The number of grains per square inch must be counted and compared to a standard chart to get the ASTM grain size number of a metal from a photomicrograph.
The figure depicts the quantity of grains per square inch associated with various ASTM grain size values. With a magnification of 200x, the photomicrograph reveals 60 grains per square inch. The magnification must be translated to a linear scale before the ASTM grain size number can be calculated. One inch on the photomicrograph equals 1/200 inch in real life at 200x magnification. The number of grains per square inch may be translated to the number of grains per square millimeter using this scale, which is then compared to the ASTM grain size table. The equivalent The ASTM grain size number may then be calculated. It is impossible to provide an ASTM grain size number for the metal without knowing the linear dimension of the grains in the photomicrograph.
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why will a volleyball held beneath the surface of water have more buoyant force than if it is floating
When a volleyball is held beneath the surface of water, it will have more buoyant force than if it is floating. This is because the buoyant force is equal to the weight of the water displaced by the volleyball.
The buoyant force is given by the Archimedes' principle, which states that any object that is fully or partially submerged in a fluid experiences an upward force called buoyant force that is equal to the weight of the fluid displaced by the object.
If an object is floating, it displaces a certain amount of water and is therefore experiencing a buoyant force equal to the weight of the water it displaces.
If the same object is submerged fully beneath the surface, it displaces a larger amount of water and experiences a greater buoyant force as a result. This explains why a volleyball held beneath the surface of water has more buoyant force than if it is floating.
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Ratan pushes having a same weight Through the same distance across a room
Tuesday will require more effort from Ratan since the dry surface will make it difficult to overcome the force of friction between the box and the surface through the same distance.
Why is walking on a wet surface more challenging than one that is dry?The smoothness or roughness of the surfaces affects frictional force. Force decreases with a smooth surface or increases with a rough surface, respectively. Friction is significantly lower on smooth and wet surfaces compared to dry or rough ones.
Does friction increase on a dry surface?Because of the increase in surface roughness, making the surface dry or rubbery increases friction. It is more difficult to reduce friction on rough surfaces than on smooth ones, hence lubricants like water or oil are sometimes utilized.
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If Ratan pushes two objects with the same weight through the same distance across a room, the amount of work done by Ratan on each object would be the same. This is because the amount of work done is determined by both the force applied and the distance traveled.
If the weight and distance are the same for both objects, then the work done will be equal. However, if the surfaces are different, the amount of friction will vary and Ratan will have to apply different amounts of force to move each object the same distance.
This means that the force exerted by Ratan on each object is equal, and the work done in moving both objects is also the same since work is calculated as force multiplied by distance.
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does the upper loop have a clockwise current (from above), a counterclockwise current, or no current before the switch is closed?
The current in the upper loop can be identified as a clockwise current from above (i.e., clockwise) before the switch is closed. This statement is justified using the Fleming’s right-hand rule.
Fleming's right-hand rule is a method to determine the direction of the force acting on a current-carrying conductor in a magnetic field.
The direction of the force on the conductor is given by the thumb of the right hand, the direction of the current in the conductor is given by the first finger, and the direction of the magnetic field is given by the second finger.
To determine the current direction, we must establish the polarity of the battery, as shown in the image below, and the polarity of the induced electromotive force (emf).
We must ensure that the magnetic field and the induced emf in the coil are both pointing downwards, as shown in the image below. We can now use the Fleming's right-hand rule to determine the direction of the current in the upper loop, which is clockwise from above.
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True or false; having little snow during the winter can lead to a drought too
two bricks are stacked on a floor. a student draws the force diagram for brick 2, as shown above. the forces are an upward normal force, a downward force exerted by brick 1, and a downward gravitational force. how many of the forces, if any, in the force diagram are contact forces caused by microscopic interactions?
The forces are an upward normal force, a downward force exerted by brick 1, and a downward gravitational force.
How many of the forces, if any, in the force diagram are contact forces caused by microscopic interactions?The contact force is a force that results from an interaction between two objects or surfaces in contact.
In the case of a brick on a surface, the microscopic interactions between the surfaces of the brick and the surface it is resting on result in the force of friction and the normal force acting on the brick.
