Suppose you watch a leaf bobbing up and down as ripples pass it by in a pond. You notice that it does two full up and down bobs each second. Which statement is true of the ripples on the pond?
They have a frequency of 2 hertz. (hertz = cycles per second)

Answer:

Explanation:

Given that

Tangential acceleration (at) =3m/s²

The propeller blade starts from rest i.e. wo=0rad/sec

And also the change in time ∆t=5sec

Also radius of blade (r)=1.5m

We have the tangential acceleration, so we need the centripetal acceleration

Which is given as

ac=v²/r

Then we need to get the final velocity using equation of motion

v=u+at

Where (a) is the tangential acceleration = 3m/s²

And the is final time at t=5sec

v=0+3×5

v=0+15

v=15m/s

Then, ac=v²/r

ac=15²/1.5

ac=150m/s²

Then, the total acceleration is given as

a=√(at)²+(ac)²

Since at=3m/s² and ac=150m/s²

Then,

a=√3²+150²

a=√22509

a=150.03m/s²

The total acceleration is 150.03m/s²

Answer: 16.57cm

Explanation:

Given

λ = 5*10^-12C/m

Mass, m = 1.67*10^-27kg

v = 1.2*10^3

Ri = 18cm

K = ?

Rf = ?

K = mv²/2

K = (1.67*10^-27)*(1.2*10^3)²/2

K = 1.2*10^-21J

Recall, Vf - Vi = K/e

Vf - Vi = 1.2*10^-21/1.6*10^-19

Vf - Vi = 7.5*10^-3

Vf - Vi = 0.0075

Also, Vf - Vi = (λ/2πE)[In(Rf/Ri)]

In Rf/Ri = (-0.0075*2*π*8.85*10^-12)/5*10^-12

In Rf/Ri = -0.083

Rf = Ri (exp -0.083)

Rf = 18 (exp -0.083)

Rf = 16.57 cm

the proton gets as close as 16.57cm to the line of charge

Answer:

a) The force between the two wires is attractive.

b) (F/L) = (μ₀I²)/(2πd)

Explanation:

a) According to Ampere's law, current in the same direction attract, while current in opposite directions repel. So, for this case of two wires carrying curremt in the same direction, the force between the wires is attractive.

b) The force of attraction between two current carrying wires carrying currents of magnitude I₁ and I₂ respectively, at some distance d, apart is given as

F = (μ₀ I₁ I₂ L)/(2πd)

(F/L) = (μ₀ I₁ I₂)/(2πd)

I₁ = I₂ = I

(F/L) = (μ₀I²)/(2πd)

Hope this Helps!!

(a) The force between the two wires is attractive.

(b) The force per unit length between the two wires is (μ₀I²)/(2πd)

(a) It is given that two wires carry current in the same direction, so the force between the wires will be attractive.

(b) The magnetic force between the two wires carrying currents I₁ and I₂ separated by a distance d, is given by:

dF = I₁dl × B₂ force on wire with current I₁ due to magnetic field of the wire with current I₂

dF = I₁dl ×  (μ₀I₂)/(2πd)

F = (μ₀ I₁ I₂ L)/(2πd)

(F/L) = (μ₀ I₁ I₂)/(2πd)

since I₁ = I₂ = I

(F/L) = (μ₀I²)/(2πd)

Learn more about magnetic force:

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Answer:

tan 75/350

Explanation:

the cliff is the height 75 and the length is 350 the other side is added to form a triangle . the tan rule is then used.

Answer:

The correct answer is Can be pronounced in many ways.

Explanation:

Typically a consultant is hired to solve a major business problem, carry out a major change and increase sales. The consultant, with experience of other companies, with methodology resources listens to the client's need, - the current situation and design an effective plan to implement, thus creating a positive impact on the business in a short time.

Answer:

Light is incident on the surface of a metal. If the wavelength of the incident photons becomes smaller, the maximum kinetic energy of the photo electrons emitted from the surface ___will decrease_______

Explanation:

when light is incident on the surface of a metal and electrons are emitted from the surface due to heating is called photoelectric effect.

