The image position is approximately -7/3 cm and the image height is approximately 7/15 cm. The negative image position indicates that the image is formed on the same side as the object, and the positive image height indicates that the image is upright compared to the object.
To calculate the image position and the image height formed by a diverging lens, we can use the lens formula and the magnification formula. Given:
Object height (h₀) = 3.0 cm
Object distance (u) = -15 cm (negative because it is in front of the lens)
Focal length (f) = -20 cm (negative for a diverging lens)The lens formula is given by:
1/f = 1/v - 1/u Where: v is the image distance.
Substituting the given values, we have:1/-20 = 1/v - 1/-15Simplifying the equation, we get:-1/20 = 1/v + 1/15To solve for v,
we can find a common denominator:
(-1/20)(15/15) = (1/v)(15/15) + (1/15)(20/20)-15/300 = 15/15v + 20/300
Combining like terms:-15/300 = (15v + 20)/300
Cross-multiplying:-15 = 15v + 20Solving for v:15v = -35v = -35/15v = -7/3 cm.
The negative sign indicates that the image is formed on the same side as the object, which is expected for a diverging lens.
Next, we can calculate the image height (hᵢ) using the magnification formula:
magnification (m) = hᵢ / h₀ = -v / u
Substituting the given values: m = hᵢ / 3.0 = (-(-7/3)) / (-15)
Simplifying, we get:
m = hᵢ / 3.0 = 7/3 / 15
Cross-multiplying:
hᵢ = (7/3) * (3.0) / 15
Simplifying further
hᵢ = 7/15 cm
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Drag the tiles to the correct boxes to complete the pairs.
Recall how Newton’s investigation of light followed one form of the scientific method. Match the statements about Newton’s experiment with the steps in the scientific method.
Tiles
White light becomes a spectrum of seven
colored lights after passing through a prism.
What happens to a single color of light
when it passes through a prism?
A single color of light will not change
when it passes through a prism.
White light passes through a prism. A slit
is used to direct only the red light through
a second prism.
When the red light goes through a second
prism, its color does not change.
The hypothesis proposed for this experiment
is true.
The colors in a spectrum are part of white
light, and the prism separates them.
Pairs
Make an observation.
arrowBoth
Ask a question.
arrowBoth
Construct a hypothesis.
arrowBoth
Test the hypothesis with an investigation.
arrowBoth
Analyze the data.
arrowBoth
Confirm whether the hypothesis is true.
arrowBoth
Explain the results.
arrowBoth
Newton's optics experiment observation and intervention. In order to make his observations, Newton used the theory of light passing through prisms and the rays that were sent by them. It was revealed that light has a variety of properties and features.
Prisms, lenses, and optical rays were the basis of Newton's inquiry into light.According to him, different coloured lights had varying degrees of re-frangibility.Newton adopted the "Proof by Experiments" method to back up his theories. Each technique was chosen to highlight a particular quality of light.Newton found a phenomenon called the Newton rings.After pressing two prisms together, Newton saw that there was a translucent area.To learn more about light, visit :
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I added an image of the answers/ Hope this helps! good luck on it.
Help pwease and tanks >:|
Answer:
B
Explanation:
Cause I think it is
At what point of a projectile motion, acceleration and velocity are perpendicular to each other?
Answer:
At the topmost point where the velocity has only horizontal component whereas the acceleration is vertical.
Explanation:
There is only a horizontal component of velocity at the ap3x of the projectile, and acceleration is vertically downwards owing to gravitation, therefore velocity and acceleration are perpendicular to one another.
A ray of light strikes a plane mirror at an angle of incidence of 60°, is reflected from the mirror and then strikes a second plane mirror placed so that the angle beftween the mirrors is 45°. The angle of reflection at the second mirror, in degrees, is
A 15
B 25
C 45
D 65
E 75
plz help me guys ASAP!
Answer:
60 - 45 = A. 15
Explanation:
Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
60 - 45 = A. 15. Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
What is Plane mirror?A flat or highly polished surface called a plane mirror reflects light or waves to create an image. It is a polished, smooth surface that creates a virtual representation of the actual object.
