An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. all the geometric parameters of the capacitor (plate diameter and plate separation) are now doubled. if the original energy density between the plates was u0, what is the new energy density?

If Rosa uses the formula (vi cos)t to do a calculation, then Rosa most likely trying to find the horizontal displacement of a projectile launched at an angle to the horizontal, therefore the correct answer is option C.

It can be defined as the motion of any object or body when thrown from the earth's surface and follows any curved path under the effect of the gravitational force of the earth.

The horizontal component of the velocity during any projectile motion is constant and is given by vicosθ.

Thus, If Rosa uses the formula (vi cos)t to do a calculation, then Rosa most likely trying to find the horizontal displacement of a projectile launched at an angle to the horizontal, therefore the correct answer is option C.

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Final answer:

The vapor pressure of cyclohexane at its normal boiling point of 81.0 ℃ is 101.3 kPa.

Explanation:

The question is asking for the vapor pressure of cyclohexane at its normal boiling point of 81.0 ℃. By definition, the normal boiling point of a liquid is the temperature at which its vapor pressure is equal to the external atmospheric pressure at sea level, which is 101.3 kPa (or 1 atmosphere). Therefore, the vapor pressure of cyclohexane at 81.0 ℃ is 101.3 kPa.

The formula for calculating the distance at constant velocity is:

d = v * t

d = 15 t

The formula for distance at constant acceleration is:

d = v0 t + 0.5 a t^2

d = 15 t + 0.5 t^2

So after a sum distance of 164 m:

15 t + (15 t + 0.5 t^2) = 164

30 t + 0.5 t^2 = 164

t^2 + 60 t = 328

(t + 30)^2 = 328 + 30^2

t + 30 = ± 35.04

t = -65.04, 5.04

Since time cannot be negative, so the two cars are 164 m apart after about 5 seconds

The components of a typical refracting telescope are basically convex object and convex eyepiece. The correct option is 1.

A typical refracting telescope is made up of a series of convex lenses. The objective lens is a convex lens positioned at the front of the telescope that collects and focuses light from distant objects. At the focus point, it creates an inverted actual picture.

The eyepiece, which is located at the telescope's back end, is likewise a convex lens. Its goal is to amplify the picture created by the objective lens so that the viewer may see a bigger, upright, magnified image.

In a standard refracting telescope, the correct combination is a convex objective lens and a convex eyepiece.

Thus, the correct option is 1.

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Your question seems incomplete, the probable complete question is:

Which are the components of a typical refracting telescope?

1.convex object and convex eyepiece

2. concave object and convex eyepiece

3. convex object and concave eyepiece

Answer:

9.83 km/h

Explanation:

Given: in a 4 kilometer race, a runner completes the first kilometer in 5.9 minutes, the second kilometer in 6.2 minutes, the third kilometer in 6.3 minutes, and the final kilometer in 6 minutes.

To Find:  the average speed of the runner for the race.

Solution:

In a 4 kilometer race,

time required to travel first kilometer = [tex]5.9[/tex] [tex]\text{minutes}[/tex]

time required to travel seoond kilometer = [tex]6.2[/tex] [tex]\text{minutes}[/tex]

time required to travel third kilometer = [tex]6.3[/tex] [tex]\text{minutes}[/tex]

time required to travel final kilometer = [tex]6[/tex] [tex]\text{minutes}[/tex]

we know that,

[tex]\text{Average speed}=\frac{\text{Total distance traveled}}{\text{Total time taken}}[/tex]

Total distance traveled = [tex]4[/tex]  [tex]\text{kilometer}[/tex]

Total time taken = [tex](5.9+6.2+6.3+6)[/tex]

                           =  [tex]24.4[/tex] [tex]\text{minutes}[/tex]

                           = [tex]\frac{24.4}{60}[/tex]  [tex]\text{hours}[/tex]

putting values,

[tex]\text{Average speed}=\frac{4}{\frac{24.4}{60}}[/tex]

 [tex]\text{Average speed}=\frac{4\times60}{24.4}[/tex]

                                            =[tex]9.83[/tex] [tex]\text{km}/ \text{h}[/tex]

the average speed of the runner for the race is approximately [tex]9.83[/tex] [tex]\text{km}/ \text{h}[/tex]

The area which is located under the curve gives us the angle in radians; we divide this by 2π to get units in revs (revolutions).