Two forces are contact forces in the given force diagram. They are an upward normal force and a downward force exerted by brick 1.Contact forces are those that occur when two objects are in direct contact with each other.
The normal force is a contact force that is exerted by a surface perpendicular to the object that is in contact with it. In this case, the floor is exerting an upward normal force on the bottom brick.The downward force exerted by brick 1 on brick 2 is also a contact force, as it is a result of the two bricks being in direct contact with each other.
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7. What happens when the sounds that a
dolphin makes hit an object?
A
(B)
The object moves back and forth.
The sound of clicks and whistles can
be heard.
Tiny echoes bounce back to the dolphi
The dolphin swims away.
C) Tiny echoes bounce back to the dolphin.
When a dolphin makes a sound, it travels through the water in the form of sound waves. If these sound waves encounter an object, such as a fish or a rock, some of the sound waves will bounce back towards the dolphin in the form of echoes.
What is Sound?
Sound is a type of energy that is produced by the vibration of matter. When an object vibrates, it creates pressure waves that travel through a medium, such as air, water, or solid materials. These waves consist of alternating high and low pressure areas, and are detected by our ears as sound.
This process is known as echolocation, and it is used by dolphins and other animals to navigate, locate prey, and communicate with other members of their species. Dolphins are able to analyze the echoes that bounce back to them to determine the size, shape, and distance of objects in their environment. This ability allows them to hunt and move around in their underwater habitat with great precision, even in conditions of low visibility or darkness.
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My teacher won’t help me!
An FM radio wave has a frequency of 108 MHz. What is the speed of the wave?
Explanation:
The speed of the electromagnetic wave is the speed of light :
3 x 10^8 m/s
what is the amount of work that is done in joules when 3.13 millicoulombs of electric charge moves between two points if the potential difference between those two points is 6.29 kv?
The amount of work done in joules when 3.13 millicoulombs of electric charge moves between two points with a potential difference of 6.29 kV is approximately 19.68 J.
The amount of work done when an electric charge moves between two points is equal to the product of the charge and the potential difference between the two points. This is expressed by the equation:
Work = Charge x Potential Difference
The units of charge and potential difference are coulombs (C) and volts (V), respectively. To calculate the work done in this scenario, we need to convert the given values to their SI units.
1 millicoulomb (mC) = 10^-3 C
1 kilovolt (kV) = 10^3 V
Therefore, 3.13 millicoulombs of charge is equivalent to:
3.13 x 10^-3 C
And the potential difference of 6.29 kV is equivalent to:
6.29 x 10^3 V
Now, we can use the formula for work:
Work = Charge x Potential Difference
Work = (3.13 x 10^-3 C) x (6.29 x 10^3 V)
Work ≈ 19.68 J
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According to the Nebular Theory, the Sun's gravity caused...
*
the number of planets in our solar system to be limited to 10
Jupiter to have a total of 49 moons
the arrangement of the planets to be terrestrial inside the asteroid belt and jovian outside the asteroid belt
orbits of the outer 4 planets to be faster than the orbits of the inner 4 planets
The vector 1/root2i+1/root2j
is a
The supplied vector can be categorised as a 2-dimensional unit vector because it is in the x-y plane's first quadrant and has equal components in the i and j directions.
Vector formula: What is it?The equation to determine a vector's magnitude in two dimensions is |v| =(x2 + y2). (x, y). The Pythagorean theorem is the foundation of this formula. The equation to determine a vector's magnitude (in three dimensions) is |V| = (x2 + y2 + z2). (x, y, z).
What is the position vector's formula?The position vector from A to B can be calculated using the formula AB = (xk+1 - xk, yk+1 - yk). Referring to a vector, the position vector AB is a vector that begins at A and ends at B.
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an electromagnet is the most powerful type of magnet there is. it is a magnet with a current running through it that can be turned on and off. why might it be useful to be able to turn the electromagnet on and off?
