Therefore, the volume of the prism is 1,934,960 cubic inches.
The prism is completely filled with 1120 cubes that have edge lengths of 12 in. Therefore, the volume of each cube can be calculated as follows:
V = (Edge length)³= (12 in)³= 1728 cubic inches.
The total volume of all the cubes in the prism is the volume of the prism itself.
Thus, the volume of the prism can be calculated by multiplying the number of cubes by the volume of one cube, which is given as follows:
Volume of prism = Number of cubes × Volume of one cube
volume of prism = 1120 × 1728 cubic inches= 1,934,960 cubic inches.
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Following data are given for a direct shear test conducted on dry sand:
• Specimen dimensions: 63 mm X 63 mm X 25 mm (height)
• Normal stress: 105 kN/m2
• Shear force at failure: 300 N
a. Determine the angle of friction, Ø’
b. For a normal stress of 180 kN/m2 , what shear force is required to cause failure?
c. What are the principal stresses at failure for the condition given in (b)?
d. Locate the pole on this Mohr’s circle and find the angle of inclination of the major and minor principal plane with the horizontal?
The correct answer is Option a. The angle of friction, Ø', can be determined using the formula:
Ø' = tan^(-1)(τ'/σn)
where Ø' is the angle of friction, τ' is the shear stress, and σn is the normal stress. In this case, the shear stress can be calculated by dividing the shear force at failure (300 N) by the area of the specimen. The area is the product of the specimen's height (25 mm) and its average perimeter [(2 * 63 mm) + (2 * 25 mm)].
Ø' = tan^(-1)(300 N / (25 mm * [(2 * 63 mm) + (2 * 25 mm)]) / 105 kN/m^2
Simplifying the equation:
Ø' = tan^(-1)(0.0256) ≈ 1.47°
b. To determine the shear force required to cause failure for a normal stress of 180 kN/m^2, we can use the formula:
τ' = Ø' * σn
Given Ø' = 1.47° and σn = 180 kN/m^2:
τ' = 1.47° * 180 kN/m^2 = 2.646 kN/m^2
c. The principal stresses at failure can be calculated using the equation:
σ1 = σn + τ'
σ3 = σn - τ'
Given σn = 180 kN/m^2 and τ' = 2.646 kN/m^2:
σ1 = 180 kN/m^2 + 2.646 kN/m^2 = 182.646 kN/m^2
σ3 = 180 kN/m^2 - 2.646 kN/m^2 = 177.354 kN/m^2
d. The pole on the Mohr's circle represents the average normal stress (σn) and is located at (σn, 0). Since σn = 180 kN/m^2, the pole would be located at (180 kN/m^2, 0).
To find the angle of inclination of the major and minor principal plane with the horizontal, we can use the equation:
θ = (1/2) * tan^(-1)((2 * τ') / (σ1 - σ3))
Given τ' = 2.646 kN/m^2, σ1 = 182.646 kN/m^2, and σ3 = 177.354 kN/m^2:
θ = (1/2) * tan^(-1)((2 * 2.646 kN/m^2) / (182.646 kN/m^2 - 177.354 kN/m^2))
Simplifying the equation:
θ ≈ 1.05°
Therefore, the angle of inclination of the major and minor principal plane with the horizontal is approximately 1.05°.
In conclusion, the angle of friction (Ø') is approximately 1.47°. For a normal stress of 180 kN/m^2, the shear force required to cause failure is approximately 2.646 kN/m^2. The principal stresses at failure for this condition are σ1 = 182.646 kN/m^2 and σ3 = 177.354 kN/m^2. The pole on the Mohr's circle is located at (180 kN/m^2, 0), and the angle of inclination of the major and minor principal plane with the horizontal is approximately 1.05°.
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2) What are the two main types of waves?
Answer:
The two types of waves are longitudinal and transverse
Explanation:
hope it helped! and i hope its correct
Here is a list of ways of producing electricity
A ) Wind farms
B ) Coal fired power stations
C ) hydroelectric power stations
D ) nuclear power stations
E ) gas fired power stations
F ) tidal power stations
G) using geothermal energy
(1) State which of these produces clean electricity
(2) State which of these uses fossils fuel
(3) state which of these uses a renewable energy resources
Please help me
Please do not answer from links
Urgent !!!!!!
Will give the brainliest!
