First lets calculate the surface area
[tex]S=4\cdot\pi\cdot r^2=4\pi\cdot0.05^2m=0.0314m^2[/tex]Now to know the surface charge density we need the next formula:
[tex]CD=\frac{q}{A}[/tex]But we are missing the amount of charge, we only have the potential
So in this case, we going to apply a different formula
[tex]V=\frac{q}{4\cdot\pi\cdot\xi\cdot r}[/tex]q=5.56*10^-10
[tex]CD=-5.56\cdot\frac{10^{-10}}{0.0314}=-1.77\cdot\frac{10^{-8}C}{m^2}[/tex]The anwer might be -1.8x10-8
What is the electric field strength at a distance of 0.9 m from a charge of 5.71 x 10^-6 C?
Given:
[tex]\begin{gathered} Q=5.71\times10^{-6}\text{ C} \\ r=0.9\text{ m} \end{gathered}[/tex]The electric field strength is given as,
[tex]E=\frac{KQ}{r}[/tex]Here, K is the electrostatic constant.
Putting the values,
[tex]\begin{gathered} E=\frac{9\times10^9\times5.71\times10^{-6}}{(0.9)^2} \\ =63444.44\text{ N/C} \end{gathered}[/tex]Therefore, the electric field strength is 63444.44 N/C.
Fill in the blanks on machines efficiency
Efficiency = ____________ energy _________ / ____________ energy ______________
Machine Efficiency = output energy/ input energy
The percent of input work that becomes work done by the machine is called efficiency. The output work is always less as compared to the input work because some of the input work gets used in overcoming friction, therefore the efficiency is always less than 100 percent.
Efficiency do not have units. It is written as a decimal or as a percentage. Energy efficiency is the use of less amount of energy to perform the same task. Energy-efficient homes and buildings use lesser energy to heat, cool, and run any appliances and energy-efficient manufacturing facilities use lesser energy to produce goods.
Efficiency measures work or energy that can conserved in a process. We can also say that efficiency is about comparing the output of the energy to the input of the energy.
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Descriptions
A. Research that is designed to describe the characteristics or behaviors of a person or particular population
B. The thing the researcher changes in the experiment
C. Research that attempts to test cause and effect between two things
D. The thing that is influenced by another variable in an experiment
E. Research that attempts to assess the relationship between two aspects of human behavior
Fill in the blank with the letter of the description that best matches the term.
Descriptive Studies
PLEASE HELP!! IF SOMEONE KNOWS THE REST PLEASE TELL ME! THANKYOU!
Answer:
I think it is C
Explanation:
Which of these does sound travel the fastest Through?A. steel SolidB. water LiquidC. Air gasD. Sound travels the same through all mediums
Speed of sound is maximum on solid.
Correct option.
A) steel Solid
A pencil is viewed through a concave lens. Which of the following best describes the image?A.RealB.InvertedC.VirtualD.Enlarged
A concave lens produces a virtual image like the one seen in the diagram (we know is virtual since it is on the same side to the original object), we also see that the image is smaller, and not inverted.
Therefore, the only option that describes this image is C which is virtual.
Which of the following best explains why Venus has a higher temperature than Mercury? And Why?
A. The atmosphere on Venus is thicker than the atmosphere on Mercury.
B. The atmosphere on Venus is thinner than the atmosphere on Mercury.
C. The length of time it takes Venus to revolve around the Sun is shorter than Mercury.
D. The length of time it takes Venus to revolve around the Sun is longer than that of Mercury.
Answer: The reason why Venus is hotter than Mercury is because it has a thick atmosphere primarily made up of carbon dioxide, which is a greenhouse gas that helps retain the heat from the Sun. In comparison to this, Mercury has almost no atmosphere, so any heat that beats down on the planet isn’t retained.
Explanation: Searched
When two coherent waves combine destructively to create a minimum, what is the smallest phase difference possible in Degrees and Radians?
