champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16-cm-high steps a 70-kg athlete could ascend in one minute while expending one horsepower is

The electric field strength at a distance of 10 cm from a charge of 2 μC is 3.6 x 10⁵ N/C.

If there's a charge present in any form, an electric field is linked with every point in space. The strength and direction of the electric field are expressed by the value of E, sometimes referred to as the strength of the electrical field, electric field intensity, or simply the electric field.

The following formula determines the magnitude of the electric field generated by a point charge:

where,

E = Electrical Field Strength = ?

k = 9 x 10⁹ Nm²/C²

q = magnitude of charge

q = 2 μC = 2x 10⁻⁶ C

r = distance = 10 cm

r = 0.10 m

Therefore,

When the values are entered into the equation, we obtain:

E = 9 x 10⁹ * (2 x 10⁻⁶) / (0.1)²

E = 3.6 x 10⁵ N/C

Because of this, the electric field intensity at 10 cm from a 2 μC charge is  3.6 x 10⁵ N/C.
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Answer:

This looks like an example of combustion

Explanation:

The kinetic energy of particle B at the instant when the particles are 3.0 m apart is 4.32 J.

The total energy of the system is conserved. The initial energy of the system is the electrostatic potential energy, which is given by:

U = k × (Q₁ × Q₂) / r

where:

U = potential energy in joules

k = Coulomb's constant (8.988 x 10⁹ N m²/C²)

Q₁ and Q₂ = charges in coulombs

r = distance between the charges in meters

In this case:

U = 8.988 x 10⁹ N m²/C² × (12 C × 5 Q) / (1.0 m) = 5.375 x 10⁻⁷ J

The final energy of the system is the kinetic energy of particle B. The kinetic energy is given by:

KE = 1/2 × m × v²

where:

KE = kinetic energy in joules

m = mass in kilograms

v = velocity in meters per second

Solve for the velocity of particle B using the conservation of energy equation:

KE = U

Substituting the expressions for KE and U gives:

1/2 × m × v² = 5.375 x 10⁻⁷ J

Solving for v gives:

v = √(2 × 5.375 x 10⁻⁷ J / m)

= 1.53 m/s

The kinetic energy of particle B is then:

KE = 1/2 × m × v²

= 1/2 × m × (1.53 m/s)²

= 4.32 J

Therefore, the kinetic energy of particle B at the instant when the particles are 3.0 m apart is 4.32 J.

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Answer:

150   kg-m/s

Explanation:

momentum = m * v

50 * 3 = 150

- The resistance of the first resistor (R₁) is 12 Ω.

- The electromotive force (EMF) of the battery is 18 V.

- The internal resistance of the battery is 12 Ω.

To solve the given problem, we can apply Kirchhoff's laws and Ohm's law to determine the resistance of the first resistor (R₁) and the electromotive force (EMF) and internal resistance of the battery.

Let's start by calculating the resistance of the first resistor (R₁):

1. Apply Ohm's law to find the voltage drop across the external circuit:

  V = I * R

  V = 1 A * 6 Ω

  V = 6 V

2. The voltage drop across the external circuit is equal to the EMF minus the voltage drop across the internal resistance of the battery:

  V = E - Ir

  6 V = E - (1 A * r)   (where r is the internal resistance of the battery)

3. We also know that the EMF of the battery is the sum of the voltage drops across each cell in the battery:

  E = 6 cells * 3 V/cell

  E = 18 V

4. Substitute the value of E in the equation from step 2:

  6 V = 18 V - r

  r = 12 Ω

Therefore, the resistance of the first resistor (R₁) is 12 Ω.

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The cost of operation for an A.C for 10 hours per day for a month will be 71,100 francs.

Power is the amount of energy transferred or converted per unit time. The unit of power is the watt, equal to one joule per second. Power is a scalar quantity.

Cost of operation for 10 hours a day;

Daily consumption = 3kW x 10 hours

Daily Consumption = 30kW

Since 1kWH = 79 francs;

Daily consumption amount = 30 x 79 francs

Daily consumption amount = 2,370 francs

Therefore, the monthly consumption (using 30days) will be;

2,370 francs x 30 = 71,100 francs

In conclusion, 71,100 francs will be spent in a month (30 days) to run the 3kW rated A.C for 10 hours a day at 1kWH.

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Answer:

  0.017 N

Explanation:

The relevant relation is ...

  F = GMm/r²

where G is the universal gravitational constant, 6.67408 × 10^-11 m^3·kg^-1·s^-2, M and m are the masses of the objects, and r is the distance between them.

__

Filling in the given numbers, we find the force to be ...

  F = (6.67408 × 10^-11 m^3·kg^-1·s^-2)(8.7 × 10^20 kg)(77 kg)/(1.6 × 10^7 m)^2

where m in this expression is the unit "meters".