A plane mirror is a surface on which an image can only be produced by at least two light beams. The intersection of these two beams can occur inside the mirror or appear to occur somewhere behind the mirror.
The image that follows illustrates how an object appears when viewed via a plane mirror.
Therefore, 60 - 45 = A. 15. Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
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In order to increase the pain of a common emitter amplifier, we have to reduce the output impedance Select one: True false . Ves V. The NMOS transtor certainly operates in saturation region Select one True False
In order to increase the gain of a common emitter amplifier, we have to reduce the output impedance. This statement is false.
To increase the gain of a common emitter amplifier, it is more common to focus on increasing the input impedance and/or the transconductance of the transistor, rather than specifically reducing the output impedance.
The NMOS transistor certainly operates in the saturation region.
False. The operating region of an NMOS transistor depends on the voltages applied to its terminals. The NMOS transistor can operate in different regions, including the cutoff, triode, and saturation regions. The specific region of operation depends on the voltages applied to the gate, source, and drain terminals of the transistor.
It's important to note that the answers provided above are based on the given options, but the questions could be more accurately answered with additional context or clarification.
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The speed of sound in wood is 3300 m s−1 and the speed of sound in air is 330 m s−1. A hammer hits one end of a 33 m long plank of wood. Find the difference in time between the sound waves being detected at the other end of the plank and the sound being heard through the air.
The difference in time between the sound waves being detected at the other end of the plank and the sound being heard through the air will be 0.09 sec.
What is a sound wave?A sound wave is produced when a medium begins to vibrate. When an entity vibrates, a pressure wave is formed, which causes sound.
Given data;
The speed of sound in wood,u= 3300 m/s
The speed of sound in air,v=330 m/sec
long plank of wood, L=33 m
The time period in the air was found as;
T₁ = 33 m / 330 m/sec
T₁= 0.1 sec
The time period in wood ;
T₂= 33 m / 3300 m/sec
T₂=0.01 sec
T = T₁ - T₂
T=0.1-0.01
T=0.09 sec
Hence, the difference in time between the sound waves being detected at the other end of the plank and the sound being heard through the air will be 0.09 sec.
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what did you learn from organize Notes, write 2 to 3 paragraphs explaining how that process is designed to help with your learning process for your classes.
Study Skills Please
Answer:
yo ni siquiera he leido Organizar Notes y quisiera responderte pero el sistema no me deja escribir bien se esta alocando
Explanation:
1. Helen's car ran out of gas and stalled 100 meters from a gas station. Helen knew she could push the car to the gas station. She put her car in neutral and pushed with a force of 40 N. How much work (in Newton meters) did Helen do to get her car to the gas station?
The amount of work (in Newton meters) that Helen did to get her car to the gas station is 4000 Newton meters
How do i determine the amount of work (in Newton meters)?Work done is defined as illustrated by the formula given below:
Work done = force (F) × distance (d)
From the question given above, we were told that:
Force applied (F)= 40 NewtonDistance to gas station (d) = 100 metersWorkdone =?The work done by Helen can be obtained as shown below:
Work done = force (F) × distance (d)
Work done = 40 × 100
Work done = 4000 Newton meters
Thus, it is evident that the work done is 4000 Newton meters
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How many seconds will it takes to stop?
In order to find the time it takes, first let's convert the distance from miles per hour to feet per second: calculate the acceleration using Torricelli's equation
\(40\text{ mph}=40\cdot1.467\text{ ft/s}=58.7\text{ ft/s}\)Then, let's :
\(\begin{gathered} V^2=V_0^2+2\cdot a\cdot d\\ \\ 0^2=58.7^2+2\cdot a\cdot50\\ \\ 100a=-3445.7\\ \\ a=-34.46\text{ ft/s^^b2} \end{gathered}\)Now, we calculate the time with the formula below:
\(\begin{gathered} \Delta S=V_0t+\frac{at^2}{2}\\ \\ 50=58.7t-17.23t^2\\ \\ -17.23t^2+58.7t-50=0\\ \\ t=\frac{-58.7\sqrt{58.7^2-4\cdot(-17.23)\cdot(-50)}}{2\cdot(-17.23)}\\ \\ t_1=t_2=1.7 \end{gathered}\)Therefore the time required is 1.7 seconds.