* please answer correctly
Answer:
1) A,B,F,G
2)B,D,E
3) A,C,F,G
Explanation:
what is the approximate tangential speed of an object orbiting earth with a radius of 1.8 × 108 m and a period of 2.2 × 104 s?
a.7.7 × 10–4 m/s
b.5.1 × 104 m/s
c.7.7 × 104 m/s
d.5.1 × 105 m/s
The approximate tangential speed of an object orbiting the Earth with a radius of 1.8 × 10^8 m and a period of 2.2 × 10^4 s is c. 7.7 × 10^4 m/s.
Orbital speed (v) is the velocity an object needs to remain in an orbit around another body.
The formula for orbital speed is:
v = 2πr / T,
where v is orbital speed, r is the radius of the orbit, and T is the period of the orbit.
In this case, the radius is given as 1.8 × 10^8 m, and the period is
2.2 × 10^4
s.π ≈ 3.14v
= (2πr) / T
= (2 × 3.14 × 1.8 × 10^8) / (2.2 × 10^4)
= (6.28 × 1.8 × 10^8) / (2.2 × 10^4)
= 51,430.91 m/s
≈ 7.7 × 10^4 m/s.
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Now assume that the oil had a thickness of 200 \rm nm and an index of refraction of 1.5. A diver swimming underneath the oil slick is looking at the same spot as the scientist with the spectromenter. What is the longest wavelength lambda_water of the light in water that is transmitted most easily to the diver?
Therefore, the longest wavelength λ_water of the light in water that is transmitted most easily to the diver is c / (1.5f).The answer cannot be found as the frequency f is not given in the problem.
Given, Thickness of the oil slick, t = 200 nm Index of refraction of oil,
n = 1.5Speed of light in vacuum, c = 3 x 10^8 m/s.
We can determine the longest wavelength λ_water of the light in water that is transmitted most easily to the diver using the relation below:
λ_wavelength = λ_0 / (n + sin(θ))
Where λ_0 is the vacuum wavelength, n is the refractive index of oil, and θ is the angle of incidence. Let's assume that the angle of incidence,
θ = 0, since the light is coming directly from the water surface to the oil slick.
The refractive index of water, n_ w = 1.33.
We can rewrite the equation as follows:
λ_wavelength = λ_0 / (n + sin(θ))
λ_wavelength = λ_0 / (1.5 + sin(0))
λ_wavelength = λ_0 / 1.5
λ_wavelength = (c / f) / 1.5 where f is the frequency of the wave.
Substituting the given values, we get;
λ_wavelength = (3 x 10^8 m/s / f) / 1.5
Since the wave travels at the same frequency in both the oil and water, we can equate the velocity in oil with that in water to find the vacuum wavelength:
1.5 * c / f = v_ water / f
where v_ water is the velocity of light in water.
So,
λ_wavelength = c / (1.5 * f)
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a radio-controlled model airplane has a momentum given by [(−0.75kg⋅m/s3)t2 (3.0kg⋅m/s)]i^ (0.25kg⋅m/s2)tj^, where t is in seconds. What is the x -component of the net force on the airplane?
Express your answer in terms of the given quantities.
The x-component of the net-force acting on the radio-controlled model airplane is given by the expression -1.5 kg·m/s^2 * t.
The x-component of the net force (F_x) on an object can be calculated using Newton's second law, which states that the net force is equal to the rate of change of momentum:
F_x = dp_x/dt
Given that the momentum of the airplane is [(−0.75kg·m/s^3)t^2 (3.0kg·m/s)]i^, we can find the x-component of the momentum (p_x) as the coefficient of the i^ unit vector. Taking the derivative of p_x with respect to time (t), we obtain the x-component of the net force:
F_x = d/dt [(−0.75kg·m/s^3)t^2] = (-0.75kg·m/s^3) * 2t
Simplifying the expression, we find:
F_x = -1.5 kg·m/s^2 * t
Therefore, the x-component of the net force on the airplane is -1.5 kg·m/s^2 * t.
The x-component of the net force acting on the radio-controlled model airplane is given by the expression -1.5 kg·m/s^2 * t, where t is the time in seconds. This equation represents the rate of change of the x-component of the momentum with respect to time.
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for another identical object initially at rest no frictional force is exerted during segment 2
The relative speeds of the two objects at the bottom of the incline will be zero.
In segment 1, the object is released from rest at the top of an inclined plane. As it rolls down the incline, the potential energy is converted into both kinetic energy and rotational energy.
Assuming no slipping occurs, the object's linear velocity increases while its angular velocity remains constant.
During segment 2, where no frictional force is exerted, there are no external forces acting on the object. As a result, there is no change in the object's kinetic energy or angular velocity. Therefore, the object's linear velocity remains constant.
