPa[/tex]
We must now locate v2. We can link the velocity and the cross-sectional area at point 2 using the mass flow rate relation and the density of the soft drink:
[tex]A2 v2[/tex] = (mass flow rate)/ρ =[tex]1.235/(1000 kg/m^3)[/tex]= [tex]0.001235 m^3/s[/tex]
Upon solving for v2, we obtain:
v2 =[tex]0.001235 m^3/s / (8.00 cm^2 / 10000 cm^2)[/tex]= [tex]0.1544 m/s[/tex]
Last but not least, we can insert this value into the P1 expression to obtain:
[tex]P1[/tex] =[tex]152 kPa + 6.75 (0.1544 m/s)^2 - 13.33 kPa[/tex] = [tex]145.2 kPa[/tex]
As a result, point 1's gauge pressure is 145.2 kPa.
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) Find mass and speed of 2 MeV electron
According to the equation E=(-1)mc2, where [tex]E=3.2 x 1013 J[/tex] and [tex]=1.0000037[/tex], a 2 MeV electron has a mass of [tex]9.11 x 1031 kg[/tex] and a speed of [tex]2.195 x 108 m/s.[/tex]
How are masses expressed in MeV?Additionally, as energy and mass are connected by Einstein's famous equation E = mc2, the masses of elementary particles are sometimes stated in electron volts as well. An electron, for instance, has a mass of 0.51 MeV/c2, where c is the speed of light.
What does 2 MeV proton mean?Moving perpendicular to a 2.5 T magnetic field is a 2 MeV proton. The proton is under a force of (1.6 10 27 kg of proton mass)
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What voltage will send a current of 5 amperes through a bell circuit if the resistance of the circuit is 4 ohms?
Answer:
Therefore, the voltage required is 20 volts
Explanation:
To find the voltage that will send a current of 5 amperes through a bell circuit with a resistance of 4 ohms, we can plug in the values into the equation and solve for V: V=IR
V=(5A)(4Ω)
V=20V
Why does a stationary bus resist being put into motion?
OA. It has no force acting on it.
OB. It is not accelerating.
OC. It has lost all of its inertia.
OD. It has a large amount of mass.
Answer:
When a passenger is sitting in a stationary bus it is under the law of inertia of rest that is the body resists any change in its state of rest.
Explanation:
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The voltage of a DC supply always _____________.
A. Points in opposite directions
B. Does not point in any direction
C. Points in various directions
D. Points in the same direction
The voltage of a DC supply always Points in the same direction. The correct answer is d.
A direct current (also known as DC) supply has voltage that always points in the same direction. A direct current (DC) is a form of electrical current in which the flow of electric charge is unidirectional. This means that it only moves in one direction through a circuit. DC is also known as a direct current. DC (Direct Current) keeps the flow of charge going in the same direction all the time, in contrast to AC (Alternating Current), which reverses its direction at regular intervals.
The voltage source in a DC circuit, which could be a battery or a DC power supply, is responsible for maintaining a consistent potential difference between the circuit's positive and negative terminals. The potential difference between the positive and negative terminals of the voltage source is greater at the positive terminal than it is at the negative terminal. As a direct consequence of this, electrons move from the negative terminal to the positive terminal, which results in the generation of an electric current that moves in the same direction consistently throughout the circuit.
When a load (such as a resistor, a light bulb, or any other type of electrical component) is connected to a DC voltage source, the DC voltage will drive the passage of electric charge through the load, which will either power the device or perform work that is of some benefit.
In a nutshell, the voltage coming from a DC supply always points in the same direction, which is from the negative terminal of the voltage source to the positive terminal of the voltage source. This results in a constant flow of electric current when the supply is connected to a DC circuit.
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Which of the following can be formed by a convergent boundary?
A. Volcanic mountains B. All of these
C. Volcanic islands
D. Deep ocean trenches
Answer:
Volcanic mountains can be formed by a convergent boundary.
A uniform beam of length and mass is inclined at an angle to the horizontal. Its
upper end is connected to a wall by a rope, and its lower end rests on a rough, horizontal surface.