So for 0 ≤ t ≤ 2,

number of revs = 20rad/s * 2s * 1rev/2π rads = 6.37 revs 

So for 2 ≤ t ≤ 3.9,

number of revs = 10rad/s * 1.9s * 1rev/2πrads = 3.02 revs 

Therefore the total is about:

6.37 revs + 3.02 revs = 9.39 revs ≈ 9.4 revs

To answer how many revolutions an object makes in 3.9 seconds, we require knowledge of the object's constant angular velocity or angular acceleration. With the angular velocity, the total radians rotated can be found and divided by 2π to get the number of revolutions.

The question "How many revolutions does the object make during the first 3.9 s?" involves calculating the number of complete rotations or revolutions an object makes over a given period of time. In physics, this is often related to concepts of rotational motion, including angular velocity and angular acceleration. However, to calculate the number of revolutions over a certain time, we need to know either the constant angular velocity of the object, the angular acceleration, or another related quantity that would allow us to determine how the angle changes over time.

For example, if we know the angular velocity (ω) in radians per second (rad/s), we can calculate the number of revolutions by integrating the angular velocity over the given time period (3.9 s) or multiplying it by time if the angular velocity is constant. Since one revolution is equivalent to 2π radians, we can determine the total number of revolutions by dividing the total angle rotated (in radians) by 2π.

Answer:

New discoveries can either provide evidence to support or refute contemporary psychological perspectives, or they can lead to the development of new theories and perspectives.Explanation:

The net force on the helicopter at t=5.0s = F = 1.65.10⁴i - 3.3.10³k

Newton's 2nd law explains that the acceleration produced by the resultant force on an object is proportional and in line with the resultant force and inversely proportional to the mass of the object

[tex]\large{\boxed{\bold{a~=~\frac{F}{m} }}}[/tex]

∑F = m. a

F = force, N

m = mass = kg

a = acceleration due to gravity, m / s²

While the speed is the first derivative of distance  

[tex]\large{\boxed{\bold{V~=~\frac{dr}{dt} }}}[/tex]

While acceleration is the first derivative of the velocity function for t

[tex]\large{\boxed{\bold{a~=~\frac{dv}{dt} }}}[/tex]

It is known that the distance function (r) = (0.020 t³i + 2.2 tj-0.06t²k

Then the speed (v)

[tex]v~=~\frac{dr}{dt}[/tex]

v = 0.06t²i + 2.2j - 0.12tk

Then acceleration (a)

[tex]a~=~\frac{dv}{dt}[/tex]

a = 0.12ti - 0.12k

While :

W = m . g

[tex]m~=~\frac{W}{g}[/tex]

m = 2.75.10⁵ : 10

m = 2.75.10⁴

so  net force :

F = m . a

F = 2.75.10⁴ . ( 0.12ti - 0.12k)

for t = 5  

F = 2.75.10⁴ . ( 0.12.5i - 0.12k)

F = 2.75.10⁴ (0.6i-0.12k)

F = 1.65.10⁴i - 3.3.10³k

Newton's second law

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Keywords : Newton's Law, acceleration, net force

The net force on the helicopter at time [tex]t = 5.0\,{\text{s}}[/tex] is [tex]\fbox{\begin\\\left( {1.68 \times {{10}^4}\,\hat i - 3.36 \times {{10}^3}\,\hat j} \right)\,{\text{N}}\end{minispace}}[/tex].

Further Explanation:

The helicopter moves under the action of the force which changes the position of the helicopter with respect to time according to the following equation.

