The length of the pendulum in cm when period is given is calculated to be 14 cm.
The period of pendulum is given as 0.755 s.
The length of the pendulum is to be found out.
We know the expression for time period as,
T = 2π √(l/g)
where,
T is time period
l is length
g is acceleration due to gravity
The value of g is 9.81 m/s².
Making l as subject, we have,
T = 2π √(l/g)
T/2π = √(l/g)
√(l/g) = T/2π
l/g = T²/4π²
Length of the pendulum l = (T²×g)/4π² = (0.755² × 9.81)/4π² = (0.57× 9.81)/39.44 = 5.59/39.44 = 0.14 m = 14 cm
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how far must two protons be placed on the earth’s surface for there to be an electrostatic force between them equal to the weight of one of the protons?
Answer:To solve this problem, we will use the following constants:
g
=
9.8
m
/
s
2
is the acceleration due to gravity
m
=
1.67
×
10
−
27
k
g
is the mass of a proton
q
=
1.602
×
10
−
19
C
is the charge of a proton
Let us first calculate the weight of a proton. To do so, we use:
F
=
m
g
We substitute:
F
=
(
1.67
×
10
−
27
k
g
)
(
9.8
m
/
s
2
)
We will get:
F
=
1.6366
×
10
−
26
N
As per the problem, the electrostatic force between the protons must be equal to the weight we derived. To calculate the electrostatic force, we use Coulomb's law:
F
=
k
q
1
q
2
r
2
Since we are dealing with two protons, we set:
q
1
=
q
2
=
q
We simplify:
F
=
k
q
2
r
2
We isolate the distance r:
r
=
√
k
q
2
F
We substitute:
r
=
√
(
9
×
10
9
N
m
2
/
C
2
)
(
1.602
×
10
−
19
C
)
2
1.6366
×
10
−
26
N
We get:
r
=
0.12
m
Explanation:
The protons must be placed at a distance of 7.42×10¹⁷ m apart so that the electrostatic force between them is equal to the weight of one proton.
Mass of the proton, = 1.67×10⁻²⁷ kg
Weight of the proton, W = 1.67×10⁻²⁷×9.81 = 1.64×10⁻²⁶ N = F
Charge on one proton, q = 1
Let the distance between proton, = d
Constant of permittivity of vacuum, ε₀ = 8.8 × 10⁻¹² C²/N-m²
Electrostatic force between two proton, F = q²/(4πε₀d²)
1.64×10⁻²⁶ = 1²/(4π × 8.8 × 10⁻¹² × d²)
d² = 5.514 × 10³⁵
d = √(5.514 × 10³⁵)
d = 7.42×10¹⁷ m
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each double bond and each ring represents one degree of
Each double bond and each ring represent: one degree of unsaturation.
What is degree of unsaturation?Degree of unsaturation is a measure to how many hydrogen atoms molecule is missing in order to be fully saturated. Compound that does not have maximum number of hydrogens per its structure is said to be unsaturated.
One degree of unsaturation is equivalent to 1 ring or 1 double bond (1 π bond) and two degrees of unsaturation is equivalent to 2 double bond, 1 ring and 1 double bond, 2 rings or 1 triple bond. General formula is CnH2n–2 and compounds containing double or triple bonds are often referred to collectively as unsaturated compounds.
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What are some some examples of estimator variables (forensics)
Answer:
Estimator variables are those that cannot be controlled by the criminal justice system. They include simple factors like the lighting when the crime took place or the distance from which the witness saw the perpetrator.
Explanation:
A beam has a square cross-section, a x a, where a is the linear dimension, and is subject to a pure bending moment, M. M is known with an uncertainty of ±10% and a is known with an uncertainty of ±5%. The strength of the material is known to an uncertainty of ±12%. Find the minimum design factor such that the beam is guaranteed not to fail
A beam has a square cross-section, a x a, where a is the linear dimension, and is subject to a pure bending moment, The minimum design factor such that the beam is guaranteed not to fail is (1.1 x M) / (1.12 x σ x (1.05 x a)^2 / 6).
