PLS HELP!! Our eyes perceive colors because of differences in which of the following properties of light?


Amplitude


Brightness


Wavelength


Source

Answer:

The answer to this is C. good luck for the rest of your work!

Answer:

Option D

Explanation:

The thought or law the scientist has implemented he has to prove it.

Although he is 100% correct he has to show evidence to the scientist community inorder to verify.

Many laws in history have been withdrawn because of lack of evidence

Answer:

the tension in the cable is \(\mathbf{F = \frac{\pi E_o v^2r^2}{2d^2}}\)

the work done by the cable is \(\mathbf{W= \frac{\pi E_ov^2r^2}{4d}}\)

Explanation:

A)

If we have two circular plate supported by a cable at a fixed distance, then the electric field formed between the two plate of the capacitor can be represented by the equation.

\(\mathbf{E = \frac{voltage \ \ V}{distance \ \ d}}\)

However; the net electric field i.e the sum of the electric filed produced is represented as:

\(\mathbf{E' = \frac{E}{2}} \\ \\ \mathbf{E' = \frac{V}{2d}}\)

So, if we assume that the lower plate and the upper plate possess the charge +q and -q respectively. Then, the tension of the cable which is the same as Force F can be written as:

\(\mathbf{F = q* E'}\)

\(\mathbf{F = \frac{q*v}{2d}}\) -----    equation (1)

Also ; we know that

\(\mathbf{C = \frac{q}{v}= \frac{E_oA}{d}}\)

\(\mathbf{\frac{q}{v}= \frac{E_o \pi r^2}{d}} \ \ \ \ \ \mathbf{since \ A = \pi r^2}\)

\(\mathbf{{q}= \frac{\pi E_o {v} r^2}{d}}\)    -----   equation (2)

Replacing equation 3 into equation (2); we have:

\(\mathbf{F = \frac{\pi E_o vr^2}{d}* \frac{v}{2d}}\)

\(\mathbf{F = \frac{\pi E_o v^2r^2}{2d^2}}\)

Therefore,  the tension in the cable is \(\mathbf{F = \frac{\pi E_o v^2r^2}{2d^2}}\)

B)

Assume that the upper plate is displaced by dz in an upward direction ; Then we can express the workdone by the tension as :

\(\mathbf{dW = T *dz} \\ \\ \mathbf{dW = F*dz} \\ \\ \mathbf{dW = \frac{\pi E_o v^2r^2}{2z^2}dz }\)

The net workdone to raise the plate from separation d to 2d is:

\(\mathbf{W = \int\limits^{2d}_{2zd} {dw} = \frac{\pi E_ov^2r^2}{2} \int\limits^{2d}_d \frac{dz}{z^2} }\)

\(\mathbf{W= \frac{\pi E_ov^2r^2}{2} [-\frac{1}{z}]^{2d}_d }\)

\(\mathbf{W= - \frac{\pi E_ov^2r^2}{2} [\frac{1}{2d}-\frac{1}{d}]}\)

\(\mathbf{W= - \frac{\pi E_ov^2r^2}{2} [\frac{-1}{2d}]}\)

\(\mathbf{W= \frac{\pi E_ov^2r^2}{4d}}\)

the work done by the cable is \(\mathbf{W= \frac{\pi E_ov^2r^2}{4d}}\)

C) To calculate the energy stored in the Electrical energy Capacitor before the top plate is raised ; we have:

\(\mathbf{U_i = \frac{1}{2}Cv^2} \\ \\ \mathbf{U_i = \frac{1}{2}(\frac{E_oA}{d})v^2} \\ \\ \mathbf{U_i = \frac{1}{2}(\frac{E_o \pi r^2}{d})v^2} \\ \\ \mathbf{U_i = \frac{E_o \pi r^2 v^2}{2d}} }\)

D) The energy stored in the plate after the  the top plate was raised is as follows:  

\(\mathbf{U_f = \frac{1}{2}C'v^2} \\ \\ \mathbf{U_f = \frac{1}{2}(\frac{E_oA}{2d})v^2} \\ \\ \mathbf{U_f = \frac{1}{2}(\frac{E_o \pi r^2}{2d})v^2} \\ \\ \mathbf{U_f = \frac{E_o \pi r^2 v^2}{4d}} }\)

