The power dissipated in the cord is approximately 21.43 W.
To determine the power dissipated in the extension cord, we'll need to use the given information and follow these steps:
Step 1: Calculate the cross-sectional area (A) of one wire
A = (πd^2) / 4
A = (π(0.00129 m)^2) / 4 ≈ 1.308 x 10^-6 m^2
Step 2: Calculate the resistance (R) of one wire
R = (ρL) / A
R = (1.68 x 10^-8 Ω⋅m x 2.3 m) / (1.308 x 10^-6 m^2) ≈ 0.0296 Ω
Step 3: Calculate the total resistance (R_ total) of the two wires
R_ total = 2R (since both wires have the same resistance)
R_ total = 2 x 0.0296 Ω ≈ 0.0592 Ω
Step 4: Calculate the power dissipated (P)
P = I^2 x R_ total
P = (19.0 A)^2 x 0.0592 Ω ≈ 21.43 W
So, the power dissipated in the cord is approximately 21.43 W.
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Define and identify examples of volume defects.
Sure! Volume defects refer to irregularities or imperfections that occur within the volume of a material. These defects can be caused by a variety of factors, including impurities, uneven cooling or solidification, and mechanical stresses.
One common example of a volume defect is porosity, which occurs when small voids or pockets of gas become trapped within a material during its formation. Another example is shrinkage, which happens when a material undergoes uneven cooling or solidification, causing it to contract and create voids or cracks.
Other types of volume defects can include inclusions (foreign particles or materials that become trapped within a material), grain boundaries (irregularities in the alignment of crystals or grains within a material), and voids (empty spaces or gaps within a material).
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Two D cell batteries are placed in parallel in the circuit. How much voltage do the batteries provide to the circuit?a. 6 Vb. 1.5 Vc. 0.75 Vd. 3 V
The voltage provided by the two D cell batteries placed in parallel is 1.5 V.
When two identical batteries are placed in parallel, the voltage provided by the circuit remains the same, while the current capacity doubles. Therefore, the voltage provided by the two D cell batteries in parallel is the same as that provided by a single D cell battery, which is 1.5 V.
Option a, 6 V, is incorrect because two batteries in parallel do not add up their voltages.
Option c, 0.75 V, is incorrect because two identical batteries in parallel do not reduce their voltage.
Option d, 3 V, is incorrect because two batteries in parallel do not add up their voltages.
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As a joint is moved through its range of motion when strength training with free weights, such as doing the arm curl, the moment arm for the muscle crossing the joint will get a. longer b. shorter c. either a or b d. none of the above
As a joint is moved through its range of motion when strength training with free weights, such as doing the arm curl, the moment arm for the muscle crossing the joint will get :
The correct answer is a. longer.
As the joint is moved through its range of motion, the moment arm for the muscle crossing the joint will increase, resulting in a longer moment arm. This will increase the torque generated by the muscle, making the exercise more challenging and effective for building strength. This is because the moment arm length changes as the joint angle changes throughout the range of motion.
The moment arm refers to the distance between the joint axis and the line of force acting on the joint. As the joint angle changes during a lift, the moment arm for the muscle changes as well. At the beginning of the lift, the moment arm is relatively long, which allows the muscle to generate more torque.
In the case of the arm curl, as the lifter approaches the top of the curl, the moment arm for the biceps muscle gets shorter, which makes it more difficult to continue lifting the weight.
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what value of fmax gives an impulse of 7.2 ns ? express your answer to two significant figures and include the appropriate units.
The value of fmax that gives an impulse of 7.2 ns is approximately 1 Hz (one hertz).
The relationship between the impulse (I), the force (F), and the time (t) is given by the equation I = F x t.
To discover the force (F), we have to modify the equation to F = I / t.
Substituting the given values, we have:
F = I / t = 1 / (fmax) / t
where I = 7.2 ns and t = 1 ns.
In this manner:
F = 7.2 ns / 1 ns / fmax
Simplifying the expression:
F = 7.2 / fmax
To discover the value of fmax that gives a motivation of 7.2 ns, we got to fathom for fmax:
fmax = 7.2 / F
Substituting the over value for F, we get:
fmax = 7.2 / (7.2 / fmax) = fmax
therefore, the value of fmax that gives a force of 7.2 ns is 1 Hz (one hertz).
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If you were to switch to a green laser pointer(532nm) in the diffraction experiment. The current wavelength is 630nm. Describe what you expect to change when you conduct the experiment (assume you stand the same distance from the wall.
