Graphically determine the magnitude and direction of the
resultant of the following three vector displacements:
1. 15 m, 30° north of east
2. 20 m, 37° north of east
3. 25 m, 45 north of east

Given parameters:Magnetic force, F = 4.5 N,Length of the wire, l = 2 m,Current flowing through the wire, I = 3 A,Surface area of the loop, A = ?,Magnetic field strength, B = 2.5 T,Angle between current and magnetic field, θ = 17.46°

We can determine the magnitude of the magnetic force by using the formula:

F = B × l × I × sinθ

Substituting the given values in the above formula, we get:

4.5 N = 2.5 T × 2 m × 3 A × sin(17.46°)

Simplifying, we find:

sin(17.46°) = 0.3

Now we can solve for the surface area of the loop using the formula:

A = F / (B × I × sinθ)

A = 4.5 N / (2.5 T × 3 A × 0.3)

Calculating the result, we find:

A ≈ 1.5 m^2

Therefore, the surface area of the loop is approximately 1.5 square meters.

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The angle, e, between the current and the magnetic field is 17.46°.

In Science, the magnitude of a force acting in a magnetic field can be modeled by the following formula:

F = BILsinθ

Where:

By making θ the subject of formula, we have:

θ = sin⁻¹(F/BIL)

By substituting the given parameters into the formula, we have;

θ = sin⁻¹(4.5/2.5 × 3 × 2)

θ = sin⁻¹(0.3)

Angle, θ = 17.46°

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Complete Question:

A magnetic force of 4.5 N is acting on a 2 meter long wire which carries a current of 3 Amps when placed in a uniform magnetic field of strength 2.5 T. What is the angle, e, between the current and the magnetic field?

Answer:

a) 756.64 ft

b) 30 degrees

c) 29.27 degrees.

Explanation:

We can represent the situation as follows:

So, we can find the magnitude of the displacement (the green line) using the Pythagorean theorem. Then:

Then, the angle of the displacement can be approximate finding the angle θ. So, using a protractor on the figure, we get that θ is approximately 30 degrees.

Now, we can find the direction using a trigonometric function as:

Because 370 is the opposite side and 660 is the adjacent side. Therefore, the value of θ is:

So, the answers are:

a) 756.64 ft

b) 30 degrees

c) 29.27 degrees.

When two strings that have different thicknesses are compared, it will affect only one parameter, and that is wavelength. The rest of the parameters, including wave frequency, wave speed, and tension, will be constant for both strings.The explanation behind this is quite simple.

When we talk about wave frequency, we refer to the number of complete waves that pass by a given point in a certain period of time. When strings vibrate, the number of waves produced is determined by the vibrating source. The wave frequency is independent of the string's physical properties.

Wave speed refers to the speed at which the wave travels through the medium. The wave speed depends only on the medium, in this case, the string. Since both strings are made of the same material, wave speed will remain the same.Tension, on the other hand, is related to the force that is applied to the string to make it vibrate. The amount of tension in the string, however, is not dependent on the string's thickness.

Wavelength is the distance between two consecutive crests or troughs of a wave. The wavelength depends on the wave speed and the frequency. Since wave speed and wave frequency are constant for both strings, only the wavelength will be different if the strings have different thicknesses.

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Answer:

Mass = 25 kg

Height = 5 m

Acceleration due to gravity = 10 m/s

Work done

We know that

W = mgh

W = 25 × 5 × 10

W = 250 × 5

W = 1250 J

\( \\ \\ \\ \)

If you increase the frequency of a sound wave four times, the speed will increase four times. The correct option is A.

Particles that are vibrating make up sound waves. These collide with other particles, causing them to vibrate, which allows the sound to escape the source.

Your ear drums vibrate as a result of air vibrations, which allows you to perceive sound. This vibration is transformed into messages, which proceed to your brain via a nerve.

