The critical angle is the smallest incident angle at which light is no longer refracted into water, but instead is totally internally reflected. This can be calculated using Snell's law, where the sine of the critical angle is the ratio of the indices of refraction for water and glass.
Explanation:The smallest value of the incident angle θa for which none of the ray refracts into water, and instead exhibits total internal reflection, is known as the critical angle. To find this critical angle, we can apply Snell's law (n1 × sin(θa) = n2 × sin(θb)), where θa is the incident angle and θb is the refracted angle when θb is 90°, the angle of refraction is at the maximum and therefore indicates the critical angle condition. Using the indices of refraction for glass (n1) and water (n2), we can solve for the critical angle which will indicate the threshold above which light will not refract into water but instead be totally internally reflected.
A man drags a 12.0 kg bag of mulch at a constant speed applying a 39.5 N force at 41°. What is the normal force acting on the bag?
At the moment the acceleration of the blue ball is 9.40 m/s2, what is the ratio of the magnitudes of the force of air resistance to the force of gravity acting on the blue ball? use 9.81 m/s2 for the standard value of g at the location of the experiment.
The ratio of the magnitudes of the force of air resistance to the force of gravity acting on the ball is approximately 1:24.
The student is asking about the ratio of the force of air resistance to the force of gravity acting on a blue ball, when the ball has an acceleration of 9.40 m/s2. To calculate this ratio, we can use Newton's second law, F = ma, where F is the force, m is the mass of the ball, and a is the acceleration of the ball due to the net force acting on it. If we denote the force of air resistance as Fair and the force of gravity as Fgrav, we can write Fnet = Fgrav - Fair, since the air resistance works in the opposite direction of gravity.
Given that the acceleration due to gravity is approximately 9.81 m/s2, the force due to gravity (weight) can be expressed as Fgrav = mg. Here, the acceleration is less than g due to air resistance, thus we can write Fnet = ma = mg - Fair. Since the acceleration of the ball is given as 9.40 m/s2, we can now express Fair as mg - ma. Taking the ratio of Fair to mg (the weight), we get:
(mg - ma) / mg = (g - a) / g = (9.81 - 9.40) / 9.81.
Therefore, the ratio of the magnitudes of the force of air resistance to the force of gravity is equal to 0.0418, which simplifies to approximately 1:24.
When populations of two species work together to obtain resources, they are
Answer:
cooperating.
Explanation:
:)
Which labels correctly identify the layers most closely associated with gamma rays and visible light? Z: Gamma rays X: Visible light X: Gamma rays Z: Visible light Z: Gamma rays Y: Visible light Y: Gamma rays Z: Visible light
Answer:
A on edge
Explanation:
Five metal samples, with equal masses, are heated to 200oC. Each solid is dropped into a beaker containing 200 ml 15oC water. Which metal will cool the fastest?
A) aluminum
B) copper
C) gold
D) platinum
Answer:
aluminum...
Explanation:
A grindstone, initially at rest, is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s. what is its angular acceleration?
The angular acceleration of a grindstone that makes 20 revolutions in 8 seconds from rest, convert the revolutions to radians and use the rotational kinematic equation, resulting in an angular acceleration of approximately 3.93 radians/s².
The angular acceleration of a grindstone that makes 20 revolutions in 8 seconds, starting from rest.
To find the angular acceleration, we can use the kinematic equation for rotational motion:
θ = ω₀t + 1/2αt²
where:
θ is the angular displacement in radians,
ω₀ is the initial angular velocity (which is 0 because it starts from rest),
t is the time in seconds,
and α is the angular acceleration in radians per second squared.
First, we convert the revolutions to radians:
20 revolutions * 2π radians/revolution = 40π radians
We then have:
40π radians = 0 + 1/2α(8²)
Solving for α gives:
α = (40π radians) / (1/2 * 64 s²)
α = 80π / 64 radians/s²
α ≈ 3.93 radians/s²
Therefore, the angular acceleration of the grindstone is approximately 3.93 radians/s².