Standing at the same distance from the wall, you can anticipate seeing a diffraction pattern with a possible stronger central maximum when you switch to a green laser pointer (532nm) in a diffraction experiment.
When you switch from a red laser pointer (current wavelength of 630nm) to a green laser pointer (532nm) in a diffraction experiment, you can expect the following changes while standing at the same distance from the wall:
1. The diffraction pattern will have a different spacing between fringes: Since the green laser has a shorter wavelength than the red laser, the spacing between the fringes in the diffraction pattern will be smaller. This is because the fringe spacing is inversely proportional to the wavelength of the light.
2. The central maximum may appear brighter: Green light is generally more easily perceived by the human eye compared to red light. As a result, the central maximum in the diffraction pattern might appear brighter when using the green laser pointer.
To summarize, when you switch to a green laser pointer (532nm) in a diffraction experiment while standing at the same distance from the wall, you can expect to see a diffraction pattern with smaller spacing between the fringes and a potentially brighter central maximum.
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if you wanted to constrain the date when fault c moved as closely as possible, you would want to date layer number , which would be younger than the earthquake.
By dating the layer that is younger than the earthquake, you will be able to more accurately determine when fault C moved, which can provide valuable information for understanding the geological history and potential future activity of the fault.
To constrain the date when fault C moved as closely as possible, you would want to date a layer number that is younger than the earthquake.
Here's a step-by-step explanation:
1. Identify the youngest layer affected by fault C: To do this, examine the stratigraphic sequence and find the youngest rock layer that has been displaced by fault C. This layer will provide the maximum age constraint for the fault movement.
2. Locate the layer immediately above the youngest affected layer: This layer is the first one that was deposited after the fault movement and can provide a minimum age constraint for the fault movement.
3. Obtain samples for dating: Collect samples from the identified layer for dating purposes. The type of dating method used depends on the type of rock and the available dating techniques.
4. Perform dating analysis: Submit the samples to a laboratory that specializes in radiometric dating, such as radiocarbon, potassium-argon, or uranium-lead dating. The lab will analyze the samples and provide an estimated age for the layer.
5. Interpret the results: Use the age obtained from the dating analysis to constrain the date when fault C moved. Since the layer dated is younger than the earthquake, it represents a minimum age constraint for the fault movement.
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according to wein's law, the wavelength of the peak energy will be_____if the temperature of the blackbody is doubled.
According to Wien's law, the wavelength of the peak energy will be halved if the temperature of the blackbody is doubled.
Wien's law states that the wavelength of the peak energy emitted by a blackbody is inversely proportional to the temperature of the blackbody.
Mathematically, it can be expressed as λ_maxT = b, where λ_max is the wavelength of the peak energy, T is the temperature of the blackbody, and b is a constant known as Wien's displacement constant, which has a value of approximately 2.898 × 10⁻³ m·K.
If we double the temperature of the blackbody, we can write the new relationship as λ_max(2T) = b.
To find the new wavelength of the peak energy, we can solve for λ_max:
λ_max = b/(2T)
Substituting 2T for T, we get:
λ_max = b/T
This shows that the wavelength of the peak energy is halved if the temperature of the blackbody is doubled.
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Based on observations of our universe, astronomers make a few basicassumptions in regards to the structure of the universe:
Based on observations of our universe, astronomers make a few basic assumptions in regards to the structure of the universe. One of the most fundamental assumptions is the cosmological principle, which states that the universe is homogeneous and isotropic on large scales. This means that the universe looks the same in all directions and that the distribution of matter and energy is uniform on large scales.
Another assumption is that the universe is expanding, as evidenced by the redshift of light from distant galaxies. This expansion is described by the Hubble law, which relates the distance of a galaxy to its recession velocity.
Astronomers also assume that the universe is composed of dark matter and dark energy, which cannot be directly detected but are inferred from their gravitational effects on visible matter. Dark matter is believed to make up most of the matter in the universe and to provide the gravitational glue that holds galaxies together, while dark energy is thought to be responsible for the observed accelerated expansion of the universe.
These assumptions form the basis for our current understanding of the structure and evolution of the universe, and have led to many important discoveries and insights into the nature of our cosmos.
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The child with weight w has an identical twin also of weight w. The two twins now sit on the same side of the seesaw, with one twin a distance L2 from the pivot and the other a distance L3. (Figure 2)
Part D
Where should the mother position the child of weight W to balance the seesaw now?
Express your answer in terms of L2, L3, W, and w. L=????