When sound is produced, air molecules shake and collide, causing vibrations to travel between air molecules. The sound is transmitted by the vibrating particles, which also cause the ear drum to vibrate.

A sound wave's frequency can be increased four times without increasing its speed.

Thus, the correct option is A.

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Answer:

b i think

Explanation:

Answer:

Soccer ball is a body at rest and does not move(because of inertia of rest) unless a force is applied on it

Explanation:

thanks for question

Utilizing the idea that Ah distance triumphs over Parallax Thus, it is seven to one over a 10.772 at 1/0, 0.7. There will come a time. the cause. One parsec and how far apart are Aaron in age? Sec. One parsec is equal to 3.262 lightyears. Therefore, assuming 3.262 light years, it would take 4.23 years.

In astronomy, a parallax is the apparent movement of an object brought on by a shift in the observer's point of view. This is used to determine how far away neighboring stars are. A star's parallax reduces as its distance from us grows, and vice versa.

The parallax formula is expressed as:

d=1/p

Where:

In arcseconds, p equals the parallax angle.

d = the separation in Parsecs

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The capacitance of the capacitor if the dielectric constant of the paper is 3.7 :  18 nF

Given data :

Thickness of aluminium capacitor = 0.022 mm

Number of sheets = 500

Thickness of ream = 5.5 cm = 0.055 m

measurement of sheets = 0.216 m by 0.279 m

dielectric constant ( k ) = 3.7

we will apply the capacitance formula below

C = Kε₀A / d

  = 3.7 * 8.85*10⁻¹² * 0.216 *0.279 / ( 0.055 / 500 )

  = 1.8 * 10⁻⁸F ≈ 18nF

Hence we can conclude that The capacitance of the capacitor if the dielectric constant of the paper is 3.7 :  18 nF

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Answer:

10.21 m/s

Explanation:

∆x =( v ^2 sin(2θ))/ g

rearrange this to get

v=√Δx·(g÷ sin(2θ))

Plug it in

v=√10·(-9.8÷sin(2·35))

Solve

v=10.21

For an ideal gas compressed isothermally, its compressibility is given by k₁ = 1/P.

The compressibility of a substance, denoted as k, is defined as the fractional change in volume (dV) of the substance for a given change in pressure (dP). Mathematically, it is expressed as:

k = -(1/V)(dV/dP) (Equation 1)

Now, let's consider an ideal gas that is compressed isothermally. Isothermal compression means that the temperature (T) of the gas remains constant during the compression process. For an ideal gas, we know that the product of pressure (P) and volume (V) is constant at constant temperature, i.e., PV = constant.

Taking the derivative of this equation with respect to pressure, we have:

P(dV/dP) + V = 0

Rearranging this equation, we get:

(dV/dP) = -V/P (Equation 2)

Substituting Equation 2 into Equation 1, we have:

k = -(1/V)(-V/P) = 1/P

Therefore, for an ideal gas compressed isothermally, its compressibility is given by k₁ = 1/P.

It's important to note that this result holds true specifically for an ideal gas undergoing isothermal compression. Different gases or non-ideal conditions may lead to different compressibility values.

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The specific gravity of this other fluid is 0,8547. The result is obtained by dividing the mass of the other fluid by the mass of the water.

The specific gravity is a ratio of the density of a substance to the density of the reference, usually water. Mathematically, it is written as

\(RD = \frac{\rho_{s}}{\rho_{r}}\)

Where

The mass of a bottle is 35.00 g when empty. It is 98.44 g when filled with water. It is 89.22 g when filled with another fluid. What is the specific gravity of this other fluid?

From that information, we have

The water and another fluid is filled in the same bottle. It means they have the same volume.

The specific gravity of this other fluid is

\(RD = \frac{ \rho_{s}}{ \rho_{r}}\)

\(RD = \frac{ m_{s}/V }{ m_{r}/V}\)

\(RD = \frac{ m_{s}}{ m_{r}}\)

\(RD = \frac{ 54.22}{ 63.44}\)

RD = 0,8547

Hence, the specific gravity of this other fluid is 0.8547.