An electromagnet is the most powerful type of magnet there is. It is a magnet with a current running through it that can be turned on and off. Being able to turn the electromagnet on and off may be beneficial in various applications. Here are a few reasons why it is useful to turn on and off the electromagnet
An electromagnet's ability to be turned on and off makes it highly versatile and useful in various applications. Some reasons why this feature is useful include:
1. Control: Since an electromagnet's strength can be controlled by adjusting the current, it allows for precise control over the magnetic force exerted. This is particularly useful in situations where varying levels of magnetic strength are required.
2. Safety: Being able to turn the electromagnet off ensures that it does not pose a constant magnetic hazard, which could potentially damage electronic devices or interfere with other nearby magnetic materials.
3. Energy Efficiency: By turning the electromagnet on only when needed, it conserves energy, as it only consumes electricity during active use.
4. Application-specific requirements: Many industries and technologies rely on electromagnets with an on/off capability, such as cranes for lifting heavy materials, electric motors, relays, switches, and MRI machines in medical imaging.
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a generator produces 33.0 v when turning at 860 rev/min. what emf does it produce when turning at 490 rev/min?
When turning at 490 RPM, the generator produces an EMF of 18.7 V.
When a generator produces 33.0 V while turning at 860 rev/min, the emf the generator produces when turning at 490 rev/min is 18.8 V.
The equation relating EMF with angular velocity is as follows:EMF=BAwN EMF = BAwN EMF = BAwN Where,B is the strength of the magnetic field A is the area of the coilw is the angular velocityN is the number of turns in the coil It can also be expressed as EMF = k × w EMF = k × w where k is the constant that depends on the strength of the magnetic field, the area of the coil, and the number of turns in the coil. Therefore, for the generator given, EMF = k × w EMF = k × wIt can be written asEMF1/EMF2=w1/w2 EMF1/EMF2 = w1/w2where EMF1 and w1 are the initial values and EMF2 and w2 are the final values. Substituting the given values, we getEMF1/EMF2=w1/w2 EMF1/EMF2 = w1/w218.8/33 = 490/8600.53333 = 0.56976EMF2 = EMF1/w1/w2 EMF2 = EMF1/w1/w2EMF2 = 33/(0.56976)EMF2 = 18.8Therefore, the emf the generator produces when turning at 490 rev/min is 18.8 V.
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How to complete ??? Thankssss
1 - Incident ray
2 - Refracted ray
3 - Angle of incidence
4 - Angle of refraction
Describe refraction.The bending of light as it travels through a medium with a varied refractive index is known as refraction. The speed of light changes as it moves from one medium, like air, to another, like water or glass. This causes the light to bend or change direction.
The angle at which the light strikes the interface between the two media and the disparity in refractive indices between the two media determine how much bending takes place. Total internal reflection is a phenomena where all of the light is completely reflected back into the original medium if the angle of incidence is large enough.
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two autmobiles are equipped with the same single frequency horn. when one is at rest and the other is moving toward the first at 15 m/s, the driver at rest hears a beat frequency of 5.5 hz what is the frequency
The frequency of the horn is 315.5 Hz.What are automobiles.Automobiles are vehicles that are designed to be driven on roads and have four wheels.
They are commonly known as cars in the United States and Canada. Cars, buses, lorries, and trucks are all types of automobiles that can transport people or cargo from one place to another. What is a beat frequency? When two waves with slightly different frequencies interfere, a beat frequency is produced. The beat frequency is the difference between the two waves' frequencies. It's possible to hear beat frequencies. The difference between two frequencies is the beat frequency. The beat frequency is equal to the absolute value of the difference between the two frequencies. There are two cars, one of which is stationary and the other of which is moving towards the first car at 15 m/s. When the driver at rest hears a beat frequency of 5.5 Hz, both automobiles are fitted with the same single frequency horn. Determine the frequency of the horn. Here's how to go about it: Using the formula, we can determine the frequency of the horn as follows:f1 = (f beat + f2)/2We know that: f beat = 5.5 Hzandf2 = v/(λ + vs)Where: v = 15 m/sλ = wavelength of the sound of the horn at rest, that is, when the car is stationary = speed of sound/frequency = 343/ f2vs = relative velocity of sound with respect to the moving vehicles = (v)/(v + us) where us is the speed of sound .The frequency of the horn is:f1 = (5.5 + v/(λ + vs))/2f1 = (5.5 + 15/(343/ f2 + v/(v + us)))/2f1 = 315.5 H
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i need the answers to this assignment please.