E) Yes,  work done by the cable equal to the change in the stored electrical energy. The Difference in energy stored before and after the top plate is raised:

\(\mathbf{U_i-U_f} = \mathbf{\frac{E_o \pi r^2 v^2}{2d}} }} - \mathbf {\frac{E_o \pi r^2 v^2}{4d}} }}\)

\(\mathbf{U_i-U_f}= \mathbf {\frac{E_o \pi r^2 v^2}{4d}} }}\)

Thus;

b)The work done in separating the plates is equal to the magnitude of the energy change in the plates. This does not mean that the work done is equal to the change in the energy stored in the plates.

The energy transferred in Joules by the radio when it has been switched on for 2 minutes would be 6000 Joules.

Power is defined as the rate of energy transfer or the rate at which work is done, and is given by the equation:

Power = Energy transferred / Time

Rearranging the equation to solve for energy transferred, we get:

Energy transferred = Power x Time

We are given:

Power = 50 W

Time = 2 minutes = 120 seconds

Therefore, the energy transferred by the radio when it has been switched on for 2 minutes is:

Energy transferred = Power x Time = 50 W x 120 s = 6000 J

In other words, the energy transferred by the radio is 6000 Joules.

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Scobie will take 10 days to drive around Earth's equator.

To calculate the time that takes Scobie to drive around Earth's equator we need to find the distance, which is given by the equation of a circumference:

\( d = 2\pi r \)

Where:

r: is the Earth's radius = 6371 km

Then, the distance is:

\( d = 2\pi r = 2\pi*6371 km = 40030.2 km \)

Now, if we divide the above distance by the speed of the car we can find the time:

\( t = \frac{d}{v} = \frac{40030.2 km}{160.0 km/h} = 250.2 h*\frac{1 d}{24 h} = 10 d \)

Therefore, Scobie will take 10 days to drive around Earth's equator.

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The total resistance of the circuit is 49 Ω. The current strength in the circuit, when connected to a voltage source of 56 V, is approximately 1.14 A.

To calculate the total resistance of the circuit, we need to determine the equivalent resistance of the resistors connected in a series.

Given:

R1 = 4 Ω

R2 = 30 Ω

R3 = 10 Ω

R4 = 5 Ω

Calculate the equivalent resistance (RT) of R1 and R2, as they are connected in series:

RT1-2 = R1 + R2

RT1-2 = 4 Ω + 30 Ω

RT1-2 = 34 Ω

Calculate the equivalent resistance (RTotal) of RT1-2 and R3, as they are connected in parallel:

1/RTotal = 1/RT1-2 + 1/R3

1/RTotal = 1/34 Ω + 1/10 Ω

1/RTotal = (10 + 34) / (34 * 10) Ω

1/RTotal = 44 / 340 Ω

1/RTotal ≈ 0.1294 Ω

RTotal ≈ 1 / 0.1294 Ω

RTotal ≈ 7.74 Ω

Calculate the equivalent resistance (RTotalCircuit) of RTotal and R4, as they are connected in series:

RTotalCircuit = RTotal + R4

RTotalCircuit = 7.74 Ω + 5 Ω

RTotalCircuit ≈ 12.74 Ω

Therefore, the total resistance of the circuit is approximately 12.74 Ω.

To determine the current strength (I) when connected to a voltage source of 56 V, we can use Ohm's Law:

I = V / RTotalCircuit

I = 56 V / 12.74 Ω

I ≈ 4.39 A

Therefore, the current strength in the circuit, when connected to a voltage source of 56 V, is approximately 4.39 A (or 1.14 A, considering significant figures).