Assume the angle is such that the static friction force between the beam and the surface is at its
maximum value. Determine what statement is true. There may be more than one answer.
a. The static frictional force relative to the pivot point does not exert a torque on the beam.
b. The torque produced by the gravitational force relative to the pivot point is equal to
= − sin /2.
c. The torque produced by the tension force relative to the pivot point is equal to
= sin where is the magnitude of the tension force.
d. If the angle were reduced from its present value, the magnitude of the tension force must
decrease in order to restore static equilibrium.
e. The coefficient of state friction must equal = /, where is the magnitude of the
tension force
Statement (a) is true: The static frictional force relative to the pivot point does not exert a torque on the beam.
What is Force?
Force is a physical quantity that describes the interaction between two objects or systems. It is defined as the push or pull that one object exerts on another, resulting in a change in the object's motion or deformation. Force is a vector quantity, which means it has both magnitude and direction.
The torque produced by a force about a pivot point is given by the product of the force and the perpendicular distance from the pivot point to the line of action of the force. In this case, the gravitational force acting on the beam can be considered to act at the center of mass of the beam, which is located at the midpoint of the beam due to its uniformity.
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As magma rises through the cracks of a spreading seafloor, it cools and adds new rock to the ocean floor.
The ribbon of magma causing the spreading is most similar to which structure?
A volcano
A sinkhole
A valley
A glacier
Answer:
zd its c
Explanation:
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A group of hikers hears an echo 4.80 s after shouting. How far away is the mountain that reflected the sound wave? (Assume the speed of sound is 345 m/s.)
Given: v = 341 m/s, t = 2.9 s.
Substitute into equation 2
x = 341(2.9)/2
x = 494.45 m.
What two forms of sound waves are there?The characteristics of sound waves should be the starting point for studying sound. Transverse and longitudinal waves are the two fundamental forms of waves, and they are distinguished by how they move through space.
Particles that are vibrating make up sound waves. These collide with other particles, causing them to vibrate, which allows the sound to escape the source. Your ear drums vibrate as a result of air vibrations, which allows you to perceive sound. This vibration is transformed into messages, which proceed to your brain via a nerve.
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With the solar photon flux of 3*10^21 m²s¹, how large area in [m²] covered by solar panels would be necessary to produce 150 kW of power? Assume yellow light (2.1 eV) and 15% power conversion efficiency.
O a. 100
O b. 50
O c. 25
O d. 10
O e. 1000
Answer: (D) 10
can't explain brainly keeps censoring the numbers out for some reason
pls help in astronomy didn’t know what subject to put it under
The subject depicted in the attached image is Astronomy and Astrophysics.
Definitely younger than the SunAO main sequence starB-type starsF-type stars (some)Possibly younger than the SunF1 main sequence starG2 main sequence starMO main sequence starDefinitely older than the SunM-type stars (some)M1, 1 Msun red giantM1, 18 Msun red supergiantWhat is Astronomy?Astronomy is the scientific study of celestial objects such as stars, planets, galaxies, and other phenomena that exist outside of Earth's atmosphere.
Astronomers use a variety of methods to observe and study these objects, including telescopes, spacecraft, and computer simulations.
Astronomy is a broad field that includes many different sub-disciplines, such as astrophysics, planetary science, and cosmology.
Astronomers study the physical properties and behavior of celestial objects, such as their composition, temperature, motion, and evolution.
They also seek to understand the structure and history of the universe as a whole.
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Which energy transformation occurs in an
operating electric motor?
(1) electrical energy - chemical - Mechanical
(2) mechanical energy - electrical - chemical
(3) chemical energy - electrical - Mechanical
(4) Chemical energy - Mechanical - Electrical
The correct answer is (2) mechanical energy - electrical - chemical.
What is Energy?
Energy is a fundamental property of the universe that allows things to happen or work. It is the ability to do work, cause changes, or produce an effect. Energy can be found in many different forms, including kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), electrical energy, chemical energy, nuclear energy, and more.