180° or π Radians is the smallest phase difference possible When two coherent waves combine destructively to create a minimum
Two waves of the same wavelength that are entirely out of phase with one another might cancel one another out or interact negatively. When there is a 180 degree or larger radian phase difference, this happens. Only when the two waves have the same amplitude do they completely cancel out. Partially destructive superposition occurs when two waves that are entirely out of phase yet have different amplitudes. The intensity is 0.
Superposition is the phenomenon in which the combined displacement of two combining waves is equal to their vector sum.
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How many kilometers does the space shuttle have to travel to complete one orbit? In terms of a circle, what is this distance called? Explain.
40,840.7 kilometers the space shuttle have to travel to complete one orbit. In terms of a circle, this distance is termed as the circumference of the circle.
The circumference of a circle is the length measured around its edge. The diameter of a circle is the distance from the center to the outside.
Here we need to find the distance of the space shuttle that completed one circle, ie, the circumference of the orbit. The Circumference or distance covered by the space shuttle can be denoted by [tex]C_{SS}[/tex] and can be calculated by application of the below formula,
[tex]C_{SS}[/tex] = 2πr
where r is the radius of earth ie, 6500Km
Therefore, the equation becomes:
[tex]C_{SS}[/tex] = 2×π×r
= 2×π×6500
=40,840.7
So, the kilometer required to travel is 40,847.7Km
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if a child on a skateboard has a total momentum of 86.94kgm/s and a speed of 2.3m/s, calculate the total mass of the child and skateboard
Monochromatic light of 605 nm falls on a single slit of width 0.095 mm. The slit is located 85 cm from a screen. How far from the center is the first dark band?540 mm5,400 mm0.5 mm5.4 mm
The wavelength of the monochromatic beam is given as,
[tex]\lambda=605\text{ nm}[/tex]The value of the width of the slit is,
[tex]d=0.095\text{ mm}[/tex]The distance of the slit from the screen is,
[tex]D=85\text{ cm}[/tex]Thus, the distance of the dark band from the center is,
[tex]y=\frac{(2m+1)\lambda D}{d}[/tex]For the first dark band,
m=0,
Substituting all the known values,
The value of the distance of the dark band becomes,
[tex]\begin{gathered} y=\frac{605\times10^{-9}\times85\times10^{-2}}{0.095\times10^{-3}} \\ y=540000\times10^{-8}\text{ m} \\ y=5.4\text{ mm} \end{gathered}[/tex]Thus, the first dark band is 5.4 mm away from the center of the screen.
Hence, the correct answer is 5.4 mm.
Aristotle's rhetorical triangle tells us that effective messages show awareness of
ethos, pathos, and logos
logic, emotion, and values
speaker, audience, and purpose
thought, voice, and opinion
Aristotle's rhetorical triangle tells us that effective messages show awareness of ethos, pathos, and logos. The correct answer to the question is option A.
What is Aristotle's rhetorical triangle?
Aristotle taught that a speaker's effective messages show awareness of the ethos, pathos, logos triangle, which expresses the idea that a good argument must be ethically, emotionally, and logically sound.
Ethos is a Latin word which means for ethics. This emphasize that that effective messages should show trust. The audience should be able to be confident of the source of information.Pathos talks about to the emotions.Logos is the Latin word for logic. The messages would be verified by the audience. The speaker would ensure there are facts backing up claims.In summary, Aristotle's rhetorical triangle shows that the Logos, Ethos, and Pathos are very important when giving an effective message.
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Ricardo, of mass 72 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 39 kg canoe. When the canoe is at rest in
the placid water, they exchange seats, which are 3.2 m apart and symmetrically located with respect to the canoe's center. Ricardo
notices that the canoe moves 46 cm horizontally relative to a pier post during the exchange and calculates Carmelita's mass. What is it?
Ricardo notices that the canoe moves 46 cm horizontally relative to a pier post during the exchange and the mass is 49 kg.
What is mass?Mass is defined as a measurement of the fundamental attribute of all stuff, inertia.
Mass is also defined as a physical body's total amount of matter.
As per question,
Let's refer to Ricardo's mass as MR and Carmelita's mass as MC.