The minimum design factor can be found by combining the uncertainties in the bending moment dimension, the cross-sectional area, and the material strength into a single factor that represents the safety margin against failure.
Let's call the design factor "n".
= n
= M / (σ.b.d^2 / 6)
here M is bending moment,
σ is material strength,
b is width of the cross-section,
d is height of the cross-section.
For a square cross-section, b = d = a.
The uncertainties in M, a, and σ can be taken into account by using the worst-case scenarios. In this case, the uncertainty in M is ±10%,
The minimum value for M is 0.9 x M
The maximum value for M is 1.1 x M.
The uncertainty in a is ±5%,
The minimum value for a is 0.95 x a
The maximum value for a is 1.05 x a.
The uncertainty in σ is ±12%,
The minimum value for σ is 0.88 x σ
The maximum value for σ is 1.12 x σ.
To find the minimum value for n, we'll use the minimum values for M, a, and σ:
= n
= (0.9 x M) / (0.88.σ.(0.95.a)^2 / 6)
To find the maximum value for n, we'll use the maximum values for M, a, and σ:
= n
= (1.1 x M) / (1.12 x σ x (1.05 x a)^2 / 6)
The minimum value for n is the larger of these two values, as it represents the worst-case scenario. If the minimum value for n is greater than 1, then the beam is guaranteed not to fail. If the minimum value for n is less than 1, then the beam is not guaranteed not to fail and must be redesigned to have a higher n value.
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A ball is tossed straight up from the surface of a small spherical asteroid with no atmosphere.
A: Only a decreasing gravitational force that acts downward
Understanding Gravity ForceAccording to Newton's law of universal gravitation, the force of attraction between two bodies is an attractive force, the magnitude of which is directly proportional to the multiples of the mass of each body and inversely proportional to the square of the distance between the two bodies.
Newton theorized that two of his objects separated by a certain distance tended to attract each other, and that this was part of the style of nature. He two objects in question are the object that falls into the center of the earth and the earth itself. This gravitational pull is called the Earth's gravitational pull.
Your question is INCOMPLETE but most probably your full question was:
A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroids radius and then falls. What forces if any act on the ball while it is traveling up?
A: Only a decreasing gravitational force that acts downward
B: Only a constant gravitational force that acts downward
C: Both a constant gravitational force that acts downward and a decreasing force that acts upward
D: No forces act at all
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how to turn a temporary magnet thats made out of magnetic materials turn into a permanent magnet
A: heat the temporary magnet then put it in a magnetic field
B: heat it then make it cool down and put it in a magnetic field
C: put the magnet in a magnetic field for a long time
D: All of the ways work
Answer: B
Explanation:
If the magnetic field applied to a temporary magnet is too strong, then the temporary magnet may align its atom and convert into a permanent magnet.
what is the mathematical relationship between spring force and the stretch of a spring?
The mathematical relationship between spring force and the stretch of a spring is F = - k x, where k is spring constant and x is the extension of the spring.
A spring is a material that may be bent by an external force before resuming its original shape.
Many of us use springs on a daily basis, yet we frequently ignore their inertia by treating them like massless objects. A spring's ability to experience displacement when stretched, compression when compacted, and return to equilibrium when free is a very casual process. This fact demonstrates that a spring compresses or stretches a body by applying an equal and opposite force.
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Which of these is the BEST example of plasticity?
A) a man who consistently drives his car too fast
B) a teenager who spends a summer in Chile and learns to speak Spanish
C) a woman who leaves her job to stay home with her newborn
D) a person who is in a coma
Plasticity is option B) a teenager who spends a summer in Chile and learns to speak Spanish. Plasticity refers to the ability of the brain to change and adapt in response to new experiences and information. It is a crucial aspect of human development and learning.
The teenager in this example is experiencing a change in their brain as they learn a new language. Through exposure to the language and practice, the brain is adapting and creates new connections to process and understand the Spanish language. This type of plastic change is known as neuroplasticity and is a prime example of the brain's ability to change in response to new experiences.
On the other hand, options A) a man who consistently drives his car too fast, C) a woman who leaves her job to stay home with her newborn, and D) a person who is in a coma do not show plasticity in the same way. While these changes may have an impact on the brain, they do not involve the same level of new learning and adaptation as the teenager who learns Spanish.
