A roller coaster works by being hoisted to the top of the highest peak on the track and then released. As the roller coaster car moves along the track the energy gets converted back and forth between kinetic and gravitational potential energy. The entire time the roller coaster car is in motion air friction and friction in the wheels act to oppose the motion of the car. At which point during the ride is the total mechanical energy of the roller coaster car the greatest?

a. At the bottom of the first dip in the track when the car is moving the fastest.
b. When the car is exactly at half its original height half way through the ride.
c. At the top of the highest peak as the very start of the ride.
d. At the end of the ride as the car nears the station.

Given that two large parallel plates are separated by 0.20 m and that the potential difference is 12V.

(a) Describe the motion of an electron released from rest at a distance "d" from the negative plate.

(b) What distance from the positive plate will the electron have a speed of 1 x 10^6 m/s?

For part (a):

The magnitude of an electric field can be given as  \(||\vec E||=\frac{\Delta V}{d}\), where "ΔV" is the potential difference and "d" is the distance between the plates.

So, \(||\vec E||=\frac{12 \ V}{0.20 \ m} \Longrightarrow \boxed{||\vec E||=60 \ \frac{N}{C} }\)

An electric field is created between the plates pointing from positive towards negative. We know that negative charges accelerate opposite the direction of electrical fields. So the electron placed "d" meters away from the negative plate will accelerate towards the positive plate at a constant rate.

For part (b):

We know that...

- the charge of an electron is \(\bold{-1.602 \times10^{-19} \ C}\).

- the mass of an electron is \(\bold{9.11 \times10^{-31} \ kg}\).

- \(\vec F_e=q\vec E\)

- \(\vec F =m\vec a\)

\(\Longrightarrow \vec F_e=(-1.602 \times10^{-19} \ C)(60 \ \frac{N}{C} }) \Longrightarrow \boxed{\vec F_e= -9.612 \times10^{-18} \ N}\)

\(\Longrightarrow \vec F =m\vec a \Longrightarrow \vec a=\frac{\vec F}{m} \Longrightarrow \vec a=\frac{-9.612 \times10^{-18}}{9.11 \times10^{-31} \ kg} \Longrightarrow \boxed{\vec a=-1.06 \times10^{13} \ m/s^2}\)

Kinematic Equation: \(\vec v_f^2=\vec v_0^2+2\vec a \Delta \vec x\)

\(\Longrightarrow 1 \times10^{12} \ m^2/s^2=-2.11 \times10^{13} \ m/s^2 \Delta \vec x \Longrightarrow \Delta \vec x= \frac{1 \times10^{12} \ m^2/s^2}{-2.12 1\times10^{13} \ m/s^2}\)

\(\Longrightarrow \boxed{\Delta \vec x= -0.047 \ m}\)

The distance from the positive plate we'll call, "D."

\(D=0.20+\Delta \vec x\)

\(\Longrightarrow D=0.20+\Delta \vec x \Longrightarrow D=0.20 \ m+(-0.047 \ m) \Longrightarrow \boxed{D=0.153 \ m} \therefore Sol.\)

Expressed in vector form, the final displacement from where the cyclist started is Δr = 3.0 km east + 6.38 km north.

Displacement is a vector quantity that represents the change in position of an object. It is the straight-line distance and direction between the initial position of an object and its final position.

To solve the problem, we can break down the motion of the cyclist into two components: one in the x-direction (east-west) and one in the y-direction (north-south).

In the x-direction, the cyclist rides 4.0 km west and then 7.0 km east, for a net displacement of 7.0 km - 4.0 km = 3.0 km to the east. In the y-direction, the cyclist rides 11.0 km at an angle of 35° west of north, which means that the component of this distance in the y-direction is 11.0 km * sin(35°) = 6.38 km to the north.

Therefore, the final displacement from where the cyclist started is the vector sum of these two components: Δr = (3.0 km, 6.38 km)

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Answer:

It could be a stringed instrument or an open pipe.

Explanation:

Let v be the speed of sound, y be wavelength and f be frequency.

v = yf

f= v/y; v is constant.

In a stringed instrument, the fundamental frequency note is heard when the length of the string, l = y/2; y= 2l

f′= v/2l

The second harmonic is heard when l= y

f"= v/y

...

f'''= 3v/2l

We can infer that f"= 2f'

f'''= 3f'

This is similar to the values in the question as;

523.26 =2(261.63) and so on.

Same thing happens with open pipes.

The change in surface area of Gaussian surface with radius (r) is 8πr.

