20. Two resistances, one 62 and the other 88
are connected in parallel. The resistors are then
connected to a 12-V battery.
a. What is the equivalent resistance of the
parallel combination?
b. What is the current through each resistor?

A golf ball will travel 166 feet before landing if it is struck with an 80 ft/s velocity.

The directional speed of an object in motion, as measured by a specific unit of time and observed from a specific point of reference, is what is referred to as velocity. The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate. Speed is the absence of direction; velocity is the presence of direction. Since velocity is a vector quantity, we must specify both the magnitude (the speed) and the direction of travel when expressing it.

Here,

(Va)x= 80cos(10+45)°= 44.886

(Va)y= 80sin(10+45)°= 65.532

S=So + Vot + 1/2at^2

d sin 10°= 0 + 65.532t + 1/2 (-32.2)t^2

0.17d= 0 + 65.532t + (-16.1)t^2

Solving the equation gives,

d=166ft

t= 3.57seconds

The distance d to where it will land is 166 feet when a golf ball is struck with a velocity of 80 ft/s.

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The power supply that technician should use 500 W.

A power supply is a component that transforms the output of an ac power line into one or more constant dc outputs. A smooth voltage is created by filtering the ac voltage after it has first been rectified to create a pulsing dc. In spite of fluctuations in the ac line voltage or circuit loads, the voltage is finally regulated to produce a consistent output level.

The power use of the server as whole is,

100 W+ 5×9 W + 200 W

Power use=445 W.

So, the power should be more than the 445 W in order that there should not be any short circuit.

and from all the given options the power supply that is feasible is 500 W.

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500 W of power should be used by the technician.

One or more consistent dc outputs are produced from an ac power line's output by a component known as a power supply. After rectifying the ac voltage to produce a pulse dc, a smooth voltage is produced by filtering the result. Despite changes in the ac line voltage or circuit loads, the voltage is eventually controlled to create a constant output level.

The entire server's energy consumption is,

100 W+ 5×9 W + 200 W

Using 445 W of power.

Therefore, the power must be more than 445 W to prevent short circuits.

Choose the power supply that is practical from the possibilities presented

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The linear density of the string is 2.86 x 10^-5 kg/m.

What is linear density?

Linear density, also known as linear mass density, is a measure of the mass of a material per unit length. It is typically used to describe the properties of thin, elongated objects such as strings, wires, and fibers. The unit of measurement for linear density is typically kilograms per meter (kg/m) or grams per centimeter (g/cm). It is calculated by dividing the mass of the material by its length.

To find the linear density of the string, we need to use the relationship between the tension, linear density, and wave properties, which is given by the equation:

Tension = (linear density) * (wave speed)^2

where wave speed is the product of the frequency and wavelength of the wave.

Given the tension, period and wavelength, we can find the linear density using the following steps:

frequency = 1 / period = 1 / 3.82 x 10^-3 s = 261.9 Hz

wave speed = wavelength * frequency = 1.26 m * 261.9 Hz = 331.9 m/s

Tension = (linear density) * (wave speed)^2

944 N = (linear density) * (331.9 m/s)^2

linear density = Tension / (wave speed)^2 = 944 N / (331.9 m/s)^2 = 2.86 x 10^-5 kg/m

Therefore, the linear density of the string is 2.86 x 10^-5 kg/m.

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Answer:

Yes

Explanation:

By adding salt.

Answer:

11

Explanation:

MA = Fout / Fin = 55 N / 5 N = 11

Explanation:

Force= mass × acceleration

= 3.6 × 4.2

= 15.12N

If the mass of the box is 3.6 kg and it is accelerating with 4.2 m/s², then the force exerted on the box is 15.12 N.

The definition of force is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. Every time two items interact, a force is exerted on each of the objects. The force is no longer felt by the two objects when the interaction ends. Only when there is interaction do forces actually exist.

The strong force, weak force, electromagnetic force, and gravitational force are the four fundamental forces operating in the universe. The formula of force is  Force = mass × acceleration.

Hence, if the mass of the box is 3.6 kg and it is accelerating with 4.2 m/s², then the force exerted on the box is 15.12 N.