Let the two-person system's center of mass, which is believed to be closer to Ricardo, be x meters from the center of the canoe's length L and mass m.
MC(L/2 +x) = mx + MR(L/2-x).
It is derived from the second law of parallel forces, which states that the sum of the moments of mass moving clockwise and counterclockwise is equal.
The canoe's center has now moved twice as far from its initial location.
So, x = 46/2 = 23 cm = 0.23 m
MC = MR (L / 2x) - mx / L / 2 + x
MC = 72 ( 3.2 / 2 - 0.23 ) - 39 x 0.23 / 3.2 / 2 + 0.23
MC = 72 ( 1.6 - 0.23 ) - 39 x 0.23 / 1.6 + 0.23
MC = 72 x 1.37 - 8.97 / 1.83
MC = 98.64 - 8.97 / 1.83
MC = 49 kg
Thus, Ricardo notices that the canoe moves 46 cm horizontally relative to a pier post during the exchange and the mass is 49 kg
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Two ways to modulate a wave are to change the wave's ___ (AM) or the wave's__ (FM).
Answer:
AM - amplitude modulation
FM - frequency modulation
a 30.0 kg child starting from rest slides down a water slide with the vertical height of 10.0 m what is the child speed (a )halfway down the slides vertical distance and (b) 3/4 of the way down
We know that
• The mass is m = 30.0 kg.
,• The vertical height is h = 10.0 m.
(a)We have to use the conservation of energy theorem, which states that mechanical energy is constant all the time. Also, halfway down means a height of 5.0 m. It's important to know that at the top the total energy is potential, while halfway is distributed as kinetic and potential, the expression below shows this
[tex]E_{p1}=E_{k1}+E_{p2}[/tex]Then, using the definition of each energy, we have
[tex]mgh_1=\frac{1}{2}mv^2+mgh_2[/tex]Now, we use the given values to find the speed.
[tex]\begin{gathered} \text{mgh}_1=m(\frac{1}{2}v^2+gh_2) \\ gh_1=\frac{1}{2}v^2+gh_2 \\ 9.81m/s^2\cdot10m=\frac{1}{2}v^2+9.81m/s^2\cdot5m \\ 98.1m^2/s^2=\frac{1}{2}v^2+49.05m^2/s^2 \\ 98.1m^2/s^2-49.05m^2/s^2=\frac{1}{2}v^2 \\ 2\cdot49.05m^2/s^2=v^2 \\ v=\sqrt[]{98.1m^2/s^2} \\ v\approx9.9m/s \end{gathered}[/tex]Therefore, the speed of the child halfway down is 9.9 meters per second.(b)In this case, we just have to use as the second height of the equation the magnitude 2.5 meters because that's 3/4 of the way down. So, let's use the same process and expression
[tex]\begin{gathered} gh_1=\frac{1}{2}v^2+gh_2 \\ 9.81m/s^2\cdot10m=\frac{1}{2}v^2+9.81m/s^2\cdot2.5m \\ v=\sqrt[]{2(98.1m^2/s^2-24.53m^2/s^2)} \\ v\approx12.1m/s \end{gathered}[/tex]Therefore, the speed of the child 3/4 of the way down is 12.1 meters per second.A ball rolls off a table and falls 0.75m to the floor, landing with a speed of 4 m/s. (A) What is the acceleration of the ball just before it strikes the ground? (B) What was the initial speed of the ball? (C) What initial speed must the ball have if it is to land with a speed of 5 m/s?
The acceleration of the ball is 21.33m/s²,
We are given that,
The ball fall's from height = d = 0.75m
The final speed of the ball = Vf = 4m/s
So that to know the acceleration of the ball we can calculate by the equation of motion in term of velocity and acceleration i.e. given as,
V = u + at
Where, V is the final velocity , u is the initial velocity , t is the time and a is the acceleration of the object.
t = d/v
t = (0.75m)/(4m/s)
t = 0.1875s
Thus, the value of t, V, and initial velocity is zero putting in equation of motion to get acceleration,
a = (4m/s)/(0.1875s)
a = 21.33m/s²
The acceleration of the ball would be 21.33m/s²
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-%deviation from expected value (show calculations) in relation between frequency and radius.
