When recording the capacitance with a measurement equipment, the user has often the choice to select a suitable circuit representation. For the series representation, the instrument attempts to predict R
S
​
and C
S
​
, while for the 33 parallel representation the prediction involves R
P
​
and C
P
​
. Which mode should be chosen if large capacitors of more than 100μF are to be measured? Is this mode also suitable for small values of less than 10μF ? Explain your answers.

Answer:

27N

Explanation: workdone = force * distance

         Hence Force= workdone/distance

                               = 405/15

                               = 27N

Explanation:

I hope this helps, you can ask any questions for clarification

Braking studies have shown that a tractor-trailer traveling at 55 mph needs two times the distance to stop as an automobile.

There are four parts that make up a vehicle's overall stopping distance i.e., Vehicle reaction time and distance, human perception time and distance, human reaction time and distance Vehicle Braking Distance and Time

The maximum distance your car will travel while braking under perfect circumstances. It may require 216 feet at 55 mph on dry pavement with decent brakes. The brakes must use more force to stop a bigger car, which increases heat absorption. On the other hand, large vehicles' brakes, tires, springs, and shock absorbers are made to function optimally when fully loaded. Trucks that are empty need longer stopping distances because they have less traction. It can lock up and bounce, providing substantially worse braking.

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Answer:

1. a = - 2.5 m/s²

2. t = 2.57 s

Explanation:

1.

The acceleration of the driver can be found using the first equation of motion:

\(v_f = v_i + at\)

where,

vf = final speed = 15 m/s

vi = initial speed = 45 m/s

a = acceleration = ?

t = time = 12 s

Therefore,

\(15\ m/s = 45\ m/s +a(12\ s)\\\\a = \frac{15\ m/s-45\ m/s}{12\ s}\)

a = - 2.5 m/s²

negative sign indicates deceleration

2.

The time taken by the biker to accelerate can be found by using the first equation of motion again:

\(v_f = v_i + at\)

where,

vf = final speed = 18 m/s

vi = initial speed = 0 m/s

a = acceleration = 7 m/s²

t = time = ?

Therefore,

\(18\ m/s = 0\ m/s +(7\ m/s^2)t\\\\t = \frac{18\ m/s}{7\ m/s^2}\)

t = 2.57 s

Answer:

1.46755 Joules

Explanation:

Applying,

E = 1/2ke²......................... Equation 1

Where E = Elastic potential energy of the spring, k = spring constant, e = extension

From the question,

Gieven: k = 559 N/m, e = (0.14-0.07) meters = 0.07 meters

Substitute these values into equation 1

E = 1/2(599×0.07²)

E = 2.9351/2

E = 1.46755 Joules

Answer:

that the acceleration is negative therefore it is directed to the left.

Explanation:

To find the acceleration of a system we must use Newton's second law

          ∑ F = m a

To apply this equation to our case we set a reference system where the direction to the right is positive.

We have 3 forces, a force F₁ = -20 N, a negative sign indicates that it is directed to the left, two forces F₂ and F₃ of magnitude 8N each directed to the right.

We substitute

            -F₁ + F₂ + F₃ = m a

           - 20 +8 + 8 = m a

             -4 = m a  

             a = -4 / m

Here we can see that the acceleration is negative therefore it is directed to the left.

Answer:

42.11 years old

Explanation:

Given that:

In 2000, a 20-year-old astronaut left Earth to explore the galaxy; her spaceship travels at 2.5 x 10^8 m/s. She returns in 2040

To find her age we use:

\(\Delta t_m=\frac{\Delta t_s}{\sqrt{1-\frac{v^2}{c^2} } }\\\)

Δtm is  time interval for the observer stationary relative to the sequence of

events = 2040 - 2000 = 40 years

Δts is is the time interval for an observer moving with a speed v relative to the  sequence of event

v = velocity = 2.5 x 10^8 m/s

c = speed of light = 3 x 10^8 m/s

\(\Delta t_s=\Delta t_m}{\sqrt{1-\frac{v^2}{c^2} } }\\\Delta t_s=40\sqrt{1-\frac{(2.5*10^8)^2}{(3*10^8)^2}}\\\Delta t_s=22.11\ yr\)

Here age in 2000 is 20 year, therefore when she appear she would be 20 year + 22.11 year = 42.11 years old

Answer:

thanks for the points

Explanation:

E4 = kQ.[2/a2 + 1/a2] appears to reflect the electric field at the fourth corner as a result.