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The answers are:

a.) The translational kinetic energy of its center of gravity:  638.144J  

b.)The rotational kinetic energy about its center of gravity 319.072 J

c.) Its total kinetic energy 957.216 J

Given:

M = 11.8 kg cylinder

V = speed of center of gravity = 10.2m/s

(a) Translational kinetic energy = 1/2mv²

1/2x 11.8kg x 10.2²

= 11.8x108.16/2

= 1276.288/2

= 638.144 J

This is the translational energy

(b) Rotational energy =1/2Iw²

I = mv²/2

w = v/r

When we substitute

1/2[mv²/2][v/r]²

= 1/4mv²

= 1/4 x 11.8 x 10.2²

= 1276.288/4

= 319.072

This is the rotational energy

(c) Total kinetic energy:

We add the values of A and B above to get this.

638.144 J + 319.072 J

= 957.216J

Complete question: A 11.8-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.2 m/s, determine the following. (a) the translational kinetic energy of its center of gravity (b) the rotational kinetic energy about its center of gravity (c) its total kinetic energy.

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c. the gravity acceleration is in the same direction as the force of gravity, and thus toward the center of the earth: accurately describes the force of gravity.

The force that pulls items toward the centre of a planetary or other body is known as gravity. The gravitational pull maintains each of the planet in orbit about the sun. The degree to which a coordinate in space-time is invisibly bent determines the intensity of the gravitational "field" at any given place in space or time. Massive items tumble down these bends in the direction of one another. The stronger the attraction between items, the more matter there is, and the closer together things are. And unlike electricity and magnetism, which may either repel or attract, gravity always draws objects together.

Thus, correct option is: c

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A box slides down a frictionless ramp, then it takes approximately 0.87 seconds for the box to reach 1.00 m/s.

The force resisting relative motion of solid surfaces, fluid layers, and material elements sliding against each other is called friction.

As, v^2 = u^2 + 2as

Given, v = final velocity = 1.00 m/s ; u = initial velocity = 0 m/s (since the box is at rest) ; a = acceleration due to gravity = 9.8 m/s^2 and s = distance covered = 1.00 m

So, s = 1.00 m = x x sin(40.0 degrees)

x = 1.00 m / sin(40.0 degrees)

(1.00 m/s)^2 = 0^2 + 2(9.8 m/s^2) (1.00 m / sin(40.0 degrees))

t = √((1.00 m/s)^2 - 2(9.8 m/s^2) (1.00 m / sin(40.0 degrees)) )/ (2(9.8 m/s^2))

Hence, t ≈ 0.87 sec

It takes approximately 0.87 seconds for the box to reach 1.00 m/s.

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Answer:

576 joules

Hope this helped :)

The amount it take to run the compressor if the electricity cost 22 cents per kilowatt-hour is 233.21 cents.

A kilowatt-hour is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ).

To calculate the the amount it takes to run the compressor daily, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Hence, the amount is 233.21 cents.

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A nickel coin contains 5.2 x 10^22 Ni atoms as coulombs of charge.

In the International System of Units, the unit of electric charge is the coulomb. It is equivalent to the electrical charge delivered by a 1 ampere constant current in 1 second in the current version of the SI. The amount of charge carried by a current of one amp for one second is measured in coulombs, which is the unit of measurement used in the SI for electric charge. It may also be a property of a substance that causes electrical and magnetic effects to occur. The symbol for it is C. According to math, 1 Coulomb equals 1 Ampere x 1/sec.

Here,

The mass of a nickel coin is 5 g.

1 mol of Ni weighs 58 g.

1 mol=6.022 x 10²³ atoms of Ni.

in 58 g,  

=6.022 x 10²³ atoms of Ni

then in 5 g the number of Ni atoms = - 6.022 x 10²³ /58 x 5

= 5.2 x 10²² Ni atoms,

Therefore number of Ni atoms as coulombs of charge are 5.2 x 10²² atoms in a nickel coin.

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The initial elastic potential energy of the block-spring system is 17.88 joules. The final speed of the block is approximately 3.15 meters per second.

Elastic potential energy is energy stored in an object as a result of application of a force to deform an elastic object. The energy is stored until the force is removed and the object springs back to its original shape and size, doing work in the process.

By applying Hooke's law and definition of work, we define the elastic potential energy (Ug), measured in joules, by the following formula:

Ug = 1/2 × k × x²

where, k = Spring constant, measured in newtons per meter

x = Deformation of the spring, measured in meters

If we know that k = 795 N/m and x = 0.045m, then the elastic potential energy is:

Ug = 1/2 × 795 × 0.045

Ug = 17.88 Joules

The initial elastic potential energy of the block-spring system is 17.88 joules.

b) According to the Principle of Energy Conservation, the initial elastic potential energy of the block-spring system becomes into translational kinetic energy, that is:

Ug = 1/2 × m × v²

where, m = Mass measured in kilograms,

v = Final speed, measured in meters per second.

