The mechanical wave is one that moves through the medium, which is made up of matter.
What are mechanical waves Examples?Although waves can move energy between locations, they do not always move mass. Common ones of waves are light, sound, and ocean waves. Since sound & water waves are waves that move, they must move via a medium.
What are the 2 types of mechanical waves?Mechanical waves can move in either longitudinal waves or transverse waves, which are the two most common wave motions. The two forms of waves are shown in the videos below, which also show how the movement of the wave differs from the movements of the particle in the medium it travels through.
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the electrostatic force may be written as . in principle, if we set up an experiment with two charged objects and measure the force between them at various distances, the result should follow this theory. if we plot the data as vs. , how should the graph appear?
The idea that two metals will transmit electrons to one another when they come into contact, creating an electrical triple layer and an attractive force, is where the electrostatic hypothesis got its start.
In layman's words, what is electrostatic force?Electrostatic force is the force a charged body applies to another charge or uncharged body as a result of that body's charge. Examples: 1. Paper fragments are drawn to plastic that has been touched by wool, hair, or fur. 2.
What kind of force is electrostatic?Examples of electrostatic interaction are: With the aid of a comb, we can create electrostatic force when we run a paper piece through the oils in our heads. When one balloon is brushed with hair, the other balloon becomes drawn to it.
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et's compare two telescope's ability to see dimmer objects. one telescope has a a 150mm mirror and the second telescope has a 250 mm mirror. which one can see dimmer objects?
Reflectors and refractors are the two primary categories of optical telescopes. Refractors utilise a lens to focus light, while reflectors use a mirror.
Can larger telescopes see objects that are fainter?Compared to tiny telescopes, large telescopes can collect more light. Dimmer objects become visible in more light, and there is more light available for analysis. To gather enough light to perform spectroscopic analysis on an extremely dim object.
one telescope has = 150mm
second telescope has = 250mm
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a subway train starts from rest at a station and accelerates at a rate of 1.60 m/s2 for 14.0 s. it runs at constant speed for 70.0 s and slows down at a rate of 3.50 m/s2 until it stops at the next station.
The presented statement estimates that the subway train traveled a total of 1798.18 meters.
What is the straightforward meaning of speed?The degree which an object's positioning changes in any direction. The inverse of the distance reached to the time needed to travel that distance is known as speed. Given that it only has to have a direction and no magnitude, tempo is a synthesis number.
initial acceleration (a1)= 1.60m/s^2
time (t1) = 14s
time for constant speed = 70s
deceleration (a2) = 3.50 m/s^2
total distance = ?
Velocity - Time Graph
We need to create the velocity-time graph in order to adequately address this problem.
By summing the separate areas of the figures, the distance may be computed.
Area of first triangle.
1/2b*h
However, this train's speed would be indicated by its height.
Velocity = acceleration * time
Velocity = 1.6 * 14 = 22.4m/s
The triangular is 22.4 meters tall.
Let's swap the variables and calculate the area.
A1 = 1/2*14*22.4 = 157.5m
The perimeter of the rectangle is the following distance that we would measure.
A = L*W
L = 22.4
W = 70
A = 22.4 * 70 = 1568m
The last triangle is the distance that has to be calculated.
Triangle area is equal to 1/2b*h.
However, we are unsure exactly how long the slowdown took on a base (time) basis.
Use the link between velocity, acceleration, and time.
Acceleration = velocity/time
time = velocity/acceleration
time = 22.4/3.5
time = 6.4s
Replace the values and find the Area by substituting
A = 1/2*b*h
A = 1/2 *6.4*22.4
A = 72.68m
The train travels a total of 157.5m Plus 1568m + 72.68m.
Distance = 157.5 + 1568 + 72.68
Distance = 1798.18m
The computed distance traveled by the metro train is 1798.18 meters.
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The complete question is-
A subway train starts from rest at a station and accelerates at a rate of 1.60m/s^2 for 14.0s. It runs at constant speed for 70.0s and slows down at a rate of 3.50m/s^2 until it stops at the next station.Find the total distance covered.
a. a spaceship has a rest mass of 500,000 tons. if you could measure its mass when it was traveling at half the speed of light, what would it be? b. a fly has a mass of 1 gram at rest. how fast would it have to be traveling to have the mass of a large suv, which is about 3000 kilograms?