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In a motor, what do the combined effect of electric currents and magnetic forces turn electrical energy into?.
Electrical energy is converted to mechanical work in a motor.
What happens when electricity is transferred in a motor?
The kinetic energy produced by the vehicle's motor is converted from the electric potential energy to the electric current. The rotation of a rotor in a motor generates kinetic energy, which is the energy of motion. The wheels can turn because of the energy the rotating rotor transfers to them.
Electrical energy is transformed into rotational kinetic energy, a type of mechanical energy, using an electric motor. Electric fans, pumps, and other devices employ electric motors. Electrical energy is transformed into kinetic energy by an electric motor, however some of the electrical energy is lost during this process to thermal energy.
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For the circuit shown in the following diagram. What is the value of(i) Current through 6Ω resistor?(ii) P.D. across 12Ω resistor ?
Part (i) Current through resistor of 6Ω: I = 0.45 V.
Part ii) P.D. across resistor of 12Ω: I = 0.27 A
Explain the term potential difference?The difference in charge carriers' energy between two places in a circuit is known as the potential difference. Voltage measured: Voltage is another name for potential difference (p.d.), which is expressed in volts (V).Part (i) Current through resistor of 6Ω
R = 6 + 3 = 9Ω
Voltage V = 4V
I = V/ R = 4/9
I = 0.45 V
Part ii) P.D. across resistor of 12Ω.
R = 12 + 3 = 15Ω
I = V/R = 4/15
I = 0.27 A
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what is the acceleration at time 11.25 s?
The acceleration at time 11.25 seconds cannot be determined without more information.
Acceleration is the rate of change of velocity, so it can be calculated by the rate of change of the velocity at 11.25 seconds. This would require knowing the velocity at 11.25 seconds and at least one other point in time.The rate at which velocity varies with respect to time is referred to as acceleration. Since acceleration has both a magnitude and a direction, it is a vector quantity. Additionally, it is the first derivative of velocity with respect to time or the second derivative of position with respect to time.
Acceleration formula is given as:
[tex]acceleration=\frac{(final velocity)-(initial velocity)}{time}\\\\acceleration=\frac{change in velocity}{time}[/tex]
Without further details, it is impossible to calculate the acceleration at time 11.25 seconds.
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the great red spot is a hurricane-like storm (twice the size of earth) that has existed on the surface of jupiter for over 300 years. how is it possible for this storm to have lasted so long?
A jet stream is a fast-flowing, narrow air current found in the upper levels of the Earth's atmosphere. It is formed due to differences in air temperature and pressure, and it can have a significant impact on the weather and climate.
Jet streams are formed as a result of the movement of air from warm to cold regions.
The Great Red Spot (GRS) on Jupiter is a long-lived, high-pressure storm that has been observed for over 300 years. Scientists believe that the stability and longevity of the GRS can be attributed to several factors, including:
Jupiter's massive size and rotation: Jupiter is much larger and rotates much faster than Earth, which creates a strong and stable jet stream that helps to maintain the storm's structure.Jupiter's deep and warm atmosphere: The atmosphere of Jupiter is much deeper and warmer than Earth's, which helps to maintain the heat and energy needed to sustain the storm.The absence of land masses: Unlike Earth, Jupiter does not have any land masses to disrupt the storm, which helps to maintain its stability.Upwelling of deep atmospheric gases: The GRS is believed to be associated with a deep, upwelling of gases from Jupiter's interior, which provides a continuous source of energy and stability to the storm.To know more about jet streams refer to:
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two ceramic balls of identical radius are placed on a lab table and shot towards one another with identical speeds. after colliding with each other, ball b recoils farther from the point of impact than does ball a. which ball has the greater density?
Based on the recoil distance of the two balls, the ball that has greater density is Ball A.
What is recoil velocity?The relationship between a substance's mass and the amount of space it occupies is known as its density (volume).
The density of a substance is determined by the mass, size, and arrangement of its atoms. Density (D) is defined as the product of a substance's mass and volume.