[tex]\vec{r}=(0.020\text{ m}/\text{s}^3)\text{ t}^3\hat{i}+(2.2\text{ m}/\text{s})\text{ t}^3\hat{j}-(0.060\text{ m}/\text{s}^2)\text{ t}^2\hat{k}[/tex]

The force acting on the helicopter at a particular time is given by:

[tex]\fbox{\begin\\F= m\cdot{a}\end{minispace}}[/tex]

Here, [tex]m[/tex] is the mass of the helicopter and [tex]a[/tex] is the acceleration of helicopter.

The helicopter has a weight of [tex]2.75 \times {10^5}\,{\text{N}}[/tex]. This weight of the helicopter can be converted into the mass of the helicopter.

The weight of the helicopter can be represented as.

[tex]\fbox{\begin\\W=m \cdot g\end{minispace}}[/tex]

Rearrange and simplify the expression for the mass of helicopter.

[tex]\begin{aligned}m&=\frac{W}{g}\\&=\frac{{2.75\times{{10}^5}}}{{9.8}}\,{\text{kg}}\\&=2.{\text{80}}\times{\text{1}}{{\text{0}}^4}\,{\text{kg}}\\\end{aligned}[/tex]

The velocity of the helicopter can be determined by the differentiation of the position vector of the helicopter with respect to time.

[tex]\begin{aligned}\vec{v}&=\dfrac{{d\vec{r}}}{{dt}}\\&=\dfrac{d}{{dt}}\ [(0.020\text{ m}/\text{s}^3)\text{ t}^3\hat{i}+(2.2\text{ m}/\text{s})\text{ t}^3\hat{j}-(0.060\text{ m}/\text{s}^2)\text{ t}^2\hat{k}]\\&=0.060{t^2}\hat{i}+2.2\hat{j}-0.12t\hat{k}\end{aligned}[/tex]

The acceleration of the helicopter is the derivative of the velocity with respect to the time.

[tex]\begin{aligned}\vec a&=\frac{{d\vec v}}{{dt}}\\&=\frac{d}{{dt}}\left({0.060{t^2}\hat i+2.2\hat j-0.12t\hat k}\right)\\&=0.12t\hat i-0.12\hat k\\\end{aligned}[/tex]

Substitute the value of [tex]t = 5.0\,{\text{s}}[/tex] in equation of the acceleration.

[tex]\begin{aligned}a&=0.12\left({5.0}\right)\hat i-0.12\hat k\\&=0.6\hat i-0.12\hat k\\\end{aligned}[/tex]

Substitute the values of the acceleration and the mass of the helicopter in the equation of force.

[tex]\begin{aligned}F&=\left( {2.80\times{{10}^4}\,{\text{kg}}}\right)\left({0.6\hat i-0.12\hat k}\right) \\&=\left({1.68\times{{10}^4}\,\hat i-3.36\times{{10}^3}\,\hat j}\right)\,{\text{N}}\\\end{aligned}[/tex]

Thus, the net force acting on the helicopter at time [tex]t = 5\,{\text{s}}[/tex] is [tex]\fbox{\begin\\\left( {1.68 \times {{10}^4}\,\hat i - 3.36 \times {{10}^3}\,\hat j} \right)\,{\text{N}}\end{minispace}}[/tex].

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Answer Details:

Grade: College

Subject: Physics

Chapter: Force and acceleration

Keywords:

Helicopter, force, time, 5s, position, velocity, derivative, acceleration, weight, net force, t=5s, 0.020t3 m/s3, 2.75x10^5 N, helicopter under test, gravity, mass of helicopter.

The liquid's index of refraction is approximately 1.88.

To find the index of refraction for the liquid, we can use the formula:

n₁ / n₂ = λ₁ / λ₂

where n₁ and n₂ are the indices of refraction for air and the liquid, respectively, and λ₁ and λ₂ are the wavelengths of light in air and the liquid, respectively.

In this problem, we are given that the wavelength of light in air is 495 nm and the wavelength in the liquid is 434 nm. Plugging in these values, we get:

n₁ / n₂ = 495 nm / 434 nm

n₂ ≈ n₁ * (434 nm / 495 nm)

n₂ ≈ 1 * (434 nm / 495 nm)

n₂ ≈ 0.876

To convert the index of refraction to its decimal form, we add 1, giving us:

n₂ ≈ 0.876 + 1

n₂ ≈ 1.876

The liquid's index of refraction is approximately 1.876, which can be rounded to 1.88.