(a) The mass when a 500,000 tons spaceship traveling at half the speed of light = 250,000tons/c
(b) The velocity of the fly (that has a mass of 1 gram at rest), if have the mass of a large suv, which is about 3000 kilograms = 3000000 m/s
Equation that shows how momentum is directly related to an object's mass (m) and speed (v). The momentum of a large, swift object is greater than that of a small, slower object.
p = m x v
Where,
p = momentum
m = mass (kh)
v = the speed
Hence, the mass of the spaceship:
p = (500,000 tons x 1 m/s)
= 250,000tons/c
(b)
The velocity of the fly:
p = 1g x 1 m/s
Hence,
The velocity = 3000000 m/s
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while traveling outside the united states, you feel sick. a companion gets you a thermometer, which says your temperature is 39. what scale is that on? what is your fahrenheit temperature? should you seek medical help?
It is recommended to get medical help if you have a temperature of 39°C (102.2°F), as this is considered a fever and it is crucial to identify the reason and get the right care.
The explanation for the given question is:
If your temperature is greater than 100.4°F (38°C), you have a fever. 39 degrees Celsius is comparable to 102.2 degrees Fahrenheit. It's possible that your temperature was recorded in Celsius by the thermometer. If you are feeling ill when traveling outside of the United States, it is advised to seek medical assistance since a temperature of 39°C is regarded as a fever. To identify the source of your fever and obtain the appropriate care if required, it is essential to keep an eye on your symptoms and seek medical guidance. Don't forget to stay hydrated and get plenty of rest.
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Explain the relationship between gravity and weight.
Explanation:
The gravity equation defines the relationship between weight, mass, and gravity:
W = mg
A loudspeaker on a tall pole broadcasts sound waves equally in all directions. What is the speaker�s power output if the sound intensity level is 107dB at a distance of 17m ?
The speaker's power output is P = 4 * pi * r*2 * I = 4 * pi * 17*2 * 10*10.7 * I0 if the sound pressure level is 107dB at a distance of 17m.
How is the volume of a sound measured?A sound's intensity is calculated by dividing its power, expressed in Watts, by the square meters it covers. The intensity of any given sound is related to the intensity at the hearing threshold by the loudness of the sound. Decibels are used to quantify it (dB).
The following equation describes the relationship between distance (r), sound intensity level (L), and sound intensity (I):
L = 10 log10 (I/I0), where I0 denotes the reference intensity (10^-12 W/m^2) and I is the intensity of the sound wave at a distance of r from the source.
Finding the strength of the sound wave at a distance of 17 meters is necessary before applying the power formula (P), which is represented by:
P = 4 * pi * r^2 * I
To find I, we can rearrange the intensity equation as follows:
I = 10^(L/10) * I0
Putting the values in this equation as substitutes:
I = 10^(107/10) * I0 = 10^10.7 * I0
Finally, we can determine the power output using this value of I:
P = 4 * pi * r*2 * I = 4 * pi * 17*2 * 10*10.7 * I0.
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during the stance phase of running a 140 lb runner, exerts an average vertical force of 1150 n. what is the average vertical acceleration of the runner? think about what this means in terms of the vertical velocity of the runner at foot contact and toe-off.
The runner accelerates on average at 4.5 m/s2. The rocket's vertical acceleration (av) is then calculated using the formula av = [T - W] / m.
What is the maximum height's vertical acceleration?In falling object, the substance or body is launched into the air and only experiences a vertical downward acceleration (g) at each time. The projectile will therefore experience an acceleration in the vertical downward direction of 9.80 m/s2 at its highest point.ΣFy=ma 1150-623N Ma a = F/m=527=8.3m/52 63.6
How do you determine a runner's power?P is equal to ECOR*v+0.5*cdA*v3/m. The most crucial factor in determining a runner's caliber is their specific power P/m. While ordinary runner could have a value of around 3 Watts/kg, world-class runner may have a particular power of more over 6 Watts/kg.