Comparing the densities of the balls show that the ball with the lesser density will recoil farther than the ball with the greater density because it has less momentum.
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What is 25 degrees Celsius in Kelvin?
25 degrees Celsius is 298 Kelvin
What is temperature?
Temperature is a unit used to represent hotness or coolness on any of a number of scales, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).
The kelvin is the fundamental unit of temperature in the International System of Units (SI). Its identifier is K. The Celsius scale, in which 0 degrees corresponds approximately to the freezing point of water and 100 degrees to its boiling point at sea level, is frequently practical for use in common applications.
The formula is °C + 273.15 = K.
So, reading on a Kelvin scale is 25∘C + 273 = 298K.
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you have watched one too many old cartoons and decide to drive around town with a giant spring that is 4 m long and attached to the front of your car. you decide to help a semi truck that is stuck and try to push them with your car. you take a running start, and when you contact the truck the spring in your car compresses 3 m. during which portion of the compression did you do the least work on the spring?
During the third-meter portion of compression least work was done on the spring.
Work is a measure of the energy transfer that occurs when an object is moved by an applied force. It is a scalar quantity with units of Joules (J) in the SI system.
Work can be calculated as the product of the force applied to an object and the distance over which the force is applied. This is described by the equation W = Fd, where W is the work done, F is the force applied, and d is the distance over which the force is applied.
The direction of the force applied is important in determining the work done. Work is only done when the force is applied in the direction of the displacement of the object. If the force is applied perpendicular to the displacement, no work is done.
Therefore, During the third-meter portion of compression least work was done on the spring.
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suppose jack’s preferences are strictly convex, and we know that for jack these two bundles (1, 9) and (9, 1) are indifferent. what is true about jack’s preferences?
Jack's preferences are strictly monotonic and exhibit diminishing marginal utility.
Strictly convex preferences mean that Jack's preferences between two bundles of goods do not change as the proportion of goods in the bundle changes. In other words, Jack values diversity of goods and the more he has of one good, the less he values additional units of that good.
The fact that Jack finds the bundles (1,9) and (9,1) to be indifferent means that he values both of these bundles equally, or in other words, he has the same utility from both of these bundles. This implies that Jack's marginal utility of the two goods decreases as he consumes more of either of them.
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Explore the program by placing red and blue figures on the rope to simulate a tug of war a. Which figure can pull with the most force? b. What is the exact measurement of force that each figure can pull the rope?
The force that each figure can pull is determined by various parameters, including the weight and strength of the figurines, the length and tension of the rope, and the location of each figure. Experiments or computations based on applicable physics concepts and equations would be required to ascertain the precise measurement of force.
What is force?A force is an effect in physics that may modify the velocity of an item. A force can cause a mass item to change its velocity, or accelerate. Intuitively, force may be characterized as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Here,
The force that each figure can pull is determined by various parameters, including the figurines' weight and strength, the length and tension of the rope, and the location of each figure. Experiments or computations employing appropriate physics concepts and equations would be required to ascertain the precise measurement of force.
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Classify each measurement as a scaled or vector a 20 books on a shelf
a) Scalar quantity, b) Vector quantity, c) Vector quantity, d) Scalar quantity, e) Vector quantity, f) Scalar quantity, g) Scalar quantity, h) Scalar quantity.
What is the difference between scalar and vector quantity?A scalar quantity is a physical quantity with a single numerical value. Scalar quantities include mass, temperature, and velocity.
A vector quantity is a physical quantity that has a magnitude as well as a direction. Displacement, velocity, and acceleration are examples of vector quantities. Scalar quantities may be stated as a single numerical value, but vector quantities must be expressed as a magnitude and a direction.
In physics, vector quantities are frequently employed to describe physical qualities such as force, velocity, and acceleration. The parallelogram technique can be used to add and subtract vector values. Scalar quantities, on the other hand, cannot be added or subtracted in the same way. Scalar quantities are easily added and subtracted.
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:As the two foci of an ellipse are brought together, the shape of the ellipse becomes ________.
A) more like a line between the foci.
B) more like a circle around the foci.
C) more like a triangle drawn around the foci.