4. An electric heater is operated by applying a potential difference of 50.0 V across a wire of total resistance 8.00 Ω. Find the current in the wire and the power rating of the heater.
Using Ohm's Law, we can find the current in the wire:
I = V/R = 50.0 V / 8.00 Ω = 6.25 A, So the current in the wire is 6.25 A.
To find the power rating of the heater, we can use the formula:
P = VI, where P is the power, V is the potential difference, and I is the current. Plugging in the values, we get:
P = 50.0 V x 6.25 A = 312.5 W
So the power rating of the heater is 312.5 W.Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. This relationship is often represented mathematically as I = V/R, where I is the current through the conductor, V is the voltage applied across the conductor, and R is the resistance of the conductor. In simpler terms, Ohm's law describes the behavior of a resistor or conductor in an electrical circuit, where the current flowing through the circuit is directly proportional to the voltage applied across it, and inversely proportional to its resistance. Ohm's law is an important concept in electrical engineering and is used to design and analyze electrical circuits, as well as to calculate the power dissipation and efficiency of electrical component
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A cube measures 3cm on each side has a mass of 25 grams. what it its density and relative density.
Answer:
Density= 2.78 g/cm³
Relative density=2.8
Explanation:
To calculate the density of the cube we have to use the formula ρ=mass/volume
ρ stands for density.
So now we don't have the volume of the cube and to find the volume of the cube we have to use the formula a³
3³= 9 cm³
Now plug in the values. ρ= 25 g/9 cm³
ρ= 2.78 g/cm³
To find the relative density, we have to use the formula ρsample/ρH20
The sample means the density of the substance earlier. We do not know the density of water but it is constant at 997 kg/m³.
Now we have to make the units same so you change the unit of the density of cube to kg/m³
So, 25/1000= 0.025 kg
9/100×100×100 (because cm³ which means that there should be 3 meters to change the unit and to conver cm to meter we need to divide by 100 so 9cm/100, 9cm²/100×100, 9cm³/100×100×100)
=0.000009 m³
The new density= 0.025 kg/ 0.000009 m³
= 2777.78 kg/m³
Now plug the values into the formula:
relative density= 2.777.78 kg/m³ / 997 kg/m³
=2.8
There is no unit since kg/m³ and kg/m³ cancels
please help me with my question I will like and mark as brainliest NO LINKS THEY DON'T WORK AND IF U DON'T KNOW THE ANSWER PLS DON'T ANSWER AT ALL
Answer:
a)
Weight in Air = 0.3N
Weight in Water = 0.25N
Weight in Liquid = 0.24N.
Upthrust /Buoyant Force = Weight in Air – Weight in Fluid(Water in this case)
= 0.3 – 0.25
= 0.5N.
b) R.D of Body = Density of Body/Density of Standard Fluid(Water).
There's a Derived Formula for RD.
I'm gonna Apply it here.
Ask me for the derivation in the Comment section if you need it.
RD = α/ρ = (Weight in Air) / (Upthrust Force)
Where
α = density of the Body(or reference substance)
ρ = density of standard fluid (water)
= 0.3/0.05 = 6.
c) RD of Liquid = (Density of Liquid) /(Density of standard Fluid(water)
Or we just go by that formula
RD of Liquid = Weight in Air/Upthrust(In Liquid)
We'll be using the Upthrust in that Liquid now.
= 0.3 – 0.24 = 0.06
RD = 0.3/0.06 = 5.
A 75-N box rests on a perfectly smooth horizontal surface. The minimum force need to start the box moving
is
A) 7.5 N. B) 75 N.
C) 750 N. D) any horizontal force greater than zero.