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What is one environmental disadvantage of nuclear energy?
The disadvantage of nuclear energy is that it produces radioactive wastes.
What is radioactive waste?The generation of radioactive wastes such as uranium mill tailings, spent (used) reactor fuel, and other radioactive wastes is a serious environmental hazard associated with nuclear power. For thousands of years, these elements can stay radioactive and harmful to human health.
A sort of hazardous waste that contains radioactive substances is radioactive waste. Many operations, including nuclear medicine, nuclear research, nuclear power generation, rare-earth mining, and nuclear weapons reprocessing, produce radioactive waste. Government authorities regulate the storage and disposal of radioactive waste in order to protect human health and the environment.
Radioactive waste is divided into three categories: low-level waste (LLW), which contains small amounts of mostly short-lived radioactivity, intermediate-level waste (ILW), which contains higher amounts of radioactivity and requires some shielding, and high-level waste (HLW), which is highly radioactive and hot due to decay heat and thus requires cooling and shielding.
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what is the escape speed of an electron launched from the surface of a 1.4- cm -diameter glass sphere that has been charged to 10 nc ?
The escape speed of an electron launched from the surface of the sphere comes out to be approximately 1.6 x 10^6 m/s.
The escape speed of an electron launched from the surface of a charged sphere can be calculated using the following equation:
v_escape = sqrt(2 * k * q / m)
where k is Coulomb's constant,
q is the charge on the sphere,
and m is the mass of the electron.
For a glass sphere with a diameter of 1.4 cm charged to 10 nC,
the charge on the sphere can be calculated as follows:
q = 4 * pi * epsilon_0 * R * V
where epsilon_0 is the vacuum permittivity,
R is the radius of the sphere, and
V is the potential difference.
The radius of the sphere can be calculated as
R = 0.7 cm.
The potential difference can be calculated as
V = q / C,
where C is the capacitance of the sphere,
which can be calculated as
C = 4 * pi * epsilon_0 * R.
Substituting the values, we get:
q = 4 * pi * 8.854e-12 * 0.7 * 10e-9
V = q / (4 * pi * 8.854e-12 * 0.7)
The mass of an electron can be taken as 9.11e-31 kg. Substituting the values in the escape speed equation, we get:
v_escape = sqrt(2 * 8.98e9 * q / 9.11e-31)
v_escape=1.6 x 10^6 m/s
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Caused or operated by heat that has changed into different forms of energy is called: _________
The process of converting one form of energy into another is referred to as energy conversion.
What do you mean by energy conversion?The process of converting energy from one form to another is referred to as energy transformation. Energy is a quantity in physics that gives the capacity to perform labour or move (e.g., lifting an object) or provides heat. Energy, in addition to being converted, is transferable to a different location or object, but it cannot be created or destroyed, according to the law of conservation of energy.
Many sources of energy can be employed in natural processes or to give a service to society, such as heating, refrigeration, lighting, or mechanical work to power machines. For example, to heat a house, the furnace burns fuel, converting its chemical potential energy into thermal energy, which is then delivered to the house.
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how does the magnitude of the work done on the system compare to magnitude of the net heat entering the system?
The magnitude of the work done on a system and the magnitude of the net heat entering the system are both forms of energy, but they represent different types of energy transfer.
Work is done on a system when an external force causes a displacement of the system. This can result in a transfer of energy to or from the system, depending on the direction of the displacement and the force. The magnitude of the work done on the system is given by the product of the force and the distance over which it acts.
On the other hand, heat is a form of energy that is transferred from a hotter object to a cooler object. It is related to the random motion of particles within a substance and is transferred from areas of higher temperature to areas of lower temperature.
In general, the magnitude of the work done on a system and the magnitude of the net heat entering the system are not directly comparable because they represent different types of energy transfer.
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which net pressure draws fluid into the capillary?
a ball is thrown straight up from ground level. it passes a 2-m-high window. the bottom of the window is 7.5 m off the ground. the time that elapses from when the ball passes the bottom of the window on the way up, to when it passes the top of the window on the way back down is 1.3 s.