In an operating electric motor, electrical energy is converted into mechanical energy through electromagnetic interactions, resulting in the motor's mechanical motion. The mechanical energy is then used to perform work, such as turning a shaft or driving a load. In some cases, the motor may also generate electrical energy through processes such as regenerative braking or back-EMF (electromotive force) during deceleration or when acting as a generator.
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of the following stars, which one has a mass less than that of our sun? The choices are Sirius B, Altair, Arcturus, Spica, and Rigel.
Answer:
Sirius BExplanation:
Here we go !!!!
Sirius B: A white dwarf star and companion to Sirius A, the brightest star in the sky. It has a mass of only about 0.98 times that of the sun, making it less massive than our sun.Arcturus: A red giant star located in the constellation Boötes, with a mass of about 1.1 times that of the sun.Spica: A binary star system composed of two hot, blue stars located in the constellation Virgo. The primary star has a mass of about 11 times that of the sun.Rigel: A blue supergiant star located in the constellation Orion, with a mass of about 17 times that of the sun. It is one of the brightest stars in the sky and is a part of Orion's Belt.Altair: A main-sequence star of spectral type A7V, located in the constellation Aquila. It has a mass of about 1.8 times that of the sun, which means it is more massive than the sun.I hope this information helps!
what is the statement of objectives in newton's second law using word to investigate, to plot,to compare, to measure
by changing the force and observing the impact on an object's acceleration, one can examine the link between force and acceleration.
What aims does Newton's second law of motion have?In conclusion, Newton's second law gives an explanation for how objects whose forces are out of balance behave. According to the law, when there are imbalanced forces acting on an item, the object will accelerate with an acceleration that is inversely proportional to the mass and directly proportional to the net force.
What is Newton's law supposed to achieve?The student should be able to relate the magnitudes of the various forces acting on an object to its state of motion, particularly the direction of acceleration. The pupil ought to be able to connect the net force.
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Two batteries supply current to the circuit in the figure. The figure shows the potential difference across two of the resistors and the value of the third resistor.(Figure 1). What current is supplied by the batteries?
The current that is supplied by the batteries is 0.01333 Amp.
How to explain the informationAn electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor. It is measured as the net rate of flow of electric charge through a surface or into a control volume.
Eeq = E1 + E2 ( batteries in series )
=> Eeq = 3+4.5 = 7.5 V
Veq = V1 + V2 + V3 ( resistances in series )
=> V3 = 7.5 - 2 - 3.5 = 2 V
=> current = V/R = 2/150 = 0.01333 Amp
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A 37-kg
child jumps to the ground from the top of a fence that is 1.6 m
high. You analyze the problem using upward as the positive x
direction
The change in the system kinetic energy during the jump is 576.32 J.
What is kinetic energy?Kinetic energy refers to the energy that an object in motion possesses due to its movement and is influenced by the object's velocity and mass.
Equation:The initial potential energy of the child-Earth system is given by mgh, where m = 37 kg is the mass of the child, g = 9.8 m/s^2 is the acceleration due to gravity, and h = 1.6 m is the height of the fence. Thus, the initial potential energy is (37 kg)(9.8 m/s^2)(1.6 m) = 576.32 J.
At the bottom of the fence, all of the initial potential energy is converted into kinetic energy. Since the child is at rest initially, the initial kinetic energy is zero. Using the law of conservation of energy, the final kinetic energy can be calculated as equal to the initial potential energy, or 576.32 J.
The change in kinetic energy during the jump is therefore:
Final kinetic energy - Initial kinetic energy = 576.32 J - 0 J = 576.32 J.
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The complete question should be:
A 37-kg child jumps to the ground from the top of a fence that is 1.6 m high. You analyze the problem using upward as the positive x direction. Taking x = 0 to be at the bottom of the fence, what are the initial potential energy of the child-Earth system and the change in the system kinetic energy during the jump? Enter your answers numerically separated by a comma.
What amount of force is required to accelerate a 20 gram toy car at 5 m/s²?