  F = 6.67408 · 8.7 · 77/2.56 × 10^(-11 +20 -2·7) N ≈ 0.017 N

The asteroid exerts a force of about 0.017 N on Sally.

__

Additional comment

That's about 0.000023 times the force of Earth's gravity.

Answer:

During heat flow, much of the energy is dissipated and cannot be used for useful work.

Explanation:

Which of the following statements is true?

During heat flow, much of the energy is lost.

During heat flow, energy is converted to matter.

During heat flow, much of the energy is dissipated and cannot be used for useful work.

ANSWER:

True

STEP-BY-STEP EXPLANATION:

Acceleration also oscillates in simple harmonic motion (SHM). If you consider a mass in a spring, when the displacement is zero, the acceleration is also zero, because the spring does not apply force. When the displacement is maximum, the acceleration is maximum, because the spring applies the maximum force; the force applied by the spring is in the opposite direction of the displacement.

Answer:

1. hold organs and other tissue in place

2. Attaches muscles to bone

Explanation:

From its name, the connective tissue has one of its most important functions to be the connection of tissues and organs.

They offer support and connection to other tissues such as tendons that attaches muscles to bones and also skeletons which offers support to the positions of the body.

Connective tissue also offer protection in various forms such as fibrous capsules and also bones that gives protection to delicate organs of the body

Answer:

x and y, or 0 and 1. These two symbols form hundreds of patterns that represent data like numbers, letters, even pictures, and videos. Digital images are made up of pixels, and each pixel contains binary code. When all that code comes together and the pixels are formed we can see things like family photo albums or we can watch a movie on our phones. We can even see a digital picture of a kitten I guess. k, bye.

Explanation:

The audience for the 9th grade physics MCAS is students in the 9th grade who are taking the Massachusetts Comprehensive Assessment System (MCAS) physics exam.

The exam is designed to assess students' knowledge and skills in physics, and it is used to make decisions about students' placement in courses, graduation requirements, and eligibility for college and career programs.

The 9th grade physics MCAS is a multiple-choice exam that consists of 50 questions. The questions are based on the Massachusetts Curriculum Framework for Science, which outlines the standards that students are expected to meet in physics.

Students who take the 9th grade physics MCAS must score at least proficient in order to meet the state's graduation requirements. Students who score below proficient may be required to take additional courses or remediation.

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Time which missile will take to reach its maximum height is 2 seconds. and The maximum height it will reach is 58.8.

What is the relation between time and acceleration?

The time, velocity and acceleration are related in such a way that time is directly proportional to velocity and time is inversely proportional to acceleration.

i.e.  t = u/g

As given in the question,

Initial velocity (u) = 39.2 m/s, and angle is 30°

initial vertical velocity = 39.2 sin30° = 19.6 m/s

So, the time taken can be calculated by:

t = u/g

t = 19.6/9.8

t = 2 seconds.

and the maximum height can be calculated by equation:

\(h = ut + \frac{1}{2} at^2\)

\(h = 39.2 + \frac{1}{2} 9.8 (2)^2\)

\(h = 39.2 + 19.6\)

h = 58.8 m

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Answer:

b. 0.20 m/s.

Explanation:

Given;

initial mass, m = 0.2 kg

maximum speed,  v = 0.3 m/s

The total energy of the spring at the given maximum speed is calculated as;

K.E = ¹/₂mv²

K.E = 0.5 x 0.2 x 0.3²

K.E = 0.009 J

If the mass is changed to 0.4 kg

¹/₂mv² = K.E

mv² = 2K.E

\(v = \sqrt{\frac{2K.E}{m} } \\\\v = \sqrt{\frac{2\times 0.009}{0.4} } \\\\v = 0.21 \ m/s\\\\v \approx 0.20 \ m/s\)

Therefore, the maximum speed is 0.20 m/s

The force constant of the spring is  866.7 N/m.

In order to fix the question that we have here we have to look at the Hooke's law. From the Hooke's law we have to note that the force that is causing the string to become expanded is proportional to the extension of the spring as long as the elastic limit has not been exceeded.

Now we know that the Hooke's law would refer to the force and the extension and that is what we would need to be able to solve in order to get the force constant as we have been asked in the problem that we have here.

Thus;

F = Ke

F = force

K = force constant

e = extension

Then;

K = F/e

K = 26 N/3 * 10^-2 m

K = 866.7 N/m

From the calculation that we have done in the lines above, we have obtained the force constant to be about  866.7 N/m.

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It takes about 4.85 seconds for the car to accelerate from a speed of 25 mi/h to a speed of 32 mi/h.