Here, if take it that you mean "perfectly smooth" to mean that there is no friction. If that is the case, then the box begins to move whenever there is a net horizontal force acting on it. (D) It goes without saying that the force increases as the box accelerates.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. The application of force is the location at which force is applied, and the direction in which the force is applied is known as the direction of the force.F = ma
Where, F is the force on the box and m is the mass of the box and a is the acceleration.
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4. Un móvil lleva una velocidad de 75 m/s, en dicho momento aplica los frenos durante tiempo de 15 segundos hasta detenerse. ¿cuál será la aceleración del frenado? ¿cuál es la distancia que recorre hasta detenerse?
Answer:
a = 5 m / s² and x = 562.5 m
Explanation:
Let's apply the kinematics relations
v = v₀ + at
v² = v₀² + 2a x
In this case, as the car stops, its final speed is zero (v = 0) and the acceleration must be opposite to the speed, that is, negative
0 = v₀ - a t
a = v₀ / t
let's calculate
a = 75/15
a = 5 m / s²
let's look for the distance
0 = v₀² - 2a x
x = v₀² / 2a
let's calculate
x = \(\frac{75^2}{2 \ 5 }\)
x = 562.5 m
Sound waves with a constant frequency of 250 hertz are traveling through air at stp. what is the wavelength of the sound waves
Answer:
wave length is 1.2m
Explanation:
since formula of wave length is v/f
v(speed of sound in air at stp is 300ms^-1)
f(frequency 250hertz)
then wave length is 300÷250 which give 1.2m
Sound waves with a constant frequency of 250 hertz are traveling through air at stp. what is the wavelength of the sound waves is 1.32 m.
What is wave ?Wave is is a disturbance in a medium that carries energy as well as momentum . wave is characterized by amplitude, wavelength and phase. Amplitude is the greatest distance that the particles are vibrating. especially a sound or radio wave, moves up and down. Amplitude is a measure of loudness of a sound wave. More amplitude means more loud is the sound wave.
Wavelength is the distance between two points on the wave which are in same phase. Phase is the position of a wave at a point at time t on a waveform. There are two types of the wave longitudinal wave and transverse wave. Longitudinal wave : in which, vibration of the medium (particle) is parallel to propagation of the wave. Sound wave is a longitudinal wave. Transverse wave : in which, vibration of the medium (particle) is perpendicular to propagation of the wave.
speed of the wave,
c = νλ
330 m/s = 250λ
λ = 330/250 = 1.32 m
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the pull cord of a lawnmower engine is wound around a drum of radius 6.43 cm. while the cord is pulled with a force of 76 n to start the engine, what magnitude torque does the cord apply to the drum?
The magnitude of the torque applied to the drum by the pull cord is approximately 4.89 Nm.
Torque is a measure of the twisting force that causes rotation. It is a vector quantity that depends on the force applied, the distance between the force and the pivot point, and the angle between the force and the lever arm (the perpendicular distance between the force and the pivot point). To find the magnitude of torque applied to the drum, you can use the formula: torque = force x radius. In this case, the force is 76 N and the radius is 6.43 cm (which needs to be converted to meters).
So first, convert the radius to meters: 6.43 cm = 0.0643 m.
Now, calculate the torque: torque = 76 N x 0.0643 m = 4.8868 Nm.
Therefore, the magnitude of the torque applied to the drum by the pull cord is approximately 4.89 Nm.
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a vibrating diaphragm sets up strong vibrations at the mouth of a horizontal tube containing air and a small amount of fine powder. the powder becomes arranged in piles i cm apart, and the speed of sound in air is 330 meters
the wavelength of this sound in air is:
(the answer is 2cm howd we get hereeee)
A sound is moving through the atmosphere at a velocity of 343 ms-1. The sound wave has a wavelength of 0.1 cm.
Sound in the air is what kind of wave?Longitudinal waves are what make up sound. Compressions and rarefactions are also present in longitudinal waves when they pass through any given medium. When particles travel in close proximity to one another, compression occurs, creating areas of intense pressure.