The electric field experienced by a charge is calculated as follows;

\(E = \frac{Q}{4\pi \varepsilon_o r^2}\)

where;

The electric field reduces by a factor of \(\frac{1}{r^2}\)

The surface area of a sphere is given as;

\(A = 4\pi r^2\)

\(\frac{dA}{dr} = 8\pi r\)

Thus, the change in surface area of Gaussian surface with radius (r) is 8πr.

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To solve this we must be knowing each and every concept related to velocity. Therefore, the amplitude and maximum velocity are 0.23 m and 2.75 m/s respectively.

V is the velocity measurement of an object's rate of motion and direction of motion. As a result, in order to calculate velocity using this definition, we must be familiar with both magnitude and direction.

For example, if an item travels west with 5 meters a second (m/s), its velocity to the west will be 5 m/s. The most frequent and simplest approach to determine velocity is using the formula shown below.

v = √(k / m) ×A

v = velocity of the mass

k= spring constant

m =mass of the object

A= amplitude of the oscillation.

substituting all the given values in the above equation, we get

2.3 m/s = √(200 N/m / 3.00 kg)×A

A = 2.3 m/s / √(200 N/m / 3.00 kg)

    = 0.23 m

v =√(200 N/m / 3.00 kg) ×0.23 m

 = 2.75 m/s

Therefore, the amplitude and maximum velocity are 0.23 m and 2.75 m/s respectively.

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Sound waves are a type of mechanical wave that propagate through a medium, typically air but also other materials such as water or solids.

Frequency: the frequency of a sound wave refers to the number of cycles or vibrations it completes per second and is measured in Hertz (Hz).

Amplitude: the amplitude of a sound wave refers to the maximum displacement or intensity of the wave from its equilibrium position. It represents the loudness or volume of the sound, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to softer sounds.

Wavelength: the wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, such as from one peak to the next or one trough to the next. It is inversely related to the frequency of the wave.

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Given,

The work function of the metal, W=4.48 eV

The work function is given by the formula,

Where ν₀ is the threshold frequency of the metal.

But the frequency is related to wavelength as,

Where c is the speed of light and λ is the wavelength.

Thus the work function will be,

Where λ₀ is the maximum wavelength needed to eject the electron from the given metal.

On substituting the known values in the above equation,

Thus the maximum wavelength of the light required is 277.48 nm.

The frequency of the light is,

Thus the frequency of the required light is 1.08×10¹⁵ Hz.

Answer:

search on the app

Explanation:

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Hi there!

a)
Since the objects are made of material of a constant area/mass density, we can simplify the process.

To calculate the value of the y-coordinate for the center of mass, we can begin by finding the y-coordinates for the center of masses for both rectangles.

Also, let the small rectangle be 'Rectangle 1', and the bigger rectangle 'Rectangle 2'.

Smaller rectangle:

Since D = 9 cm and B = 32 cm, the remaining width of the small rectangle is  equal to B - D = 32 - 9 = 23 cm. The midpoint of this width is:
\(w_{1m} = \frac{23}{2} = 11.5 cm\)

Now, the height of this rectangle is 10 cm. The midpoint of this height is 10/2 = 5 cm. However, this is not the actual y-coordinate. Since the height of the block below is 5 cm, we must add the two because this rectangle is on top of the other.

\(h_{1m}= 5 + 5 = 10 cm\)

Larger rectangle:
We can simply take the midpoints of its dimensions to solve for its center of mass.

\(w_{2m} = \frac{B}{2} = \frac{32}{2} = 16 cm\)

\(h_{2m} = \frac{A-C}{2} = \frac{15-10}{2} = 2.5 cm\)

Now, take the averages of the coordinates for both rectangles to solve.

y-coordinate:
\(y_{cm} = \frac{10 + 2.5}{2} = \frac{12.5}{2} = \boxed{6.25 cm}\)

x-coordinate:
\(x_{cm} = \frac{11.5 + 16}{2} = \frac{27.5}{2} = \boxed{13.75 cm}\)

The acceleration of the car is determined as 0.35 m/s².

The acceleration of the car is calculated by applying the formula for Newton's second law of motion as follows;

F(net) = ma

where;

Fy = F sinθ

200 = F x sin(30)

F = 200 / sin(30)

F = 400 N

The tension in horizontal direction;

Fₓ = 400 N x cos(30)

Fₓ = 346.4 N

The acceleration of the car is calculated as;

a = Fₓ / m

a = 346.4 / 1000

a = 0.35 m/s²

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In order to determine the length of the wire, use the following formula for the force exterded on a wire in a magnetic field:

where,

I: current through the wire = 2.0A

L: length of the wire = ?