A characteristic of matter called an electric discharge generates multiple objects to either attract or repel each other depending on how it is charged (positive or negative). A region of space surrounding a static electricity particle or object known as an electrostatic potential is one in which an electricity would experience force.

A personality electromagnetic field like light also requires a grasp of the electric field idea. We now have a mechanism to explain how starlight traverses enormous stretches of vacant desert in order to reach our eyes thanks to the electric field notion.

Number of point charges = 3

E4 = E1 + E2 + E3

E4 = kQ/a2 + kQ/√(2a2) + kQ/a2

E4 = kQ.[ 1/a2 + 1/√(2a2) + 1/a2 ]

E4 = kQ.[ 2/a2 + 1/a√2 ]

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Answer:

F/L = μ₀I₁I₂/2πr

when a force of 2 x 10⁻⁷ N is produced between two conductors 1 m apart from each other and having a cross-sectional radius 1 m. The current on each conductor in this situation is 1 Ampere

Explanation:

Consider two conductors of same length parallel to each other. The Magnetic field due to current in 1st conductor is given by Ampere's Law as:

B₁ = μ₀I₁/2πr

where,

B₁ = Magnetic Field due to Conductor 1

μ₀ = permeability of free space = 4π x 10⁻⁷ N/A²

I₁ = Current through conductor 1

r = radius of cross section of conductor

Now, the force of the conductors on each other is given by:

F₁₂ = B₁I₂L

where,

F₁₂ = Force of conductor 1 on conductor 2

B₁ = Magnetic Field of Conductor 1

I₂ = Current through conductor 2

L = Length

Therefore,

F₁₂ = μ₀I₁I₂L/2πr

The force of conductor 2 on conductor will also have same magnitude but opposite direction:

F₁₂ = |- F₂₁| = F

F/L = μ₀I₁I₂/2πr

F/L = μ₀I₁I₂L/2πr

Now, to define S.I unit of current (Ampere) we substitute values:

F/(1 m) = (4π x 10⁻⁷ N/A²)(1 A)(1 A)/2π(1 m)

F = 2 x 10⁻⁷ N

So, when a force of 2 x 10⁻⁷ N is produced between two conductors 1 m apart from each other and having a cross-sectional radius 1 m. The current on each conductor in this situation is 1 Ampere

Answer:

Third Law Of Motion.

Explanation:

The law of interaction, the third one, explains that if one body exerts a force on a second body, the second body exerts a force equal in magnitude and opposite in direction on the first body.

The force of gravity will become one fourth of the original force when the masses of the objects remain the same but their distance of separation doubles.

Force of gravity is an attraction force which holds the object towards the ground surface.

The gravitational force depends directly on the masses of two objects and indirectly on the square of the distance between them.

Let

m₁ and m₂ be the two different masses

r₁ be the initial distance between the the two masses

r₂ be the distance when their separation doubles.

i.e. r₂ = 2r₁

So, according to the formula,

F₁ =   \(\frac{Gm1m2}{r1^{2} }\)

F₂ =   \(\frac{Gm1m2}{r2^{2} }\)

since masses are same:

\(\frac{F1}{F2} = \frac{r2^{2} }{r1^{2} }\)

\(\frac{F1}{F2} = \frac{4r1}{r1}\)

F₁ = 4F₂

F₂ = \(\frac{1}{4}\)F₁

The resultant force is one fourth of the original force.

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When you place an extremely small almost point source of light at the primary focal point of a parabolic mirror, the reflected wave front will be a plane wave.

This plane wave is characterized by parallel wavefronts. The focal point of a parabolic mirror is defined as the point on the principle axis at which parallel light rays converge when they are parallel to the principle axis.

According to the principles of reflection, all light rays incident on a parabolic mirror are reflected such that they converge at the focal point. In the case of a point source of light positioned at the focal point of a parabolic mirror, all the light rays coming from that point are reflected in a parallel fashion. The wavefronts of the reflected light are thus parallel, resulting in a plane wavefront.

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The line of evidence that is not consistent with the theory of evolution of the horse is: "The fossils of the limbs are different from each other, which indicates these organisms are not related and evolved separately from each other."