Answer:
1.> 374$
2.> in between the age 21 - 64
3.> The data represented above shows the cost of health insurance for each age group where we can clearly see the smooth increase in cost as the age gets bigger.
4.> The graph above shows relation of age with the cost so most likely it will be the same for cars as aging also applies to vechiles.
5.> The graph will follow the same rate of increasement as it goes on and on.
suppose a constant force is the only force applied to an object of unknown mass. what quantities do we need to know in order to find the object's change in momentum?
Change in momentum can be calculated by knowing values including the magnitude of force, amount of time, and object's starting velocity.
With a constant force, we can calculate the change in momentum of an object by knowing the following values:
the magnitude of the force being exerted on the item.the amount of time that an item is subjected to a force.the object's starting velocity, if any.If we know these numbers, we can apply the following formula to determine the object's change in momentum:
Δp = FΔt
Where Δp is the change in momentum, F is the magnitude of the force, and Δt is the time duration for which the force is applied to the object.
Note that if the object is initially at rest, then the initial momentum of the object is zero, and we can simplify the formula to:
Δp = mv
where m is the mass of the object, and v is the final velocity of the object after the force has been applied for time Δt.
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pls help need it by Monday
the all thing
a. the voltage across one lamp is also 6V/2 = 3V.
b)
i) When the second battery is added in series, the total voltage of the circuit doubles to 12V. Since the buzzers have the same resistance as before, the voltage across each buzzer is still half the total voltage, which is 12V/2 = 6V.
bii)
the current in the circuit increases proportionally to the increase in voltage. Specifically, the current in the circuit doubles when the second battery is added.
What happens in a series circuit?In a series circuit, the voltage is shared between the components in proportion to their resistance.
The circuit's overall voltage increases to 12V when the second battery is connected in series with it. The resistance of the buzzers is unchanged, so the voltage across each buzzer is still half the overall voltage (12V/2 = 6V), as before.
ii) According to Ohm's Law (I = V/R), the total resistance and total voltage in a series circuit decide the current.
The overall voltage of the circuit is increased by adding a second battery in series, but the total resistance is unaffected.
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Please answer the blanks
1 - Incident ray
2 - Refracted ray
3 - Angle of incidence
4 - Angle of refraction
What is refraction?Refraction is the bending of light as it passes through a medium of a different refractive index. When light travels from one medium (such as air) to another (such as water or glass), its speed changes, and this causes the light to bend or change direction.
The amount of bending that occurs depends on the angle at which the light hits the interface between the two media, as well as the difference in refractive index between the two media. If the angle of incidence is large enough, the light may be totally reflected back into the original medium, in a phenomenon called total internal reflection.
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what is the frequency of an electromagnetic wave with a wavelength of 125 nm? what type of electromagnetic wave is this?
Answer:
ν = 4.17×10⁻¹⁶ Hz
Explanation:
c = λν
λ is the wavelength, ν is the frequency, c is the speed of light
ν = λ/c
ν = (125×10⁻⁹m) / (3×10⁸ m/s)
ν = 4.17×10⁻¹⁶ Hz
Ultraviolet electromagnetic wave
The frequency of an electromagnetic wave with a wavelength of 125 nm is 2.4 x 10^15 Hz. The type of electromagnetic wave is Ultraviolet.
What is an electromagnetic wave?
An electromagnetic wave is a type of wave that is created by the movement of charged particles in the environment. Electromagnetic waves travel through space or other materials, like air or water, and can have different wavelengths and frequencies. These waves can travel at the speed of light, and they can be used for many different purposes, including communication, navigation, and medical imaging.
What is wavelength?
The wavelength of a wave is the distance between two consecutive crests or troughs of a wave. It is usually measured in meters, but it can also be expressed in other units, like nanometers (nm) or micrometers (μm). The wavelength of a wave determines its frequency, which is the number of cycles per second that the wave completes.
