Answer:
\(F_g=461lb_f\)
Explanation:
First calculate the mass of the asteroid. To do so, you need to find the volume and know the density of iron.
If r = d/2 = 645ft, then:
\(V = \frac{4}{3} \pi r^3\)
\(V = \frac{4}{3} \pi r^3\\V = 1.124\times10^{9}ft^3\delta_{iron}=m/V=491lb/ft^3m=V\times\delta=5.519\times10^{11}lb\)
In order to find force, use Newton's universal law of gravitation:
\(F_g=G\frac{m_1m_2}{d^2}\)
Where,
G= the gravitational constant:
\(G= 1.068846 \times10^{-9} ft^3 lb^{-1} s^{-2}\)
\(F_g=461lb_f\)
The amplitude of oscillations reduces to one-sixth of its original value in 10 oscillations. Find the logarithmic decrement.
Answer:
Explanation:To describe a damped harmonic oscillator, add a velocity dependent term, bx, where b is the vicious damping coefficient.
how can an object have the same speed and mass but change its momentum?
Answer: It can change its direction
Explanation:
Momentum is a vector, which has magnitude and direction. An object can have the same speed and mass (magnitude) but if it changes direction, it just changed its momentum
During a normal reaction to a stressful event, muscles are moved to their maximum capacity, and sensitivity is
Answer:
The paper focuses on the biology of stress and resilience and their biomarkers in humans from the system science perspective. A stressor pushes the physiological system away from its baseline state toward a lower utility state. The physiological system may return toward the original state in one attractor basin but may be shifted to a state in another, lower utility attractor basin. While some physiological changes induced by stressors may benefit health, there is often a chronic wear and tear cost due to implementing changes to enable the return of the system to its baseline state and maintain itself in the high utility baseline attractor basin following repeated perturbations. This cost, also called allostatic load, is the utility reduction associated with both a change in state and with alterations in the attractor basin that affect system responses following future perturbations. This added cost can increase the time course of the return to baseline or the likelihood of moving into a different attractor basin following a perturbation. Opposite to this is the system's resilience which influences its ability to return to the high utility attractor basin following a perturbation by increasing the likelihood and/or speed of returning to the baseline state following a stressor. This review paper is a qualitative systematic review; it covers areas most relevant for moving the stress and resilience field forward from a more quantitative and neuroscientific perspective.
Explanation:
During a normal reaction to a stressful event, muscles are moved to their maximum capacity, and sensitivity is increased.
What is Sensitivity?This is defined as the ability of an organism to respond to stimuli such as touch, sensation etc.
During exercise, sensitivity to substances such as insulin when glucose transport wears off helps to balance energy supply.
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A uniform electric field is directed upward and has a magnitude of 24 N/C. A charge of -6 C is placed in this
field.
The direction of the force on the charge placed in the electric field is upward.
True or False
The statement" The direction of the force on the charge placed in the electric field is upward" is false because the direction of the force on a negative charge (-6 C) placed in an upward-directed uniform electric field of magnitude 24 N/C would be downward.
The direction of the force on a charged particle placed in an electric field is determined by the charge of the particle and the direction of the electric field. In this case, a charge of -6 C is placed in an electric field directed upward with a magnitude of 24 N/C.
The force on a charged particle in an electric field can be calculated using the formula:
F = q * E
Where F is the force, q is the charge of the particle, and E is the electric field.
Since the charge q in this case is negative (-6 C) and the electric field E is directed upward, we can substitute the values into the formula:
F = (-6 C) * (24 N/C)
F = -144 N
The negative sign in the force value indicates that the force is in the opposite direction to the electric field. Therefore, the force on the charge placed in the electric field is downward, not upward.
The force on a negative charge is always opposite to the direction of the electric field. This is because negative charges experience an attractive force towards positive charges, and electric fields are directed from positive charges to negative charges.
Therefore, the statement "The direction of the force on the charge placed in the electric field is upward." is false.
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A charge +Q is located at the origin and a second charge, +4Q, is at distance (d) on the x-axis.
a. Where should a third charge, Q , be placed, so that all three charges will be in equilibrium? Express your answer in terms of d.
b. What should be its sign, so that all three charges will be in equilibrium?
c. What should be its magnitude, so that all three charges will be in equilibrium? Express your answer in terms of Q.