What is the air wavelength formula?As with all waves, the relationship between the speed of sound (vw), its frequency (f), and its wavelength () is provided by vw=f. vw=(331m/s)T273K describes how the sound's velocity in the air relates to air temperature T. For any and all frequencies and wavelengths, vw is constant.
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calculate the wavelength (in m) of a 650.00 hz sound in air at room temperature and pressure, where the velocity of sound is 344 m/s.
The wavelength of a 650.00 Hz sound in air at room temperature and pressure, where the velocity of sound is 344 m/s, is approximately 0.529 m.
What is the wavelength of a 650.00 Hz sound in air at room temperature and pressure?Sound waves travel through a medium by creating compressions and rarefactions. The wavelength of a sound wave is the distance between two consecutive points that are in phase, such as two compressions or two rarefactions. To calculate the wavelength, we can use the formula: wavelength = velocity of sound / frequency.
In this case, the frequency of the sound is 650.00 Hz, and the velocity of sound in air at room temperature and pressure is 344 m/s. Plugging these values into the formula, we get: wavelength = 344 m/s / 650.00 Hz = 0.529 m.
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Do ocean currents affect aquatic life? What do you think and why?
Answer: By moving heat from the equator toward the poles, ocean currents play an important role in controlling the climate. Ocean currents are also critically important to sea life.
Explanation: Plzz mark me as brainliest !!
what is the half-life of lithium-8 if the decay constant is 0.825/s? what is the half-life of lithium-8 if the decay constant is 0.825/s? A. 0.572s B. 2.42s
C. 1.19s
D. 0.840s
0.840s is the half-life of lithium-8 if the decay constant is 0.825/s. The decay constant is unique to each radioactive substance and measures the speed of radioactive decay. Therefore, the correct answer is option D.
The half-life of lithium-8 can be calculated using the formula:
\(t1/2 = ln(2) / \lambda\)
Where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay constant. Substituting the given decay constant of 0.825/s into the formula:
t1/2 = ln(2) / 0.825/s
t1/2 ≈ 0.840s
Therefore, the half-life of lithium-8 is approximately 0.840s. The formula for half-life is a fundamental concept in nuclear physics, which determines the time required for a radioactive substance to decay by half of its original quantity. The decay constant, which is specific to each radioactive substance, measures the rate at which radioactive decay occurs.
The higher the decay constant, the shorter the half-life, indicating that the substance is more unstable and decays faster. In this case, the decay constant of lithium-8 is 0.825/s, indicating that it is relatively unstable and has a short half-life of approximately 0.840s.
In summary, the half-life of lithium-8 is approximately 0.840s with a decay constant of 0.825/s. Therefore, the correct answer is option D.
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A 10.0 N force is applied to a 2.00 kg mass, what is its velocity of the mass at 10.0 s?
Answer:
The velocity of the mass after 10.0 seconds is 50.0 m/s.
Explanation:
Explanation: We can use the formula v = (F t)/m to calculate the velocity of the mass. Given that the force applied is 10.0 N, the mass is 2.00 kg, and the time elapsed is 10.0 s, we can substitute these values into the formula to get:
v = (10.0 N * 10.0 s) / 2.00 kg = 50.0 m/s
Therefore, the velocity of the mass after 10.0 seconds is 50.0 m/s.
a 1.06den silk fiber has reached its maximum tenacity value. how many grams (force) would it take to rupture such fiber when dry?
It would take approximately 4.77 grams (force) to rupture a 1.06 denier silk fiber when dry at its maximum tenacity value.
To calculate the force needed to rupture a 1.06 denier silk fiber at its maximum tenacity value when dry, you can follow these steps:
1. Convert the denier (den) to grams per meter (g/m): 1.06 den is equal to 1.06 grams per 9,000 meters (1 den = 1 g/9,000 m).
2. Calculate the length of the fiber in meters: 1.06 g / (1.06 g/9,000m) = 9,000 meters.
3. Determine the maximum tenacity value of silk fiber, which is typically around 4-5 grams/force per denier (g/den) when dry. Let's assume a maximum tenacity value of 4.5 g/den.
