How do you add non-collinear vectors?

Answer:

 The state when the two objects have reached the same temperature is known as thermal equilibrium.

The electrostatic force between these electrons will be 2.3×10⁻²⁰ N.

The force of attraction between two charges, according to Coulomb's law, is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Charges that are similar repel each other, whereas charges that are diametrically opposed attract each other.

They will repel, moving in opposite directions at the same speed. Because the magnitude and nature of the charge are same.

The electrostatic force between these electrons is;

\(\rm F= \frac{Kq_1q_2}{r^2} \\\\ F=\frac{9 \times 10^9 \times -1.6 \times 10^{-19} \times- 1.6 \times 10^{-19} }{(0.10 \times 10^-3)^2} \\\\F= 2.3 \times 10^{-20} \ N\)

Hence, the electrostatic force between these electrons will be. 2.3×10⁻²⁰ N.

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The firefighters must exert a force of approximately 266 Newtons to hold the hose steady.

The force required to hold the hose steady can be calculated using Newton's Second Law, which states that force (F) is equal to the mass (m) of the water flowing through the hose multiplied by the acceleration (a) of the water:

F = ma

The mass of water flowing through the hose per second is given as 9.5 kg/s. The acceleration of the water can be calculated using the formula:

v = at

where v is the velocity of the water and t is the time it takes for the water to reach that velocity. Assuming that the water starts from rest, we can rearrange the formula to solve for acceleration:

a = v/t

The velocity of the water is given as 28 m/s. The time it takes for the water to reach that velocity is not given, but we can assume that it is a short time, since the water is expelled at a high speed. Let's assume a time of 1 second, for simplicity.

Substituting the given and calculated values, we get:

a = v/t = 28 m/s / 1 s = 28 m/\(s^2\)

F = ma = (9.5 kg/s) * (28 m\(/s^2\)) = 266 N

Therefore, the firefighters must exert a force of approximately 266 Newtons to hold the hose steady.

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vf = vi + at

vf = 0

a = - (to stop (deceleration))

input the value:

0 = 4 m/s -a.8

8a = 4

a = 0.5 m/s²

F = m.a

F = 75 kg x 0.5 m/s²

F = 37.5 N

The expression for the energy stored (E) in a stretched wire of original length (L), cross-sectional area (A), tension (T), and Young's modulus (Y) is given by E = Y * e * ln(L) * A

The work done to stretch the wire can be calculated by integrating the force applied over the displacement. In this case, the force applied is the tension (T) in the wire, and the displacement is the change in length (ΔL) from the original length (L) to the stretched length (L + ΔL).

The tension in the wire is given by Hooke's law, which states that the tension is proportional to the extension of the wire:

T = Y * (ΔL / L)

where Y is the Young's modulus of the material of the wire.

Now, let's calculate the work done to stretch the wire:

dW = T * dL

Integrating this expression from L to L + ΔL:

W = ∫ T * dL = ∫ Y * (ΔL / L) * dL

W = Y * ΔL * ∫ (dL / L)

W = Y * ΔL * ln(L) + C

Here, C is the constant of integration. Since the energy stored in the wire is zero when it is unstretched (ΔL = 0), we can set C = 0.

Finally, the expression for the energy stored in the wire (E) is:

E = W = Y * ΔL * ln(L)

or, if we substitute the cross-sectional area (A) and strain (e) of the wire, where e = ΔL / L:

E = Y * e * ln(L) * A

Thus, the expression for the energy stored (E) in a stretched wire of original length (L), cross-sectional area (A), tension (T), and Young's modulus (Y) is given by:

E = Y * e * ln(L) * A

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The final temperature of the air is (c) 193°C.

Explanation:-

Given,

The initial pressure, P1 = 1 MPa

The initial temperature, T1 = 400 °C

The final pressure, P2 = 110 kPa

The polytropic exponent, n = 1.2

We need to determine the final temperature of the air.

Solution:

For the polytropic process with a given polytropic exponent n, the work done can be given as;

W = P1V1 (1 - n) / (n - 1) [1 - (P2 / P1) ((n - 1) / n)] -------------- [1]

Where,V1 = (mRT1) / P1 ------------- [2]

V2 = (mRT2) / P2 ------------- [3]

Combining equations [2] and [3], we get;

V2 / V1 = P1 / P2 * T2 / T1T2

= T1 (V2 / V1) * (P2 / P1) --------------- [4]

Now, substituting equation [2] into equation [1],

we get;

W = (mRT1) / P1 * (1 - n) / (n - 1) [1 - (P2 / P1) ((n - 1) / n)]

Also, substituting equation [4] into equation [1],

we get;

W = (mR T1) / P1 (1 - n) / (n - 1) [1 - (P2 / P1) ((n - 1) / n)]T2

= T1 (1 - n) / n [1 - (P2 / P1) (n - 1)] ------------ [5]

where m is the mass of the gas and R is the gas constant.