Answer:
a) x = ⅔ d , b) the charge must be negative, c) Q
Explanation:
a) In this exercise the force is electric between the charges, we are asked that the system of the three charges is in equilibrium, we use Newton's second law. Balance is on the third load that we are placing
∑ F = 0
-F₁₂ + F₂₃ = 0
F₁₂ = F₂₃
let's replace the values
k Q Q / r₁₂² = k Q 4Q / r₂₃²
Q² / r₁₂² = 4 Q² / r₂₃²
suppose charge 3 is placed at point x
r₁₂ = x
r₂₃ = d-x
we substitute
1 / x² = 4 / (d-x) 2
1 / x = 2 / (d-x)
x = 2 (x-d)
x = 2x -2d
3x = 2d
x = ⅔ d
b) The sign of the charge must be negative, to have an attractive charge on the two initial charges
c) Q
How much more efficient is organic farming than "regular" farming?
Answer:
Organic systems used 45% less energy overall than conventional systems. Production efficiency was 28% higher in the organic systems, with the conventional no-till system being the least efficient in terms of energy usage.
Answer: 65%
Explanation: i took the quiz
A 75 kg bungee jumper leaps from a bridge. When he is 30 meters above the water, and moving at a speed of 20 m/s, the bungee cord begins to stretch. The cord stops his motion exactly at the water surface. Determine the spring constant of the bungee cord. Assume no thermal losses.
Answer:
k = 52.2 N / m
Explanation:
For this exercise we are going to use the conservation of mechanical energy.
Starting point. When it is 30 m high
Em₀ = K + U = ½ m v² + m g h
Final point. Right when you hit the water
\(Em_{f}\) = K_{e} = ½ k x²
in this case the distance the bungee is stretched is 30 m
x = h
as they indicate that there are no losses, energy is conserved
Em₀ = Em_{f}
½ m v² + m g h = ½ k h²
k = \(\frac{m (v^{2} + 2 g h)}{h^{2} }\)
let's calculate
k = \(\frac{75 \ ( 20^{2} + 2 \ 9.8 \ 30)}{30^{2} }\)
k = 52.2 N / m
A frictionless roller-coaster is given a maximum possible initial speed v0= 9.1 m/s when it is at height y0 = 6 m above the ground and moves freely afterwards, see figure below. What will be the roller-coaster’s speed when it reaches the lowest point at y1 = 4.4 m?
Explanation:
The equation of motion for a frictionless roller coaster is given by: v2 = v02 + 2ay, where v0 is the initial velocity, a is the acceleration due to gravity (9.8 m/s2), and y is the height.
Plugging in the given values of v0, y0 and y1, we get: v2 = 92 + 2(9.8)(-2.6) = 77.88 m/s2.
Therefore, the speed of the roller coaster at the lowest point (y1) will be v = √77.88 m/s = 8.82 m/s.
Why must humans limit their exposure to X-rays and gamma rays?
A. The rays can change molecules and atoms in the body into ions.
B. Exposure can cause the human body to give off heat.
O C. Even a small amount of radiation can burn the skin.
D. These rays act similarly to microwaves on the human body.
Answer:
A. The rays can change molecules and atoms in the body into ions.
What do I have to do on these help me out
Momentum After ∞ The velocity of the truck after the collision is 10m/s.
What is velocity ?Velocity is a vector quantity that measures the rate of change of an object's position with respect to time. It is a physical quantity that describes both the speed and direction of an object's motion. Velocity is the rate of change of an object's position, and is equal to the total distance traveled divided by the total time it took to travel that distance. It is represented by the symbol v, and its SI unit is m/s. Velocity is an important concept in physics, as it is used to describe the motion of objects in the universe.
This is because the total momentum before the collision (5000kg*20m/s) is equal to the total momentum after the collision (5000kg*10m/s + 1200kg*0m/s). So, the velocity of the truck after the collision is equal to 10m/s.
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A car accelerates at a rate of 9 ft/s/s for a time of 11 seconds. How far does the car go?
A ball starts from rest and accelerates at 0.470 m/s2 while moving down an inclined plane 9.45 m long. When it reaches the bottom, the ball rolls up another plane, where, after moving 16.1 m, it comes to rest. What is the speed of the ball at the bottom of the first plane?
How long does it take to roll down the first plane?
What is the acceleration along the second plane?