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The power that must be delivered to the object by the force is 50 W

Power is defined as the rate of doing work. The power of an object in relation to the force and velocity is given by the following equation:

Power (P) = Force (F) × velocity (v)

P = F × v

From the question given above, the following data were obtained:

P = F × v

P = 10 × 5

Thus, the power that must be delivered to the object by the force is 50 W

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The expression for the velocity of the sixth ball is

 \(v_2 = \frac{u_1 sin\theta }{sin \phi cos\theta + cos \phi sin\theta}\)

Explanation:

From the question we are told that

     The mass of the 8 ball is  \(m_1 =  0.5 \  kg\)

      The initial velocity of the 8 ball is  \(u_1  =  3.7 \  m/s\)

      The initial velocity of the 6 ball is  \(u_2  =  0  \  m/s\)

         The mass of the 6 ball is  \(m_2 =  0.5 \  kg\)

Generally from the law of momentum conservation is  

     \(m_1 *u_1 + m_2 * u_2 = m_1 * v_1 +m_2 *v_2\)

Now along the y  axis

      \(u_1 =u_y_1 =  0 \  m/ s\)

      \(u_2 =u_y_2=  0 \  m/ s\)

      \(v_1 =v_y_1=  v_1 sin \theta  \  m/ s\)

      \(v_2 =v_y_2=  v_2 sin \phi  \  m/ s\)

So

  \(m_1 *0 + m_2 * 0 = m_1 * (v_1 sin \theta) +m_2 *(v_2 sin \phi )\)

=>  \(v_1 = \frac{v_2 sin \phi }{ sin \theta}\)

Now along the x  axis

      \(u_1 =u_x_1 =  u_1 \  m/ s\)

       \(u_2 =u_2_2=   0 \  m/ s\)

        \(v_1 =v_x_1=  v_1 cos \theta  \  m/ s\)

        \(v_2 =v_x_2=  v_2 cos \phi  \  m/ s\)

So

        \(m_1 *u_1 + m_2 * 0 = m_1 *(v_1 cos \theta) +m_2 *(v_2 cos \phi)\)

=>\(m_1 *u_1  = m_1 *(v_1 cos \theta) +m_2 *(v_2 cos \phi)\)    

substituting for \(v_1\) in the above equation

=>\(m_1 *u_1  = m_1 *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m_2 *(v_2 cos \phi)\)      

=>\(m_1 *u_1  = m_1 *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m_2 *(v_2 cos \phi)\)

 given that  \(m_1 = m_2 = m\)

=>\(m *u_1  = m *([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) +m *(v_2 cos \phi)\)

=>\(m *u_1  = m [([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) + (v_2 cos \phi)]\)

=>\(u_1  = ([ \frac{v_2 sin \phi }{ sin \theta}] cos \theta) + (v_2 cos \phi)\)

=>\(u_1  = v_2 sin\phi cot \theta + v_2 cos\phi \)

\(v_2 = \frac{u_1  }{sin\phi cot\theta + cos\phi }\)

converting \(cot \phi\) back  to  \(\frac{cos \theta}{sin\theta }\)

So

    \(v_2 = \frac{u_1  }{sin\phi [\frac{cos \theta}{sin\theta }] + cos\phi }\)

multiply through by  \(\frac{sin \theta}{sin \theta }\)

   \( \frac{sin \theta}{sin \theta } *v_2 = \frac{sin \theta}{sin \theta } * \frac{u_1  }{sin\phi [\frac{cos \theta}{sin\theta }] + cos\phi }\)

=>  \(v_2 = \frac{u_1 sin\theta }{sin \phi cos\theta + cos \phi sin\theta}\)

C. The average acceleration is positive and smaller in magnitude than the initial acceleration.

Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs.

a = Δv/Δt

where;

a = (250 - 248) / (70 - 40)

a = 0.067 m/s²

Thus, we can conclude that the average acceleration is positive and smaller in magnitude than the initial acceleration.

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After several contacts with a charged ball, the charge on the rod will become negatively charged on end A with end B remaining almost neutral.

When the charged ball is touched to end A, some of its negative charges will be transferred to the rod and deposited at end A, increasing the negative charge on that end. End B will remain neutral or nearly neutral since no charge has been transferred to it.

The process of charging a rod by contact with a charged ball is called "contact charging." In this process, electrons from the charged ball transfer to the rod, causing the rod to become charged.

When the charged ball is touched to end A of the rod, electrons from the ball are transferred to the rod and accumulate at that end, giving it a negative charge.