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To explain the tangent plane to the surface, `z = 53 − x² − 2y²` at the point `(3, 2, 6)`, let us first determine the partial derivatives of `z` with respect to `x` and `y`.

Partial derivative of `z` with respect to `x`, `∂z/∂x = -2x`Partial derivative of `z` with respect to `y`, `∂z/∂y = -4y`Now, let's find the gradient vector `grad z` at `(3, 2, 6)` and the value of `z` at `(3, 2)`.gradient vector `grad z = (-2x, -4y, 1)`gradient vector `grad z = (-6, -8, 1)` at `(3, 2, 6)`.Value of `z` at `(3, 2)` is given by `z = 53 - 3² - 2(2)² = 39`.

Therefore, the equation of the tangent plane to the surface `

z = 53 − x² − 2y²` at `(3, 2, 6)` is:

`z - 6 = -6(x - 3) - 8(y - 2)`

which can be written as:`6x + 8y + z = 50`Thus, the equation of the tangent plane to the surface `z = 53 − x² − 2y²` at the point `(3, 2, 6)` is `6x + 8y + z = 50`.

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An electric field is defined along the x-axis by the function then if g=1.5m and h=6m, then v(g)-v(h) = 7768.40V.

When charge is present in any form, a point in space has an electric field that is connected to it.

The value of E, often known as the electric field strength, electric field intensity, or just the electric field, expresses the strength and direction of the electric field.

Each location in space where a charge exists in any form can be considered to have an electric field attached to it. The electric force per unit charge is another name for an electric field. The electric field’s equation is given as E = F / Q.

E = + 5 x^4 x^n

Also, E = -x^n r/rx (v)

⇒ 5 x^4 x^n = -x^n r/rx (v)

⇒ v = - ∫ 5 x^4 dx

⇒ v = -5 x^5/5

⇒ v = - x^5 v

So, v(g) - v(h) = - (1.5)^5 + (6)^5

= -7.59375 + 7776

=7768.40 V

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Answer:

330m/s

Explanation:

v= total distance/ time

=3300/10

The molar mass of a compound can be found by adding the molar masses of all of the atoms in the compound.

The molar mass of an atom can be found on the periodic table by looking at the atomic mass listed for that element.

For example, to find the molar mass of water (H2O), we would add the molar masses of two hydrogen atoms (2 x 1.01 g/mol) and one oxygen atom (16.00 g/mol) to get a total molar mass of 18.02 g/mol.

Another way is by finding the molecular formula of the compound, it can be done by analyzing the compound's chemical and physical properties and then using the mass spectrometer to determine the molecular weight.

In conclusion, the molar mass of a compound can be found by adding the molar masses of the atoms in the compound using the atomic masses listed on the periodic table, or by determining the molecular formula of the compound and using a mass spectrometer to find the molecular weight.

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Answer:

it won't depend on the frequency of the wave

Explanation:

Answer:

The statements that describe the relationship between history and geography are:

Geography is the setting of the history's story.

Geography plays a role in historic events.

History affects geography, and geography influences history.

The second, third, and the fifth statements are the correct answers.

Answer:

Convergent boundaries. When two plates collide and one is pushed over the other, forming a mountain.

The time taken for the man to reach the ground is 0.64 s and his velocity on reaching the round is 6.26 m/s.

Given that we can be able to use the equations of kinematics to obtain the time that it took the man to fall to the floor. Using the equation;

v^2 = u^2 + 2gh

v = final velocity

u = initial velocity

g = acceleration due to gravity

h = height attained

Note that u= 0 m/s since he dropped from a height;

v= √2gh

v = √2 * 9.8 * 2

v = 6.26 m/s

Again;

v = u + gt

Again  u= 0 m/s

v = gt

t = v/g

t = 6.26 m/s/9.8 m/s

t = 0.64 m/s

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Answer:

Nuclear power is presently a sustainable energy source, but could become completely renewable if the source of uranium changed from mined ore to seawater. Since U extracted is continuously replenished through geologic processes, nuclear would become as endless as solar.