What is the ball's speed 7.35 m along the second plane?
The ball's speed 7.35 m along the second plane 3.20m 2 /s 2
What is the ball's speed ?At the top and bottom of the first inclination, respectively, measure the starting and ending locations. If the ball is at rest when it begins, v I =0, a =0.470m/s 2, and x f -x I =9.45m. Consequently, v f 2 = v I 2 + 2a(x f x I )=0 2 + 2(0.470m/s 2 )(9.45m) v f =3.00m/s
(b) In order to determine the time interval, we utilize the formula x f x I =v I t+ 2 1 at 2.
Upon plugging in, 9.00=0+ 2 1 (0.470m/s 2 )t 2
t=6.00s
(c) Consider the beginning and end locations as being, respectively, at the bottom of the first plane and the top of the second plane: v I = 3.00 m/s, v f = 0, and x f -x I = 16.1 m. We employ the formula v f 2 = v I 2 + 2a(x f x i), where
This results in the expression a= 2(x f x i) v f 2 v I 2
= 2(15.0m) 0−(3.00m/s 2 )=−0.300m/s 2
(d) Calculate the velocity at the beginning point at the bottom of the first plane and the end position along the second plane as follows: v I = 3.00 m/s, x f -x I = 7.35 m, a=-0.300 m/s 2.
The formula is v f 2 = v I 2 + 2a(x f x I )=(3.00m/s)
2 +2(−0.300m/s 2 )(7.35m) =3.20m 2 /s 2
v f=2.05m/s.
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A north magnetic pole is facing another north magnetic pole with a distance x. If the distance between the poles becomes 12x, what happens to the magnitude of the field energy between them?
The answer is "The field energy will increase"
What will happen to the magnitude of the field energy between them is that
The field energy will increaseWhenever there is a stored energy in an object at rest, the object will move in the direction that causes the energy stored to decrease, which will be replaced by movement energy.
Therefore, if two magnets with like poles are pointing together, then the energy stored will decrease as they move apart. Hence, as the distance between poles decreases, field energy increases.
What are magnetic poles?Magnetic pole are region at each end of a magnet where the external magnetic field is strongest.
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What is the momentum of a 6.5 kg bowling ball with a velocity of 3.0 m/s?
Answer:
19.5
Explanation:
momentum = mass * velocity
momentum = 6.5 * 3
momentum = 19.5
A tennis ball and a bag filled with sand have the same mass. They are dropped from the same height and they hit the ground. The bag of sand stays on the ground, while the tennis ball rebounds. Which experiences the larger impulse from the ground?
Answer:
The bag of sand
Explanation:
I think it is the bag of sand because according to the definition of impulse, impulse is the average force acting on a particule when an external force is being acted on it.
The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as 89 cm across (see Google Earth), and the telescopes on military surveillance satellites reportedly can resolve objects as small as 13 cm across. Assume first that object resolution is determined entirely by Rayleigh's criterion and is not degraded by turbulence in the atmosphere. Also assume that the satellites are at a typical altitude of 414 km and that the wavelength of visible light is 542 nm. What would be the required diameter of the telescope aperture for (a) 89 cm resolution and (b) 13 cm resolution? (c) Now, considering that turbulence is certain to degrade resolution and that the aperture diameter of the Hubble Space Telescope is 2.4 m, what can you say about the answer to (b), i.e. is the military surveillance resolution accomplished?
Answer:
Explanation:
minimum angle that can be resolved is given by the expression
1.22 λ / D , λ is wavelength of light , D is aperture of telescope.
distance that can be resolved = d x 1.22 λ / D
d is the distance by which observation is being made.
a )
89 x 10⁻² = 1.22 x 542 x 10⁻⁹ x 414 x 10³ / D₁
D₁ = 30.76 cm
b )
13 x 10⁻² = 1.22 x 542 x 10⁻⁹ x 414 x 10³ / D₂
D₂ = 2.1 m
c ) Hubble space telescope diameter is 2.4 m which is more than that of military surveillance telescope . Since diameter increases the power of resolution , it is capable of resolving two points situated even less than 13 cm apart . But , due to atmospheric turbulence , this power may not be achieved .
IMAGE PROVIDED Please HELP! I Will MARK BRAINLIEST
Answer:
5m
Explanation:
The area under the curve of velocity is the displacement. So From 0 to 5 there's a rectangle with height 1.