When an object moves in a circular trajectory with a uniform speed, a centripetal force is needed to keep it in that trajectory. In the experiment, the hanging mass is used to keep the tension of the string constant. The tension is equal to the weight of the hanging mass, and it is responsible for keeping the rubber stopper in a circular trajectory.
The centripetal acceleration of a particle in a circular trajectory with radius r and frequency f is:
[tex]a_c=(2\pi f)^2r[/tex]On the other hand, if the mass of the hanging object is M and the mass of the rubber stopper is m, according to Newton's Second Law of Motion, the relationship between the tension of the string and the centripetal acceleration is:
[tex]\begin{gathered} \Sigma F=ma_c \\ \\ \Rightarrow T=m(2\pi f)^2r \\ \\ \Rightarrow Mg=m(2\pi f)^2r \end{gathered}[/tex]If we isolate f from that expression, we get a theoretical relationship between the radius and the frequency:
[tex]\begin{gathered} \Rightarrow(2\pi f)^2=\frac{Mg}{mr} \\ \Rightarrow2\pi f=\sqrt{\frac{Mg}{mr}} \\ \\ \therefore f=\frac{1}{2\pi}\sqrt{\frac{Mg}{mr}} \end{gathered}[/tex]To find the expected value for the frequency for different values of r, replace M=200g, m=15.3g, g=9.81m/s^2 and the different values of r:
[tex]\begin{gathered} f_{10cm}=\frac{1}{2\pi}\sqrt{\frac{(200g)(9.81\frac{m}{s^2})}{(15.3g)(0.10m)}}\approx5.70Hz \\ \\ f_{15cm}=\frac{1}{2\pi}\sqrt{\frac{(200g)(9.81\frac{m}{s^2})}{(15.3g)(0.15m)}}\approx4.65Hz \\ \\ f_{20cm}=\frac{1}{2\pi}\sqrt{\frac{(200g)(9.81\frac{m}{s^2})}{(15.3g)(0.20m)}}\approx4.03Hz \\ \\ f_{25cm}=\frac{1}{2\pi}\sqrt{\frac{(200g)(9.81\frac{m}{s^2})}{(15.3g)(0.25m)}}\approx3.60Hz \\ \\ f_{30cm}=\frac{1}{2\pi}\sqrt{\frac{(200g)(9.81\frac{m}{s^2})}{(15.3g)(0.30m)}}\approx3.29Hz \end{gathered}[/tex]On the other hand, we can find the experimental measurements for the frequency depending on the radius using the information provided in the table.
To do so, remember that the frequency is equal to the average number of spins from the three trials over the time.
The experimental values for the frequencies are:
[tex]\begin{gathered} f_{10cm-exp}=\frac{35+34+32}{3\times10s}\approx3.37Hz \\ \\ f_{15cm-exp}=\frac{31+29+27}{3\times10s}\approx2.90Hz \\ \\ f_{20cm-exp}=\frac{27+27+25}{3\times10s}\approx2.63Hz \\ \\ f_{25cm-exp}=\frac{25+23+24}{3\times10s}\approx2.40Hz \\ \\ f_{30cm-exp}=\frac{26+23+20}{3\times10s}\approx2.30Hz \end{gathered}[/tex]To find the percent deviation from the expected value, use the following formula:
[tex]\%dev=\frac{f_{exp}-f}{f}\times100\%[/tex]Then, the percent deviations from the expected values are:
[tex]\begin{gathered} \%dev_{10cm}=\frac{3.37Hz-5.70Hz}{5.70Hz}\times100\%\approx-40.9\% \\ \\ \%dev_{15cm}=\frac{2.90Hz-4.65Hz}{4.65Hz}\times100\%\approx-37.6\% \\ \\ \%dev_{20cm}=\frac{2.63Hz-4.03Hz}{4.03Hz}\times100\%\approx-34.7\% \\ \\ \%dev_{25cm}=\frac{2.40Hz-3.60Hz}{3.60Hz}\times100\%\approx-33.3\% \\ \\ \%dev_{30cm}=\frac{2.30Hz-3.29Hz}{3.29Hz}\times100\%\approx-30.1\% \end{gathered}[/tex]4. Betsy wants to use her own weight to lift a 1,500-newton box. She weighs 500 newtons. Suggest input and output arm lengths that would allow Betsy to lift the box with a lever. Draw a lever and label the input and output arms with the lengths and forces.