D) more like a sphere around the foci.
As the two foci of an ellipse are brought together, the shape of the ellipse becomes B) more like a circle around the foci.
What is the Foci of an Ellipse?The two reference points that aid in drawing the ellipse are its foci. The ellipse's foci are equidistant from the origin and located on its primary axis.
The locus of a point, whose sum of the distances from the two fixed points is a constant value, is represented by an ellipse.
Hence, as they come closer and closer, the shape of the ellipse becomes B) more like a circle around the foci.
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A 50,000kg comet is at rest in space. A nuclear explosion spilts the comet into two pieces. If the 35,000kg piece moves away +5m/s, what is the velocity of the second piece?
Answer:
-11.67 m/s.
Explanation:
The velocity of the second piece can be determined by the law of conservation of momentum, which states that the total momentum of a closed system remains constant.
Let's call the velocity of the second piece "v".
Before the explosion, the total momentum of the comet is 0 (since it is at rest). After the explosion, the total momentum of the two pieces is
(35,000 kg)(5 m/s) + (15,000 kg)(v).
Using the law of conservation of momentum, we can set these two momenta equal to each other and solve for v:
0 = (35,000 kg)(5 m/s) + (15,000 kg)(v)
0 = 175,000 kg m/s + 15,000 kg v
-175,000 kg m/s = 15,000 kg v
v = -11.67 m/s
So the velocity of the second piece is -11.67 m/s.
the graph below shows the velocity versus time for an object from t = 0 to t = 10 s. what is the total distance traveled by the object during this time interval?
Distance travelled by object from 0 to 10 seconds is 50 m. We can calculate it using equation of motion.
We need to calculate the distance from 0 to 10 seconds for the object.
As in the question, acceleration is constant, we can thus utilize the equation of motion to calculate the value of distance using magnitudes of time and acceleration.
The equations of motion describe the time evolution of an object's position and velocity in a given force field.
[tex]s = ut + (1/2)at^{2}[/tex]
Insert the given values, and we get:
s = 2*10 + (1/2)*0.6*10*10S = 50 m
Therefore, distance is 50 m. As velocity is continuously increasing in magnitude, displacement will also be equivalent to the distance.
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Complete question: Image of the graph has been uploaded.
2. according to grove & gray (2019), what are the potential biases of convenience sampling?
Convenience sampling has several potential biases that can impact the validity of a study. It is important for researchers to be aware of these biases and to consider alternative sampling methods, such as stratified or random sampling, to ensure that their sample is representative of the population of interest.
Convenience sampling is a type of sampling method where the researcher selects participants who are easily accessible and willing to participate in the study. It is often used in qualitative research and in situations where the researcher has limited resources, such as time and budget. However, convenience sampling has several potential biases that can impact the results of a study and compromise its validity.
One of the main biases of convenience sampling is selection bias. This occurs when the sample is not representative of the population of interest, leading to an over- or under-representation of certain groups. For example, if a researcher conducts a survey on drug use among high school students and only surveys students who are present during lunchtime, they may miss the experiences and perspectives of students who are absent during that time or have different lunch periods.
Another potential bias of convenience sampling is response bias, which occurs when participants do not answer questions truthfully or accurately. This can happen if participants feel pressure to provide socially desirable answers, or if they are not motivated to participate in the study. For example, if a researcher conducts a survey on alcohol use among college students and only surveys students who are present in the student union building, they may miss the experiences and perspectives of students who do not use that building.
Finally, convenience sampling can also lead to bias in the results if the participants are not diverse enough in terms of their demographic characteristics, such as age, gender, ethnicity, or socio-economic status. This can limit the generalizability of the results to other populations, as the findings may not be representative of the broader population of interest.
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it takes 250.0 j to raise the temperature of a 50.0 g sample of a metal by 10.0°c. what is the specific heat capacity of this metal?
The specific heat capacity of this metal is 0.5J/g°C when it takes 250.0 j to raise the temperature of a 50.0 g sample of a metal by 10.0°C.
Given the mass of metal (m) = 50g
The temperature of metal is raised to (T) = 10.0°C.