Einstein proposed the statement that light has a particle nature which exist in the form of small small packets known as photons.

He said that when light is incident on the surface of a metal then electrons are emitted due to head=ting effect of the surface and electrons emitted are called photo electrons.

This theory of photoelectric effect states that energy of photo electrons is directly proportional to amplitude of the light and it's frequency. That's why if wavelength/amplitude of incident photons becomes smaller then the maximum kinetic energy of  photo electrons emitted from the surface will decrease

Answer: Antibody molecules

Explanation:

The immune system is categorised into two functional systems:

-Innate (natural) immune system and

-Acquired (adoptive) immune system.

The acquired immune system plays a major role against all the microbes capable of producing diseases and they are classified into two namely: Humoral and cell mediated immunity. The humoral immunity involves the B cells and the production of antibodies which are specific to invading antigens of disease causing organisms.

Antibodies are molecules of the adaptive defence system that provides humoral immunity by circulating freely in the blood and lymph.

Answer:

Yes, It is easier to balance a long rod with a mass attached to it when the mass is farther from your hand.

Explanation:

There it is illustrated how we can hold a long rod while the hand is further away from the surface.

Rotational inertia depends on whether the mass is closer to or further to the rotation point.

The more the mass is, the greater the acceleration of the rotation.

The explanation for this is that the mass variance is directly proportional to the roational inertia height.

When the mass attached to a long rod is closer to your hand, the rod is easier to balance. This is because the center of gravity and mass concentration is closer to the axis of rotation, which reduces the force needed to maintain balance.

In the context of balancing a long rod with a mass attached to it, it's crucial to consider the concept of the center of gravity, and moment of inertia. The center of gravity is the point at which the weight of an object is concentrated. When the mass is closer to your hand, the center of gravity is also closer, making the rod easier to balance as less torque-force is required.

This is analogous to two people carrying a load – whoever is closer to the center of gravity carries more of the weight, making it easier for them. Furthermore, the moment of inertia, a measure of an object's resistance to changes to its rotation, also plays a role. Objects with their mass concentrated closer to the axis of rotation have a lower moment of inertia and are thus easier to rotate or balance. This is reflective of the rod's behavior – when the mass is closer to your hand (essentially the axis of rotation), balancing it becomes easier.

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Answer:

Chang live 480 miles from the mountains

Explanation:

Constant Speed Motion

An object is said to have constant speed if it takes the same time t to travel the same distances x. The speed is calculated as

[tex]\displaystyle v=\frac{x}{t}[/tex]

From that equation, we can solve for x

[tex]x=v\cdot t[/tex]

and for t

[tex]\displaystyle t=\frac{x}{v}[/tex]

Let's assume the distance from the mountains and Chang's house is x. We know he took t1=12 hours in heavy traffic at an average speed v1, thus we can set

[tex]x=v_1\cdot t_1[/tex]

In his way back home Chang took t2=8 hours at a speed v2, thus:

[tex]x=v_2\cdot t_2[/tex]

Since the distance is the same

[tex]v_1\cdot t_1=v_2\cdot t_2[/tex]

The speed back is 20 mph more than the speed to the mountain:

[tex]v_2=v_1+20[/tex]

Replacing in the above equation

[tex]v_1\cdot t_1=(v_1+20)\cdot t_2[/tex]

[tex]v_1\cdot t_1=v_1\cdot t_2+20\cdot t_2[/tex]

[tex]v_1\cdot 12=v_1\cdot 8+20\cdot 8[/tex]

Solving for v1

[tex]v_1\cdot 4=160[/tex]

[tex]v_1=40\ mph[/tex]

Now we can compute the value of x

[tex]x=40\cdot 12[/tex]

[tex]\boxed{x=480 \ miles}[/tex]

Chang lives 480 miles from the mountains

Answer:

The incidence angle is 27°

Explanation:

As the complete question is not given, the complete question is given here

The angle between the Sun and a rescue aircraft is 54 degrees. What should be the angle of incidence for sunlight on a plane mirror so that the rescue pilot sees the reflected light?