The theory of evolution suggests that organisms share a common ancestor and have evolved through gradual changes over time. Therefore, the presence of similar structures and traits among fossilized limbs is consistent with the theory, indicating that these organisms are related and evolved from a common ancestor. If the fossils of the limbs were significantly different from each other, it would suggest that these organisms evolved separately and do not share a common ancestry. However, this would contradict the theory of evolution, which states that species are connected through common ancestors and have undergone a process of gradual change.

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v= constant

mass of the cart = 1.5 kg

m2 (added)= 7.5 kg

The altitude of the satellite is 883.89 km

Generally, The Rayleigh criterion for resolution states that the minimum angle, θ, between two point sources that can be resolved is given by:

θ = 1.22 * λ / D

where

λ is the wavelength of light and

D is the diameter of the lens.

The minimum distance, d, between two point sources that can be resolved is given by:

d = θ * L

where

L is the distance from the lens to the image.

Given the green lights have a wavelength of 508 nm, we can convert it to meters:

λ = 508 * 10^-9 m

Given the diameter of the lens is 49.8 cm, we can convert it to meters:

D = 49.8 cm * (1 m / 100 cm)

= 0.498 m

Using the Rayleigh criterion, we can find the minimum resolvable angle:

θ = 1.22 * λ / D

= 1.22 * 508 * 10^-9 / 0.498

= 1.24449799*10^{-6} radians

We know the lights on the satellite are spaced 1.1 m apart, so:

d = 1.1 m

Solving for the distance from the lens to the image, L:

L = d / θ

= 1.1 m / 1.24449799*10^{-6} radians

=883890.53 m

Finally, converting the distance to kilometers:

L = 883890.53 m * (1 km / 1000 m)

= 883.89 km

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Using the half-life formula, the concentration of cyclopropane after 234 seconds is 3.70M.

Since 1934, cyclopropane, also known as trim ethylene, has been utilized in medicine as a general cosmetic. Both mucous membrane irritation and respiratory depression are not caused by cyclopropane. Cyclopropane anesthesia is typically quickly induced and smoothly exhaled.

It is clear that this is a first order reaction from the units of k.

We can use the integrated rate law \([A]=[A]_0 e^{-k t}\) or we can use half life.

0.693/k = 0.693/6.7x10-4 s-1 is the first order half life.

1034s = t(1/2)

No. of half lives elapsed  =234sec x 1 half life/1034 sec = 0.226 half lives elapsed

Fraction remaining = 0.5ⁿ

where n is half lives elapsed

Fraction remaining = 0.5⁰·²²⁶

Fraction remaining = 0.855

Concentration remaining =

4.33 M x 0.855 = 3.70 M

Using the half-life formula, the concentration of cyclopropane after 234 seconds is 3.70M.

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A. The given model can be rewritten as y = 13 + 14 · sin^2(t + arctan(13 / 14)). B. The amplitude of the oscillations of the weight is 14.

A. To write the given model in the form y = a! + b! · sin(Bt) + C, we'll use the provided identity and compare the terms.

Given model: y = 13sin^2(t) + 14cos^2(t)

Using the identity a · sin^2(θ) + b · cos^2(θ) = a + b · sin^2(θ + C) where C = arctan(a / b), and a > 0:

Comparing the given model with the identity, we can see that a = 13,

b = 14, and

C = arctan(13 / 14).

Therefore, we can rewrite the model as follows:

y = 13 + 14 · sin^2(t + arctan(13 / 14))

B. The amplitude of the oscillations of the weight can be determined from the rewritten model. In the given model, the amplitude is represented by the coefficient of sin(Bt).

From the rewritten model: y = 13 + 14 · sin^2(t + arctan(13 / 14))

The coefficient of sin(Bt) is 14, which represents the amplitude of the oscillations of the weight.

A. The given model can be rewritten as y = 13 + 14 · sin^2(t + arctan(13 / 14)).

B. The amplitude of the oscillations of the weight is 14.

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The Carnot heat engine absorbs 8.3 J of heat per cycle from the high-temperature reservoir.