Answer:
Explanation:
Given:
F₁ = 500 N
F₂ = 1.500 N
____________
L₁ - ?
L₂ - ?
Moment rule:
M₁ = M₂
F₁*L₁ = F₂*L₂
F₂ / F₁ = 1.500 / 500 = 3
L₁ / L₂ = 3
L₁ = 3*L₂
If L₂ = 0.5 m
then L₁ = 3*0.5 = 1.5 m
- If we start an experiment with 191.3 g of a substance, how much should we end with?
More than 191.3 g
191.3 g
Less than 191.3g PLEASE NOW
If we start an experiment with 191.3 g of a substance, we should be ending with 191.3 g
We know that matter cannot be created out of nothing. So that is why the number of atoms of products must be equal to the number of atoms of reactants. That is why a chemical reaction is written as a balanced reaction equation. This is the law of conservation of mass.
During a combustion reaction or during decomposition reaction, the products mass might seem to be different than that of reactants either higher or lower. This is due to the involvement of environment. So while considering mass environment should also be included.
Therefore, if we start an experiment with 191.3 g of a substance, we should be ending with 191.3 g
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Gravitation always does negative work. Is this true or false?
The given statement 'Gravitation always does negative work' is false.
The work done by the gravitation depends upon the reference level of the system. Therefore, according to reference level it is taken as positive or negative.
In a parallel circuit with a 12 V battery and three 6 Ohm resistors, what is the total current in the entire circuit? Select one:a.36 Ampsb.6 Ampsc.4 Ampsd.2 Amps
First, let's find the equivalent resistance. Since they are in parallel, we can find it as follows:
[tex]\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{R1}+\frac{1}{R2}+\frac{1}{R3} \\ so: \\ \frac{1}{R_{eq}}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{1}{2} \\ Hence: \\ R_{eq}=2\Omega \end{gathered}[/tex]Now, we can use ohm's law to calculate the current:
[tex]\begin{gathered} V=IR \\ so: \\ I=\frac{V}{R}=\frac{12}{2}=6 \end{gathered}[/tex]Answer:
b.
6 Amps
A parking lot is going to be 60 m wide and 240 m long. which dimensions could be used for a scale model of the lot?A. 90 in x 360 cmB. 1 m x 3 mC. 20 cm x 80 cmD. 120 cm x 480 m
Answer:
C. 20 cm x 80 cm
Explanation:
The dimensions of the scale model have the same ratio of the original dimensions. The ratio of the original dimenstions is
240/60 = 4
Then, the ratio for each option is
A. 360/90 = 4
B. 3/1 = 3
C. 80/20 = 4
D. 480/120 = 4
Therefore, B is not a correct option.
Additionally, we don't use A because the units for length and width are different
And we don't use D because the measures are too long for a model.
Therefore, the answer is
C. 20 cm x 80 cm
What is the mass of a truck if it produces a force of 13,607 N while accelerating at a rate of 2.9 m/s²?
Newton's Second Law.
We have the following data, provided in the exercise:
Mass (m) = ?
Force (F) = 13607 N
Acceleration (a) = 2.9 m/s²
To calculate the mass, we solve the following formula:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{F=m*a \ \ < ====Formula \ clear==== > \ \frac{F}{a}=\frac{m*\not{a}}{\not{a}} } \end{gathered}$}}[/tex][tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{F}{a}=m \ \iff \ Address \ is \ changed \Rightarrow \ m=\frac{F}{a} } \end{gathered}$}}[/tex]
We substitute the data in the clear formula.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{13607 \ N}{2.9 \ \frac{m}{s^{2} } } } \end{gathered}$} }[/tex]
We break down the units of Newton = Kg * m/s².