The lowest gear on a bicycle provides the greatest mechanical advantage by amplifying the force exerted on the pedals, requiring the rider to pedal more but with less effort per stroke, due to the conservation of energy.

In order to climb a steep hill on a bicycle, a rider shifts to the lowest gear. The lowest gear has the greatest mechanical advantage because it allows the rider to apply a force over a greater distance. When a gear with many teeth drives a gear with fewer teeth, the driven gear spins more times but with a smaller turning force, amplifying the force the rider exerts on the pedals.

However, this means the rider will have to spin the pedals more times to cover the same distance, which is a trade-off.

This concept of mechanical advantage applies to all machines and is governed by the conservation of energy, which states that work input is equal to work output, minus any losses due to inefficiency like friction.

Answer:

a=5.20 m/s²

Explanation:

Given Data

Thrust = T (N)=3.0×10⁵N

Mass=m=20000kg

To find

acceleration=a=?

Solution

Newton Second law states that

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

(resultant force F)=ma

a=(resultant force F)/m

where

(resultant force F) is (Thrust-weight)  

Weight = mg = 2.0^4 kg*9.8 N/kg = 1.96^5 N

a = (resultant force F) / mass

a = (T - mg)/m = (3.0^5 N - 1.96^5 N)/ 2.0^4 kg

a=5.20 m/s²

The rocket's initial upward acceleration is 5.2m/s²

According to Newton's second law of motion

[tex]\sum F = ma[/tex]

The sum of forces is the difference between the weight and the thrust

[tex]\sum F = T -W[/tex]

[tex]T - W = ma\\a=\frac{T-W}{a}[/tex]

Given the following parameters:

T = [tex]3.0 \times 10^5 N[/tex]

W = [tex]20,000 \times 9.8 = 1.96 \times 10^5 N[/tex]

m = [tex]20,000kg[/tex]

Substitute the given parameters into the formula to have:

[tex]a=\frac{(3.0-1.96)\times 10^5}{2\times 10^4} \\a=\frac{1.04\times 10^5}{2\times 10^4} \\a = 0.52 \tmes 10\\a = 5.2m/s^2[/tex]

Hence the rocket's initial upward acceleration is 5.2m/s²

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Answer:

Continuity vs. Stages

Explanation:

Continuity is the gradual changes that a person may experiment throught their life, good examples are the ones given in the question, height and weght increasing or changing over time, but stages start whenever something happens that changes the way of life of the person, for example graduating college and going into the labor force, or getting married.

Use the expression -

P²k = a³---(i)

Where P is time in years, a is in AU, k is the function of the Sun's mass and set to unity.

Further, we're looking for the mass of the new star we have slightly modified Kepler's Third Law. After all, the inverse of a constant is also a constant. The reason we do it is because we want an answer in the form of K:1, where K is the mass of the HD 10180 and the mass of the Sun is 1, so k needs to start out on the other side.

Convert 600 days in years = 600/365 = 1.64 years

Put this in the expression mentioned at (i) -

1.64²k = a³

You gave us a = 1.4 AU

1.64²k = 1.4³ ; isolating k

k = 1.4³/1.64²

k = 2.744/2.702 = 1.015

So, the requisite ratio = 1.015 : 1

The ratio of the star's mass to the sun's mass is about 1.02 : 1

[tex]\texttt{ }[/tex]

Centripetal Acceleration can be formulated as follows:

[tex]\large {\boxed {a = \frac{ v^2 } { R } }[/tex]

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

[tex]\texttt{ }[/tex]

Centripetal Force can be formulated as follows:

[tex]\large {\boxed {F = m \frac{ v^2 } { R } }[/tex]

F = Centripetal Force ( m/s² )

m = mass of Particle ( kg )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

mass of the sun = M_sun = 1.99 × 10³⁰ kg

radius of the orbit = R = 1.4 AU = 2.094 × 10¹¹ m

Orbital Period of planet = T = 600 days = 600 × 24 × 3600 = 5.184 × 10⁷ seconds

Asked:

mass of the star = M = ?