Then, the final speed is cleared:

v = [tex]\sqrt{2Ug/m}[/tex]

If we know that Ug = 17.88 Joules and m = 3.60kg, then the final speed of the block is:

v = √(2 × 17.88J)/ 3.60kg

v = 3.15m/s.

The final speed of the block is approximately 3.15 meters per second.

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The speed of each seat is 3.2 m/s.

The speed of each seat is calculated by applying Newton's second law of motion as shown below.

T cos (θ)  = mg

T sin (θ) = mv² / r

where;

T  = mg / cos(θ)

T = ( 10 x 9.8 ) / ( cos 15.9 )

T = 101.9 N

The speed of each seat is calculated as;

v² = (Tr sin(θ) ) / m

v = √ [ (Tr sin(θ) ) / m ]

v = √ [ (101.9 x 3.6 x  sin(15.9) ) / 10 ]

v = 3.2 m/s

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Pluto masses 1.3e22 kg, and its average distance from the sun is about 6e15 km. The sun’s mass is 2e30 kg. G is 6.7e−11 m^3 / kg⋅s^2.

What is meant by mass?

So the force of gravity is

f = G M1 M2 / d^2

= 6.7e-11 x 1.3e22 x 2e30 / 5e15^2

= .7e11 N = 70 billion newtons.

One might say, not insignificant.

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In this situation, the pressure will change in direct proportion to the temperature. Double both the pressure and the temperature.

When the temperature is held constant, pressure decreases as volume increases and vice versa. As a result, when the volume is cut in half, the pressure is also cut in half, and vice versa.

According to Boyle's Law, pressure and volume have an inverse relationship. The volume reduces as the pressure rises, and the volume rises as the pressure falls.

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Because a system's resonant frequency is related to its mass, the resonant frequency of a system falls as the level of fluid in the system drops.

Natural frequency, as it is commonly understood, is the usual supply source frequency, which is often 50 or 60 hertz. The resonant frequency is 1/2pi multiplied by 1/LC.

Depending on where you reside, the natural frequency is either 50Hz or 60Hz. Resonance can happen at any multiple of the fundamental frequency (natural).

A larger amplitude of sound waves signifies a higher sound pressure and hence a bigger volume in acoustics. In general, resonant frequencies are unfavourable for loudspeakers.

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a) The change in the angular velocity is - 3.40 rad/s.

b) The angular acceleration is -1.36rad/s^2.

We have to note that the change in the angular velocity would be obtain as the difference between the initial and the final angular velocity of the bicycle tire.

Then we would have that;

Change in the angular velocity = 0 rad/s - 3.40 rad/s = - 3.40 rad/s

We know that the angular acceleration = Change in the angular velocity/Time

= - 3.40 rad/s/2.5 s

= -1.36rad/s^2

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Minimum: 75.64; maximum: 48.36 is the nearest hundredth unless otherwise noted.

The given values of n and p to find the minimum usual value and the maximum usual value μ

−2σ

n = 248, p = Detailed explanation:

Considering the characteristics of the binomial distribution

n = 248, p = 4/5

To determine the necessary values, we must determine the mean and the standard deviation.

The steps are listed below.

Identify the mean.

μ = n·p = 248*(4/5) = 570.4

Find the variation in 2.

σ² = np(1 - p) = 248*(4/5)*(1 - 4/5) =

Discover the standard deviation in 3.

Minimum: 75.64; maximum: 48.36

Minimum: 75.64; maximum: 48.36 the nearest hundredth unless otherwise noted.

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Answer:

Approximately [tex]0.042\; {\rm kg \cdot m^{-3}}[/tex].

Explanation:

Note the unit conversion for mass:

[tex]1\; {\rm g} = 10^{3}\; {\rm mg}[/tex].

[tex]1\; {\rm kg} = 10^{3}\; {\rm g}[/tex].

Therefore:

[tex]\begin{aligned}& 10\; {\rm mg} \times \frac{1\; {\rm g}}{10^{3}\; {\rm mg}} \times \frac{1\; {\rm kg}}{10^{3}\; {\rm g}} \\ =\; & 10\; {\rm mg} \times \frac{1\; {\rm kg}}{10^{6}\; {\rm mg}} \\ =\; & 10^{-5}\; {\rm kg}\end{aligned}[/tex].