HELP When the forces are applied in the same direction, how do you determine net force?
Answer:
Explanation:
If two forces act on an object in the same direction, the net force is equal to the sum of the two forces.
4. 9.222 m/s5. 5.523 m/s27. Answer: Dv²=85.04v² = 9.2217=19.22228.) Under the influence of some forces, the speedof a 21.325 kg object changed from 6 m/s to a certain speed.If the net work done on the object is 1450 J.Calculate its final speed.1. 13.115 m/s2. 15.634 m/s19.322 m/s4. 7.263 m/s3.5. 21.714 m/s29. Answer: A
By the work energy theorem we know that the net work done on an object is equal to its change in kinetic energy, that is:
\(W=\Delta K\)where
\(K=\frac{1}{2}mv^2\)Then, the work energy theorem can be express as:
\(W=\frac{1}{2}mv_f^2-\frac{1}{2}mv_0^2\)In this case we know that the work done is 1450 J, that the mass is 21.325 kg and the initial velocity is 6 m/s; plugging these values and solving for the final velocity we have:
\(\begin{gathered} \frac{1}{2}(21.325)v_f^2-\frac{1}{2}(21.325)(6)^2=1450 \\ \frac{1}{2}(21.325)v_f^2=1450+\frac{1}{2}(21.325)(6)^2 \\ v_f^2=\frac{2}{21.325}(1450+\frac{1}{2}(21.325)(6)^2) \\ v_f=\sqrt{\frac{2}{21.325}(1450+\frac{1}{2}(21.325)(6)^2)} \\ v_f=13.115 \end{gathered}\)Therefore, the final velocity is 13.115 m/s and the correct option is A.
A spacecraft heading for Pluto will take pictures of several other planets on its way. The above equation gives the distance, ddd, in millions of kilometers, of the craft from its first photo opportunity with Mars in terms of the time, ttt, in days. What is the meaning of the 212212212 in this equation
Answer:
The maximum number of days for the trip
Explanation:
Given
\(d = 1.06(212 - t)\) --- Missing Equation
Required
What does d represent?
From the question, we understand that t represent the number of days;
So, by default 212 represent days
Going further:
For the equation, \(d = 1.06(212 - t)\) to be valid; the value of t must be within the interval;
\(0 \le t \le 212\)
When \(t = 0;\)
that is the beginning of the journey
As t increases;
212 - t decreases
Until the point where t = 212,
This signifies the end of the journey
So: 212 - t indicates a particular day between 0 and 212.
Hence, 212 represents the maximum number of days for the trip.
4. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface? how to draw the question?
It is to be noted that the magnitude of the electric flux through the hemisphere surface is πR²E. (Option D)
What is an Electric Flux?
The characteristic of an electric field known as electric flux may be thought of as the quantity of electric lines of force (or electric field lines) that cross a certain region.
According to this theory, electric field lines begin with positive electric charges and end with negative charges.
What is the calculation for the above?
Recall that the A hemispherical surface (half of a spherical surface) of radius R.
In order to derive the Magnitude of the electric flux we use the following formula:
Ф = ∈ x Area of the Curve Surface
⇒ Ф = ∈ x πR²
⇒ Ф = πR²∈
Thus, option D is the correct answer.
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Full Question:
A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface?
A) 2πR²∈
B) 0
C) 4 πR²∈/3
D) πR²∈
1. Which object would have more inertia — a 1,000 kg car or a 150 kg golf cart?
Answer:a car with 1,000kg
Explanation: A car with a mass of 1,000kg has more inertia than 150 kg
Out of the two objects a 1000-kilogram car and a 150-kilogram golf cart, the 1000-kilogram cart will have more inertia as the inertia of any object is directly proportional to its mass.
What is Newton's first law?According to Newton's first law, until pushed to alter its condition by the intervention of an external force, every object will continue to be at rest or in uniform motion along a single direction.
The larger the mass of the object, the greater would be the inertia of the object.
Thus, a 1000-kilogram automobile will have higher inertia than a 150-kilogram golf cart since any object's inertia is directly proportionate to its mass.
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The photograph shows a mixture of beach sand. A student
wants to separate the shell bits, rocks, and sea animals
from the sand.
Which method is the best way for the student to separate the mixture?