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{13607 \ Kg*\not{\frac{m}{s^{2}} } }{2.9 \not{\frac{m}{s^{2}} } } } \end{gathered}$} }[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=4692.07 \ Kg } \end{gathered}$} }[/tex]
The mass of the truck is: 4692.07 Kilograms (Kg).1) Prove that for the adiabatic process of gas pVr =const ; r=Cp/Cv *
2) Write down the expression for the number of molecules of N2 gas having speeds in the interval (100m/s ; 102m/s) for one mole of gas at T=300K
3) Demonstrate how to obtain the Boltzmann Distribution of Energies from the Maxwell-Boltzmann distribution of speeds.*
For an adiabatic process of gas PV(^r)= Constant, where r = Cp/Cv , Cp, and Cv are constants for a particular gas.
What is an ideal gas?It is an imaginary gas for which the volume occupies by it is negligible, this gas does not exist in a practical situation and the concept of an ideal gas is only the theoretical one.
Universal Gas Equation for the ideal gas,
PV=nRT
By differentiating on both sides: P.dV + V.dP = n.R.dT…. (1)
For the adiabatic process, the expansion or compression of gas occurs at a very fast rate which makes no heat transfer. Therefore, dQ= 0
A/c to First Law of TD: dQ=dU+ dW, implies dU= -dW=-P.dV ….. (2)
But dU= n.Cv. dT …. (3) Combining 2 and 3, we get: n.dT= -P.dV/Cv …..(3)
Using R= Cp-Cv, the gas law gives: from 1 and 3.
n.dT= (P.dV + V.dP)/(Cp-Cv) = -PdV/Cv
On rearranging terms we get, (dP/P)+((Cp/Cv)*(dV/V))=0
Cp and Cv are constants for a particular gas, hence integrating,
Ln(P)+ r.Ln(V)=constant (replacing Cp/Cv = r or Gamma)
Hence, P.V(^r)= constant is termed an adiabatic equation.
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Increasing the mass wouldIncreasing the mass would_______can increase or decrease the value of the gravitational force depending on the initial valuehave no effect on the gravitational forceincrease the gravitational forcedecrease the gravitational force
We will have that:
Increasing the mass would increase the gravitational force.
The force diagram below is for a 10 kg object. Determine its acceleration.
As the buoyant force balances the weight of the object.
Thus, there is no motion of the object in the vertical direction.
Whereas, the force acting on the object towards the right is more than the drag force.
Thus, the net force acting on the object along the horizontal direction is,
[tex]F_{net}=F_T-F_{drag}[/tex]Substituting the known values,
[tex]\begin{gathered} F_{\text{net}}=35-10 \\ F_{\text{net}}=25N_{} \end{gathered}[/tex]According to Newton's second law, the net force acting on the object in terms of the acceleration of the object is,
[tex]F_{\text{net}}=ma[/tex]where m is the mass, and a is the acceleration,
Substituting the known values,
[tex]\begin{gathered} 25=10\times a \\ a=\frac{25}{10} \\ a=2.5ms^{-2} \end{gathered}[/tex]Thus, the acceleration of the object is 2.5 meters per second.
H
An Olympic diver is on a diving platform 8.40 m above the water. To start her dive, she runs off of the platform with a speed of 1.2 m/s in the horizontal direction. What is the diver speed, in m/s, just before she enters the water?m/s
Given data
*The given distance above the water is s = 8.40 m
*The given initial speed of the Olympic diver is u = 1.2 m/s
*The value of the acceleration due to gravity is a = 9.8 m/s^2
The formula for the diver speed, in m/s, just before she enters the water is given by the equation of motion as
[tex]v^2=u^2+2as[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} v^2=(1.2)^2+2\times9.8\times8.40 \\ v=12.88\text{ m/s} \end{gathered}[/tex]Hence, the diver speed, in m/s, just before she enters the water is v = 12.88 m/s
Compare(how they are the same) and contrast(how they are different) psychoanalysis and behaviorism as two of the early schools of psychology. Offer the major names associated with each and explain how each explained behavior.