From the question, the total angle between the Sun and the aircraft is 54 degrees which is the sum of the incidence and the reflected angle so

[tex]\theta_{total}=\theta_{incidence}+\theta_{reflection}=54[/tex]

Also from the law of reflection

[tex]\theta_{incidence}=\theta_{reflection}[/tex]

So now the equation becomes

[tex]\theta_{total}=\theta_{incidence}+\theta_{reflection}=54\\\theta_{total}=\theta_{incidence}+\theta_{incidence}=54\\2\theta_{incidence}=54\\\theta_{incidence}=27\\[/tex]

So the incidence angle is 27°

The angle of incidence for sunlight on a plane mirror should be set so that the angle of reflection directs the light towards the rescue pilot. The mirror's orientation is crucial, and light reflects at the same angle relative to the normal. Practical adjustments have to be made based on the positions of the sun and pilot.

For sunlight to be reflected from a plane mirror to a rescue pilot, the angle of incidence should be such that the angle of reflection directs the light towards the pilot. Since the angle of reflection is equal to the angle of incidence, the mirror must be tilted to reflect the light into the pilot's eyes.

According to the law of reflection, light incident on a mirror will reflect off at the same angle relative to the normal (an imaginary line perpendicular to the surface of the mirror). Hence, for the rescue pilot to see the reflected light, the angle of incidence must be adjusted accordingly based on the position of the sun and the pilot's location in the sky.

It is important to note that if we wish to maximize the reflection towards the pilot, utilizing the mirror's orientation is key. At very high angles of incidence, approaching 90 degrees, almost all the light is reflected, according to physical principles. However, such angles may not be practical when trying to target a specific viewer such as a pilot.

Answer:

Explanation:

kinetic energy of alpha particle

= Q X V ( Q is charge on the particle and V is potential difference )

= 3.2 x 10⁻¹⁹ x 3.45 x 10⁻³

= 11.04 x 10⁻²² J

1/2 m v² = 11.04 x 10⁻²²

1/2 x 6.68 x 10⁻²⁷ x v² = 11.04 x 10⁻²²

v² = 3.305 x 10⁵

v = 5.75 x 10² m /s

Final answer:

To find the speed of the alpha particle after it has moved through a potential difference, we can use the conservation of energy. Using the given values for charge and potential difference, we can calculate the speed using the formula for change in kinetic energy. The speed of the alpha particle is approximately 1.91x10^5 m/s.

Explanation:

To find the speed of the alpha particle after it has moved through a potential difference of -3.45x10^-3 V, we can use the conservation of energy.

The potential difference is given by ΔV = qΔV, where q is the charge of the alpha particle and ΔV is the potential difference. Plugging in the values, we get ΔV = (3.20x10^-19 C)(-3.45x10^-3 V).

The change in kinetic energy is given by ΔKE = (1/2)mv^2, where m is the mass of the alpha particle and v is its velocity. Setting ΔV equal to ΔKE, we can solve for v. Plugging in the values, we get (1/2)(6.68x10^-27 kg)v^2 = (3.20x10^-19 C)(-3.45x10^-3 V).

Solving for v, we find that the speed of the alpha particle is approximately 1.91x10^5 m/s.

Answer: The Rate constant is 1.209

Explanation:

in the attachment

Explanation:

Below is an attachment containing the solution.

Answer:

The answer to the question is

The two balls, although of different masses, could be made to have the same demolishing force by setting the velocity of the 100 kg ball to 1.5 times the velocity of the 150 kg ball.

That is if V₁ is the velocity of the 150 kg ball and  V₂ is the velocity of the 100 kg ball then V₂  = 1.5×V₁ for the demolishing effect of the two balls to be equal.