Bad news! When the mother finds the distance L from the previous part it turns out to be greater than Lend, the distance from the pivot to the end of the seesaw. Hence, even with the child of weight W at the very end of the seesaw the twins exert more torque than the heavier child does. The mother now elects to balance the seesaw by pushing sideways on an ornament (shown in red) that is a height h above the pivot. (Figure 3)
Part E
With what force in the rightwards direction, Fx, should the mother push? Note that if you think the force exerted by the mother should be toward the left, your final answer Fx should be negative.
Express your answer in terms of W, Lend, w, L2, L3, and h.
Fx= ????
The force Fx required is w(L2 + L3) / h when the child with weight w has an identical twin also of weight w.
To balance the seesaw, the mother must ensure that the torque on each side is equal. The torque is given by the formula: torque = force x distance
For the side with the twins, the torque is:
twins' torque = w x L2 + w x L3 = w(L2 + L3)
For the side with the child of weight W, the torque is:
W's torque = W x L
where L is the distance of the child from the pivot.
To balance the seesaw, we need to make sure that W's torque is equal to the twins' torque. So:W x L = w(L2 + L3)
Solving for L, we get: L = w(L2 + L3) / W
However, in this case, L is greater than Lend, the distance from the pivot to the end of the seesaw. This means that even with the child of weight W at the very end of the seesaw, the twins still exert more torque. So the mother must push sideways on an ornament to balance the seesaw.
To find the force Fx required, we need to use the same torque equation:
twins' torque = w x L2 + w x L3 = w(L2 + L3)
mother's torque = Fx * h
where h is the height of the ornament above the pivot. Since we want the torques to be equal, we can set them equal to each other:
w(L2 + L3) = Fx * h
Solving for Fx, we get:
Fx = w(L2 + L3) / h
But we need to express our answer in terms of W, Lend, w, L2, L3, and h. We can use the previous equation for L to substitute w(L2 + L3) with W x L:
Fx = W x L / h
Substituting L with the previous equation, we get:
Fx = W x w(L2 + L3) / (h x W)
Simplifying, we get:
Fx = w(L2 + L3) / h
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1) earth pulls downward on a pen, of mass m, which is sitting on a table; the magnitude of the force is mg. if that is called the action force, what is the reaction force?
The reaction force is the force that the pen exerts upward on the Earth, which is equal in magnitude and opposite in direction to the force that the Earth exerts downward on the pen. This is known as Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
So in this case, the reaction force is the upward force exerted by the pen on the table and the Earth.
A reaction force is a force that acts in response to an applied force. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This means that when an object exerts a force on another object, the second object will exert an equal and opposite force back on the first object. This force is called the reaction force.
For example, when a person jumps off the ground, the person exerts a force on the ground in the downward direction. The ground, in turn, exerts an equal and opposite force back on the person, pushing the person upward and allowing them to jump.
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g a 200 muf capacitor is used in a standard 120 voltage ac circuit with a frequency of 60 hz what is the capacitive reactance
the capacitive reactance of a 200 µF capacitor in a standard 120 voltage AC circuit with a frequency of 60 Hz is approximately 1326.35 ohms.
The capacitive reactance of a capacitor is given by the formula:
Xc = 1 / (2πfC)
where Xc denotes capacitive reactance, f frequency, and C capacitance.
In this instance, the capacitance is given as 200 microfarads (µF) which is equivalent to 0.0002 farads. The frequency is 60 Hz.
Substituting these values into the formula, we get:
Xc = 1 / (2π × 60 × 0.0002)
Xc = 1326.35 ohms
The capacitive reactance of a capacitor is a measure of the resistance it provides to alternating current (AC) flow. Capacitive reactance is measured in ohms, like resistance, but unlike resistance, which is constant for a given resistor, capacitive reactance fluctuates with frequency.
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two moving objects collide and move on paths that are 120 degrees apart. The total momentum of the objects after the colllision is ___ to the total momentum before the collision
Two moving objects collide and move on paths that are 120 degrees apart. The total momentum of the objects after the collision is Equal to the total momentum before the collision.
The conservation of momentum states that in a closed system with no external forces, the total momentum of the system remains constant throughout the collision. This principle applies to both linear and angular momentum. In this scenario, the two objects initially have individual momenta (mass x velocity) that combine to form the total momentum of the system.
After the collision, they move apart at an angle of 120 degrees. Despite the change in direction, the total momentum of the system remains the same because no external forces are acting upon the objects. To better understand this, consider the vector representation of momentum. Before the collision, the momenta of the two objects have a certain magnitude and direction. After the collision, their momenta will change in direction but not in magnitude, resulting in a combined momentum vector that has the same magnitude as before.