O 150 N
O 100 N
O 50 N
Ο ΟΝ
Answer:
100
Explanation:
F = m * a
Given that the mass (m) of the toy car is 20 grams (or 0.02 kilograms, since 1 kilogram = 1000 grams) and the acceleration (a) is 5 m/s^2, we can plug these values into the formula to calculate the force (F):
F = 0.02 kg * 5 m/s^2 = 0.1 N
So, the amount of force required to accelerate the 20 gram toy car at 5 m/s^2 is 0.1 N, which is equivalent to 100 N when rounded to the nearest whole number. Therefore, the correct answer is 100 N.
Need Help! The diagram shows a cross section of the Earth near its surface.
In the diagram, continental crust is labeled ___, and oceanic crust is labeled ____
A. 1; 2
B. 3; 1
C. 2; 1
D. 1; 3
In the diagram, continental crust is labeled 1 and oceanic crust is labeled 2.
option A.
What are the characteristics of Continental and ocean crust?
Continental crust:
Generally thicker, averaging about 30-40 kilometers in depth.Composed mostly of granite, which is a type of igneous rock.Less dense compared to oceanic crust.Contains a wide range of rock types, including sedimentary, metamorphic, and igneous rocks.Forms the continents and the shallow shelves extending from the continents under the oceans.Oceanic crust:
Generally thinner, averaging about 5-10 kilometers in depth.Composed mostly of basalt, which is a type of igneous rock.More dense compared to continental crust.Mostly consists of igneous rocks, specifically basaltic lava flows and volcanic rocks.Forms the ocean basins and the deep ocean floor.Learn more about Continental and ocean crust here: https://brainly.com/question/5637320
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If a→=4i^+7j^-5k^ and b→=3i^+4j^+k^, find the direction cosines of a→-b→.
The direction cosines of a→ - b→ are:
l_x = 1 / √46
l_y = 3 / √46
l_z = -6 / √46
What are the directions?The direction cosines of a vector can be found by dividing the components of the vector by its magnitude.
Here's how you can find the direction cosines of the vector a→ - b→:
Step 1: Subtract the vectors a→ and b→ to get a new vector, let's call it c→:
c→ = a→ - b→
In this case, a→ = 4i^ + 7j^ - 5k^ and b→ = 3i^ + 4j^ + k^, so we can subtract them component-wise:
c_x = 4 - 3 = 1
c_y = 7 - 4 = 3
c_z = -5 - 1 = -6
So, c→ = 1i^ + 3j^ - 6k^.
Step 2: Find the magnitude of vector c→ using the formula:
|c→| = √(c_x^2 + c_y^2 + c_z^2)
Substituting the values we found earlier:
|c→| = √(1^2 + 3^2 + (-6)^2)
|c→| = √(1 + 9 + 36)
|c→| = √46
Step 3: Divide the components of vector c→ by its magnitude to find the direction cosines:
l_x = c_x / |c→|
l_y = c_y / |c→|
l_z = c_z / |c→|
Substituting the values we found earlier:
l_x = 1 / √46
l_y = 3 / √46
l_z = -6 / √46
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the direction cosines of the vector a→ - b→ are (0.155, 0.466, -0.932).
How do we calculate?we first calculate the vector a→ - b→:
a→ - b→ = (4i^ + 7j^ - 5k^) - (3i^ + 4j^ + k^)
= (4-3)i^ + (7-4)j^ + (-5-1)k^
= i^ + 3j^ - 6k^
Next, we find the magnitude of the vector a→ - b→:
|a→ - b→| = √(1^2 + 3^2 + (-6)^2) = √46
We then find the direction cosines of the vector a→ - b→:
cos α = (1/√46) = 0.155
cos β = (3/√46) = 0.466
cos γ = (-6/√46) = -0.932
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If enough experimental data supports a hypothesis, then it:
A. Is accepted as true until proven false.
B. Becomes an Observational Law
C. Is proven 100% true.
D. Is falsified.
If enough experimental data supports a hypothesis, it is considered a well-supported scientific theory, but it is not considered to be 100% true or proven. Scientific theories are always open to further investigation and revision based on new evidence. Therefore, option C ("Is proven 100% true") is incorrect.