The heat required to raise the temperature of metal (Q) = 250j
Let the specific heat of metal = c
We know that q = mcΔT where q is the heat absorbed , m is the mass, c is the specific heat heat and T is the temperature change.
Such that, c = q/mΔT
c = 250/50 x 10 = 0.5J/g°C
Hence, the required specific heat capacity of the metal is 0.5J/g°C
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please help!! i’ve been trying to do this for an hour and a bit and i still have no clue what to do and it’s too late to email my teacher asking for help..
We have from the question on the proportionality that;
a) 147 m
b) 11 s
What is direct proportionality?Direct proportionality is a mathematical relationship between two variables where a change in one variable is accompanied by a proportional change in the other variable. In other words, if the values of two variables are directly proportional, they change in such a way that the ratio of the two variables remains constant.
We know that we have to find the constant of the proportionality first as such we have that;
s α t
s = kt^2
k = s/t^2
k = 75/5^2
k = 3
a) s = 3 * (7)^2
= 147 m
b) t =(s/k)^1/2
t = (363/3)^1/2
t = 11 s
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how is heat capacity ratio determined experimentally
Heat capacity ratio is determined experimentally by measuring the change in temperature of a gas in response to the addition or removal of heat.
The heat capacity ratio, also known as the adiabatic index, is defined as the ratio of the heat capacity at constant pressure to the heat capacity at constant volume.
To experimentally determine the heat capacity ratio, a sample of gas is subjected to changes in temperature while its pressure and volume are carefully monitored. The change in temperature can be caused by adding or removing heat, or by changing the pressure of the gas through a piston or other mechanism.
The heat capacities at constant pressure and constant volume can then be calculated from the data, and the heat capacity ratio can be determined as their ratio. This measurement can provide valuable information about the thermodynamic properties of gases and can be used to better understand their behavior in different conditions.
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Ariana is accelerating her car at a rate of 4. 6 m/s2 for 10 seconds. Her starting velocity was 0 m/s.
The final velocity of car is 46 m/s.
We know that from newton's equation of motion,
v = u+at
Where,
v = final speed
u = initial speed = 0
a = acceleration = 4.6 m/s^2
t = time= 10 sec
Putting these these values in above equation we get: v = 46 m/s.
The action of one body on another in the form of pull or push is called a force. Mutual interaction between two bodies, which produce a force on one body, also produces a force on another body. The force applied by the body the other is known as reaction and the force on the body under study is known as Action.
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Three identical charges of 4.00 μC are placed at the positions (0.20 m, 0, 0), (0, 0.20 m, 0) and (0, 0, 0.20 m). What is the magnitude of the force on any one of the charges?
a.3.6 N
b.0.0 N
c.3.1 N
d.7.2 N
Option a. The three charges are placed at the vertices of an equilateral triangle, with each side length equal to 0.20 m. Since the charges are identical and the distances between them are equal.
The force on a point charge q due to another point charge Q is given by Coulomb's law:
[tex]F = k * (q * Q) / r^2[/tex]
where k is the Coulomb constant ([tex]8.99 * 10^9 N m^2 / C^2[/tex]), q and Q are the magnitudes of the charges, and r is the distance between the charges.
In this case,[tex]q = 4.00 * 10^-6 C[/tex] and [tex]Q = 4.00 * 10^-6 C[/tex], so the magnitude of the force between two charges is given by:
[tex]F = k * (q * Q) / r^2\\ \\ = (8.99 * 10^9 N m^2 / C^2) * (4.00 * 10^-6 C)^2 / (0.20 m)^2\\ \\ = 3.6 N[/tex]
Since there are three charges, each charge experiences three forces in different directions due to the other two charges. The net force on a charge is the vector sum of these three forces. If the charges are placed at the given positions, the net force on a charge will be zero, as the forces cancel each other out.
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Two particles A and B start from rest at the origin s = 0 and move along a straight line such that aA = (6t - 3) ft/s2 and aB = (12t2 - 8) ft/s2, where t is in seconds. Determine the distance between them when t = 4s and the total distance each has traveled in t = 4s.