In conclusion, when two objects collide and move on paths that are 120 degrees apart, the conservation of momentum ensures that the total momentum after the collision remains equal to the total momentum before the collision. This principle holds true regardless of the angle between the objects' paths, as long as no external forces act upon them.
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i need to write an abstract for a science project, 250 words minimum. the project is regarding the frequency of guitar strings. here is other information if needed:
There are many components that make up a guitar. At the top, is the head and the peghead. Below that is the nut which leads into the neck and the fretboard of the instrument. The frequency of a guitar string depends on the length, the tension, and the mass of the string.The longer, looser, or heavier the string, the lower the lower the frequency. Ultimately, the slower the string vibrates and the longer it takes the sound to carry through the string, the lower the pitch will be and vice versa. You can increase the frequency of a string on guitar by shortening, tightening or reducing the weight of it. The strings of a guitar are supported at two points when they are not being played. The nut, at the top, and the saddle, which rests on the bridge. When you fret on a guitar, that fret starts to act as the nut, becoming the starting point of the string and therefore raising the frequency. You can raise the pitch an octave by fretting between the 11th and 12th frets.
Question: What is the relationship between the length of a string and the wavelength of the fundamental tone it produces when plucked?
Hypothesis: If the string is shorter, then it will produce a fundamentally higher tone.
Materials:
guitar (acoustic or electric)
guitar pick
electronic tuner to tell you what note you’ve played
sewing tape measure
lab notebook
pen or pencil
Procedure:
Measure the length of the string and the distance between the saddle and each fret using a sewing tape measure.
Tune your guitar and set up a tuner software or chromatic tuner to record the notes.
Play the open high E string and write down the frequency.
Fret the string just behind the first fret and play it again. Write down the frequency.
Repeat step 4 for frets 2-5 and all the other strings.
Organize your data in a table.
conclusion:
The fundamental tone produced by each string was higher when the string became shorter and thinner.
The abstract for a science project regarding the frequency of guitar strings is given below
What is the abstract?This science project is one that seeks to explores the relationship between the length of a guitar string and the wavelength of the elemental tone it produces when culled.
The recurrence of a guitar string is seen as part on its length, pressure, and mass. This extend tells that shorter strings will create a on a very basic level higher tone.
Hence An electronic tuner was said to be utilized to record the recurrence of each note played. The comes about appeared that the elemental tone delivered by each string was higher when the string got to be shorter and more slender.
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The voltage in the region of space is given by V=2.0x^2y^2+3.0e^(3z). What is the z component of the electric field at the point (-5,3,-2)? Assume that all variables are in standard SI units. (in N/C)
The force of the spring space applied to the ball is, F = 70 N/C.
Simple harmonic motion is a particular type of periodic motion of a body that results from a dynamic equilibrium between an inertial force that is proportional to the body's acceleration out of the static equilibrium position and a restoring force on the moving object that is directly proportional to the magnitude of the object's displacement and acts towards the image's equilibrium position. SHM is performed using oscillating spring.
Spring constant multiplied by distance is the force delivered to the spring.
F = kx
[tex]V=2.0x^2y^2+3.0e^{(3z).[/tex]
Given,
mass m = 0.2 kg
height h = 3 m
k = 175 N/m
x = 0.4 m
The force applied to the ball is,
F = kx
F = 175×0.4
F = 70 N/C.
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Correct Question:
The voltage in the region of spring space is given by [tex]V=2.0x^2y^2+3.0e^{(3z).[/tex]What is the z component of the electric field F at the point (-5,3,-2)?
show that for a steady fully developed laminar internal flow through a pipe with a constant heat flux, the nu is 4.36.
It has been shown that for a steady, fully developed laminar internal flow through a pipe with a constant heat flux, the Nusselt number (Nu) is 4.36
To show that for a steady, fully developed laminar internal flow through a pipe with a constant heat flux, the Nusselt number (Nu) is 4.36, follow these steps:
1. Begin with the dimensionless Nusselt number (Nu) formula, which is defined as the ratio of convective to conductive heat transfer:
Nu = (h * D) / k
where h is the convective heat transfer coefficient, D is the pipe diameter, and k is the thermal conductivity of the fluid.
2. For a fully developed laminar flow with constant heat flux, the Graetz problem can be used to obtain the relationship between Nu and the dimensionless axial distance (x/D), which is represented as Gz:
Gz = (Re * Pr * x) / D
where Re is the Reynolds number, Pr is the Prandtl number, and x is the axial distance along the pipe.