The efficiency of a Carnot heat engine is given by the equation:

Efficiency = 1 - (Tc/Th)

where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

In this case, the temperatures are given as 500°C and 30°C, respectively. We can calculate the efficiency of the engine using these values:

Efficiency = 1 - (30 + 273.15)/(500 + 273.15) ≈ 0.8208

The efficiency of a Carnot heat engine is also defined as the ratio of the work done by the engine to the heat absorbed from the high-temperature reservoir:

Efficiency = Work/Heat absorbed from high-temperature reservoir

We know that the engine does 2.2 J of work per cycle, so we can rearrange the equation to solve for the heat absorbed from the high-temperature reservoir:

Heat absorbed from high-temperature reservoir = Work/Efficiency

Heat absorbed from high-temperature reservoir = 2.2 J / 0.8208 ≈ 2.68 J

Therefore, the Carnot heat engine absorbs approximately 2.68 J of heat per cycle from the high-temperature reservoir.

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Answer:

his acceleration rate is -0.00186 m/s²

Explanation:

Given;

initial position of the car, x₀ = 100 miles = 160, 900 m ( 1 mile = 1609 m)

time of motion, t₀ = 60 minutes = 60 mins x 60 s = 3,600 s

final position of the car, x₁ = 150 miles = 241,350 m

time of motion, t₁ = 100 minutes = 100 mins x 60 s = 6,000 s

The initial velocity is calculated as;

u = 160, 900 m / 3,600 s

u = 44.694 m/s

The final velocity is calculated as;

v = 241,350 m / 6,000 s

v = 40.225 m/s

The acceleration is calculated as;

\(a = \frac{\Delta V}{\Delta t} = \frac{v- u}{t_1 - t_ 0} = \frac{40.225 - 44.694}{6000-3600} = -0.00186 \ m/s^2\\\\\)

Therefore, his acceleration rate is -0.00186 m/s²

Answer:

its very simple this list the items that you have in your house that have electric energy

Explanation:

The time it will take her to land on the other side is 0.5 seconds.

In a triangle with three angles of 30°, 60°, and 90°, the hypotenuse is twice as long as the shorter leg and three times as long as the latter. To understand why this is the case, consider that the triangle is a right triangle given these numbers according to the Converse of the Pythagorean Theorem. The lengths of the three sides in a triangle of this kind are referred to as a Pythagorean triple.

distance = velocity x time

In this case, the distance is 3 meters and the velocity is 6 m/s, so:

3 = 6 x time

Solving for time, we get:

time = 3/6 = 0.5 seconds

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A 500 N force is applied to a 25m/s2 object. The mass of the object is 20kg. The correct answer is option: A.

The force applied to an object is related to its mass and acceleration through the equation:

F = ma,

where F is the force, m is the mass, and a is the acceleration. Rearranging this equation, we get:

m = F/a.

In the given problem, a force of 500 N is applied to the object, and its acceleration is 25 m/s^2.

Substituting these values in the formula, we get :

m = 500 N / 25 m/s^2 = 20 kg.

Therefore, the mass of the object is 20 kg, which is option A.

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Answer:

Potential energy refers to the stored up energy within an object, that builds up and can potentially be used to propel that object.

Explanation:

A famous example, would be water behind a dam. The rushing water fills up behind the dam, and since it's being held in one place, it will build up until of course the dam is either moved or lifted, and then all the water will be forced (due to all the energy that was being stored) down the rest of the stream.

I hope the explanation makes sense. If it doesn't, please let me know and I'll try to find another one for you :)

Answer:

P = (1/2 * m * V ^ 2)/t = 1/2 * ((0.12 * 10 ^ - 3) * c)/0.020

= 2.7*10^ -2 w

The average power developed by the legs of the grasshopper will be 2.7 × 10⁻² W.

Average power is a ratio of total work done by the body to the total time. Its unit is the watt.

The given data in the problem is ;

mass (m)=  0.12 g

time to run up = 0.020 s

According to the law of conservation of energy,

Work = change in Potential energy

Power is defined as the rate of work done which is found as;

\(\rm P = \frac{W}{t} \\\\ P= \frac{\frac{1}{2}mv^2 }{t} \\\\ P= \frac{\frac{1}{2}(0.12)(10^{-3})(3)^2}{0.020} \\\\P=2.7 \times 10^{-2}\ sec\)

The average power developed by the legs of the grasshopper will be 2.7 × 10⁻² W.

Hence,option C is correct.

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