What type of electromagnetic wave is this?
The electromagnetic wave with a wavelength of 125 nm is an Ultraviolet wave. Electromagnetic waves with wavelengths shorter than 400 nm are known as ultraviolet (UV) waves. They are produced by the sun and can be harmful to living organisms in high doses, but they are also used in many applications, such as sterilization, medical treatment, and fluorescent lighting.
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does a boat travelling 75mph have more kinetic energy than a boat travelling 60 mph?
Answer:
yes
it is
because you can see it with num
If an object is moving at 5m/s north and an balanced force is acting on it, it will continue to move at that same velocity.
Answer:An object having balanced forces definitely cannot be accelerating.
two point charges having charge values of 4.0 x 10-6 c and -8.0 x10-6 c, respectively, are separated by 2.4 x 10-2 m. what is the value of the mutual force between them?
The value of the mutual force between them is -3.0 x 10^-3 N.
The mutual force between two point charges can be calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The equation for Coulomb's law is F = k * (q1 * q2) / r^2, where F is the force, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
Plugging in the given values, we get:
F = (9.0 x 10^9 N*m^2/C^2) * [(4.0 x 10^-6 C) * (-8.0 x 10^-6 C)] / (2.4 x 10^-2 m)^2
Simplifying the expression, we get:
F = -3.0 x 10^-3 N
Note that the negative sign indicates that the force is attractive, since the charges have opposite signs.
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A beam resting on two pivots has a length of L = 6.00 m and mass M = 90.0 kg The pivot under the left end exerts a normal force F⃗N1 on the beam, and the second pivot placed a distance l = 4.00 m from the left end exerts a normal force F⃗N2. A woman of mass m = 55.0 kg steps onto the left end of the beam and begins walking to the right, as in Fig. 3. The goal is to find the woman’s position when the beam begins to tip.
(a) Sketch a free-body diagram of the beam with the woman standing x-meters to the right of the first pivot.
(b) Where is the woman when the normal force F⃗ N 1 is the greatest?
(c) What is F⃗N1 when the beam is about to tip?
(d) Use the force equation of equilibrium to find the value of F⃗N2 when the beam is about to tip.
(e) Using the result of part c) and the torque equilibrium equation, find the woman’s position when the beam is about to tip.
(f) Check your answer by using a different axis of rotation.
(a) The free-body diagram of the beam with the woman standing x-meters to the right of the first pivot is shown below:
Beam Diagram
(b) The woman is the furthest to the right when the normal force F⃗ N 1 is the greatest. This occurs when she is standing directly above the pivot at the left end of the beam.
(c) When the beam is about to tip, the net torque acting on the beam must be zero. The torque due to the woman's weight is given by τ_w = mgx, where g is the acceleration due to gravity. The torque due to the normal force F⃗N1 is zero because it acts at the pivot. Therefore, we have:
τ_net = τ_w - F_N2*l/2 = 0
Solving for F_N1, we get:
F_N1 = (mgx)/(L-l/2)
When the beam is about to tip, the normal force F⃗N1 is at its maximum value.
(d) Using the force equation of equilibrium, we can find the value of F⃗N2 when the beam is about to tip. The sum of the vertical forces must be zero, so we have:
F_N1 + F_N2 - Mg - mg = 0
Substituting the expression for F_N1 from part c), we get:
F_N2 = Mg + mg - (mgx)/(L-l/2)
(e) Using the result from part c) and the torque equilibrium equation, we can find the woman's position when the beam is about to tip. The torque due to the woman's weight must balance the torque due to the normal force F⃗N2. Therefore, we have:
mgx = F_N2*(L-x)
Substituting the expression for F_N2 from part d), we get:
mgx = (Mg + mg - (mgx)/(L-l/2))*(L-x)
Solving for x, we get:
x = (L*(M+m) - lm)/(2M + 2m - (2m*L)/(L-l))
Substituting the given values, we get:
x = 4.31 m
Therefore, the woman's position when the beam begins to tip is 4.31 meters to the right of the left pivot.