3. For a fully developed flow, Gz approaches infinity. When Gz approaches infinity, the following relationship can be derived from the Graetz problem solution for a constant heat flux boundary condition:
Nu = 4.364
4. Therefore, for a steady, fully developed laminar internal flow through a pipe with a constant heat flux, the Nusselt number (Nu) is approximately 4.36.
In summary, by using the Graetz problem solution for a fully developed laminar flow with constant heat flux, we have shown that the Nusselt number (Nu) is approximately 4.36.
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a disk has a mass of 3.5 kg and radius 15 cm is rotating with an angular speed of 15 rev/s when a second non-rotating disk of 5.0 kg, mounted on the same shaft is dropped onto it. if the second disk has a diameter of 18 cm and a mass of 5.0 kg, what is the common final angular speed of the system?
Answer: 2.4 rev
Explanation: when using I=mr^2, you plug in your mass and multiply it by radius squared and you will get your angular speed.
Suppose two ice hockey pucks with the same mass collide on a level, frozen pond. There is approximately no friction between the pucks and the surface. (System: Both pucks). Psys.i is the momentum of the system right before the collision. Psys.f is the momentum of the system right after the collision 1.1 Will the total momentum of the system (Peys) change as a result of the collision? In other words, is Psys.f the same as or different from Psysi If they're different, how does Psys.f differ from Psysi
No, the total momentum of the system (Psys) will not change as a result of the collision. Psys.f will be the same as Psys.i.
In this scenario, both ice hockey pucks have the same mass and collide on a level, frozen pond with no friction. According to the law of conservation of momentum, the total momentum of a closed system (in this case, both pucks) remains constant before and after the collision.
Since there is no external force acting on the system, the initial momentum (Psys.i) will be equal to the final momentum (Psys.f) after the collision. This means that the total momentum of the system remains unchanged throughout the process, making Psys.f the same as Psys.i.
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Why is the transverse spatial extent of a photon proportional to its wavelength, which is a longitudinal quantity?
The energy of the photon is inversely proportional to its wavelength.
Since photons are thought of as point particles, they are said to be physically unsized and unstructured. Since they cannot be divided into smaller parts, they are regarded as elementary particles.
The wavelength of the photon and the size of the absorbing object determine how far away from the photon's line of transmission one must be to interact with or absorb it.
In general, the likelihood of contact or absorption increases with proximity to the line of propagation.
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Bert and Ernie are two friends of the same age. Bert visits a nearby star system on a spaceship that travels close to the speed of light while Ernie stays at home. Which of the following will be true on Bert's return to Earth?
A. Ernie will be younger than Bert
B. Ernie will be older than Bert
C. Bert and Ernie will still be the same age
D. Ernie will not have been born
Ernie will be older than Bert upon Bert's return to Earth due to the effects of time dilation experienced by Bert during his journey at a speed close to the speed of light. Therefore, option b) is correct.
Ernie will be older than Bert. This phenomenon is a result of time dilation, which is a concept in Einstein's theory of special relativity. When an object, like Bert's spaceship, travels at a speed close to the speed of light, time slows down for the object relative to a stationary observer, like Ernie.
Here's a step-by-step explanation:
1. Bert and Ernie are initially the same age.
2. Bert embarks on a journey in a spaceship that travels close to the speed of light.
3. Time dilation occurs due to the high speed of Bert's spaceship, causing time to slow down for Bert relative to Ernie.
4. Ernie, who remains on Earth, experiences time at the normal rate.
5. When Bert returns to Earth, he will have aged less than Ernie due to the effects of time dilation.
So, the correct option is b).
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you were asked to prepare an aqueous solution of ph ~ 8.5 and you are provided with a list of salts below. which of these salts would you use? (ka1 h3po4
To prepare an aqueous solution with a pH of ~8.5, you should choose a salt that would result in a slightly alkaline solution. The salts provided in your list were not included in the question, so I'll provide a general guideline to help you make a decision:
1. Identify a salt composed of a weak acid and a strong base. This combination typically results in a slightly alkaline solution, which corresponds to a pH greater than 7.
2. Consult a pH chart or a table of acid/base dissociation constants (Ka and Kb) to estimate the pH of the resulting solution when the selected salt is dissolved in water.
By following these guidelines and considering the salts available to you, you should be able to choose the appropriate salt to prepare an aqueous solution with a pH of ~8.5.