At the bottom of the incline, both objects will have the same linear velocity. Since they are identical objects, the relative speed between them will be zero.
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--The complete Question is, For another identical object initially at rest, no frictional force is exerted during segment 2. If the first object is released from rest at the top of an inclined plane in segment 1, and both objects roll down the incline, what will be the relative speeds of the two objects at the bottom of the incline?--
Question
If you are tracking the energy in a system, but the total energy seems to be going down, where has the energy gone ?
how long would it take a leopard, running at an average speed of 20 m/s to travel 500 m?
Answer:
25 seconds
Explanation:
500/20
a block of mass 3kg slides along a horizontal surface that has neglitjble friction except dor one section what is the magntiude of acerage frictional force exerted on the block by rough section of surface
6. Let u(x, y) = xy. (a) Show that u is harmonic. (b) Find a harmonic conjugate of u.
a. u is harmonic for let u(x, y) = xy because ∂²u/∂x² + ∂²u/∂y² = 0.
b. A harmonic conjugate of u is v = (x² - y²)/2.
To determine that u is harmonic, we need to verify whether u satisfies Laplace's equation or not. Laplace's equation is given by:
∂²u/∂x² + ∂²u/∂y² = 0
On differentiating u(x, y) = xy partially, we get,
∂u/∂x = y∂u/∂y = x
On differentiating partially again, we get,
∂²u/∂x² = 0∂²u/∂y² = 0
Therefore, ∂²u/∂x² + ∂²u/∂y² = 0
Thus, u is harmonic.
To find a harmonic conjugate of u, we need to find v(x, y) such that u + iv is analytic. In other words, v must satisfy the Cauchy-Riemann equations. The Cauchy-Riemann equations are given by:
∂u/∂x = ∂v/∂y∂u/∂y = -∂v/∂x
On substituting u = xy in the above equations, we get,
∂v/∂y = x∂v/∂x = -y
On integrating the above equations, we get
v = (x² - y²)/2 + C
Thus, a harmonic conjugate of u is v = (x² - y²)/2.
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An oil drop whose mass is 2.9×10^−15 kg is held at rest between two large plates separated by 1.2 cm (Figure 1) when the potential difference between the plates is 360 V . Part A How many excess electrons does this drop have? Express your answer as an integer.
The oil drop has an excess of 4 electrons when the potential difference between the plates is 360 V.
The excess charge on the oil drop can be determined by equating the electric force on the oil drop with the gravitational force acting on it. The electric force is given by Coulomb's law:
Felectric = qE,
where Felectric is the electric force, q is the charge, and E is the electric field.
The gravitational force on the oil drop is given by:
Fgravity = mg,
where Fgravity is the gravitational force, m is the mass of the oil drop, and g is the acceleration due to gravity.
Since the oil drop is at rest, the net force on it is zero:
Felectric - Fgravity = 0.
Substituting the expressions for the electric and gravitational forces:
qE - mg = 0.
Solving for the charge q:
q = mg/E.
We are given that the mass of the oil drop is 2.9 × 10^(-15) kg, the potential difference between the plates is 360 V, and the electric field E is related to the potential difference by E = V/d, where d is the separation between the plates (1.2 cm = 0.012 m).
Substituting the values:
q = (2.9 × 10^(-15) kg × 9.8 m/s^2) / (360 V / 0.012 m).
q ≈ 6.4 × 10^(-19) C.
Since the charge of a single electron is approximately 1.6 × 10^(-19) C, we can calculate the number of excess electrons:
Number of excess electrons = q / (1.6 × 10^(-19) C).
Substituting the value of q:
Number of excess electrons ≈ (6.4 × 10^(-19) C) / (1.6 × 10^(-19) C).
Number of excess electrons ≈ 4.
The oil drop has an excess of 4 electrons.
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are positively charged ions form when atoms lose electrons
Answer: Atoms that lose electrons acquire a positive charge as a result because they are left with fewer negatively charged electrons to balance the positive charges of the protons in the nucleus. Positively charged ions are called cations. Most metals become cations when they make ionic compounds.
Explanation: hope this helps
When the image of an object is seen in a plane mirror, the distance from the mirror to the image depends on?
A. The Wavelength of light used for viewing
B. The distance from the object to the mirror
C. The distance of both the observer and the object to the mirror.
When the image of an object is seen in a plane mirror, the distance from the mirror to the image depends on the distance from the object to the mirror.