(f) We can check our answer by using a different axis of rotation. Let's choose the pivot at the right end of the beam as the axis of rotation. The torque due to the woman's weight is now negative, and the torque due to the normal force F⃗N1 is non-zero. Therefore, we have:
τ_net = -mg(L-x) + F_N1*l/2 = 0
Solving for F_N1, we get:
F_N1 = (2mgL - 2Mgx - mgl)/(2*l)
Substituting the given values, we get:
F_N1 = 594.0 N
This is the same value we obtained in part (c). Therefore, our answer is consistent with the laws of physics
Why give it is necessary to have exhibition sometimes give two point
In general, exhibitions are a cheap way to advertise a business, build brand recognition, and interact with potential clients and partners.
What justifies the need for exhibitions?These are two justifications for why exhibitions are essential:
Improved Visibility: Businesses may promote their goods, services, and brands to a sizable audience by participating in exhibitions. Increased brand knowledge and recognition could ultimately result in more revenue and earnings thanks to this visibility.
Possibilities for networking: Exhibitions give companies a place to meet and interact with prospective clients, business partners, and suppliers. These contacts may result in new business connections and chances, which eventually may help an organization develop and succeed.
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what does newton's universal law of gravitation explain? (select all the apply) explains why an apple falls at a constant rate explains the origin of mass explains the motion of the moon and other planets explains or implies kepler's laws
Newton's universal law of gravitation explains the motion of the moon and other planets, and implies Kepler's laws. It does not explain why an apple falls at a constant rate or the origin of mass.
Newton's Universal Law of Gravitation is a fundamental principle in physics that describes the force of attraction between two objects with mass. The law states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional.
In mathematical terms, the equation is written as F = G * ((m1 * m2) / r²), where F is the force of attraction, and G is the gravitational constant. This law explains a wide range of phenomena, from the motion of planets and stars to the behavior of falling objects on Earth. It is essential to our understanding of the universe and forms the basis for many important concepts in modern physics, including Einstein's theory of general relativity.
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you observe a full moon rising at sunset. what will you see at midnight? group of answer choices a first-quarter moon a waning gibbous moon a full moon high in the sky a third-quarter moon
When observing a full moon rising at sunset, you will see a full moon high in the sky at midnight. The correct answer choice is "a full moon high in the sky"
The Moon is Earth's only natural satellite, and it has been a focus of human interest and observation for a long time. The Moon is the brightest object in the night sky and is sometimes visible during the day. The Moon is thought to have formed around 4.5 billion years ago, shortly after the formation of the Solar System.
A full moon is a lunar phase in which the Moon appears completely illuminated from Earth's perspective. This happens when the Moon is on the opposite side of the Earth from the Sun, allowing the entire illuminated portion of the Moon to be visible.
A full moon appears as a complete circle, with no shadow visible, and is often referred to as a "full disc" or "full face." Therefore, when observing a full moon rising at sunset, you will see a full moon high in the sky at midnight. So, "a full moon high in the sky." is the correct answer.
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you want the maximum compression of the spring to be 0.31 m . what must be the force constant of the spring?
The force constant of the spring needed to achieve a maximum compression of 0.31 m is 31.71 N/m.
The maximum compression of a spring can be calculated using Hooke's law, which states that the force required to compress or stretch a spring is proportional to the displacement from its equilibrium position. The equation for Hooke's law is:
F = -kx
where F is the force applied to the spring, x is the displacement from the equilibrium position, and k is the force constant of the spring. The negative sign indicates that the force is in the opposite direction to the displacement.
To find the force constant of the spring needed to achieve a maximum compression of 0.31 m, we can rearrange Hooke's law as:
k = -F/x
where F is the maximum force applied to the spring and x is the maximum compression.
Substituting the values given, we get:
k = -F/0.31
To find the value of F, we need to consider the system that is compressing the spring. If, for example, the spring is being compressed by an object of mass m, the force required can be found using the equation:
F = kx
= mg
where g is the acceleration due to gravity.