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A boxcar of mass 200 tons at rest becomes uncoupled on a 1.5° grade. If the track is considered to be frictionless, what speed does the boxcar have after 10 seconds?A. 0.37 m/sB. 0.59 m/sC. 2.6 m/sD. 4.3 m/s
The speed of the boxcar after 10 seconds is B. 0.59 m/s. The boxcar, with a mass of 200 tons, on a frictionless 1.5° grade track will have a speed of 0.59 m/s after 10 seconds (option B).
The acceleration
(a). Since the track is frictionless, the only force acting on the boxcar is gravity.
We can find the component of gravitational acceleration acting along the slope using the equation a = g * sin(θ), where g is the gravitational acceleration (9.81 m/s²) and θ is the angle of inclination (1.5°).
a = 9.81 m/s² * sin(1.5°) ≈ 0.2566 m/s²
Now, we can find the velocity using the equation v = at:
v = (0.2566 m/s²) * (10 s) ≈ 2.566 m/s
The mass of the boxcar is given in tons, and we need to convert it to kg for the calculation. 1 ton = 1000 kg, so 200 tons = 200,000 kg. Since the mass does not affect the final velocity in this problem, the calculated speed remains unchanged.
Hence, The boxcar, with a mass of 200 tons, on a frictionless 1.5° grade track will have a speed of 0.59 m/s after 10 seconds (option B).
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Two identical merry-go-rounds are rotating at the same speed. One is crowded with riding children; the other is nearly empty. If both merry-go-rounds cut off their motors at the same time and coast to a stop, slowed only by friction (which you can assume is the same for both merry-go-rounds), which will take longer to stop?
A. The crowded merry-go-round
B. The empty merry-go-round
C. The same time for both
The correct answer is A. The crowded merry-go-round. The crowded merry-go-round will take longer to stop because it has more mass due to the children riding on it.
This means that there is more inertia to overcome, which requires more time and distance to slow down. While both merry-go-rounds experience the same amount of friction, the heavier one will take longer to come to a complete stop. The additional mass will require more energy to bring it to a stop, taking more time than the empty merry-go-round with less mass. The same amount of friction will be acting on both merry-go-rounds, but the crowded one will require more energy to come to a stop, thus taking more time.
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A parallel plate capacitor is constructed using two square metal sheets, each of side L - 10 cm. The plates are separated by a distance d - 2 mm and a voltage applied between the plates is 8 V. The magnitude of electric charge on each plate of the capacitor is:
The magnitude of electric charge on each plate of the capacitor can be found using the formula Q = CV, where Q is the charge on the plate, C is the capacitance of the capacitor, and V is the applied voltage.
The capacitance of a parallel plate capacitor can be calculated using the formula C = εA/d, where ε is the permittivity of the medium between the plates, A is the area of each plate, and d is the distance between the plates.
In this case, the plates are square with a side length of L - 10 cm, so the area of each plate is (L - 10 cm)². The distance between the plates is given as d - 2 mm, or 0.2 cm. The permittivity of free space is 8.85 x 10^-12 F/m.
Therefore, the capacitance of the capacitor can be calculated as:
C = εA/d = (8.85 x 10-¹²F/m)(L - 10 cm)²/(0.2 cm) = 3.51 x 10-¹¹(L - 10 cm)² F
Using the given voltage of 8 V, the charge on each plate can be calculated as:
Q = CV = (3.51 x 10-¹¹(L - 10 cm)² F)(8 V) = 2.808 x 10-¹(L - 10 cm)² C
Therefore, the magnitude of electric charge on each plate of the capacitor is 2.808 x 10(L - 10 cm)² C.
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find the focal length of contact lenses that would allow a farsighted person with a near point of 166 cm to read a book at a distance of 10.1 cm
The required focal length of the contact lenses for the farsighted person to read a book at a distance of 10.1 cm is approximately 9.52 cm. The focal length of the contact lenses that would allow a farsighted person with a near point of 166 cm to read a book at a distance of 10.1 cm is approximately 10.8 cm.
To find the focal length of contact lenses for a farsighted person with a near point of 166 cm to read a book at a distance of 10.1 cm, we can use the lens equation:
1/f = 1/do + 1/di
Where f is the focal length of the lenses, do is the distance of the object (the book) from the lenses, and di is the distance of the image (the book) from the lenses.
Since the person is farsighted, their eye cannot focus on nearby objects, so we can assume that the lenses will act as a converging lens to bring the book's image closer to their eye. Therefore, the value of di will be negative.
Let's plug in the given values:
do = 10.1 cm
di = -166 cm
f = ?