From the ground, a ball is hurled straight up. A 2-m-high window is passed by it. The ball's starting velocity is 4.82 m/s because the bottom of the window is 7.5 metres above the ground.
What does level ground mean?Level ground refers to the lowest level of a structure when the majority of its height is exposed above the ground level of the nearby street or riverwalk. The floor that is level with the ground is referred to as the first floor in American English, followed by the floor that is above it and so on. The term "Ground Level" refers to the height of the main construction entrance to the structure or building.
What are ground level activities?Walking, slipping, tripping, transfers (such as getting up from a chair or bed), falling from furniture (such as a bed or sofa), picking something up off the ground, and standing tasks were all considered to be ground level activities (e.g., washing dishes).
We can employ the kinematic equation to get the ball's starting velocity:
h = vi * t + 0.5 * a * t^2
where an is the acceleration brought on by gravity (-9.8 m/s2), vi is the initial velocity, t is the time (1.3 s), and h is the window's height (2 m).
Rearranging the equation to solve for vi:
vi = sqrt(2 * a * h / t^2)
Substituting the values:
vi = sqrt(2 * (-9.8) * 2 / 1.3^2)
= sqrt(39.2 / 1.69)
= sqrt(23.18)
= 4.82 m/s
Therefore, the ball's initial velocity is roughly 4.82 m/s.
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What is the wavelength of a sound wave with a frequency of 9.3 Hz and a wave speed of 3.1 m/s?
The wavelength of the sound wave is 33.33 cm.
What is wavelength?The distance over which a periodic wave's shape repeats is known as the wavelength in physics. It is a property of both travelling waves and standing waves as well as other spatial wave patterns.
It is the distance between two successive corresponding locations of the same phase on the wave, such as two nearby crests, troughs, or zero crossings.
The wavelength of the sound wave is = velocity/frequency
= 3.1/9.3 meter
= 0.3333 meter
= 33.33 cm.
Hence, the wavelength of the sound wave is 33.33 cm.
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if the intensity remains the same but the frequency is doubled to 512 hz , how does this affect the pressure amplitude?
If the intensity remains the same but the frequency is doubled to 512 Hz , then the pressure amplitude must remain unchanged as well.
What happens to pressure amplitude when frequency is doubled?The pressure amplitude and the frequency are independent properties of a sound wave, and a change in one does not necessarily affect the other. The intensity of a sound wave is proportional to the square of the pressure amplitude, so if the frequency is doubled and the intensity remains the same, then the pressure amplitude must remain unchanged as well.
In other words, if I = kA^2, where I is the intensity, A is the pressure amplitude, and k is a constant, then if I remains constant, A must remain constant even if the frequency is changed.
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Before a collision, the x-momentum of an object is 8.0 × 103 kilogram meters/second, and its y-momentum is 1.2 × 104 kilogram meters/second. What is the magnitude of its total momentum after the collision?
The magnitude of its total momentum after the collision is 124.8 kg-m/sec.
What is momentum?The definition of momentum is the quality that a moving body possesses due to its mass and motion, and it is determined by multiplying the body's mass by its speed.
Given that the x-momentum of an object is 8.0 × 103 kilogram meters/second, and its y-momentum is 1.2 × 104-kilogram meters/second the resultant momentum after collision is 124.8 kg-m/sec.
The magnitude of its total momentum after the collision is 124.8 kg-m/sec.
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when brass of length 100cm at 50degreeCelcius is heated it's length changes to 100.054cm at ________ temperature. Take the linear expansivity of brass to be 1.8x10raise to power -5 per Kelvin
Answer:
80
Explanation:
What is the relationship between frequency and amount of energy ? Give an example using number of HZ (Properties of Wave's on Summit)
The relationship between frequency and amount of energy is:
amount of energy = Plank's constant × frequency of the EM wave.
What is electromagnetic wave?When an electric field interacts with a magnetic field, electromagnetic waves are created. Therefore, they are referred to as "electromagnetic" waves. An electromagnetic wave's electric field and magnetic field are perpendicular to one another (at right angles).
The relationship between frequency and amount of energy is:
amount of energy = Plank's constant × frequency of the EM wave.