Solution:

Firstly , we will use this following formula to find the mass of the star:

[tex]F = ma[/tex]

[tex]G \frac{ Mm}{R^2}=m \omega^2 R[/tex]

[tex]G M = \omega^2 R^3[/tex]

[tex]\frac{GM}{R^3} = \omega^2[/tex]

[tex]\omega = \sqrt{ \frac{GM}{R^3}}[/tex]

[tex]\frac{2\pi}{T} = \sqrt{ \frac{GM}{R^3}}[/tex]

[tex]M = \frac{4 \pi^2 R^3}{GT^2}[/tex]

[tex]M = \frac{4 \pi^2 (2.094 \times 10^{11})^3}{6.67 \times 10^{-11} \times (5.184 \times 10^7)^2}[/tex]

[tex]\boxed {M \approx 2.0 \times 10^{30} \texttt{ kg} }[/tex]

[tex]\texttt{ }[/tex]

Next , we will calculate the ratio of the star's mass to the sun's mass as follows:

[tex]M : M_{sun} = (2.0 \times 10^{30}) : (1.99 \times 10^{30})[/tex]

[tex]\boxed{M : M_{sun} \approx 1.02 : 1}[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Circular Motion

From Newton’s law of motion, the relation for velocity, acceleration and displacement is given by v^2 = vo^2 + 2as. Where v and vo are final and initial velocity respectively, and a, s are the acceleration and displacement respectively. From Newton’s second law, F = ma. Where m is the mass.

The magnitude of the frictional fore can be calculated only before estimating the ston’s acceleration. The initial speed of stone is mentioned in the problem as 3 m/s. Also, after 40m, the stone will stop. This means that its final speed is 0 m/s and the displacement is 40m.The acceleration of rock is calculated as:

(0 m/s)^2 = (3 m/s)^2 + 2a (40m).

9 m^2/s^2 = -2a(40m)

a= -9m^2/s^2/80m = 0.1 m/s^2.

This means that deceleration will occur and this will stop the stone. Substituting to Newton’s second law of motion,

-F = 20kg * -0.1 m/s^2. Further solve,

F = 20kg * 0.1 m/s^2 = 2N. Hence, the magnitude frictional force is 2N. 

In curling, the final position of the stone depends on its initial speed and the force of friction. Team members can use brooms to adjust the stone's speed and trajectory. The force of friction opposes the stone's motion.

In the winter sport of curling, the final position of the stone depends on the initial speed at which it is launched and the force of friction between the ice and the stone. Team members can use brooms to sweep the ice, which can adjust the stone's speed and trajectory. By judicious sweeping, they can lengthen the travel of the stone by a few meters. The force of friction between the ice and the stone will oppose the motion of the stone and slow it down.

The initial speed at which the stone is launched will determine how far it travels before coming to rest. If the stone is launched with a higher initial speed, it will travel a farther distance. The force of friction between the ice and the stone will also influence the distance the stone travels. A higher frictional force will cause the stone to slow down more quickly, resulting in a shorter travel distance.

Correct answer choice is:

B. forefinger in the direction of the lines of force.

Explanation:

The direction of the force - and consequently the transfer of the wire - can be defined by applying Fleming’s left-hand rule.

The forefinger tends to the direction of the magnetic field. The middle finger points in the course of the current. The thumb supplies the direction of force or movement working on the conductor. Fleming's Left Hand Rule is applied in electronic engines which are utilized in coolers, appliances, printers, etc.

Answer: The correct answer is constructive interference.

Explanation:

Interference is the phenomenon in which there is superposition of the two waves. Interference are of two types: Constructive interference and Destructive interference.

Constructive interference occurs when the there is a superposition of the two waves. The resulting wave has a large amplitude.

Destructive interference occurs when the there is a superposition of the two waves. The resulting wave has a low amplitude.

Therefore, Constructive interference occurs when two waves overlap and the resulting wave has a larger amplitude.

Answer:

B. Constructive