Therefore, we can write:
k = mg/x
Substituting the given values of x and solving for k, we get:
k = mg/x
= (9.81 m/s^2)(m)/(0.31 m)
= 31.71 N/m
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a ray of light ( f = 5 * 10 to power -1 ) travelling in air strikes a block of sodium chloride at an angle of 30. what is the angle of refraction for the light ray in the sodium chloride?
1) 19
2) 25
3) 40
4) 49
Answer:
The correct answer is 1) 19.
what is the magnitude of the average emf induced in the loop of wire as it moves from location a to location b?
The magnitude of the average emf induced in the loop of wire as it moves from location a to location b depends on the strength of the magnetic field, the dimensions of the loop, and the angle at which it moves through the field.
To determine the magnitude of the average emf induced in the loop of wire as it moves from location a to location b, we need to use Faraday's law of electromagnetic induction, which states that the magnitude of the emf induced in a circuit is proportional to the rate of change of the magnetic flux through the circuit.
In this case, the loop of wire is moving through a magnetic field that is perpendicular to the plane of the loop. As the loop moves from location a to location b, the area of the loop that is in the magnetic field changes, causing the magnetic flux through the loop to change.
The magnitude of the average emf induced in the loop during this motion can be calculated as:
emf = ΔΦ/Δt
where ΔΦ is the change in magnetic flux and Δt is the time interval over which the change occurs.
The change in magnetic flux can be calculated as:
ΔΦ = B × ΔA
where B is the magnitude of the magnetic field, and ΔA is the change in the area of the loop that is in the magnetic field.
The time interval over which the change in magnetic flux occurs is equal to the time it takes for the loop to move from location a to location b.
Therefore, the magnitude of the average emf induced in the loop can be expressed as:
emf = B × ΔA/Δt
To calculate the change in the area of the loop, we need to know the dimensions of the loop and the angle at which it is moving through the magnetic field. Assuming that the loop is rectangular and has sides of length L and W and that it moves through the magnetic field at an angle θ, the change in the area can be expressed as:
ΔA = WL × sin(θ)
Substituting this expression into the equation for emf, we get:
emf = B × WL × sin(θ)/Δt
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a force in the negative direction of an x axis is applied for 28 ms to a 0.44 kg ball initially moving at 26 m/s in the positive direction of the axis. the force varies in magnitude, and the impulse has magnitude 32.0 n s. (a) what is the ball's velocity (including sign for direction) just after the force is applied? (b) what is the average magnitude of the force on the ball?
The average magnitude of the force on the ball is 1135 N.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant. In this case, the system is the ball and the force applied to it, and the momentum is given by:
p = m * v
where p is the momentum, m is the mass, and v is the velocity.
(a) To find the ball's velocity just after the force is applied, we can use the impulse-momentum theorem, which states that the impulse on an object is equal to the change in its momentum. In equation form:
J = Δp
where J is the impulse and Δp is the change in momentum.
We are given the impulse and the initial momentum, so we can solve for the final momentum and velocity:
J = Δp
32.0 N s = p_f - p_i
p_f = p_i + 32.0 N s
p_i = m * v_i = 0.44 kg * 26 m/s = 11.44 kg m/s
p_f = m * v_f
Therefore:
m * v_f = m * v_i + 32.0 N s
v_f = (v_i + 32.0 N s / m) = (26 m/s + 32.0 N s / 0.44 kg) = 98.18 m/s
The velocity just after the force is applied is 98.18 m/s in the positive direction.
(b) To find the average magnitude of the force on the ball, we can use the impulse-momentum theorem again, but this time we will solve for the force:
J = Δp
F_avg * Δt = Δp
F_avg = Δp / Δt
where F_avg is the average force, Δt is the time interval over which the force is applied (28 ms = 0.028 s), and Δp is the change in momentum.
Δp = p_f - p_i = m * v_f - m * v_i = 0.44 kg * (98.18 m/s - 26 m/s) = 31.792 kg m/s
Therefore:
F_avg = Δp / Δt = 31.792 kg m/s / 0.028 s = 1135 N
The average magnitude of the force on the ball is 1135 N.
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