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The amount the needle on the meter is deflected A. increases

This phenomenon can be explained by Faraday's law of electromagnetic induction. According to this law, when a magnetic field (created by the bar magnet) passes through a coil of wire, it induces an electric current in the wire. This induced current generates its own magnetic field, which interacts with the magnetic field of the bar magnet.

The deflection of the meter needle is a result of this induced current. When the number of coils of wire is increased, there is a greater number of wire loops for the magnetic field to pass through. This leads to a stronger induction of electric current, resulting in a larger deflection of the meter needle.

By increasing the number of coils, more magnetic flux is linked with the wire, resulting in a higher induced electromotive force (emf) and a greater current. This increased current produces a stronger magnetic field around the wire, leading to a larger deflection on the meter. Therefore, increasing the number of coils of wire enhances the magnetic field interaction, resulting in an increased deflection of the meter needle. Therefore, Option A is correct.

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The heaviest liquid is mercury. In order to equalize the air pressure, it only climbs 76 cm. Water will rise to a 13.6 because it is 13.6 times lighter than mercury. By a factor of 13.6, mercury is 13.6 times denser than water.

Therefore, the barometer's height would be 13.6 times higher if water were employed in place of mercury. Since water expands when it freezes, the glass tube would be broken.

Because of its high density, mercury is frequently employed in barometers, allowing for a column height that is appropriate for measuring atmospheric pressure. For example, a mercury barometer would need to be 13.6 times taller than a water barometer to measure the same change in pressure.

This is the primary justification for using mercury in thermometers. Mercury will provide accurate readings in comparison to water since it lacks the condensation property that water possesses. Mercury can be used to measure both negative and positive temperatures, whereas water cannot be used to measure either.

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gear C and Z will run at the same RPM

RPM is not a unit, according to the International System of Units (SI). The word "revolution" is a semantic annotation rather than a unit, which explains this. RPM formula sign must be f for (rotational) frequency and or for angular velocity due to the measured physical quantity. s−1  or Hz is the basic SI-derived unit that corresponds. The radians per the second unit are used to express angular speed.

As a result, a disc rotating at 60 RPM  is considered to be rotating at either 2 rad/s or 1 Hz, where the former refers to angular velocity and the latter to the rate of revolutions per second.

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The electrostatic interactive force between electrical charges is exactly the same as the gravitational interaction between them is referred to as the incorrect statement and is denoted as option A.

This is defined as the force of attraction or repulsion which exists in a charged body and it is different from the gravitational force interaction between two bodies.

This is because gravitational force is the force of objects as a result of its mass while  electrostatic force is the force of an object due to charge which is therefore the reason why option A was chosen.

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Jonathan needs to maintain a separation of 0.543 mm between the plates to get the desired charge, and a dielectric constant of 92.6 to achieve a separation of 5 mm with a dielectric.

(a) Using the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage, we can solve for the capacitance: C = Q/V =\((8.15 x 10^-9 C) / (50 V) = 1.63 x 10^-10 F.\)

Then, using the formula for capacitance of parallel plate capacitors: C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the separation distance, we can solve for the separation distance: d =\(_{3}OA/C = (8.85 x 10^-12 F/m) x (0.01 m^2) / (1.63 x 10^-10 F) = 0.543 mm.\)

(b) To find the dielectric constant, we can use the formula for capacitance of a parallel plate capacitor with a dielectric: C = εrε0A/d, where εr is the relative permittivity or dielectric constant of the material. Solving for εr, we get: εr = Cd / ε0A = \((1.63 x 10^-10 F)\) x (0.005 m) / \((8.85 x 10^-12 F/m)\) x \((0.01 m^2)\) = 92.6.

Therefore, Jonathan should use a dielectric with a relative permittivity of 92.6 to achieve a separation of 5 mm.