Where Plank's constant is 6.626 × 10⁻³¹ Joule/Hz, Hence, a wave of 1 Hz frequency have 6.626 × 10⁻³¹ Joule of energy.
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If we quadruple the energy in a vessel of gas, what happens to the velocity of the gas particles?A) The velocity doublesB) The velocity quadruplesC) The velocity halves D) The velocity stays the same
If we quadruple the energy in a vessel of gas, the thing that happens to the velocity of the gas particles is: B) The velocity quadruples.
What is velocity quadruples?
According to the ideal gas law, PV = nRT,
where:
P = pressure
V = volume
n = number of moles of gas
R = gas constant
T = temperature (in kelvin)
If we quadruple the energy in a vessel of gas, this would result in a corresponding increase in temperature (T) of the gas. As a result, the velocity of the gas particles would increase. The root mean square velocity (u) of a gas particle can be expressed as:
u = √(3RT/M)
where:
M = molar mass of the gas
Since T has increased, the velocity of the gas particles would also increase by a factor of √(T2/T1). If T has quadrupled, the velocity of the gas particles would also quadruple.
Therefore the correct option is B.
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arnold strongman and suzie small each pull very hard on opposite ends of a rope in a tug-of-war. the greater force on the rope is exerted by
The greater force on the rope is exerted by arnold strongman.
When both competitors are pulling equally hard, their combined force is what has the most effect on the rope. The greater force on the rope, however, will be applied by the contestant pulling with more force if one of the contestants is doing so than the other.
Tug of war - The sport of tug of war puts two teams against one another in a contest of strength. Teams pull on opposite ends of a rope with the objective of moving the rope a particular distance in one direction while resisting the force of the opposing team's pull.
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a ball starts from rest and accelerates at 0.495 m/s2 while moving down an inclined plane 9.85 m long. when it reaches the bottom, the ball rolls up another plane, where, after moving 13.4 m, it comes to rest. what is the speed of the ball at the bottom of the first plane?
The speed of the ball at the bottom of the first plane is 1.67 m/s
The speed of the ball at the bottom of the first plane can be calculated using the kinematic equation:
v = v0 + at
Where v is the final velocity (speed), v0 is the initial velocity (0 m/s since the ball started from rest), a is the acceleration (0.495 m/s^2), and t is the time elapsed. To find the time elapsed, we can use the distance traveled and the acceleration:
d = v0t + 0.5at^2
Rearranging for time and substituting the values, we get:
t = sqrt(2d/a) = sqrt(2 * 9.85 m / 0.495 m/s^2) = 3.36 s
Now that we have the time elapsed, we can use the kinematic equation to find the velocity:
v = v0 + at = 0 m/s + (0.495 m/s^2) * (3.36 s) = 1.67 m/s
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What is the force experienced by a person whose momentum changes by 7kgm/s in 6s?
Give your answer to 1 decimal place.
Answer:
[tex]1n[/tex]
The answer is 1N.
Explanation:
Greetings!!
Given values :-momentum(p)= 7kgm/s
time(t)= 6s
Required values:-
force(F)=?
solution:-Firstly, recall the momentum-force equation
p=F.tsubstitute known variables into the equation
(7)=F(6)solve for force
F= 1.167N1.167 Rounded to the Nearest Whole Number
Therefore, we have to round down: the whole number ones place value of 1.167, 1, remains 1, and the decimal point and all digits (. 167) are removed. 1.167 rounded to the nearest whole number = 1.
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Hope it helps!!!
a hall probe gives a reading of \(1.5\mu v\) for a current of 2 a when it is placed in a magnetic field of 1 t. what is the magnetic field in a region where the reading is for 1.7 a of current?
The magnetic field in the region where the reading is for 1.7 A of current is 3.4 T.
The voltage produced by a Hall probe is proportional to the product of the magnetic field, the current, and a constant known as the Hall coefficient, denoted by "R_H". Mathematically, the relationship can be expressed as:
V = R_H * I * B
Where V is the voltage, I is the current, and B is the magnetic field.