Abstract of American Intercontinental University
This paper will compare and contrast three of the 10 main early psychology views. This assignment's three approaches are behavioral, humanistic, and cognitive. Three Early Psychology Perspectives are compared and contrasted. Psychology, like anything else, offers a plethora of theories and methods. One idea may be beneficial to one patient while being ineffective to another. The trick is to discover the optimal method for each patient. The concept that behaviors arise as a result of conditioning is known as behaviorism. This theory does not acknowledge the presence of interior mental factors such as thoughts, feelings, and moods, nor does it take free will into account.
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Emily and Gemma did a Reaction time lab. Emily dropped the ruler while Gemma tried to catch it. She caught the ruler 5 times and her average catching distance is 0.12 m. What is Gemma's reaction time?
The average reaction time of Gemma is 0.1564 seconds.
As we know, Gemma is catching the scale and Emily is dropping the scale.
The whole experiment is taking place under gravity, so the acceleration is constant.
As we know, the scale is dropped, it means that the initial velocity of the scale is zero.
We can use the equation of motion,
The equation is,
S = Ut + 1/2at²
Where,
S is the displacement, which is 0.12 m in our case,
U is initial velocity which is 0m/s because the stone is dropped,
t is the time taken, this is equal tot he reaction time here,
a is the acceleration due to gravity whose value is 9.8m/s.
Now, putting all the values,
0.12 = 1/2(9.8)(t)²
t² = 0.24/9.8
t = 0.1564 seconds.
Gemma reacts in 0.1564 seconds to catch the scale.
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A spring with spring constant 175 N/m has 20 J of EPE stored in it. How much is it compressed?
Given:
• Spring constant = 175 N/m
,• Energy = 20 J
Let's find by how much it is compressed.
Apply the formula:
[tex]E=\frac{1}{2}kx^2[/tex]Where:
E is the energy = 20 J
k is the sring constant = 175 N/m
x is the compression in meters
Rewrite the formula for x:
[tex]x=\sqrt{\frac{2E}{k}}[/tex]Input values and solve for x:
[tex]\begin{gathered} x=\sqrt[]{\frac{2\times20}{175}} \\ \\ x=\sqrt[]{\frac{40}{175}} \\ \\ x=\sqrt[]{0.2285} \\ \\ x=0.48\text{ m} \end{gathered}[/tex]ANSWER:
0.48 m
In Young's double-slit experiment, two slits are separated by 5.0 mm and illuminated by light with a wavelength of 480 nm. The screen is 3.0 m from the plane of the slits. Calculate the separation between the eighth bright fringe and the third dark fringe observed with respect to the central bright fringe.
We are given the following information.
Seperation between slits: d = 5.0 mm
Wavelength of light: λ = 480 nm
Distance from the plane of slits: D = 3.0 m
We are asked to calculate the separation between the 8th bright fringe and the 3rd dark fringe observed with respect to the central bright fringe.
The position of the 8th bright fringe is given by
[tex]\begin{gathered} x_n=\frac{n\lambda D}{d} \\ x_8=\frac{8\cdot480\times10^{-9}\cdot3}{5\times10^{-3}} \\ x_8=2.304\times10^{-3}\;m \end{gathered}[/tex]The position of the 3rd dark fringe is given by
[tex]\begin{gathered} x_n=(\frac{2n-1}{2})\frac{\lambda D}{d} \\ x_3=(\frac{2\cdot3-1}{2})\frac{480\times10^{-9}\cdot3}{5\times10^{-3}} \\ x_3=7.2\times10^{-4}\;m \end{gathered}[/tex]Finally, the separation between the 8th bright fringe and the 3rd dark fringe is
[tex]\begin{gathered} x_8-x_3=2.304\times10^{-3}-7.2\times10^{-4} \\ x_8-x_3=1.584\times10^{-3}\;m \end{gathered}[/tex]Therefore, the separation between the eighth bright fringe and the third dark fringe observed with respect to the central bright fringe is 1.584×10⁻³ m.