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For a rectangular storage tank filled with paraffin to a depth of 2 m, the volume, weight, mass of paraffin, and pressure at the bottom of the tank are:

a. The volume is 24 m³.

b. weight is 240,000 N,

c. mass is 24,490 kg, and

d. pressure is 23,530 Pa.

a) The volume of paraffin in the rectangular storage tank can be calculated using the formula:

Volume = Length x Width x Depth

Given:

Length = 4 m

Width = 3 m

Depth = 2 m

Substituting the values into the formula, we have:

Volume = 4 m x 3 m x 2 m

Volume = 24 m³

Therefore, the volume of paraffin in the tank is 24 cubic meters.

b) The weight of the paraffin can be calculated using the formula:

Weight = Volume x Density x Acceleration due to gravity

The density of paraffin varies, but we can assume a typical value of 10,000 kg/m³. The acceleration due to gravity is approximately 9.8 m/s². Substituting these values into the formula:

Weight = 24 m³ x 10,000 kg/m³ x 9.8 m/s²

Weight = 240,000 N

Therefore, the weight of the paraffin in the tank is 240,000 Newtons.

c) The mass of the paraffin can be calculated using the formula:

Mass = Density x Volume

Substituting the given values:

Mass = 10,000 kg/m³ x 24 m³

Mass = 24,490 kg

Therefore, the mass of the paraffin in the tank is 24,490 kilograms.

d) The pressure at the bottom of the tank due to the paraffin can be calculated using the formula:

Pressure = Weight / Area

The area of the bottom of the tank is equal to the length multiplied by the width. Substituting the values:

Area = 4 m x 3 m

Area = 12 m²

Pressure = 240,000 N / 12 m²

Pressure = 20,000 Pa

Therefore, the pressure at the bottom of the tank due to the paraffin is 20,000 Pascals (Pa).

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The radio waves travels between the two boxes and they were travelling through air,

In that way, the radio waves from box A to B through air, the box A will gets the signal, and then modulates, amplifies and then it send out radio waves. Through the air, Box B will captures, amplifies and demodulates radio waves.

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So the velocity of light in a material with an index of 2.0 is approximately 149,896,229 m/s.

Velocity is a vector quantity that refers to the rate at which an object changes its position in a particular direction. It is defined as the displacement of an object over time, or in other words, the distance an object moves in a specific direction per unit of time. Velocity is measured in units of distance per time, such as meters per second (m/s) or kilometers per hour (km/h). Unlike speed, which is a scalar quantity that only describes how fast an object is moving without regard to its direction, velocity includes both the speed and the direction of the motion. For example, a car traveling at 60 km/h due east has a velocity of 60 km/h in the eastward direction. A change in velocity can result from a change in speed, direction, or both.

Here,

The velocity of light in a material with an index of refraction n is given by:

v = c/n

where c is the speed of light in a vacuum (approximately 299,792,458 m/s).

Substituting n = 2.0, we get:

v = c/n

= (299,792,458 m/s)/2.0

= 149,896,229 m/s

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HERE IS YOUR ANSWER!

The time it would take it to reach Earth if the Sun remained at its current position is 978,349.5 years.

The time of motion of the giant molecular cloud is the time take for the giant molecular cloud to reach the earth.

Mathematically, the time taken for the giant molecular cloud to reach the earth is given as;

time = distance / speed

where;

time of motion = (6.48 x 10¹⁴ km) / (21 km/s)

time of motion = 3.086 x 10¹³ seconds = 978,349.5 years.

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Theories help scientists to determine whether a claim is false. Thus, the correct option for this question is C.

A Scientific theory may be defined as a type of explanation that significantly deals with the natural world and universe that has been repeatedly tested in order to prove some facts and understanding.

A scientific theory not only illustrates known facts but also authorizes scientists in order to make predictions on the basis of observation of the theory whether it is true or false. Scientific theories are testable in nature.

Scientific theories are always constructed with the utilization of scientific methods which are well-explained and systematically arranged. It brings out many facts and hypotheses together.

Therefore, theories help scientists to determine whether a claim is false. Thus, the correct option for this question is C.