The given information includes the acceleration rate of a certain car which is 0.65 m/s², and the initial speed of the car which is 25 miles per hour. The question is asking about the time taken by the car to accelerate from the initial speed of 25 miles per hour to a speed of 32 miles per hour. This is a simple problem in kinematics that can be solved by using the formula of acceleration. Here’s how:
First, convert the initial and final speeds of the car into meters per second.
Given that:
Initial speed of the car, u = 25 miles/hour
Final speed of the car, v = 32 miles/hour
To convert miles/hour to meters/second, multiply it by 0.447:
u = 25 miles/hour × 0.447 = 11.175 meters/second
v = 32 miles/hour × 0.447 = 14.324 meters/second
Now, let’s use the formula of acceleration:
v = u + at
Where,
v = final speed = 14.324 m/s
u = initial speed = 11.175 m/s
a = acceleration = 0.65 m/s²
t = time taken
Substitute the given values in the formula:
14.324 = 11.175 + (0.65)t
Solve for t:
t = (14.324 - 11.175) / 0.65
t = 4.85 seconds
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Answer:

i hop this help you :)

Explanation:

How Does Radiant Energy Work? Radiant energy moves from one place to another in the form of electromagnetic waves or electromagnetic radiation. At its most elementary level, electromagnetic waves are made up of photons, which have no mass and move at the speed of light.

Answer:

Explanation:Radiant energy is used for radiant heating. It can be generated electrically by infrared lamps, or can be absorbed from sunlight and used to heat water. The heat energy is emitted from a warm element (floor, wall, overhead panel)

(a) The average acceleration of this sprinter is 3.31 m/s².

(b) The time taken for the sprinter to reach the speed is 3.5 s.

The average acceleration of this sprinter is calculated as follows;

v² = u² + 2as

where;

v² = 0 + 2as

a = v² / 2s

a = ( 11.5² ) / ( 2 x 20 )

a = 3.31 m/s²

The time of motion of the sprinter is calculated as follows;

v = u + at

v = 0 + at

t = v / a

t = ( 11.5 ) / ( 3.31 )

t = 3.5 s

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Answer:

There are 5 general layers; organism, population, community, ecosystem, and biosphere.

Explanation:

Hope this helps!

equal in magnitude but opposite in direction

Answer:

The  diameter is  \(d = 6.5 *10^{-4} \ m\)

Explanation:

From the question we are told that

   The length of the cylinder is  \(l = 120 \ m\)

     The resistance is  \(\ 6.0\ \Omega\)

     The  resistivity of the metal is \(\rho = 1.68 *10^{-8} \ \Omega \cdot m\)

Generally the resistance of the cylindrical wire is  mathematically represented as

         \(R = \rho \frac{l}{A }\)

The cross-sectional area of the cylindrical wire is  

        \(A = \frac{\pi d^2}{4}\)

Where  d is the diameter, so

         \(R = \rho \frac{l}{\frac{\pi d^2}{4 } }\)

=>     \(d = \sqrt{ \rho* \frac{4 * l }{\pi * R } }\)

       \(d = \sqrt{ 1.68 *10 ^{-8}* \frac{4 * 120 }{3.142 * 6 } }\)

       \(d = 6.5 *10^{-4} \ m\)

In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.

This relationship is described by the equation for the generated emf in a DC generator:

Emf = Φ * N * A * Z / 60

Where:

Emf is the generated electromotive force (in volts),

Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),

N is the number of turns in the armature winding,

A is the effective area of the armature coil (in square meters),

Z is the total number of armature conductors, and

60 is a constant representing the conversion from seconds to minutes.

From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.

The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.

The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.

Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.

By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.

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The acceleration with which the car uniformly increases its speed from zero to the given speed is 5m/s².

Given the data in the question

Since the car was initially at rest

Acceleration of the car; \(a = \ ?\)

Using the First Equation of Motion:

\(v = u + at\)

Where u is the initial velocity, v is the final velocity, a is the acceleration and t is the time taken.

We substitute our given values into the equation and solve for "a"

\(10m/s = 0m/s\ +\ ( a * 2s ) \\\\10m/s = a * 2s\\\\a = \frac{10m/s}{2s}\\\\a = 5m/s^2\)

Therefore, the acceleration with which the car uniformly increases its speed from zero to the given speed is 5m/s².

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Frequency, is defined as the rate of rotation, or the number of rotations in some unit of time. Angular frequency, , is the rotation rate measured in radians. These three quantities are related by f = 1 T = ω 2 π .

The frequency is the number of oscillation per unit time and it is used for defining the cyclic process like rotation, oscillation, wave etc.

The SI unit of the frequency is denoted as Hertz and the symbol λ represents it where one hertz means the wave completed one cycle in one second.

The frequency which explains the phenomenon of oscillatory and vibration like the mechanical vibration, sound signals, light, frequency waves etc. The  “period” represented as the time required by the wave for one oscillation, i.e., it is inversely proportional to the frequency.