Explanation:

To answer the we are required to explain the meaning of momentum and state its properties

Momentum is a physical property of an object in motion. It indicates the amount of motion inherent in the object.  An object in motion is said to have momentum

The types of momentum possessed by an object can be classified into either

1, Linear momentum or

2. Angular momentum

An object moving with a velocity, v has linear momentum while a spinning object has an angular momentum

The momentum is given by the formula

P = m × V

Where m = mass and

V = velocity

Newtons second law of motion states that, the force acting on an object is equivalent to the rate of change of momentum produced and acting in the direction of the force

Properties of momentum

From the above statements it means that the two balls can be made equivalent by having the appropriate amount of speed. That iis the two balls can have the same momentum thus for equal momentum effect, we have

150 kg × V₁ = 100 kg × V₂

or V₂ = 1.5×V₁

Answer:

The answer to the question is

A 100 lb person would weigh 300.33 lbf at the upper atmosphere of Jupiter

Explanation:

To solve the question we note that

Mass of object = 100 lb =‪ 45.35924‬ kg

Mass of Jupiter = 300×Mass of Earth = 300×5.972 × 10²⁴ kg =1.7916×10²⁷ kg

Radius of Jupiter = 10× Radius of Earth = 10×6,371 km = 63710 km

Gravitational constant, G = 6.67408 × 10⁻¹¹ m³ kg-1 s-2

Gravitational force is given by [tex]F_G= \frac{Gm_1m_2}{r^2}[/tex]

Plugging in the values we get

[tex]F_G[/tex] = [tex]\frac{6.67408*10^{-11}*45.35924*1.7916*10^{27}}{63710^2}[/tex] = 1335.93 N

Converting into lbf gives 1335.93 N *0.2248 lbf/N = 300.33 lbf

On Jupiter, you would weigh 2.5 times more than on Earth due to its stronger gravity. Therefore, if you weighed 100 lb on Earth, you would weigh approximately 250 lb in the upper atmosphere of Jupiter though your weight may slightly vary with altitude. It is important to note that while weight changes with location, mass remains constant.

If you weighed 100 lb on Earth, it is interesting to calculate what you would weigh in the upper atmosphere of Jupiter. Since gravitational force is what we perceive as weight, and gravity varies with the mass of the planet and the distance from its center, we can determine the comparative weight. Jupiter has a mass approximately 318 times that of Earth and a radius about 11 times greater. However, for simplicity, the student question references Jupiter's mass as 300 times that of Earth and a radius 10 times that of Earth. This would normally impact the surface gravity calculation significantly.

Now, since it's stated that on Jupiter you would weigh 2.5 times more than on Earth, if you weigh 100 lb on Earth, you would weigh 250 lb on Jupiter. But note that in the upper atmosphere, your weight might be slightly less than this because you would not be at Jupiter's surface, and gravity decreases with altitude.

Lastly, remember the important conceptual distinction: While your weight changes depending on the gravity of the celestial body you are on, your mass remains constant. Your mass represents the amount of matter within you and does not change with location.

Explanation:

∴  The Correct option is (b)

Final answer:

To determine the height a rocket needs to go above the Earth's surface so that its weight is reduced to 58.8% of its weight at the Earth's surface, we can use the concept of gravitational force.

Explanation:

To determine the height a rocket needs to go above the Earth's surface so that its weight is reduced to 58.8% of its weight at the Earth's surface, we can use the concept of gravitational force. The force of gravity between two objects is given by the equation: F = (G * m1 * m2) / r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the objects. We can set up a ratio of the weight of the rocket at a certain height to its weight at the Earth's surface:

Weight at height / Weight at surface = (G * m1 * m2) / (r + h)^2 / (G * m1 * m2) / r^2

By substituting the given values, such as the radius of the Earth and the weight reduction percentage, we can solve for h, which represents the height the rocket needs to reach. The final answer should be in units of kilometers, which can be obtained by converting the radius of the Earth from meters to kilometers.

Answer:

684J

Explanation:

So basically the formula for gravitational potential energy is Mass X Gravity X height. That is G.p.e = mgh

We don't have the mass but since we have the height, we multiply directly with the height since the quantity of weight is already given.

so G.p.e = 360 X 1.9 = 684J

Note that; The answer is in joules because g.p.e is work done.