It is because a Plane Mirror is the incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of incidence is equal to the angle of reflection. So, the distance from the object to the mirror equals the distance from the image to the mirror. Thus whoever the person viewing this image must sight at this image location.
A skier traveling downhill has this type of energy
Answer:
potential energy
Explanation:
The purple arrow on the graph shows speed and direction.
What is this arrow called?
A. an acceleration arrow
B. a vector
C. a force arrow
D. a speed arrow
The purple arrow on the graph that shows speed and direction, this arrow called B. a vector.
Vectors have magnitude (size) and direction. They are represented graphically as arrows, in which the direction of the arrow denotes the direction of the vector, while the length of the arrow represents the vector's magnitude (size). Furthermore, the term "vector" is used in physics to refer to a quantity that has both magnitude and direction, such as velocity, force, and acceleration.
They are essential in physics since they enable scientists to precisely describe how objects move and interact. Moreover, vector quantities, such as velocity and force, are often depicted with arrows in physics diagrams, with the direction of the arrow representing the vector's direction and the arrow's length representing its magnitude. The use of vectors in physics and other fields has made a significant contribution to the advancement of science and technology. So therefore the correct answer is B. a vector, the purple arrow on the graph that shows speed and direction.
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What must the charge (sign and magnitude) of a particle of mass 1.46 g be for it to remain stationary when placed in a downward-directed electric field of magnitude 630 N/C?
Use 9.81 m/s^2 for the magnitude of the acceleration due to gravity.
The particle remains stationary in a downward-directed electric field, the charge must be negative to balance the gravitational force.
The two forces acting on the particle are the gravitational force and the electric force. The gravitational force is given by F_gravity = m * g, where m is the mass of the particle and g is the acceleration due to gravity (9.81 m/s^2). The electric force is given by F_electric = q * E, where q is the charge of the particle and E is the magnitude of the electric field.
For the particle to remain stationary, the electric force must exactly balance the gravitational force, i.e., F_electric = F_gravity. Therefore, we can equate the two expressions and solve for the charge.m * g = q * E
Given that the mass of the particle is 1.46 g (0.00146 kg) and the magnitude of the electric field is 630 N/C, we can substitute these values into the equation:0.00146 kg * 9.81 m/s^2 = q * 630 N/C
Solving for q, we have:
q = (0.00146 kg * 9.81 m/s^2) / 630 N/C ≈ 2.262 x 10^-5 C.
Therefore, the charge of the particle must be approximately 2.262 x 10^-5 C. Since the particle remains stationary in a downward-directed electric field, the charge must be negative to balance the gravitational force.
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oil (sg = 0.9) with a kinematic viscosity of 0.007 ft2/s, flows in a 3-in diameter pipe at 0.01 ft3/s. determine the head loss per unit length of this flow.
The head loss per unit length of the flow is obtained by the use of the Darcy-Weisbach equation which is expressed as hf = f (L/D) (V^2/2g), where hf is the head loss, f is the friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the mean velocity of flow, and g is the acceleration due to gravity.
Calculate the Reynolds number first which is defined as the ratio of inertial forces to viscous forces and is expressed as Re = ρVD/μ where ρ is the density, V is the velocity, D is the diameter, and μ is the kinematic viscosity of the fluid given.
Re = (ρVD/μ) = (0.9*0.01*3/0.007) = 38.57.
The fluid is characterized by a Reynolds number of less than 2300, thus it is laminar.
Using the Moody diagram, for a laminar flow regime, we have that f = 16/Re = 16/38.57 = 0.4144.
Substituting the values for L, D, V, g, and f, we get
= f (L/D) (V^2/2g)hf = (0.4144) (1) (0.01^2/(2*32.2))hf = 0.00000079 ft/ft.
Let's round the value to 8.0 × 10^-7 ft/ft.
Hence, the head loss per unit length of this flow is 8.0 × 10^-7 ft/ft.
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What is the work done by gravity on a 4 kg ball
a. as it goes from point B to point A?
b. As it goes from point A to C?
(horizontal distance between A and B is 8 m; between B and C is 3.2 m)
Answer:
a. Work done = 313.92 Joules
b. Work done = 439.49 Joules
Explanation:
Work done = Force x distance
Where: Force = mass x gravity
Thus,
Work done = Force x gravity x distance
The earth's acceleration to gravity = 9.81 m/[tex]s^{2}[/tex].
a. The work done as it goes from B to A can be determined as;
work done = 4 x 9.81 x 8
= 313.92 Joules
b. The distance between A and C is the total horizontal distance covered from A to C.
i.e 8 + 3.2 = 11.2 m
The work done as the ball goes from point A to C can be determined as:
work done = 4 x 9.81 x 11.2
= 439.488
work done = 439.49 Joules
What makes water a natural resource?