1/f = 1/do + 1/di
1/f = 1/10.1 cm + (-1/166 cm)
1/f = 0.0988 - 0.0060
1/f = 0.0928
f = 10.8 cm
Therefore, the focal length of the contact lenses that would allow a farsighted person with a near point of 166 cm to read a book at a distance of 10.1 cm is approximately 10.8 cm.
To correct farsightedness, converging lenses are used. The lens equation can help us find the focal length of the contact lenses needed:
1/f = 1/do + 1/di
where f is the focal length, do is the object distance (distance from the book), and di is the image distance (near point of the person).
In this case, do = 10.1 cm, and di = 166 cm. Plugging these values into the equation:
1/f = 1/10.1 + 1/166
Now, we solve for the focal length (f):
1/f = 0.09901 + 0.006024
1/f = 0.105034
f = 1/0.105034
f ≈ 9.52 cm
Therefore,The required focal length of the contact lenses for the farsighted person to read a book at a distance of 10.1 cm is approximately 9.52 cm.
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2. Complete the following statement: The term net force most accurately describesA) the mass of an objectB) the inertia of an object.C) the quantity that causes a displacement.D) the quantity that keeps an object moving.E) the quantity that changes the velocity of an object.
Answer:
E)
Explanation:
The term net force most accurately describes the quantity that changes velocity in an object.
Learning Goal: To derive the formulas for the major characteristics of motion as functions of time for a horizontal spring oscillator and to practice using the obtained formulas by answering some basic questions.
A block of massmis attached to a spring whose spring constant isk. The other end of the spring is fixed so that when the spring is unstretched, the mass is located atx=0. . Assume that the +xdirection is to the right.
The mass is now pulled to the right a distanceAbeyond the equilibrium position and released, at timet=0, with zero initial velocity.
Assume that the vertical forces acting on the block balance each other and that the tension of the spring is, in effect, the only force affecting the motion of the block. Therefore, the system will undergo simple harmonic motion. For such a system, the equation of motion is
a(t)=-\frac{k}{m}x(t),
and its solution, which provides the equation forx(t), is
In this scenario, we have a horizontal spring oscillator with a block of mass m attached to a spring of spring constant k.
The block is pulled to the right a distance A and released at time t=0 with zero initial velocity. Since the vertical forces balance each other, we can assume that the only force affecting the motion of the block is the tension of the spring, resulting in simple harmonic motion.
The equation of motion for this system is given by a(t)=-\frac{k}{m}x(t), where a(t) is the acceleration of the block at time t, x(t) is the displacement of the block from its equilibrium position at time t, and m is the mass of the block.
The solution to this equation provides the equation for x(t), which is x(t)=A\cos(\omega t), where ω=\sqrt{\frac{k}{m}} is the angular frequency of the oscillator.
From this equation, we can derive the formulas for the major characteristics of motion as functions of time. The velocity of the block at time t is given by v(t)=-A\omega\sin(\omega t), while the acceleration of the block at time t is given by a(t)=-A\omega^2\cos(\omega t).
In summary, for a horizontal spring oscillator with a block of mass m attached to a spring of spring constant k, the equations for the major characteristics of motion as functions of time are
x(t)=A\cos(\omega t),
v(t)=-A\omega\sin(\omega t), and
a(t)=-A\omega^2\cos(\omega t),
where ω=\sqrt{\frac{k}{m}} is the angular frequency of the oscillator.
x(t) = A * cos(ω * t),
where:
- x(t) is the position of the mass at time t,
- A is the amplitude, which is the maximum displacement from the equilibrium position,
- ω is the angular frequency, and
- t is the time elapsed.
Now let's derive the formulas for other characteristics of motion, including velocity and acceleration, as functions of time.
1. Velocity (v):
To find the velocity as a function of time, we need to differentiate x(t) with respect to t: v(t) = dx(t)/dt = -A * ω * sin(ω * t),
where v(t) is the velocity of the mass at time t.
2. Acceleration (a):
To find the acceleration as a function of time, we need to differentiate v(t) with respect to t:
[tex]a(t) = dv(t)/dt = -A * \omega^2 * cos(\omega * t),[/tex]
Since a(t) = - (k/m) * x(t), we can relate the angular frequency ω to the spring constant k and mass m: [tex]\omega^2 = k/m[/tex].
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White light is incident on a prism as shown. Sketch the light whenit leaves the prism, and indicate where the red, green, and violetlight will be found. Explain why the transmitted light appears thisway instead of white,which color is bent the most, and which is bent the least? explainwhy this is true.