If the flashes, then the period is the time between the two flashes. And the frequency is the total number of flashes per second.

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The moment of a couple is significant in various applications, such as analyzing the equilibrium and rotational motion of objects, understanding the behavior of rotating systems, and studying the effects of torques in mechanics and engineering.

In physics, the moment of a couple, also known as torque, refers to the rotational effect produced by two equal and opposite forces acting on an object but not along the same line of action.

A couple consists of two forces that have the same magnitude, act in parallel lines, and are opposite in direction. These forces create a rotational moment or torque around a particular point, known as the pivot or axis of rotation. The moment of a couple is a measure of the tendency of the couple to rotate an object.

The magnitude of the moment of a couple is given by the product of one of the forces and the perpendicular distance between the lines of action of the two forces. Mathematically, it can be expressed as:

Moment of couple = Force × Perpendicular distance

The SI unit of moment of a couple is the newton-meter (Nm). It is also important to note that the moment of a couple is a vector quantity and follows the right-hand rule for determining its direction.

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Answer: A. Light always travels in a straight line.

Explanation: Light follows rectilinear motion. Rectilinear motion is also known as linear motion. For example; the motion of a bullet fired from a gun, a ray of the torch.

Light always travels in a straight line. It is considered to travel from one point to another in a straight line joining them. The path of light is called a ray of light.

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Answer:

Answer:

1) the mass of the toy is 0.304 kg

2) the amplitude of the motion is 0.1524 m

3) the maximum speed obtained by the object during its motion is 4.87 m/s

Explanation:

Given the data in the question;

force constant of spring k = 310 N/m

position of toy x = 0.120 m

speed v = 3 m/s

Total energy E = 3.6 J

let m represent mass of toy.

1.) Find the mass of the toy.

we know that; The total energy of the system equals the sum of kinetic energy of the toy and the potential energy of the spring;

E = \(\frac{1}{2}\)kx² + \(\frac{1}{2}\)mv²

we substitute

3.6 = ( \(\frac{1}{2}\) × 310 × (0.120)² ) + ( \(\frac{1}{2}\) × m × (3)² )

3.6 = 2.232 + 4.5m

3.6 - 2.232 = 4.5m

1.368 = 4.5m

m = 1.368 / 4.5

m = 0.304 kg

Therefore, the mass of the toy is 0.304 kg

2) Find the amplitude of the motion.

we know that;

E = \(\frac{1}{2}\)kA²

where A is the amplitude of the motion,

we substitute

3.6 = \(\frac{1}{2}\) × 310 × A²

3.6 = 155 × A²

A² = 3.6 / 155

A² = 0.0232258

A = √0.0232258

A = 0.1524 m

Therefore, the amplitude of the motion is 0.1524 m

3) Find the maximum speed obtained by the object during its motion;

we know that;

E = \(\frac{1}{2}\)m\(v_{max\)²

where \(v_{max\) is the maximum speed

so we substitute

3.6 = \(\frac{1}{2}\) × 0.304 × \(v_{max\)²

3.6 = 0.152 × \(v_{max\)²

\(v_{max\)² = 3.6 / 0.152

\(v_{max\)² = 23.6842

\(v_{max\)² = √23.6842

\(v_{max\)² = 4.8664 ≈ 4.87 m/s

Therefore, the maximum speed obtained by the object during its motion is 4.87 m/s

Answer:

The resultant velocity has a magnitude of 38.95 m/s

Explanation:

Vector Addition

Given two vectors defined as:

\(\vec v_1=(x_1,y_1)\)

\(\vec v_2=(x_2,y_2)\)

The sum of the vectors is:

\(\vec v=(x_1+x_2,y_1+y_2)\)

The magnitude of a vector can be calculated by

\(d=\sqrt{x^2+y^2}\)

Where x and y are the rectangular components of the vector.

We have a plane flying due west at 34 m/s. Its velocity vector is:

\(\vec v_1=(-34,0)\)

The wind blows at 19 m/s south, thus:

\(\vec v_2=(0,-19)\)

The sum of both velocities gives the resultant velocity:

\(\vec v =(-34,-19)\)

The magnitude of this velocity is:

\(d=\sqrt{(-34)^2+(-19)^2}\)

\(d=\sqrt{1156+361}=\sqrt{1517}\)

d = 38.95 m/s

The resultant velocity has a magnitude of 38.95 m/s

The kinematics equation to determine v₀ is  Δx = (v + v₀/2) Δt; option B

Kinematic equations are equations which describe the motion of moving bodies.

Kinematic equations are also known as equations of motion.

The equations of motion are given below:

where;

Given that the values for the following are given;  Δx, v, and Δt, the equation to determine v₀ will be Δx = (v + v₀/2) Δt

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