A.
It is a natural material that can be easily replaced.
B.
It is a material found in nature that people can use.
C.
It is a material that people can easily make and use.
D.
It is a energy source that cannot be replaced.
Answer:
I belive is the answer is B. It is a material found in nature that people can use. Because water is technically a natural resource.
How fast would a 20 kg dog have to run, to reach a momentum of 120 kg x m/s? Include unit in your answer. Worth 40 points!
Answer:
6 m/s
Explanation:
momentum= mass times velocity
120 = 20v
v = 120/20
Answer:
7
Explanation:
7
there is a 3-way switch in the bedroom hallway leading into the living room. show your calculation of how to determine the box size for this switch. the box contains cable clamps.
Therefore, the minimum box size for this switch will be 2.5 cubic inches, while the recommended size is at least 18 cubic inches for a 14-gauge wire. However, the calculated box volume is 13 cubic inches. Hence, the box size required will be greater than 13 cubic inches.
In order to determine the box size for a 3-way switch in the bedroom hallway leading into the living room, the calculation needs to be done. Also, the box contains cable clamps.
So, here is how to determine the box size for this switch:
Calculation:
Firstly, we need to calculate the box volume. For that, we need the formula:
Box volume = Number of wires x 2 + Box fill volume Box fill volume is 2.0 cubic inches for each 14-gauge wire or 2.25 cubic inches for each 12-gauge wire or larger plus clamps for each box.
The box size of switch can be found out as follows:
The minimum box size for a three-way switch is 2.5 cubic inches.
However, the National Electrical Code recommends at least 18 cubic inches for a 14-gauge wire or 20 cubic inches for a 12-gauge wire.
The volume of the cable clamps is also to be included in the calculation. So, let's say the wire gauge used is 14-gauge.
Then,
the box volume = (2 x number of wires) + (2.0 cubic inches for each 14-gauge wire x number of wires) + volume of cable clamps.
Let the number of wires be 3 and the volume of each cable clamp be 0.5 cubic inches.
The calculation will be as follows:
Box volume = (2 x 3) + (2.0 x 3) + (0.5 x 2) = 6 + 6 + 1 = 13 cubic inches.
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What is one way that testing helpes scientists determing which solution for a problem works best?
What is the relationship between large amplitude waves and small amplitude waves?
A Both waves have variable energy.
B Large amplitude waves have more energy than small amplitude waves.
C Large amplitude waves have less matter than small amplitude waves.
D Both waves have constant matter.
Answer:
c.large amplitude waves have less matter than small amplitude waves
15 points!
Five good work habits are:
be trustworthy
let others start
get by
be dependable
be efficient
slow and steady
punctuality
courtesy
Developing good work habits is essential for professional success and personal growth. Here are five commendable work habits:
1. Trustworthiness: Being trustworthy builds strong relationships with colleagues and clients. It involves fulfilling commitments, maintaining confidentiality, and being honest and transparent.
2. Initiating Collaboration: Allowing others to start and actively participating in collaborative efforts fosters teamwork and encourages diverse perspectives. It shows respect for colleagues' expertise and encourages collective problem-solving.
3. Dependability: Demonstrating reliability and consistency in meeting deadlines and delivering quality work builds trust and credibility. Being dependable ensures that others can rely on you and reduces stress within the workplace.
4. Efficiency: Striving for efficiency maximizes productivity and minimizes wasted time and resources. Effective time management, prioritization, and streamlining processes contribute to a productive work environment.
5. Punctuality and Courtesy: Being punctual demonstrates respect for others' time and sets a positive example. Additionally, practicing courtesy, such as using polite language, active listening, and showing appreciation, promotes a harmonious and respectful workplace.
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PLEEEEASE HELP ME PLEASE WILL GIVE BRAINLIEST
in a pig-calling contest, a caller produces a sound with an intensity level of 87 db.
In a pig-calling contest, the caller produces a sound with an intensity level of 87 dB. Understanding the intensity level of the sound helps evaluate its potential impact on the surrounding environment and human hearing.
The intensity level of a sound is a measure of its loudness and is expressed in decibels (dB). The decibel scale is logarithmic, meaning that each increase of 10 dB represents a tenfold increase in sound intensity.
To calculate the intensity level in decibels, we use the formula:
dB = 10 * log10(I/I₀)
where I is the sound intensity and I₀ is the reference intensity (typically the threshold of hearing, which is approximately 10^(-12) W/m^2).