Option A ("Is accepted as true until proven false") is also incorrect because scientists do not accept a hypothesis as true until it has been rigorously tested and supported by a large body of evidence. Even then, scientists recognize that any scientific theory is subject to revision or falsification if new data or evidence emerges that contradicts it.
Option B ("Becomes an Observational Law") is also incorrect because scientific laws are typically descriptive, rather than explanatory. They describe what happens in a given set of circumstances, but they do not explain why it happens. Hypotheses and theories, on the other hand, attempt to explain why certain phenomena occur, and they are supported by experimental evidence.
Therefore, none of the options are completely accurate, but the most appropriate answer is that the hypothesis becomes a well-supported scientific theory.
During the earliest stages of the universe, the only things that existed were
During the earliest stages of the universe, the only things that existed were subatomic particles such as protons, neutrons, and electrons. These particles came together to form the first atoms, which were primarily hydrogen and helium.
The universe was also filled with a hot, dense plasma of particles and radiation, known as the cosmic microwave background radiation.
Hence, as the universe expanded and cooled, these atoms and radiation would play a key role in the formation of galaxies, stars, and the larger structures we see today.
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(c) At what angle of incidence will the light reflected from water (u= 1.3) be completely polarized?
Answer:
When unpolarized light is reflected off a non-metallic surface at a specific angle of incidence, the reflected light becomes polarized. This angle of incidence is known as Brewster's angle and can be calculated using the formula:
tan θp = n
where θp is Brewster's angle and n is the refractive index of the medium the light is passing into.
In this case, the light is passing from air (which has a refractive index of approximately 1) into water with a refractive index of 1.3. Therefore, we can plug in the values into the formula and solve for θp:
tan θp = 1.3
θp = tan^-1(1.3)
Using a calculator, we get θp = approximately 53.1 degrees.
Therefore, light reflected from water will be completely polarized at an angle of incidence of approximately 53.1 degrees.
Determine the resultant x and y components, when one vector is equal to 26.5 and the other 44 with angles of 56 and 28 degrees
The resultant x and y components are 53.23 and 41.51, respectively.
What are the components?
To determine the resultant x and y components of the vectors, we can use the following equations:
Rx = ΣFx = F1x + F2x + ...
Ry = ΣFy = F1y + F2y + ...
where F1x, F2x, ... are the x components of the vectors, F1y, F2y, ... are the y components of the vectors, and ΣFx and ΣFy are the total x and y components of the resultant vector, R.
First, we need to find the x and y components of each vector:
Vector 1: magnitude = 26.5, angle = 56°
F1x = 26.5cos(56) = 14.28
F1y = 26.5sin(56) = 21.44
Vector 2: magnitude = 44, angle = 28°
F2x = 44cos(28) = 38.95
F2y = 44sin(28) = 20.07
Now we can add the x and y components of the vectors to find the total x and y components of the resultant vector:
ΣFx = F1x + F2x = 14.28 + 38.95 = 53.23
ΣFy = F1y + F2y = 21.44 + 20.07 = 41.51
Therefore, the resultant x and y components are 53.23 and 41.51, respectively.
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A person fires a gun close to a wall (40m). An echo is heard 0.24 after the original shot. Based on this information only, find the speed of sound in air?
The speed of sound in air can be calculated using the following formula:speed of sound = distance / timeIn this case, we know that the distance between the person and the wall is 40 meters, and the time it takes for the echo to be heard after the original shot is 0.24 seconds. However, we need to account for the fact that sound travels to the wall and back, so the total distance the sound wave covers is twice the distance to the wall, or 2 x 40 = 80 meters.Thus, using the formula above, we can calculate the speed of sound:speed of sound = distance / time = 80 m / 0.24 s ≈ 333.33 m/sTherefore, the speed of sound in air is approximately 333.33 meters per second.