Hope that was helpful!!

To find out after how many years the activity level of a sample with a half-life of 10 years decreases from 2 curies to 0.25 curie, we calculate that it takes 30 years.

The question asks, "A sample of radioactive waste has a half-life of 10 years and an activity level of 2 curies. After how many years will the activity level of this sample be 0.25 curie?" To solve this problem, we follow the basic principle of half-lives, which states that the amount of a radioactive substance decreases to half its initial amount after one half-life period.

In this example, the activity decreases from 2 curies to 0.25 curies. To go from 2 curies to 1 curie, it takes one half-life (10 years). To go from 1 curie to 0.5 curies takes another half-life (adding up to 20 years in total). Finally, to decrease from 0.5 curies to 0.25 curies requires a third half-life period, adding another 10 years, for a total of 30 years.

Therefore, it will take 30 years for the activity level of the sample to reduce to 0.25 curie.

Answer:

Therefore the volume of cube is change at the 29.4 cube in./s at that instant time.

Explanation:

Formula

Cube :

The volume of a cube is = [tex]side^3[/tex]

The side of length is x in.

Then volume of the cube is (V) = [tex]x^3[/tex]

∴ V = [tex]x^3[/tex]

Differentiate with respect to t

[tex]\frac{d}{dt}(V)=\frac{d}{dt} (x^3)[/tex]

[tex]\Rightarrow \frac{dV}{dt} =3x^2\frac{dx}{dt}[/tex]....(1)

Given that the side of the cube is increasing at the rate of 0.2 in/s.

i.e [tex]\frac{dx}{dt} = 0.2[/tex]  in/s.

And the sides of the cube are 7 in i.e x= 7 in

Putting [tex]\frac{dx}{dt} = 0.2[/tex]  and  x= 7 in equation (1)

[tex]\therefore \frac{dV}{dt} =3 \times 7^2 \times 0.2[/tex]  cube in./s

       =29.4 cube in./s

Therefore the volume of cube is change at the 29.4 cube in./s at that instant time.

To find the rate at which the volume of the cube is changing, differentiate the volume formula with respect to time. For a cube with sides of 7 in length growing at 0.2 in/s, the rate of volume change is 6.3 in³/s.

The volume of a cube is determined by the formula V = x³, where x is the length of the side of the cube.

Given that the sides of the cube are 7 in long and increasing at 0.2 in/s, we can calculate how fast the volume is changing by differentiating the volume formula with respect to time. By taking the derivative of V = x³, we find that the rate of change of the volume at that instant of time is 6.3 in³/s.

Answer:

(a) 0.1134 L

(b) 2.009 L

(c) 0.07 cm from the top

Explanation:

The volume of the aluminum container and the turpentine is 2.000 L at  23 °C.

(a) When the entire system is heated to from 23 °C to 91 °C. The volume of the aluminum container is:

Vf = Vi*(1 + 3α*ΔT)

where:

Vi is the initial volume, Vf the final volume, α is the linear expansion coefficient and ΔT is the temperature change.

Vf = 2*[1 + 3*2.4 *10^-5*(91 - 23)] = 2.009 L

The volume of the turpentine is

Vf = Vi*(1 + β*ΔT)

where:

β is the  volume expansion coefficient

Vf = 2*[1 + 9.0*10^-4*(91 - 23)] = 2.1224 L

The overflow is:

2.1224  - 2.009 = 0.1134 L

(b) the volume of turpentine remaining in the cylinder at 91 °C is the same volume of the hollow aluminum cylinder, that is, 2.009 L

(c) Cooling the system back to 23 °C means the aluminum container is back to 2.000 L. The  volume of turpentine is:

Vf = 2.1224*[1 + 9.0*10^-4*(23-91)] = 1.9925 L

The following proportion must be  satisfied:

Volume of turpentine / Volume of container = deep turpentine / deep of container

1.9925 / 2.000 = deep turpentine/19

deep turpentine = (1.9925 / 2.000)*19 = 18.93 cm

This is 19 - 18.93 = 0.07 cm from the top

Answer:

Impedance = 19.44ohms

Current = 5.14A

Power factor = 0.62

Explanation:

Impedance in an RLC AC circuit is defined as the total opposition to the flow of current in the resistor, inductor and capacitor.