For air, the value of R is 0.287 kJ/kg.K.

Substituting the values in equation [5],

we get;T2 = 400 × (1 - 1.2) / 1.2 [1 - (110 / 1000) (1.2 - 1)]

= -220.34 K (-53.81°C)

However, the final temperature of the air cannot be negative.

Therefore, the process must be irreversible or isothermal.

Thus, the option (c) 193°C is the correct answer.

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When the Bowen ratio is low and negative, it means the surface is wet, and the latent heat flux is significant, while the sensible heat flux is minor. Because of Arctic sea ice's nature, the Bowen ratio is expected to be small and negative.

During summer, the Arctic sea ice's surface temperatures are often above 0° C, with a temperature inversion expanding from the surface to altitudes of some hundred meters.

For such conditions, the sensible heat flux H is expected to be positive, while the latent heat flux H L is expected to be small or zero. The Bowen ratio B is expected to be small and negative.

Let us discuss each term in more detail. Sensible heat flux (H):The rate of heat transfer from the Earth's surface to the atmosphere due to the temperature difference is referred to as the sensible heat flux. The earth surface warms up due to solar radiation, and then the warm surface transfers heat to the cooler air. The air then heats up and rises, creating convection currents that aid in the heat transfer process.

Sensible heat flux is positive when heat moves from the surface to the atmosphere.Latent heat flux (H L ):The heat required for a phase transition, such as a liquid converting to a gas, is referred to as latent heat. The energy required to convert a material from one phase to another is referred to as latent heat. Evaporation and transpiration are the two main processes that contribute to the latent heat flux.

Because Arctic sea ice's surface temperature is typically above the melting point of ice during summer, the latent heat flux is expected to be small or zero.

Bowen ratio (B):The Bowen ratio is a measure of the ratio of sensible heat flux to latent heat flux. It's a dimensionless quantity that helps to understand the surface's evapotranspiration efficiency.

When the Bowen ratio is low and negative, it means the surface is wet, and the latent heat flux is significant, while the sensible heat flux is minor. Because of Arctic sea ice's nature, the Bowen ratio is expected to be small and negative.

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1. Sensible heat flux (H) is negative, indicating heat transfer from the surface to the atmosphere.
2. Latent heat flux (H_L) is positive, indicating heat transfer from the atmosphere to the surface through evaporation.
3. Bowen ratio (B) is negative, indicating that the sensible heat flux is larger than the latent heat flux. The magnitude of the Bowen ratio can vary depending on the specific conditions.

In summer, surface temperatures over Arctic sea ice are often above 0°C, and there is a temperature inversion that extends from the surface to altitudes of a few hundred meters.

1. Sensible heat flux (H): The sensible heat flux is the transfer of heat between the surface and the atmosphere due to temperature differences. In this case, the sensible heat flux is expected to be negative. This means that heat is being transferred from the surface (warmer) to the atmosphere (cooler). The magnitude of the sensible heat flux can vary depending on the temperature difference between the surface and the atmosphere, but it is generally larger when the temperature difference is greater.

2. Latent heat flux (H_L): The latent heat flux is the transfer of heat between the surface and the atmosphere due to the evaporation and condensation of water. In this case, the latent heat flux is expected to be positive. This means that heat is being transferred from the atmosphere (warmer) to the surface (cooler) through the process of evaporation. The magnitude of the latent heat flux depends on factors such as the availability of moisture and the temperature difference between the surface and the atmosphere. It can be larger when there is more moisture available for evaporation and when the temperature difference is greater.

3. Bowen ratio (B): The Bowen ratio is the ratio of sensible heat flux to latent heat flux. It provides information about the relative importance of sensible and latent heat transfer processes. In this case, the Bowen ratio is expected to be negative. This indicates that the sensible heat flux is larger than the latent heat flux. The magnitude of the Bowen ratio can vary depending on the specific conditions, but it is generally larger when the sensible heat flux is dominant.

To summarize:
- Sensible heat flux (H) is negative, indicating heat transfer from the surface to the atmosphere.
- Latent heat flux (H_L) is positive, indicating heat transfer from the atmosphere to the surface through evaporation.
- Bowen ratio (B) is negative, indicating that the sensible heat flux is larger than the latent heat flux. The magnitude of the Bowen ratio can vary depending on the specific conditions.