Similarly, for volume:

[tex]1\; {\rm mL} = 1\; {\rm cm^{3}}[/tex].

[tex]1\; {\rm m^{3}} = 10^{3}\; {\rm dm^{3}} = 10^{6}\; {\rm cm^{3}}[/tex].

Thus, [tex]1\; {\rm m^{3}} = 10^{6}\; {\rm mL}[/tex].

[tex]\begin{aligned}& 240\; {\rm L} \times \frac{1\; {\rm m^{3}}}{10^{6}\; {\rm mL}} = 2.40\times 10^{-4}\; {\rm m^{3}}\end{aligned}[/tex].

Divide mass by volume to find the mass-to-volume ratio:

[tex]\begin{aligned}\frac{10^{-5}\; {\rm kg}}{2.40 \times 10^{-4}\; {\rm m^{3}}} \approx 0.042\; {\rm kg \cdot m^{-3}}\end{aligned}[/tex].

-Borrows = 0 , -Returns > 0, Since these two statements have the same truth value, they are both indicating that a particular laptop is not currently borrowed.

What is Equivalence theory?

This question is using the Theory of Equivalence, which states that two statements are logically equivalent if they have the same truth value.

In this case, the two statements are:

1) Borrows = 0

2) Returns > 0

Both choices indicate that a particular laptop is not currently borrowed from the library.

Borrows = 0 indicates that the laptop has not been borrowed at all. Since the library keeps track of the number of times a laptop is borrowed, if the number is zero, then it has not been borrowed.

Returns > 0 indicates that the laptop has been borrowed before, but it is not currently borrowed.

Since the library keeps track of the number of times a laptop is returned, if the number is greater than zero, then it has been returned and is therefore not currently borrowed.

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Through the decomposition of organic matter, CO₂ is released into the atmosphere as part of this natural process.

One carbon atom is covalently doubly bound to two oxygen atoms in each of the molecules that make up carbon dioxide, which has the chemical formula CO 2.

At room temperature, it exists as a gas. In the atmosphere, carbon dioxide serves as a greenhouse gas because it absorbs infrared radiation despite being transparent to visible light. It has increased from pre-industrial levels of 280 ppm to a trace gas in the Earth's atmosphere at 421 parts per million (ppm), or roughly 0.04% by volume (as of May 2022).

The fundamental driver of both these elevated CO2 concentrations and climate change is the burning of fossil fuels. Groundwater, lakes, ice caps, and ocean all contain dissolved carbon dioxide. 

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When a wave travels through a medium, the particles in that medium vibrate in a direction perpendicular to the direction the wave travels it is a transverse mechanical waves only.

When a wave travels through a medium, the particles in that medium vibrate in a direction parallel to the direction the wave travels it is a longitudinal mechanical waves only .

Then a wave travels through a medium, the wave speed will depend on an inertial property of that medium it is for both transverse and  longitudinal mechanical waves .

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The government derive its power according to the Declaration of Independence is the document that declare the freedom of the people. The document was approved by the Continental Congress on July 4, 1776.

Below are the main messages of the declaration of independence.

(1) God made all men equal and gave them the rights of life, liberty, and the pursuit of happiness.

(2) The main business of government is to protect these rights.

(3) If a government tries to withhold these rights, the people are free to revolt and to set up another government.

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(a) The number of electrons on the T-shirt is 700 electrons.

(b) The mass of the particle attached to your T-shirt is 1.5 x 10⁻²⁴ kg.

The number of electrons on the T-shirt is calculated as follows;

Let the number of electrons = e

Let the number of protons = p

p + e = 1596 ------ (1)

p = 1596 - e ------ (2)

qp - qe = -3.14 x 10⁻¹⁷ ------- (3 )

The equation (3) can be simplified as;

q ( p - e ) = -3.14 x 10⁻¹⁷ -------- (4)

Now substitute the value of p into (4)

q (1596 - e - e) = -3.14 x 10⁻¹⁷

q (1596 - 2e) = -3.14 x 10⁻¹⁷

1596 - 2e = ( -3.14 x 10⁻¹⁷ ) / ( q )

1596 - 2e = ( -3.14 x 10⁻¹⁷ ) / ( 1.6 x 10⁻¹⁹ )

1596 - 2e = 196.25

2e = 1596 - 196.25

2e = 1399.75

e = 1399.75 / 2

e = 700 electrons

The mass of the particle attached to your T-shirt is calculated as follows;

m = (700 x me ) + ( 896 x mp)

m = ( 700 x 9.1 x 10⁻³¹ ) + ( 896 x 1.67 x 10⁻²⁷ )

m = 1.5 x 10⁻²⁴ kg

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The road force on the wheel weigh is 690.