Impedance Z = √R²+(Xl-Xc)²

Where R is the resistance = 12Ω

Inductance L = 0.15H

Capacitance C = 100uF = 100×10^-6F

Since Xl = 2πfL and Xc = 1/2πfC where f is the frequency.

Xl = 2π×50×0.15

Xl = 15πΩ

Xl = 47.12Ω

Xc = 1/2π×50×100×10^-6

Xc = 100/π Ω

Xc = 31.83Ω

Z =√12²+(47.12-31.83)²

Z = √144+233.78

Z = 19.44Ω

Impedance = 19.44ohms

To calculate the circuit current, we will use the expression V=IZ where V is the supply voltage = 100V

I = V/Z = 100/19.44

I = 5.14Amperes

To calculate the power factor,

Power factor = cos(theta) where;

theta = arctan(Xl-Xc)/R

theta = arctan(47.12-31.83)/12

theta = arctan(15.29/12)

theta = arctan1.27

theta = 51.78°

Power factor = cos51.78°

Power factor = 0.62

Answer:

The circuit impedance [tex]=19.4 \Omega[/tex]

The circuit's current [tex]=5.14 A[/tex]

Circuit Power Factor [tex]=0.62[/tex]

Explanation:

Given:

Resistance [tex]R=12 \Omega[/tex]

Inductance [tex]=0.15H[/tex]

Capacitance [tex]=100uF[/tex]

Voltage [tex]=100V[/tex]

Step 1:

To calculate the inductive reactance, [tex]$X_{L}$[/tex].

[tex]X_{L}=2 \pi f L=2 \pi \times 50 \times 0.15=47.13 \Omega[/tex]

To calculate the Capacitive reactance,

[tex]X_{C}=\frac{1}{2 \pi f C}[/tex]

[tex]=\frac{1}{2 \pi \times 50 \times 100 \times 10^{-6}}[/tex]

[tex]=31.83 \Omega[/tex]

Step 2:

Circuit impedance,

[tex]$$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}$$[/tex]

where R is the resistance,

[tex]$$&Z=\sqrt{12^{2}+(47.13-31.83)^{2}}[/tex]

[tex]&Z=\sqrt{144+234}=19.4 \Omega\end{aligned}$$[/tex]

Step 3:

Circuits Current, I

[tex]$I=\frac{V_{S}}{Z}[/tex]

[tex]=\frac{100}{19.4}[/tex]

[tex]=5.14 \ A[/tex]

Step 4:

Voltages across the Circuit, [tex]$\mathrm{V}_{\mathrm{R}}, \mathrm{V}_{\mathrm{L}}, \mathrm{V}_{\mathrm{C}}$[/tex]

[tex]V_{R}=I \times R=5.14 \times 12=61.7$ volts[/tex]

[tex]V_{L}=I \times X_{L}=5.14 \times 47.13=242.2$ volts[/tex]

[tex]V_{C}=\ I \times X_{C}=5.14 \times 31.8=163.5$ volts[/tex]

Step 5:

Circuits Power factor

[tex]$=\frac{R}{Z}=\frac{12}{19.4}=0.619$[/tex]

Therefore,

The circuit impedance [tex]=19.4 \Omega[/tex]

The circuit's current [tex]=5.14\ A[/tex]

Power Factor [tex]=0.62[/tex]

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Answer:

Age

Depth

Explanation:

Viscosity is referred to as a measure of a material's resistance to flow

Rise in temperature or heat, burial, exposure to existing magmas, dissolved gases, exposure to mantle plumes, decreasing pressure, and high water content, crystal composition are factors that affect the viscosity of magma;

However, age and depth are two of the factors that do not affect the viscosity of magma/lava

Answer:

The question is incomplete because it lacked the options. These are the options..

a. composition

b. age

c. temperature

d. dissolved gases

Answer is B. Age.