A. Flisering
B. Settling
C. Exaporation
D. Magnetism
Sand and salt and water will be separated by decanting. The student's best option for separating the mixture is to leave the sand in the original container.
How can you divide the components of saltwater using the best technique?The salt will be left behind as a solid even if you boil or evaporate the water. Distillation is an option if you wish to collect the water. Salt has a far greater boiling point than water, which explains why this is effective.
How can components be separated with the least amount of effort?Filtration. Filtration is among the most straightforward techniques for separating mixtures. Filtration is simple if one component is a liquid and the other is a solid. In this case, the mixture can simply be poured through filter paper.
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Super fine 40-gauge copper wire has a diameter of only and weighs only . Suppose a spool of 40-gauge wire weighs less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used
This question is incomplete, the complete question is;
Super fine 40-gauge copper wire has a diameter of only 0.080 mm and weighs only 44.5 g/km. Suppose a spool of 40-gauge wire weighs 205 g less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used ?
Answer: length of wire to be used is 4.6067 km
Explanation:
Circular diameter = d mm
Linear mass density of wire = μ g/km
let m be the mass of wire un-winded from spool to wind a magnet.
If M is mass of wire initially
then
Δm = M - m { which represents decrease of mass }
Also if L rep the length of wire pulled off,
then
Δm = μ × L grams
⇒ L = Δm/μ km
now given that weight Δm = 205 g and length per unit weight μ = 44.5 g/km
we substitute
L = 205 g / 44.5 g/km
L = 4.6067 km
Therefore length of wire to be used is 4.6067 km
Explain/Describe how atoms in domains determine whether a material is magnetic or not. (Please help this is due today)
Answer:
In a material, the magnetic behavior depends on the alignment of magnetic moments of the atoms. Magnetic moments are generated by the motion of the electrons in the atoms. When the magnetic moments of atoms in a material are aligned in a specific pattern, it creates a magnetic field which results in the material being magnetic.
In many materials, the magnetic behavior arises due to the alignment of magnetic domains, which are regions of atoms with magnetic moments aligned in the same direction. When many domains with aligned magnetic moments are present in a material, the material becomes magnetic.
The magnetic behavior of a material depends on the number of electrons and the arrangement of those electrons in the atoms. In particular, for an atom to have a magnetic moment, it must have unpaired electrons, meaning electrons that are not paired with another electron with the opposite spin. When these unpaired electrons in the atoms are aligned, they generate a magnetic moment. If all electrons are paired, there will not be a net magnetic moment, so the material will not be magnetic.
So, in summary, the magnetic behavior of a material is determined by the alignment of magnetic moments of atoms. When the magnetic moments of many atoms in a material align in the same direction, it creates a magnetic field, leading to a material being magnetic. This alignment is usually present in magnetic domains consisting of atoms with unpaired electrons.
Compared to using analog signals, what is an advantage of transmitting
information using digital signals?
A. Digital signals become stronger as the distance from their source
increases.
B. Digital signals are more secure.
C. Digital signals have a continuous range of values.
D. Digital signals can use the cloud to store and access data.
Answer:
B. Digital signals are more secure
Explanation:
You want to know an advantage of transmitting information using digital signals.
Digital signalsDigital signals are characterized by having a few discrete states. In the simplest case, those states are {transmitting, not transmitting}. Modern digital signals are often transmitted using numerous combinations of phases, frequencies, and amplitudes.
Analog signalsAnalog signals are characterized by a continuum of the characteristic used to convey the information. When amplitude modulation is used, the information of interest is conveyed by the amplitude of the signal. Similarly, when frequency or phase modulation is used, the information is conveyed by the frequency or phase of the signal, respectively.
That is, analog signals have a continuous range of values.
DistanceAny signal that is broadcast will have a signal level that decreases with distance from the source of the broadcast. Any signal conveyed through a medium will be subjected to distortions and losses due to the interaction of the signal and the medium. Hence all signals become weaker as the distance from the source increases.
NoiseThe receiver of a signal will, in general, receive signals other than the one intended. These are referred to as "noise." A transmission channel may have many sources of noise, including other transmitters, Cosmic Background Radiation, thermal noise in the components of the receiver or transmission medium, and others.
For analog signals, noise can directly affect the amplitude or phase being used to represent the signal of interest. Hence it changes the received value so it is not the same as the transmitted value.