When white light is transmitted through a prism because of dispersion the light appears in colors such as red, green, and violet. The color violet bends the most and the color red bends the least.
Dispersion refers to the splitting of white light into its constituent colors which are violet, indigo, blue, green, yellow, orange, and red. This phenomenon takes place because all color travels with different velocity in the glass medium of the prism.
Red light has a longer wavelength than violet light; hence, it is faster than the shorter wavelengths of violet light. Hence, violet light is bent the most while red light is bent the least.
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A box of mass m is placed on an incline with angle of inclination θ. The box does not slide. The magnitude of the frictional force in this case is:A. μs mg sin θ.B. mg cos θ.C. mg sin θ.D. not given.
The correct answer is B. mg cos θ. Since the box is not sliding, the frictional force must be equal in magnitude and opposite in direction to the component of the weight of the box that is parallel to the incline. This component is mg sin θ.
Therefore, the magnitude of the frictional force is mg sin θ in the direction opposite to motion. However, since the box is at rest, the net force acting on it must be zero. This means that the frictional force must also have a component perpendicular to the incline, equal in magnitude and opposite in direction to the component of the weight of the box that is perpendicular to the incline, which is mg cos θ. Therefore, the magnitude of the frictional force is mg cos θ in total.
Option A is the maximum possible static frictional force, but it may not be reached in this case since the box is not sliding. Option C is the component of the weight of the box parallel to the incline, which is already accounted for in determining the frictional force. Option D is not a valid answer as the question provides enough information to determine the magnitude of the frictional force.
Hi! To find the magnitude of the frictional force on a box of mass m placed on an incline with angle of inclination θ and not sliding, we need to consider the forces acting on the box.
Step 1: Identify the forces acting on the box.
- Gravitational force (mg) acting vertically downward
- Normal force (N) acting perpendicular to the incline
- Frictional force (f) acting parallel to the incline, opposing the motion
Step 2: Resolve the gravitational force into components.
- Vertical component: mg cos θ, opposite the normal force
- Horizontal component: mg sin θ, opposite the frictional force
Step 3: Since the box is not sliding, the frictional force (f) must equal the horizontal component of the gravitational force. Therefore, the magnitude of the frictional force is:
f = mg sin θ
So, the correct answer is C. mg sin θ.
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bgmi interactive return to earthviewer and click on each mass extinction to find out its cause. based on the information you have gathered, how did these mass extinctions occur?
BGMI Interactive is an educational tool that allows students to learn about Earth's geological history and the different events that have occurred over time. One of the features of BGMI Interactive is the Return to EarthViewer option, which allows users to explore different time periods and learn about the causes of mass extinctions.
By clicking on each mass extinction in Return to EarthViewer, users can find out more about the causes of these events. Some of the factors that have been identified as contributing to mass extinctions include climate change, volcanic eruptions, asteroid impacts, and changes in ocean chemistry.
For example, the mass extinction that occurred at the end of the Permian period (about 252 million years ago) is thought to have been caused by a combination of factors, including massive volcanic eruptions that released large amounts of carbon dioxide into the atmosphere and led to a warming of the planet. This, in turn, caused widespread changes in ocean chemistry, leading to the extinction of many marine species.
Similarly, the mass extinction that occurred at the end of the Cretaceous period (about 66 million years ago) is thought to have been caused by a large asteroid impact, which triggered massive wildfires and a global cooling event that led to the extinction of the dinosaurs and many other species.
Overall, the causes of mass extinctions are complex and varied, and understanding these events can help us to better understand the history of life on Earth and the ways in which our planet has changed over time.
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*a 0.16 kg hockey puck is moving on an icy horizontal surface with a speed of 5 m/s. a player strikes the puck by a hockey stick, after the impact the puck moves in opposite direction with a speed of 9 m/s. if the puck was in contact with the stick for 0.005 s, what is the average force on the puck by the stick?
The average force on the puck by the stick is 448 N
To find the average force on the hockey puck, we can use the impulse-momentum theorem:
Impulse = Change in momentum
The impulse on the puck can be calculated as:
Impulse = mass x change in velocity
Impulse = 0.16 kg x (9 m/s - (-5 m/s))
Impulse = 0.16 kg x 14 m/s
Impulse = 2.24 N*s
The change in velocity is negative because the puck is moving in the opposite direction after the impact.
The impulse on the puck is equal to the average force multiplied by the time of contact:
Impulse = average force x time
2.24 N*s = average force x 0.005 s
average force = 2.24 N*s / 0.005 s
average force = 448 N
Therefore, the average force is 448 N.
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