Distance between the particles when t = 4s:To find the distance between A and B, we need to find their positions as a function of time.
The position of particle A can be found using the equation:
[tex]x A = (1/2)at^2 + v0t + x0,[/tex]
where[tex]v0 = 0 m/s[/tex] (since both particles start from rest), [tex]x0 = 0 m[/tex], and[tex]a = 6 m/s^2.[/tex]
So,[tex]x A = (1/2)(6 m/s^2)(4 s)^2 = 48 m[/tex]
The position of particle B can be found using the equation:
[tex]x B = (1/2)at^2 + v0t + x0,[/tex]
where [tex]v0 = 0 m/s[/tex] (since both particles start from rest), [tex]x0 = 0 m[/tex], and [tex]a = (12t^2 - 8) m/s^2.[/tex]
So, [tex]x B = (1/2)((12)(4^2) - 8) (4s)^2 = 64 m[/tex]
The distance between the two particles at t = 4 s is [tex]|x A - x B| = |48 m - 64 m| = 16 m.[/tex]
Total distance traveled by each particle in t = 4s:
The total distance traveled by particle A in 4 seconds can be found using the equation:
[tex]d A = (1/2)at^2 + v0t + x0[/tex],
where[tex]v0 = 0 m/s[/tex] (since both particles start from rest), [tex]x0 = 0 m[/tex], and[tex]a = 6 m/s^2.[/tex]
So,[tex]d A = (1/2)(6 m/s^2)(4 s)^2 = 48 m[/tex]
The total distance traveled by particle B in 4 seconds can be found using the equation:
[tex]dB = (1/2)at^2 + v0t + x0[/tex],
where [tex]v0 = 0 m/s[/tex](since both particles start from rest), [tex]x0 = 0 m[/tex], and [tex]a = (12t^2 - 8) m/s^2.[/tex]
So, [tex]dB = (1/2)((12)(4^2) - 8) (4s)^2 = 64 m[/tex]
In 4 seconds, particle A travels a total of 48 m and particle B travels a total of 64 m.
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a car starts at rest and accelerates with an acceleration of 4.51 m/s2. after the car travels a distance of 355 m, it slows down with an acceleration of -2.34 m/s2 until its speed reaches 25.4 m/s. what is the total displacement of the car?
The total displacement of the car is the sum of the displacement during acceleration and deceleration, which is 155.44 - 254.24 = -98.8 m. So, the car moves backwards 98.8 m during the entire motion.
The total displacement of the car can be calculated as follows:
The car accelerates from rest to 25.4 m/s with an acceleration of 4.51 m/s2. The time taken to reach this speed can be calculated as t = v / a = 25.4 / 4.51 = 5.6 s
During the time t, the car travels a distance x = 0.5at^2 + v_0t, where v_0 is the initial velocity, which is zero.
The distance covered during acceleration is x = 0.5 * 4.51 * 5.6^2 = 155.44 m
The car then slows down with an acceleration of -2.34 m/s2. The time taken to slow down from 25.4 m/s to 0 m/s can be calculated as t = v / a = 25.4 / 2.34 = 10.8 s
During this time, the car travels a distance x = 0.5at^2 + v_0t = 0.5 * -2.34 * 10.8^2 + 25.4 * 10.8 = -254.24 m
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how strong is the electric field between the plates of a 0.80 μf air-gap capacitor if they are 3.0 mm apart and each has a charge of 72 μc ?
The required value of electric field between the plates of the capacitor which contain a specified charge is calculated to be 30 × 10³ V/m.
The value of capacitance is given as,
C = 0.8 μ F = 0.8 × 10⁻⁶ F
The following is the value of the space between the plates:
d = 3 mm = 3 × 10⁻³ m
The value of the charge is:
Q = 72 μc = 72 × 10⁻⁶ c
The value of the potential difference is: Q = C V
Making V as subject,
V = Q/C = (72 × 10⁻⁶)/(0.8 × 10⁻⁶) = 90 V
Substitute all the values in the potential difference calculation, then simplify it to account for the electric field.
90 = E × 3 × 10⁻³
E = 90/(3 × 10⁻³) = 30 × 10³ V/m
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