The states of digital signals are designed to be sufficiently far apart that any corruption by noise will not affect the value as interpreted by the receiver. Thus, in terms of corruption of the information, we can say digital signals are more secure.
__
Additional comment
In radio transmission, noise is generally an addition to the signal. The weaker the analog signal, the greater the effect of noise. Broadcast radio began as AM radio: amplitude modulated. As the signal weakens, noise becomes a greater portion of the amplitude, so the receiver hears "static" where they want to hear voice or music.
FM, frequency modulated, radio replaced AM radio in order to avoid this issue with noise. The frequency of a signal is less likely to be corrupted. However, as the signal weakens, it can be difficult to determine its frequency, so that method of analog transmission also succumbs to noise.
Digital transmission in a noisy channel can also be corrupted by noise. Ultimately, the rate of information transmission in a given channel depends on the channel bandwidth and the signal-to-noise ratio. The integrity of a signal can be improved through coding that allows missing or corrupted bits of information to be determined based on the other bits that are received.
"Security" of a transmission can have different meanings. Here, we understand it to refer to the integrity of the information being conveyed. It could also relate to the difficulty of intercepting the transmission, or the difficulty of understanding the meaning of the received signal. Digital signals may or may not be more "secure" in these other meanings of the word.
Particles q₁ +8.0 μC, q2 +3.5 μC, and
93-2.5 μC are in a line. Particles q₁ and q2 are
separated by 0.10 m and particles q2 and q3 are
separated by 0.15 m. What is the net force on
particle q₂?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
+8.0μ.C
+91
0.10 m
+3.5 C
+92
0.15 m
-2.5μ C
93
The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.
To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.
The force between two charged particles can be calculated using Coulomb's law:
F = k * |q₁ * q₂| / r²
Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.
First, let's calculate the force exerted on q₂ by q₁:
F₁₂ = k * |q₁ * q₂| / r₁₂²
F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²
F₁₂ ≈ 252000 N
The force is positive because q₁ and q₂ have opposite charges.
Next, let's calculate the force exerted on q₂ by q₃:
F₂₃ = k * |q₂ * q₃| / r₂₃²
F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²
F₂₃ ≈ -63000 N
The force is negative because q₂ and q₃ have the same charge.
Finally, we can find the net force on q₂ by summing the individual forces:
Net force = F₁₂ + F₂₃
Net force = 252000 N + (-63000 N)
Net force ≈ 189000 N
The net force on particle q₂ is approximately 189000 N.
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How to calculate magnitude of tension if given an angle of 10°
Answer:
Mag isip ka po wag Kang tanong ng tanong kac kami po Yung nahihirapan mag hanap ng answer
Old Faithful geyser in Yellowstone National Park shoots water every hour to a height of 40.0 m. With what velocity does the water leave the ground? (Assume no air resistance and that g 9.81 m/s2)
Answer:
Vo = 28 [m/s]
Explanation:
To solve this problem, use the following equation of kinematics.
\(v_{f}^{2}= v_{o}^{2}-(2*g*y)\)
where:
Vf = final velocity = 0
Vo = initial velocity [m/s]
g = gravity acceleration = 9.81 [m/s²]
y = elevation = 40 [m]
Note: when the geyser water reaches the maximum height, the speed is zero. Another important observation is that the negative sign in the equation indicates that the movement of water is contrary to the direction of the acceleration of gravity.
0 = Vo² - (2*9.81*40)
Vo = (784.8)⁰⁵
Vo = 28 [m/s]
g What is the CD's moment of inertia for rotation about a perpendicular axis through the edge of the disk
Answer:
Explanation:
A CD has an OD of 120 mm and an ID of 15 mm and has a mass between 14 and 33 grams. Let's call it m
Lets call the outer and inner radii R and r respectively
Find the moment of inertia about a line perpendicular to the surface of the disc through its center. We can integrate or look up the result from standard tables
I = ½m(R² + r²)
then use the parallel axis theorem to shift the position of the axis
I = ½m(R² + r²) + md²
where d is the distance of the shift. In this case d = R
I = ½m(R² + r²) + mR²
I = m(1.5R² + 0.5r²)
If we select a mass of say 20 grams
I = 0.020(1.5(0.060²) + 0.5(0.0075²))
I = 0.0001085625 kg•m²