Given that the intensity level is 87 dB, we can rearrange the formula to solve for I:
87 = 10 * log10(I/I₀)
8.7 = log10(I/I₀)
I/I₀ = 10^(8.7)
I = (10^(8.7)) * I₀
In the pig-calling contest, the caller produces a sound with an intensity level of 87 dB. The calculation of the sound intensity requires knowledge of the reference intensity and the logarithmic relationship of the decibel scale.
By using the formula and considering the logarithmic nature of the scale, we can determine the actual sound intensity. Remember that the decibel scale is logarithmic, so even a small increase in decibels represents a significant increase in sound intensity. Understanding the intensity level of the sound helps evaluate its potential impact on the surrounding environment and human hearing.
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What is the relationship between the kinetic energy of molecules in an object and the object's temperature? Responses As the kinetic energy of the molecules decreases, the temperature increases. The total kinetic energy of the molecules is not affected by a change in temperature. As the temperature increases, the kinetic energy of the molecules increases. The kinetic energy always increases whether the temperature increases or decreases.
As the temperature increases, the kinetic energy of the molecules also increases.
The relationship between the kinetic energy of molecules in an object and the object's temperature is that as the temperature increases, the kinetic energy of the molecules also increases.
This relationship is governed by the kinetic theory of gases, which states that the temperature of a gas is directly proportional to the average kinetic energy of its molecules.
Temperature is a measure of the average kinetic energy of the particles in a substance. When the temperature of an object increases, the molecules within it gain more energy and move faster.
As a result, their kinetic energy increases. Conversely, when the temperature decreases, the molecules lose energy and their kinetic energy decreases.
The kinetic energy of a molecule is directly related to its mass and velocity. As the temperature increases, the molecules move with greater speed and collide more frequently with each other and the walls of their container.
These collisions transfer energy, leading to an overall increase in kinetic energy.
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An object is placed +15 cm in front of a concave mirror. A real image is formed +30 cm in front of the mirror. What is the focal distance, f, for this mirror? O +10 cm O +30 cm 0 -30 cm O -10 cm
From the given data the focal distance for the given concave mirror is +30 cm.
The focal distance, f, for a concave mirror, can be determined using the mirror formula:
1/f = 1/v - 1/u
Where:
f is the focal distance,
v is the image distance,
u is the object distance.
In this case, the object distance, u, is given as +15 cm (in front of the mirror), and the image distance, v, is given as +30 cm (in front of the mirror). We can substitute these values into the mirror formula:
1/f = 1/30 - 1/15
Simplifying the equation, we get:
1/f = (2 - 1) / 30
1/f = 1/30
f = 30 cm
Therefore, the focal distance, f, for this concave mirror is O +30 cm.
In conclusion, the focal distance for the given concave mirror is +30 cm.
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An airplane flies due north at 150 km/h relative to the air. There is a wind blowing at 125 km/h to the east relative to the ground. What is the direction plane's velocity relative to the ground?
a. 30 degrees with east.
b. 45 degrees with east.
C. 60 degrees with east.
d. Due east.
Hence, the direction of plane's velocity relative to the ground is at 34.08° with the East or 90 - 34.08 = 55.92° with the North. Thus, the correct option is D. Due East
The direction plane's velocity relative to the ground, The given data is: Airplane velocity relative to air = 150 km/h, Wind velocity = 125 km/h. Direction of wind velocity = East,
Using Pythagoras theorem, we can calculate the magnitude of the plane's velocity relative to the ground. Let Vp be the velocity of the plane relative to the ground and let theta be the angle between the velocity vector and the horizontal velocity vector (east).
Then the component of velocity of the plane in the East direction is given by
cos(theta) × Vp, and the component of velocity of the plane in the North direction is given by sin(theta) × Vp.
Using the given data and equation of relative velocity, the velocity of the plane with respect to the ground is:
Vp = √(150² + 125²) km/h
Vp= √(22500 + 15625) km/h
Vp= √(38125) km/h= 195.04 km/h.
So the speed of the airplane relative to the ground is 195.04 km/h.
We have to find out the direction plane's velocity relative to the ground. In order to find the direction of the plane's velocity relative to the ground, we have to find the angle of the plane's velocity relative to the East (horizontal) direction.
Using the components of velocity and taking the inverse tangent, we get:θ = tan⁻¹(sin⁻¹(125/195.04))= tan⁻¹(0.6414)= 34.08°
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