4. Calculate the force required to rupture the fiber: 1.06 den × 4.5 g/den = 4.77 grams (force).
Therefore, it would take approximately 4.77 grams (force) to rupture a 1.06 denier silk fiber when dry at its maximum tenacity value.
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Suppose you have two metal cubes, one made of iron and one made of aluminum. You transfer the same amount of heat Q to each of them. Which cube will have the higher final temperature, given they have the same masses and initial temperatures?
a. Iron Cube
b. Aluminum Cube
The iron cube will have the higher final temperature if both cubes have the same mass and are initially at the same temperature.
What are the characteristics of iron?
1. Iron is a malleable and ductile metal, meaning it can be bent and shaped without breaking.
2. It has a high melting point, making it useful in a variety of applications.
3. Iron is relatively abundant and inexpensive, making it an ideal material for a variety of construction and manufacturing uses.
4. Iron is highly reactive and can corrode easily, so it must be protected with a coating or alloying elements like chromium or nickel to prevent rusting.
5. Iron is a strong and durable metal, making it ideal for structural applications.
The equation for the final temperature is, Delta*T = Q/(c.m) The specific heat, c of aluminum is greater than that of iron. Iron has a higher heat capacity than aluminum, which means that it takes more heat to raise the temperature of a given mass of iron by a certain amount compared to aluminum. When the same amount of heat Q is transferred to both the iron and aluminum cubes, the iron cube will absorb more heat due to its higher heat capacity, resulting in a higher final temperature for the iron cube.
Therefore, iron cube is the correct answer.
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assume that an intercontinental ballistic missile goes from rest to a suborbital speed of 7.90 km/s in 57.0 s (the actual speed and time are classified). what is its average acceleration in m/s2 and in multiples of g (9.80 m/s2)?
The average acceleration in multiples of g (9.80 m/s²) is 14.13.
Initial speed = 0 km/s
Final speed = 7.90 km/s
Time taken = 57.0 s
Firstly, we need to convert km/s to m/s:1 km/s = 1000 m/s
Therefore, Final speed = 7.90 km/s = 7900 m/s
Initial speed = 0 km/s = 0 m/s,
The formula to calculate average acceleration is given by :a = (v - u)/t
Where, a is the average acceleration
v is the final velocity
u is the initial velocity
t is the time taken
We need to put all the values in the above formula to get the answer:
a = (v - u)/ta = (7900 - 0)/57.0a = 138.60 m/s²
Therefore, the average acceleration in m/s² is 138.60 m/s².
To find the average acceleration in multiples of g (9.80 m/s²),
we will divide the average acceleration by the acceleration due to gravity.
a = 138.60 m/s²a(g) = a/9.80 m/s²a(g) = 138.60/9.80a(g) = 14.13
Therefore, the average acceleration in multiples of g (9.80 m/s²) is 14.13.
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Electrons are charged particles. The amount of charge that passes per unit time is called potential. current. voltage.
The amount of charge that passes per unit of time is called current. Current is a measure of the flow of electric charge through a circuit or conductor.
It is defined as the amount of charge passing through a given point per unit time, typically measured in amperes (A). Electric current is caused by the movement of charged particles, such as electrons, in a conductor under the influence of an electric field. Current can be either direct current (DC), which flows in one direction, or alternating current (AC), which periodically reverses direction. The flow of current is essential for the operation of many electrical devices, including lights, motors, and electronic devices.
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Which number would be 16,000 when rounded to the nearest thousand? *
15,472
15,518
16,511
16,739
On what does the magnitude of an applied torque depend?
Answer:
See below
Explanation:
The force applied and the length of the arm
The magnitude of an applied torque depend on force vector, 'θ' is the angle between r and F, and the distance vector.
What is torque?
The force that can cause an object to rotate along an axis is measured as torque. Similar to how force accelerates an item in linear kinematics, torque accelerates an object in an angular direction. A vector quantity is a torque.
Torque is defined as Γ=r×F=rFsin(θ). In other words, torque is the cross product of the force vector, where 'θ' is the angle between r and F, and the distance vector (the distance between the pivot point and the place where force is applied).