Your automobile advances under the influence of static friction. The power to turn the tires is provided by the engine, which pushes the vehicle rearward against the road.

Example:

The axle of the wheel that is in touch with the road receives a 200 mN torque from a car's engine.

The vehicle moves rightward at a steady speed:

The automobile wheel measures 0.58 meters in diameter. What does the horizontal component of the road force on the wheel weigh?

Radius: 0.29 m

When formula is used, we obtain

Force = Torque / Radius = 200/0.29

=690.

It is the necessary response as a result.

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According to collision theory, the quantity of reactant molecule collisions determines how quickly a chemical reaction proceeds. The pace of reaction increases with the frequency of reactant-molecule collisions.

The average pace of particles increases with temperature, which increases the rate of particle collisions. The average kinetic power of collisions increases with temperature, increasing the proportion of collisions that require the least amount of energy to react.

Reactant particles need to have a certain minimum energy in order to make an efficient collision. The activation energy is the energy that starts the reaction.

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According to legend, young Isaac Newton came up with first law of gravity after getting hit on the head by a piece of fruit that had fallen from an apple tree while he was sitting underneath it.

Newton's gravitational law states that every piece of matter in the universe is drawn to every other piece with a force than varies directly with the mass-to-mass ratio and inversely with the distance between them.

The product of the masses of two objects multiplied by two is the gravitational force between them. The gravitational pull here between objects will also triple if one of them triples in mass. When two objects' masses double, for example, the gravitational force between them is multiplied by two, and so on.

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A gas expands from I to f along the three paths shown in the diagram. compute the work done on the gas along paths (a) W = 810.4 J (b) W = 506.5 J (c) Wtot = 202.6 J

Along pathIAF,

the work done is the area under the curve,

W = (4 atm)(2 L)

W = 8 L-atm

Now, what's a liter-atmosphere? We solved that in the last chapter. But let's do it again here. 1.0 atm =1.013 x 10 + 5 Pa = 1.013 x 10 5N/m2

1 L-atm = 1 L-atm [ 10 - 3m3 / L] [(1.013 x 105 N/m2) /atm]

1 L-atm = 101.3 N-m = 101.3 J

W = 8 L-atm [101.3 J/L-atm]

W = 810.4 J

Along pathIBF,

the work done is still the area under the curve. Now we can describe that as the area of the rectangle BFDA plus the area of the triangle IBF.

W = ABFDA +AIBF

W = (1 atm)(2 L) +(1/2)(3 atm)(2 L)

W = 5 L-atm

W = 5 L-atm [101.3 J/L-atm]

W = 506.5 J

Along pathIAF,

There is no work done along the path IB; this is a constant volume process (this is also known as an isometric process). Along path BF, there is work done.

Wtot = WIB +WBF

Wtot  = 0 + 2L-atm

Wtot  = 2 L-atm

Wtot = 202.6J

Gas, along with liquid, solid, and plasma, is one of the four natural states of matter. A gas has neither a fixed shape nor a fixed volume. The gas's atoms or molecules fill the container. Even when gravity is present, the gas expands until it is uniformly distributed throughout the container.

Correct question is:

A gas expands from I to F along the three paths indicated in the figure below. Calculate the work done on the gas along each of the following paths.

(a) IAF (in J) =

(b) IF (in J) =

(c) IBF (in J) =

The images supporting question is attached below

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The particles in a liquid have enough energy to transform into gases at a specific temperature. Boiling (or vapourization) is the conversion of a liquid into a gas; condensation is the conversion of a gas into a liquid.

Melting is the process through which a solid transforms into a liquid (an older term that you may see sometimes is fusion). It is known as solidification when a liquid turns into a solid. Any pure substance's melting point, or the temperature at which melting starts, is a property of that substance. For a solid to turn into a liquid, energy is needed. Each pure material requires a specific quantity of energy to transform from a solid to a liquid. The symbol for this quantity, Hfus, stands for the substance's enthalpy of fusion (also known as heat of fusion). In Table 10.2, "Enthalpies of Fusion for Various Substances," a number of Hfus values are provided;

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