Two tuning forks of frequency 480 hz and 484 hz are struck simultaneously. what is the beat frequency resulting from the two sound waves?
Does someone have this??
A child goes down a playground slide with an acceleration of 1.12 m/s2 .find the coefficient of kinetic friction between the child and the slide if the slide is inclined at an angle of 27.0 ∘ below the horizontal.
The coefficient of kinetic friction is obtained by considering the forces acting on the child as they slide. These are the force of gravity (mg sin θ) and the force of kinetic friction (μk mg cos θ). Setting these forces equal gives us an equation that can be solved to find the coefficient of kinetic friction, μk.
Explanation:To figure out the coefficient of kinetic friction, we need to consider the forces acting on the child as they slide down the playground. There are two key forces to consider, the force caused by gravity which is pulling the child down the slide, and the force of kinetic friction which is trying to slow the child down.
The force of gravity working to pull the child down the slide, or the component of the weight down the slope is given as mg sin θ. Here m is the mass of the child, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the slide. The force of kinetic friction, which opposes the motion, is expressed as μk mg cos θ, where μk is the coefficient of kinetic friction we're trying to find.
Since the child is sliding down the slide with an acceleration of 1.12 m/s², the force due to gravity exceeds the force of friction. Setting up the equation μk mg cos θ = mg sin θ - ma, where a is the acceleration of 1.12 m/s², and solving for μk gives us the coefficient of kinetic friction between the child and the slide.
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what is air resistance?
Air resistance is the pushing of air against an object that is moving. Both the air and the object rub together and this slows the down the object and making it use more energy to reach a required speed. If an object moves faster, the greater the air resistance it encounters.
After harvesting their main crops, such as corn and wheat, many farmers plant a second crop called a cover crop. This cover crop grows during the fall and winter and is then plowed over in the spring. What is the main purpose of a cover crop?
A.
to get rid of excess seed rather than storing during the winter
B.
to provide food and shelter for birds and animals during the winter
C.
to prevent water runoff into other parts of the farmers' field
D.
to prevent erosion of the topsoil by wind and water
Answer:
Option (D)
Explanation:
A cover crop is usually defined as a special type of crop that is cultivated in order to increase the productivity of the soil, rather than focusing on the productivity of the crop. These are very commonly used and it helps in the decreasing amount of weeds, controlling pests and diseases, increasing the fertility of the soil, reduction of soil erosion. It also enhances the biodiversity.
Thus, the main purpose of the cover crop is to prevent the erosion of the topsoil by the agents such as water and wind.
Hence, the correct answer is option (D).
A person drives to the top of a mountain. On the way up, the person’s ears fail to “pop,” or equalize the pressure of the inner ear with the outside atmosphere. The pressure of the atmosphere drops from 1.010 x 10^5 Pa at the bottom of the mountain to 0.998 x 10^5 Pa at the top. Each eardrum has a radius of 0.40 cm. What is the pressure difference between the inner and outer ear at the top of the mountain?
a.
1.2 x 10^3 Pa
b.
1.1 x 10^5 Pa
c.
1.0 x 10^2 Pa
d.
1.2 x 10^2 Pa
The pressure difference between the inner and outer ear at the top of the mountain is given by option a. 1.2 × 10³ Pa.
The pressure difference between the inner and outer ear at the top of the mountain can be calculated by evaluating the difference between atmospheric pressure at top and bottom of the lift. Let this difference be denoted as ΔP, then:
Δ P = P₁ - P₂
P₁ = pressure at the top of the lift = 1.010 × 10⁵ Pa
P₂ = pressure at the bottom of the lift = 0.998 × 10⁵ Pa
or, Δ P = (1.010 × 10⁵ Pa - 0.998 × 10⁵ Pa)
or, Δ P = 0.012 × 10⁵ Pa
or, Δ P = 1.2 × 10³ Pa
If electrons of energy 12.8 ev are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?