The magnitude of an applied torque depend on force vector, 'θ' is the angle between r and F, and the distance vector.
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What two things related to sedimentary rocks do you see at the Grand Canyon ?
Answer:
sandstone and mudstone
Explanation:
a guitar string is 90 cmcm long and has a mass of 3.6 gg . the distance from the bridge to the support post is l=62cml=62cm, and the string is under a tension of 540 nn .. What are the frequencies of the fundamental and first two overtones? Express your answers using two significant figures. Enter your answers in ascending order separated by commas.
The frequency of the fundamental can be calculated using the formula f = (1/2L) * sqrt(T/m), where L is the length of the string, T is the tension, and m is the mass per unit length of the string.
Plugging in the values, we get f = (1/2*0.9) * sqrt(540/(3.6/0.9)) = 196.1 Hz (rounded to two significant figures).
The frequency of the first overtone can be calculated as f1 = 2f, so f1 = 392.2 Hz.
The frequency of the second overtone can be calculated as f2 = 3f, so f2 = 588.3 Hz.
Therefore, the frequencies of the fundamental and first two overtones are 196.1 Hz, 392.2 Hz, and 588.3 Hz, respectively, when rounded to two significant figures and listed in ascending order.
To find the frequencies of the fundamental and first two overtones for a guitar string with a mass of 3.6 g, length of 90 cm, distance from the bridge to the support post (l) of 62 cm, and tension of 540 N, you can follow these steps:
Step 1: Convert mass and length to appropriate units.
Mass (m) = 3.6 g = 0.0036 kg
Length (L) = 90 cm = 0.9 m
Step 2: Calculate the linear mass density (µ) of the string.
µ = mass/length = 0.0036 kg / 0.9 m = 0.004 kg/m
Step 3: Calculate the speed of the wave (v) on the string using the tension (T) and linear mass density.
v = sqrt(T/µ) = sqrt(540 N / 0.004 kg/m) ≈ 164.32 m/s
Step 4: Calculate the frequencies of the fundamental and first two overtones.
Fundamental frequency (f1): f1 = v / (2L) = 164.32 m/s / (2 × 0.9 m) ≈ 91.29 Hz
First overtone (f2): f2 = 2 × f1 ≈ 182.58 Hz
Second overtone (f3): f3 = 3 × f1 ≈ 273.87 Hz
So, the frequencies of the fundamental and first two overtones are approximately 91.29 Hz, 182.58 Hz, and 273.87 Hz. Using two significant figures, the answer is 91 Hz, 180 Hz, and 270 Hz.
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what is ωmax , the magnitude of the dipole's angular velocity when it is pointing along the y axis? express your answer in terms of quantities given in the problem introduction. view available hint(s)
The magnitude of the dipole's angular velocity (ωmax) when it is pointing along the y-axis can be determined using the given information.
To find the magnitude of the dipole's angular velocity (ωmax) when it is pointing along the y-axis, we need to consider the properties of a dipole and its rotational motion.
A dipole consists of two opposite charges separated by a distance, forming a vector pointing from the negative charge to the positive charge. The dipole moment (p) is defined as the product of the charge magnitude (q) and the separation distance (d) between the charges: p = q * d.
The angular velocity (ω) of a dipole rotating about its axis is related to its dipole moment and moment of inertia (I) by the equation ω = p / I.
When the dipole is pointing along the y-axis, it implies that the dipole moment vector is in the y-direction. Therefore, the magnitude of the dipole moment can be expressed as p = p_y, where p_y represents the component of the dipole moment along the y-axis.
The moment of inertia for a dipole rotating about its axis can be determined based on its shape and mass distribution. Without specific details or values provided in the problem introduction, it is not possible to determine the exact moment of inertia or provide a specific expression for ωmax in terms of the given quantities.
Therefore, to calculate the magnitude of the dipole's angular velocity (ωmax) when it is pointing along the y-axis, we would need additional information, such as the specific shape and mass distribution of the dipole, in order to determine the moment of inertia.
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