Explanation:

Viscosity is simply described or explained as the resistance to flow.

Magma is known to be the molten rock material under the Earth's crust. It known to come out from the rock or mountain through the vent during volcano eruption.

All the other options except the age, that is , composition, temperature and dissolved gases  contribute to the viscosity of the magma.

Magma with higher SiO and, increase in temperature tends to increase viscosity of the magma.

Explanation:

The statement can become true by changing 'increase' to 'decrease'. Hence, when the velocity of a fluid increases, its pressure decreases as per Bernoulli's Principle.

The false statement can be rewritten to say 'Bernoulli's Principle indicates that an increase in the velocity of a fluid will cause its pressure to decrease.

This principle is utilized in various applications such as the lift on an aircraft wing and the functioning of a curve ball in baseball. It states that, in an inviscid flow of a non-conducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid potential energy.

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Answer:

Conservation

Explanation:

She has observation conservation because If the temperature of the liquids stays constant and the container is insulated and not heat or cool the liquid much would not change the density of the liquid very much so that it's original volume could remain constant.

The interesting thing is not that the child assumes the taller glass holds more liquid but that they fail to understand conservation: the fact that the water from one glass is going to be the same amount after being poured into any other container. It's as if they did not realize the water came from the same glass.

Answer with Explanation:

We are given that

Diameter of coil=d=0.115mm

Radius, r=[tex]\frac{d}{2}=\frac{0.115}{2}=0.0575mm=0.0575\times 10^{-3} m[/tex]

Using [tex]1mm=10^{-3} m[/tex]

Electric field=E=0.235V/m

T=55 degree C

[tex]T_0=20^{\circ} C[/tex]

[tex]\rho_0=2.82\times 10^{-8}\Omega m[/tex]

[tex]\alpha=3.9\times 10^{-3}/C[/tex]

(a).We know that

[tex]\rho=\rho_0(1+\alpha(T-T_0))[/tex]

Substitute the values

[tex]\rho=2.82\times 10^{-8}(1+3.9\times 10^{-3}(55-20))[/tex]

[tex]\rho=3.2\times 10^{-8}\Omega m[/tex]

(b).Current density,[tex]J=\frac{E}{\rho}[/tex]

Using the formula

[tex]J=\frac{0.235}{3.2\times 10^{-8}}=7.3\times 10^6A/m^2[/tex]

c.Total current,I=JA

Where [tex]A=\pi r^2[/tex]

[tex]\pi=3.14[/tex]

Using the formula

[tex]I=7.3\times 10^6\times 3.14\times (0.0575\times 10^{-3})^2[/tex]

I=0.076A

d.Length of wire=l=2m

[tex]V=El[/tex]

Substitute the values

[tex]V=0.235\times 2=0.47 V[/tex]

Answer:

did you get the answer?

Explanation:

Answer:

did you get anything?

Explanation:

Answer:

Therefore the magnitude of tangential velocity is 20 m/s.

Explanation:

Tangential velocity:The tangential velocity is the straight line velocity of at any point of rotating object.

It is denoted by [tex]v_t[/tex]

[tex]v_t= \omega r[/tex]

ω= angular velocity

r = radius of rotating object.

Angular velocity: Angular velocity is ratio of angle to time.

Here ω= 50 rad/s and r = 0.4 m

Tangential velocity=(50 ×0.4)m/s

                                =20 m/s

Therefore the magnitude of tangential velocity is 20 m/s.

Answer:

The resultant force is F=6i-j-14k while the resultant Moment is about point O (M_o) is 1.3i +3.3 j -0.45k.