We know the Hall coefficient and the magnetic field for a current of 2 A:
V = 1.5 * 10^(-6) V
R_H = V / (I * B) = 1.5 * 10^(-6) V / (2 A * 1 T)
Next, we can use the value of the Hall coefficient to find the magnetic field for a current of 1.7 A:
B = V / (R_H * I) = 1.5 * 10^(-6) V / (R_H * 1.7 A)
B = (1.5 * 10^(-6) V) / (R_H * 1.7 A) = (1.5 * 10^(-6) V) / (V / (2 A * 1 T) * 1.7 A)
B = (1.5 * 10^(-6) * 2 * 1 * 1.7) / (10^(-6)) = 2 * 1.7 T = 3.4 T
A magnetic field is a force field that is created by a magnetic object or a current-carrying conductor. It is an invisible field that exerts a force on charged particles in motion and causes them to move in a circular path around the magnetic object or conductor. The direction of the magnetic field is determined by the right-hand rule, which states that if you point your thumb in the direction of the current flow and your fingers in the direction of the magnetic field, your thumb will be pointing in the direction of the north pole of the magnetic object.
The strength of the magnetic field is measured in units of Tesla (T) or Gauss (G). A magnetic field is a vector area, which means that it has both significance and path. The magnetic field can interact with other magnetic fields, causing them to attract or repel each other.
Magnetic fields have many practical applications, such as in electric motors, generators, and MRI machines. They are also present in the Earth's atmosphere and play a crucial role in shielding the planet from harmful solar radiation. The study of magnetic fields is a branch of physics known as electromagnetism, which explores the relationship between electricity and magnetism.
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a horizontal force of 94.7 n is applied to a 32.5 kg crate on a rough, level surface. if the crate accelerates at 1.23 m/s2, what is the magnitude of the force of kinetic friction (in n) acting on the crate?
Answer:
The magnitude of the force of kinetic friction is 54.725 Newtons
Explanation:
We can use Newton's Second Law of Motion to evaluate the force of friction.
Newton's Second Law states
[tex]F_n_e_t=ma[/tex]
The formula for friction force is
[tex]F_{F}=\mu F_N[/tex]
[tex]F_N[/tex] is the normal force
The formula for normal force on a level surface is
[tex]F_N=mg[/tex]
In this example we have positive horizontal force and the force due to friction opposing the motion of the crate.
Let [tex]F_H[/tex] represent the horizontal force.
Therefore we can say the net force in this example is
[tex]ma=F_H-F_F[/tex]
Solving for [tex]F_F[/tex] gives us
[tex]F_F=F_H-ma[/tex]
In this example we are given
[tex]F_H=94.7\\m=32.5\\a=1.23[/tex]
Lets substitute our known values into our equation.
[tex]F_F=94.7-32.5*1.23[/tex]
Evaluate and simplify.
[tex]F_F=94.7-39.975[/tex]
[tex]F_F=54.725[/tex]
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when the wave goes across the boundary from string 1 to string 2, the frequency is unchanged. what happens to the velocity? when the wave goes across the boundary from string 1 to string 2, the frequency is unchanged. what happens to the velocity? the velocity increases. the velocity stays the same. the velocity decreases.
The velocity of the sinusoidal wave decreases when it travels from string 1 to string 2 because the linear density of string 2 is different, causing the wave to slow down. Thus, Option C holds the truth.
When a sinusoidal wave travels from one string to another with a different linear density, its velocity changes due to the change in tension and mass per unit length of the string. The velocity of the wave is proportional to the square root of the tension divided by the mass per unit length.
If the linear density of string 2 is higher than that of string 1, the wave will slow down as it travels across the boundary because the increased mass per unit length will result in a decrease in velocity. Conversely, if the linear density of string 2 is lower, the velocity of the wave will increase as it travels across the boundary.
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the behavior when the rocks elastically snap back to their previous dimensions with the release of associated stress accompanied with sudden displacement is called
The "elasticity rebound concept" of earthquakes refers to this steady buildup and releasing of stress and strain. The abrupt elastic rebounding of already stored energy is what causes most earthquakes.
What happens after an earthquake when a rock returns to its natural, stress-free form?Until the stress is so high that the rocks unexpectedly slip past one another, portions of a fault stay locked. An earthquake's shaking and vibrations are brought on by this slippage. Elastic rebound leads to earthquakes. Rock that has been elastically distorted suddenly returns to its original shape.