Answer:

Explained below.

Explanation:

The ball doesn't fall behind the moving cart because the horizontal motion of the ballistic cart is not affected by the forces that act in the vertical direction. Therefore, when the cart is pushed, it means that the ball will shoot up and then it will land right back in the barrel.

Answer:

\(K.E = \frac{1}{2} m {v}^{2} \\ {v}^{2}_i = {v}^{2} _x + {v}^{2} _y \\ = {(6)}^{2} + {( - 2)}^{2} = 36 + 4 = 40m. {s}^{ - 1} \\ K.E_i = \frac{1}{2} (3) (40) = 60J \\ \\ {v}^{2}_f = {v}^{2} _x + {v}^{2} _y \\ = {(8)}^{2} + {(4)}^{2} = 80m. {s}^{ - 1} \\ K.E_i = \frac{1}{2} (3) (80) = 120J \\ W_{net}=K.E_f-K.E_i \\ = 120J - 60J \\ = 60J\)

Two similarities between electric and magnetic field lines are:
1. Direction: Both electric and magnetic field lines represent the direction of the force exerted on a charged particle or a magnetic pole.

Electric field lines originate from positive charges and terminate at negative charges, while magnetic field lines show the direction a north magnetic pole would move within the field.
2. Field strength: In both electric and magnetic fields, the field strength is proportional to the density of the field lines. More closely spaced lines indicate a stronger field, and the strength decreases as the lines become farther apart.
Two differences between electric and magnetic field lines are:
1. Origin and termination: Electric field lines originate from positive charges and terminate at negative charges, indicating the direction of the electric force.

Magnetic field lines, however, form closed loops, as they originate from the north pole of a magnet and terminate at the south pole, representing the continuous nature of the magnetic field.
2. Flux through a closed surface: For electric fields, the net electric flux through a closed surface is proportional to the total enclosed charge, as described by Gauss's Law.

In contrast, for magnetic fields, the net magnetic flux through any closed surface is always zero.

This is because magnetic field lines form closed loops, and there are no isolated magnetic poles (monopoles) in nature, which means that the magnetic field lines that enter a closed surface must also exit it.

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We may use trigonometry to address this issue by dividing the forces into their horizontal and vertical components.

...... 'S,""" '

T horizontal equals Tension * cos(19°)

T vertical = 1437.61 N

Then, we may determine the tension force's vertical component:

T vertical equals Tension * Sin(19°)

T horizontal = 484.94 N

We can now calculate the horizontal component of the sail's force on the rider:

F horizontal is equal to F sail * cos(30°).

vertical = 25.98 N

Last but not least, we may determine the vertical component of the sail's force on the rider:

F vertical is F sail times sin(30°).

F horizontal = 14.99 N

The net horizontal force must be zero since the rider is not accelerating in the horizontal direction. In light of this, the horizontal component of the tension force and the horizontal component

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Answer:

Average speed = 40.50 km/h (Approx)

Explanation:

Distance = Time × Speed

Total distance = (40/60) 50 + (8/60) 70 + (35/60) 35

Total distance = 33.33 km + 9.33 km + 20.17 km

Total distance = 62.80 km

Average speed = Total distance / Total time taken

Average speed = 62.80 / [(40+8+35+40)/60]

Average speed = 62.80 / 1.55

Average speed = 40.50 km/h (Approx)

Answer:

2 minutes or 120 seconds

Explanation:

The answer is 2 minutes or 120 seconds because 36 km is 36000 m and 36000 divided by 300 is 120, so the answer is 120 seconds, and converted to 2 minutes. Hope it helps!