When 12.8 eV energy electrons excite hydrogen atoms, the atoms are elevated to an energy level just below ionization. To determine the specific energy state, the energy formula for hydrogen atoms is used, then the energies of emitted photons are found by calculating the energy difference between the excited and final states.
Explanation:If electrons with an energy of 12.8 eV are incident on hydrogen atoms in their ground state, we first need to determine the energy level to which the hydrogen atoms are excited. The ground state energy of hydrogen is -13.6 eV. If 12.8 eV is provided, the electron reaches an energy level just below 0 eV (ionization energy), since 12.8 eV is not sufficient to completely ionize the atom (13.6 eV needed).
To find out which energy level the electron will jump to, we use the formula for the total energy of an electron in a hydrogen atom, En = (- 13.6 eV/n²), and solve for n.
Once the electron is excited, it will eventually drop back to a lower energy state, emitting a photon in the process.
The energy of the emitted photon can be calculated using the difference in energy levels, ΔE = E1 - Ef.
You are at home in your air conditioned garage. You are planning a family road trip from New York to Florida. You are lnfating the tires of your suv. You fill each car-tire with about 10 Liters of air. The temperature inside your air conditioned garage is about 10 degrees Celsius. Your family packs the car, and you begin your trip to Florida. The temperature in New York is about 21 degrees Celsius, and the happen temperature in Florida is 32 degrees Celsius. Assuming the pressure stays constant from the garage all the way to Florida, what could to your car tires during your road trip.
Write a paragraph that makes a claim about what happen to the car tires
To determine an epicentral distance scientists consider the arrival times of what wave types
A force of 35 n acts on an object which has a mass of 5.4 kg. what acceleration (in m/s2) is produced by the force
"a metal sphere of radius 5.00 cm is initially uncharged. how many electrons would have to be placed on the sphere to produce an electric field of magnitude 1.53 ✕ 105 n/c at a point 8.64 cm from the center of the sphere?"
A water bed weighs 1025 N, and is 1.5 m wide by 2.5 m long. How much pressure does the water bed exert if the entire lower surface of the bed makes contact with the floor?
a.
3.6 x 10^2 Pa
b.
2.7 x 10^4 Pa
c.
1.2 x 10^3 Pa
d.
2.7 x 10^2 Pa
a 13 kg sled is moving at a speed of 3.0 m/s. at which of the following speeds will the sled have tace as mucb as the kinetic
You are asked to design a horizontal curve with a 40-degree central angle (' = 40) for a two-lane road with 11-ft lanes. the design speed is 70 mi/h and superelevation is limited to 0.06 f
a. True
b. Falset. give the radius, degree of curvature, and length of curve that you would recommend. 3.43 for the h
To design a horizontal curve for a two-lane road, you can calculate the radius, degree of curvature, and length of the curve using formulas.
Explanation:To design a horizontal curve, we need to calculate the radius, degree of curvature, and length of the curve. First, we can calculate the radius using the formula: R = (V2) / (15 * f), where R is the radius in feet, V is the design speed in miles per hour, and f is the superelevation. Plugging in the values, we get: R = (702) / (15 * 0.06) = 43,333.33 feet. The degree of curvature can be calculated using the formula: (180 * L) / (π * R), where L is the length of the curve in feet. Since the central angle is given as 40 degrees, the degree of curvature is also 40 degrees. Finally, we can calculate the length of the curve using the formula: L = (π * R * d) / 180, where d is the degree of curvature. Plugging in the values, we get: L = (π * 43,333.33 * 40) / 180 = 9,632.87 feet.
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A sinusoidal wave travels with speed 250 m/s . its wavelength is 3.5 m . part a what is its frequency
A ball is thrown at an angle of 45° to the ground. if the ball lands 87 m away, what was the initial speed of the ball? (round your answer to the nearest whole number. use g â 9.8 m/s2.)