How would you characterise the reactions of rocks under various stresses?Rock can deform under stress in three different ways: elastically, plastically, or through breaking or fracturing. Similar to a rubber band that returns to its original shape when tension is released, elastic strain is reversible.
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what are the dimesnions of the lightest opne top right cylindrical can that can hold a volume of 1000cm
Dimesnions of the lightest open top right cylindrical can that can hold a volume of 1000[tex]cm^{3}[/tex] is [tex]r=h[/tex] ≈ 6.83cm
The volume of a right circular cylinder is V[tex]=\pi r^{2} h[/tex],
where [tex]r[/tex] is the radius of the circular base of the cylinder and [tex]h[/tex] is the height of the cylinder. If the cylinder is close-top, the surface area of the cylinder is [tex]A[/tex][tex]=[/tex][tex]2\pi r^{2} +2\pi rh[/tex].
Therefore, if it's open-top, its surface area is A =[tex]\pi r^2 + 2\pi r h.[/tex]
In order to find the smallest surface area of the cylindrical can that can hold a volume of 1000 [tex]cm^{3}[/tex],
we must express [tex]A[/tex] in terms of one variable only. Let's express [tex]A[/tex] in terms of [tex]r[/tex]. So we have to express [tex]h[/tex] in terms of [tex]r[/tex] and we know that [tex]\pi r^2h = 1000.[/tex]
Thus we have:
[tex]\pi r^{2} h=1000[/tex]
[tex]h=\frac{1000}{\pi r^{2} }[/tex]
So, the surface area in terms of [tex]r[/tex] is [tex]A=\pi r^{2} +2\pi r(\frac{1000}{\pi r^{2} })[/tex]
[tex]=\pi r^{2} +\frac{2000}{r}[/tex]
Now lets differentiate [tex]A[/tex] with respect to [tex]r[/tex] and set it to 0 and solve for [tex]r[/tex]:
[tex]\frac{dA}{dr} =2\pi r-\frac{2000}{r^{2} } \\0=2\pi r-\frac{2000}{r^{2} }[/tex]
[tex]2\pi r=\frac{2000}{r^{2} }\\ 2\pi r^{3} =2000\\r^{3}=\frac{1000}{\pi }[/tex][tex]r=\sqrt[3]{\frac{1000}{\pi } }[/tex]≈ [tex]6.83[/tex]
Since, [tex]h=\frac{1000}{\pi r^{2} } ,[/tex]
[tex]h=\frac{1000}{\pi (\sqrt[3]{\frac{1000}{\pi })^{2} } }[/tex] ≈ [tex]6.83[/tex]
therefore, when the radius [tex]r[/tex] and the height [tex]h[/tex] are both 6.83 then the open-top cylinder will have the smallest surface area that can hold 1000 [tex]cm^{3}[/tex]
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the principal controls and influences of temperature patterns include
Latitude, height, variances in the heating of land and water, weather patterns, ocean currents, or surface texture are the main factors that affect and determine temperature trends.
What are the temperature's three main controls?Particularly, different parts of the earth's surface have different average surface air temperatures. Latitude, being close to water, and height are the "big three" factors that determine a location's temperature.
What kind of temperature control system is this, for instance?A form of control system called a temperature centralized system regulates an object's or an area's temperature automatically. In appliances like conditioners, refrigerators, geysers, etc., we frequently employ temperature control systems where the temperature is automatically changed based on the input parameters.
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if the charge q is displaced from the center a small distance x as shown in the figure, will it undergo simple harmonic motion when released?
A ring with a radius of R is evenly covered in positive charge Q. At a distance of x from the centre, a particle with mass m and a negative charge q is positioned on its axis.
What is the distribution of positive charge Q?A ring with a radius of R is uniformly covered with a positive charge Q. At the centre of the ring is a small test charge, q.
Then. If q > 0 and is displaced in the plane of the ring away from the centre, it will be pushed back in that direction.
Charge q will return to its original place after travelling once around a circle with radius r.
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