Explanation:

As the complete question is not given, the complete question is attached herewith

The coordinates of the points from the Free-body diagram are given as

0=(0,0,0) m

A=(0.15,0,0.3) m

B=(0,-0.25,0.3) m

the position vector of OA is

roa=(0.15-0)i +(0-0)j +(0.3–0)k

= 0.15i +0j +0.3k

the position vector of OB is

rob =(0-0)i +(-0.25 - 0); +(0.3–0)k

= 0i -0.25j +0.3K

Now

The equivalent resultant force is expressed as,

F = F1+ F2

Substitute 6i - 3j -10k for  F1, and 2j -4K for F2.

F =6i -3j -10k +2j - 4k

= 6i - 1j -14k

So the resultant force is F=6i-j-14k.

Resultant couple moment at point O is expressed as,

[tex]M_o=r_{OA}\times F_1+r_{OB}\times F_2\\M_o=\left|\begin{array}{ccc}i&j&k\\0.15&0&0.3\\6&-3&-10\end{array}\right|+\left|\begin{array}{ccc}i&j&k\\0&-0.25&0.3\\0&2&-4\end{array}\right|\\M_o=0.9 i+3.3j-0.45 k+0.4 i+0 j+0k\\M_o=1.3 i+3.3 j-0.45 k[/tex]

The moment of the resultant force about point O (M_o) is 1.3i +3.3 j -0.45k.

Answer:

The angular velocity of the woman will decrease when she extends her arms outwards.

Explanation:

We know that the angular momentum of a body is the product of its angular velocity and the moment of inertia.

So, mathematically:

[tex]L=I.\omega[/tex]

where:

[tex]I=[/tex] moment of inertia (second moment of mass that depends upon the radial distance of the mass from the center of rotation)

[tex]\omega=[/tex] angular velocity

When the woman extends her arms she increases the radial distance of her mass form the axis of rotation thus increasing the moment of inertia of her body. As the angular momentum in this case remains constant so proportionately the angular velocity of her body increases.

[tex]I'\times \omega'=I\times \omega[/tex]

The angular velocity will  increase and angular momentum remains constant, when she extends her arms outward.

The given problem is based on the concept of angular momentum. The angular momentum of a body is the product of its angular velocity and the moment of inertia.  So, mathematically:

[tex]L = I \times \omega[/tex]

Here,

I is the moment of inertia.

[tex]\omega[/tex] is the angular velocity.

Note: - The moment of inertia (I) depends on the radial distance and mass of object.

So in the given problem, when the woman extends her arms she increases the radial distance of her mass and form the axis of rotation. Thereby increasing the moment of inertia of her body. As the angular momentum in this case remains constant so proportionately the angular velocity of her body increases.

Thus, we can conclude that the angular velocity increases and  angular momentum remains constant, when she extends her arms outward.

Learn more about the angular momentum here:

https://brainly.com/question/25303285

Answer:

R1 = 4.8Ω

Explanation:

The loop circuit has an initial voltage of  V = IR

I = 2 A , R1 = R

V = 2R1

with the current reduced to 1.5A with an additional 1.6Ω resistor

the total resistance of the circuit is 1.6 + R1

the voltage of the two scenarios has to be equal , since the same voltage flows through the circuit

therefore V = 2R1

from Ohms law V = IR

2R1= 1.5 (1.6 + R1)

2R1 = 2.4 + 1.5R1

collecting like terms

2R1 - 1.5R1 = 2.4

0.5R1 = 2.4

R1 = [tex]\frac{2.4}{0.5}[/tex]

R1 = 4.8Ω

Answer:

4.8 Ω

Explanation:

From Ohm's Law,

Using,

I = E/(R+r)................. Equation 1

E = I(R+r)................. Equation 2

Where I = current, E = emf, R = external resistance, r = internal resistance

Given: I = 2 A, R = R1, r = 0 Ω

Substitute into equation 2

E = 2(R1)

E = 2R1.

When an additional 1.6 Ω  resistor is added in series,

E = 1.5(R1+1.6)

2R1 = 1.5R1+2.4

2R1-1.5R1 = 2.4

0.5R1 = 2.4

R1 = 2.4/0.5

R1 = 4.8 Ω