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Answer:

t = 26.8 s

Explanation:

Here, we can use the second equation of motion to calculate the required time:

\(s = v_it + \frac{1}{2}at^2\)

where,

s = distance = 1800 m

vi = initial speed = 0 m/s

t = time needed = ?

a = acceleration = 5 m/s²

Therefore,

\(1800\ m = (0\ m/s)t+\frac{1}{2}(5\ m/s^2)t^2\\\\t^2 = \frac{(1800\ m)(2)}{5\ m/s^2}\\\\t = \sqrt{720\ s^2}\)

t = 26.8 s

Answer:

F

Explanation: Its common sence

Answer:

It’s false

Explanation:

2020 (WORST YEAR EVER) on Edge ;-)

The amplitude of the object is 1.6m, the angular speed, position, velocity and acceleration of the object at t = 0 ate 3.5rad/s,  0.256m, 4.459m/s and 3.136m/s² and the maximum acceleration is 19.6m/s².

The object is undergoing Simple Harmonic Motion along x-axis and its position is described by,

x(t) = 1.6cos(3.5t-1.4)

t is the time.

(a) The standard equation of simple harmonic motion is,

X = Acos(wt)

So, comparing the given equation with the standard equation, we get,

Amplitude = 1.6m.

(b) Again comparing the given equation with standard equation, we get the angular velocity as,

W = 3.5rad/s.

(c) To find the position of the object at t=0,

Putting t=0 in x(t) = 1.6cos(3.5t-1.4).

x = 1.6cos(-1.4)

x = 1.6 × 0.16

x = 0.256m.

(d) To find the speed of the object,

Differentiating x(t) = 1.6cos(3.5t-1.4) with respect to x,

v(t) = 1.6sin(3.5t-1.4)3.5

Putting t = 0

v(t) = 1.6 x -0.98 x 3.5

v(t) = 4.459m/s.

(e) To find the acceleration of the object,

Double Differentiating x(t) = 1.6cos(3.5t-1.4) with respect to x,

a(t) = -1.6(3.5)²cos(3.5t-1.4)

Putting t = 0,

a(t) = -1.6 x (3.5)² x 0.16

a(t) = 3.136m/s².

(f) For maximum acceleration,

cos(3.5t-1.4) = 1

a(t) = -19.6m/s².

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Answer:

The elevator is stationary

The question is incomplete. Here is the complete question.

Suppose the mass of a loaded elevator is 1600 kg.

(a) What force, in Newtons, must be supplied by the elveator's cable to produce an acceleration of 0.745 m/s² upwards against a 185N frictional force?

(b) How much work, in joules, is done by the cable in lifting the elevator 21m?

(c) What is the final speed, in meters per second, of the elevator if it starts from rest?

(d) How much work, in kilojoules, went into thermal energy produced by friction?

Answer: (a) F = 1377 N

              (b) W = 28917 J

              (c) v = 5.6 m/s

              (d) W = 3.885 kJ

Explanation:

(a) According to Newton's Second Law: \(F_{net}=m.a\), in which, \(F_{net}\) is the vetorial sum of all the forces in a system and its unit is [F] = kg.m/s² or newton (N).

In the elevator's case, and assuming going upwards is positive:

\(F-F_{f}=m.a\)

F - 185 = 1600(0.745)

F = 1377 N

For an elevator to produce an acceleration of 0.745m/s² upwards, the cables have to supply a force of 1377 newtons.

(b) Work is the energy transferred to an object while is being moved. It is calculated as: W = F.s. Its unit is [W] = N.m or Joule (J)

In the elevator's cable:

W = 1377.21

W = 28917 J

The work done by the elevator's cable is W = 28917 joules.

(c) Acceleration is variation in velocity along time. Since we know the displacement of the elevator:

\(v^{2}=v_{0}^{2}+2a\Delta x\)

where:

v₀ is initial velocity, which is this case v₀=0 because it starts from rest;

a is acceleration;

Δx is the displacement

Replacing values:

\(v^{2}=2(0.745)(21)\)

\(v=\sqrt{31.29}\)

v = 5.6 m/s

Final speed of the elevator is 5.6 m/s.

(d) \(W=F_{f}.s\)

W = 185(21)

W = 3885 J

Work transferred into thermal energy because of friction is W = 3.885 kJ.

Answer:

it's b  

a\p\e\x\

Explanation:

Answer:

20*365=7300

Explanation:

1 Year=365day

20years = x days