A charge of 50 µC is pushed by a force of 25 µN a distance of 15 m in an electric field. What is the electric potential difference? Recall that Fe = qE.
The electric potential difference is 7.5 V.
Electric potential difference between two points is defined as the work done in moving unit positive charge between the two points. Electric potential difference can also be defined as the work done W per unit charge q in an electric field.
[tex]\Delta V=\frac{W}{q}[/tex]......(1)
Work done by a force is the product of the force F and the displacement s made in the direction of the force. Assuming that the displacement is parallel to the line of action of the force,
[tex]W=F.s[/tex]......(2)
Rewrite equation (1) using equation (2).
[tex]\Delta V=\frac{Fs}{q}[/tex]......(3)
Substitute the given values of force, displacement and charge in the equation (3).
[tex]\Delta V=\frac{Fs}{q}\\ =\frac{(25*10^-^6N)(15m)}{(50*10^-^6C)} \\ =7.5V[/tex]
The potential difference between the two points is 7.5 V
A proton moves perpendicularly to a uniform magnetic field b with a speed of 3.7 × 107 m/s and experiences an acceleration of 5 × 1013 m/s 2 in the positive x direction when its velocity is in the positive z direction. the mass of a proton is 1.673 × 10−27 kg. find the magnitude of the field. answer in units of t.
What potential difference is needed to accelerate a he+ ion (charge +e, mass 4u) from rest to a speed of 1.0×106 m/s ? express your answer using two significant figures?
The potential difference required to accelerate the helium ion to a speed of [tex]1.0 \times {10^6}\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}[/tex] is [tex]\boxed{21\,{\text{kV}}}[/tex] or [tex]\boxed{20875\,{\text{V}}}[/tex].
Further Explanation:
The potential difference, through which the helium ion passes, provides the potential energy and this potential energy provided by the potential difference to the Helium ion leads to the increase in the kinetic energy of the ion.
The charge on the [tex]H{e^ + }[/tex] ion is equal to the charge of one electron and the mass of the helium atom is equal to the mass of [tex]4\,{\text{amu}}[/tex].
The expression for the conservation of the energy of the Helium ion in the potential difference is:
[tex]\Delta PE = \Delta KE[/tex]
Substitute [tex]q\Delta V[/tex] for [tex]\Delta PE[/tex] and [tex]\dfrac{1}{2}m{v^2}[/tex] for [tex]\Delta KE[/tex] in above expression.
[tex]\begin{aligned}q\Delta V &= \frac{1}{2}m{v^2} \hfill \\\Delta V &= \frac{{m{v^2}}}{{2q}} \hfill \\\end{aligned}[/tex]
Here, [tex]\Delta V[/tex] is the potential difference, [tex]m[/tex] is the mass of the ion, [tex]q[/tex] is the charge over the ion.
Substitute [tex]1.6 \times {10^{ - 19}}\,{\text{C}}[/tex] for [tex]q[/tex], [tex]\left( {4 \times 1.67 \times {{10}^{ - 27}}\,{\text{kg}}} \right)[/tex] for [tex]m[/tex] and [tex]1.0 \times {10^6}\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}[/tex] for [tex]v[/tex] in above expression.
[tex]\begin{aligned}\Delta V &= \frac{{\left( {4 \times 1.67 \times {{10}^{ - 27}}\,{\text{kg}}} \right){{\left( {1.0 \times {{10}^6}\,{{\text{m}} \mathord{\left/{\vphantom {{\text{m}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}} \right)}^2}}}{{2\left( {1.6 \times {{10}^{ - 19}}\,{\text{C}}} \right)}} \\&= \frac{{6.68 \times {{10}^{ - 15}}}}{{3.2 \times {{10}^{ - 19}}}}\,{\text{V}} \\&= 2{\text{0875}}\,{\text{V}} \\&\approx {\text{21}}\,{\text{kV}}\\\end{aligned}[/tex]
Thus, the potential difference required to accelerate the helium ion to a speed of [tex]1.0 \times {10^6}\,{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right.\kern-\nulldelimiterspace} {\text{s}}}[/tex] is [tex]\boxed{21\,{\text{kV}}}[/tex] or [tex]\boxed{20875\,{\text{V}}}[/tex].