B: strength of magnetic field = 0.20T

θ: angle between the axis of the wire and the direction of B = 60 degrees

F: force = 0.40N

Solve the equation above for L, replace the values of the other parameters and simplify:

Hence, the length of the wire is approximately 1.15m

Answer:

Final speed after 2 seconds = 34.6 m/s

Explanation:

Given:

Initial speed of coin (u) = 15 m/s

Time taken = 2 seconds

Find:

Final speed after 2 seconds

Computation:

Gravitational acceleration of earth = 9.8 m/s²

Using first equation of motion;

v = u + at

or

v = u + gt

where,

v = final velocity

u = initial velocity

g = Gravitational acceleration

t = time taken

v = 15 + 9.8(2)

v = 15 + 19.6

Final speed after 2 seconds = 34.6 m/s

Answer:

f

Explanation:

f

The information provided above demonstrates that the range of the tube's radius within which we are certain is from 23.7 to 24.3.

Accurate findings are desired when any quantity is being measured. Closeness of the measurements to a particular value is referred to as accuracy (like the theoretical value). It is not insignificant that measurements can contain inaccuracies; as a result, the outcome frequently includes a margin error. The sentence above displays the radius's measured value along with its margin of error.

In other words, the aforementioned statement represents a quantity's numerical value along with its tolerance, or the only permissible (and conceivable) values to ensure that the measurement is accurate. The information provided above demonstrates that the range of the tube's radius within which we are certain is from 23.7 to 24.3.

These are all valid radius values, along with all others within this interval. By increasing the number of trials in a measurement, the value for the upper and lower bounds of the error can be decreased.

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The mechanisms by which out-of-plane deformation in the laser forming process can occur include:

This is the mechanism which involves bending the sheet to a laser light source.

The experiment shown in this scenario depicts it as one plane of the sheet can be seen raised.

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Answer:

215.5 m/s

Explanation:

Given that:

the wavelength λ = 668 km

distance (d) = 3180 km

time t = 4.81 hr

\(a) speed (v) =\dfrac{distance}{time}\)

\(speed (v) =\dfrac{3180}{4.1}\)

\(speed (v) =775.61 \ km/h\)

\(speed (v) =(\dfrac{775.61\times 1000 }{3600}) \ m/s\)

\(speed(v) = 215.5 \ m/s\)

The frequency is:

\(f = \dfrac{v}{\lambda}\)

\(f = \dfrac{215.5 }{668 \times 1000}\)

\(f = 3.226 \times 10^{-4} \ Hz\)

c)

The period:

\(T = \dfrac{1}{f}\)

\(T = \dfrac{1}{3.226 \times 10^{-4}}\)

T = 3099.8 seconds

Answer:Magnetic fields from two sources add up as vectors at each point, so the strength of the field is not necessarily the sum of the strengths1. Magnetic fields are vectors, which means they have direction as well as size. Therefore, the sum of two magnetic fields is not simply the sum of their magnitudes2.

Explanation:

Answer:

i dont know

Explanation:

i dont know

The final amount of pressure caused by the force is 90 N/m².

Initial amount of force, F₁ = 22 x 10³ N

Initial amount of pressure produced, P₁ = 110 N/m²

Final amount of force exerted, F₂ = 18 x 10³ N

Pressure is defined as the amount of force acting on an object per unit area of the object.

So, we can say that the force and pressure are directly proportional.

F ∝ P

So, F₁/P₁ = F₂/P₂

Therefore, the final amount of pressure caused by the force is,

P₂ = F₂P₁/F₁

P₂ = 18 x 10³x 110/22 x 10³

P₂ = 18/0.2

P₂ = 90 N/m²

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To calculate the volume of a parallelepiped given the sides, we can use the scalar triple product. The formula for the volume of a parallelepiped with sides a, b, and c is:

Volume = |a · (b × c)|

where · represents the dot product and × represents the cross product.

Using the given sides:

a = (7, 2, 4)

b = (4, 7, 6)

c = (3, 4, 7)

First, calculate the cross product of b and c:

b × c = (7*7 - 4*4, 6*3 - 7*7, 4*4 - 2*3)

      = (49 - 16, 18 - 49, 16 - 6)

      = (33, -31, 10)

Next, calculate the dot product of a and the cross product (b × c):

a · (b × c) = 7*33 + 2*(-31) + 4*10

           = 231 - 62 + 40

           = 209

Finally, take the absolute value of the result to obtain the volume:

Volume = |209| = 209 cubic units

Therefore, the correct answer is:

209 cubic units

Either A or C most likely A though

This method of responding to stimulus, due to the memory of another stimulus is called priming. So, the correct option is A.

Priming is defined as the method by which a person responds to a stimulus, due to the influence of any previous stimuli the person had come across.

Here,

The test question on the brain allowed the student to recall the memory of a previous stimuli the student has come across.

This is a method of implicit memory effect. This happens because, the person has a previous exposure to a similar stimulus.

This type of technique is called priming. This creates an effect of getting connections with the previous incidents, with the similar new ones.

Hence,

This method of responding to stimulus, due to the memory of another stimulus is called priming. The correct option is A.

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The primary means by which heat is transferred through fluids is convection currents (option D).

Convection is the transmission of heat in a fluid by the circulation of currents.

Heat can be transferred by different methods depending on the medium. Fluids like gases and liquids transfer heat through the process of convection.

Therefore, the primary means by which heat is transferred through fluids is convection currents.

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Answer:

Having the inside dimensions (ID) and the outside dimensions (OD) will allow you to figure out the wall thickness on tubing. You would need to subtract the ID from the OD and then divide by two. This number is the wall thickness.

Explanation:

The law of conservation of matter stated that during a chemical reaction, the amount of matter stays the same. Thus, option B is correct.

Matter can be changed into other forms either by physical or chemical changes. But through any of these changes matter remains constant. The amount of matter present before the chemical reaction will remain the same after the chemical reaction. Thus, the matter can neither be created nor destroyed.

The law of conservation of matter is defined as the law of conservation of mass. Hence, in a system, the mass or matter remains conserved, before and after the chemical reaction and it was given by Antonie Lavoisier.

The law of conservation of matter states that during a chemical reaction, the amount of matter remains the same. Thus, the ideal solution is option B.

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Astronomers conclude that distant galaxies are moving away from the Earth based on the observation of redshift in their light. The redshift is a result of the Doppler effect caused by the stretching of light waves due to the expansion of the universe. This redshift provides evidence for the ongoing expansion and supports the concept of an expanding universe.

Astronomers have observed a phenomenon known as redshift, where the light from distant galaxies appears redder than the light from nearer galaxies. This redshift is a crucial piece of evidence that supports the conclusion that distant galaxies are moving away from the Earth. To understand this, we need to consider the concept of the Doppler effect and the nature of light.

The Doppler effect describes how the perceived frequency of a wave changes when the source of the wave is moving relative to the observer. For light waves, this effect manifests as a shift in the wavelength of the light. When an object emitting light is moving away from an observer, the wavelength of the light is stretched, causing it to shift towards the red end of the spectrum.

In the case of distant galaxies, astronomers observe a significant redshift in the light they receive. This redshift indicates that the galaxies' light is being stretched to longer wavelengths. Based on the Doppler effect, this implies that the galaxies are moving away from us.

The reason behind this phenomenon is the expansion of the universe. The universe is not static but rather undergoing a continuous expansion, causing galaxies to move away from each other. As a galaxy moves away from the Earth, the light it emits becomes stretched due to the expanding space between us. This stretching of the light waves causes an observable redshift.

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The given velocity is 54km/hr, which, when converted to m/s using 1km = 1000m and 1 hour = 3600 seconds, equals 15m/s.

Now substitute the initial speed u = 15m/s values.

v = 0m/s as the final velocity

Time is 6 seconds.

In the a= -3 m/ s2 equation,

s= ut + 1/2at2 s= 15 6+ 1/2(-3)(6)2 s= 90-45 s = 45m

As a result, after using the brakes, the car will halt for up to 45 meters.

The inverse of acceleration is deceleration. The deceleration will be calculated by dividing the final velocity minus the initial velocity by the time required for the velocity drop.

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Answer:

Explanation:

To find the speed of the tsunami:

Speed = Distance / Time

Converting the distance from miles to meters and the time from hours to seconds:

Distance = 6500 miles × 1609.34 m/mile = 10,460,210 m

Time = 17 hours × 3600 s/hour = 61,200 s

Speed = 10,460,210 m / 61,200 s ≈ 171 m/s

To convert the speed to miles per hour:

Speed = 171 m/s × 2.24 mi/hr / 1 m/s ≈ 383 mi/hr

So the speed of the tsunami is approximately 171 m/s or 383 mi/hr.

To find the average frequency:

Wave speed = frequency × wavelength

The wavelength is twice the width of the wave:

Wavelength = 2 × 22 m = 44 m

Frequency = wave speed / wavelength

Frequency = 171 m/s / 44 m ≈ 3.9 Hz

So the average frequency of the tsunami is approximately 3.9 Hz.

Answer:

29.4m/s

Explanation:

Given.

Time (t) = 3.0s

Required

Determine the final velocity

Since, it's a vertical motion, we make use of the following formula to solve for the final velocity (v).

v = u + gt

Where u = 0, g = 9.8m/s² and t = 3s

v = 0 + 9.8m/s² *3s

v = 0 + 29.4m/s

v = 29.4m/s

Hence, the final velocity is 29.4m/s