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Grade: College
Chapter: Electrostatics
Subject: Physics
Keywords: Potential energy, potential difference, accelerate, kinetic energy, speed, helium ion, charge, significant figures, rest to a speed.
A heat engine takes in 840 kJ per cycle from a heat reservoir. Which is not a possible value of the engine's heat output per cycle?
for a bohr model,how many protons,electrons,and neutron does Sodium has
What is the energy of the spring-mass system when the mass first passes through the equilibrium position? (you may wish to include a logical test to help you find when this occurs)?
A rock is thrown vertically upward from ground level at time t = 0. at t = t, it passes the top of the tower and ât later (i.e., when t = t + ât) it reaches the maximum height. what is the height of the tower? leave g as g â do not substitute with numbers
"The height of the tower is given by the equation:
[tex]\[ h = \frac{1}{2} g (t + \hat{t})^2 - \frac{1}{2} g t^2 \][/tex]
This equation represents the difference in height between the maximum height the rock reaches and the height it reaches at time \( t \) when it passes the top of the tower. Here, \( g \) is the acceleration due to gravity, \( t \) is the time it takes for the rock to reach the top of the tower, and \( \hat{t} \) is the additional time it takes for the rock to reach the maximum height after passing the top of the tower.
To find the height of the tower, we can simplify the equation:
[tex]\[ h = \frac{1}{2} g ((t + \hat{t})^2 - t^2) \][/tex]
[tex]\[ h = \frac{1}{2} g (t^2 + 2t\hat{t} + \hat{t}^2 - t^2) \][/tex]
[tex]\[ h = \frac{1}{2} g (2t\hat{t} + \hat{t}^2) \][/tex]
[tex]\[ h = g t\hat{t} + \frac{1}{2} g \hat{t}^2 \][/tex]
Since [tex]\[ u = g \hat{t} \][/tex]is the time it takes for the rock to reach the maximum height from the top of the tower, and at the maximum height the velocity of the rock is zero, we can use the kinematic equation for the final velocity \( v \) at the maximum height:
[tex]\[ v = u + g t \][/tex]
Here, \( u \) is the initial velocity (which is the velocity of the rock at the top of the tower), \( g \) is the acceleration due to gravity, and \( t \) is the time taken to reach the maximum height, which is \( \hat{t} \). At the maximum height, \( v = 0 \), so:
[tex]\[ 0 = u - g \hat{t} \][/tex]
[tex]\[ u = g \hat{t} \][/tex]
Now, we can substitute \( u \) back into the height equation:
[tex]\[ h = g t\hat{t} + \frac{1}{2} g \hat{t}^2 \][/tex]
[tex]\[ h = g t\left(\frac{u}{g}\right) + \frac{1}{2} g \left(\frac{u}{g}\right)^2 \][/tex]
[tex]\[ h = u t + \frac{1}{2} \frac{u^2}{g} \][/tex]
Since \( u t \) represents the distance the rock would have traveled in time \( t \) if it continued at a constant velocity \( u \), and \( \frac{1}{2} \frac{u^2}{g} \) represents the total height the rock would reach if it continued to move upward with initial velocity \( u \) and was only acted upon by gravity, the term \( u t \) is actually the height of the tower. Thus, the height of the tower is:
[tex]\[ h = u t \][/tex]
This is the final answer, and it shows that the height of the tower is the product of the initial velocity of the rock at the top of the tower and the time it takes to reach the top of the tower. The term[tex]\( \frac{1}{2} \frac{u^2}{g} \)[/tex]is not needed for the height of the tower, as it represents the additional height the rock reaches after passing the top of the tower until it reaches the maximum height."
What is a property of a transparent object?