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Answer:

5kg

Explanation:

p = mv

m = p/v

m = 35/7

m = 5kg

Answer:

5 kilograms

Explanation:

Mass can be found using the following formula.

\(m=\frac{p}{v}\)

where p is the momentum and v is the velocity.

The object has a momentum of 35 kg m/s and a velocity of 7 m/s. Therefore,

p= 35 kg m/s

v= 7 m/s

Substitute these values into the formula.

\(m= \frac{35 kg- m/s}{ 7 m/s}\)

Divide 35 kg m/s  by 7 m/s. (35/7=5)

The m/s in the numerator and denominator cancel each other out.

\(m= 5 kg\)

The mass of the object is 5 kilograms.

Answer:

Add Ff from Fa

Explanation:

Fnet = sum of all force

horizontal net force = Ff + Fa

The correct answer for the given question for the distance that the piston on the right will move is 0.1 m option (A).

When an explosion occurs in the left piston, it exerts a force on the fluid, which in turn exerts an equal and opposite force on the right piston due to the enclosed volume.

The cross-sectional area of the left piston is 0.25 m², and assuming the force is uniformly distributed over the entire area, the force exerted by the left piston is given by F = P × A, where P is the pressure and A is the area.

Using the work-energy principle, the work done by the left piston is equal to the work done on the right piston. Therefore, the work done on the right piston is equal to the force exerted on it multiplied by the distance it moves.

The force exerted on the right piston can be calculated using the same formula as before (F = P × A), where the cross-sectional area A is 0.5 m².

Since the force exerted on the right piston is equal to the force exerted by the left piston, we can equate the two expressions for force and solve for the distance moved by the right piston.

Using the equation F_left = F_right, we have P_left × A_left = P_right × A_right.

Plugging in the given values, we get (P_left × 0.25) = (P_right × 0.5).

Since the pressure is the same throughout the fluid, P_left = P_right.

Simplifying the equation, we have 0.25 = (0.5 × A_right).

Solving for A_right, we get A_right = 0.25 / 0.5 = 0.5 m².

The distance moved by the right piston can be calculated using the work formula:

Work_right = Force_right × Distance_right.

Plugging in the values, we have (P_right × A_right) × Distance_right = (P_left × A_left) × Distance_left.

Since P_left = P_right, we can further simplify the equation:

A_right × Distance_right = A_left × Distance_left.

Plugging in the given values, we get (0.5 × Distance_right) = (0.25 × 0.2).

Solving for Distance_right, we have Distance_right = (0.25 × 0.2) / 0.5 = 0.1 m.

Hence, the correct answer is option A: 0.1 m.

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Answer:

The linear speed of the car is approximately 27.30 m/s

Explanation:

The question parameters are;

The mass of the person on the rollercoaster, m = 57.0 kg

The radius of the rollercoaster track, r = 42.7 m

The normal force felt by the person, F = 995 N

The centripetal force acting on the person keep the circular motion is given by the following equation;

\(Centripetal \, force \ F_c = \dfrac{m \times v^2}{r}\)

Where;

v = The linear velocity of motion = The linear speed of the car

The centrifugal force, F, is the force normal force felt by the person and is equal to the centripetal force, therefore, we have;

\(Centripetal \, force \ F_c = Centrifugal \, force \ F = \dfrac{m \times v^2}{r}\)

From which we have;

\(F = 995 = \dfrac{57 \times v^2}{42.7}\)

\(\therefore v = \sqrt{\dfrac{995 \times 42.7}{57} } \approx 745.38\)

The linear speed of the car = v ≈ 27.30 m/s

The angular speed of the car, ω = v/r ≈ 27.30/42.7 ≈ 0.639 rad/s

Answer: 18.1 m/s

Explanation:

The provided text contains information about the microscopic structures and crystal diagrams of dental plaster, dental stone, and die stone. It also mentions the gauging water ratios and procedures for manipulating and pouring compound impressions using these materials.

The text describes the microscopic structure of dental plaster, which consists of fibrous aggregates of fine cupotal with capitany pares. Dental stone is described as having prior crystals in the form of mods, while die stone is characterized by its cuboidal shape.

The crystal diagrams are mentioned for each material: Dental plaster, dental stone, and die stone.

The text then outlines three different demonstrations, each with a specific aim and gauging water ratio. The demonstrations involve studying the manipulation of dental plaster, dental stone, and die stone, as well as pouring compound impressions using these materials. The procedures for each demonstration are provided.

To learn more about the manipulation of dental plaster, dental stone, and die stone, as well as the pouring of compound impressions, further information can be explored in dental textbooks or dental laboratory manuals.

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Answer:

B)a tool to drop temperatures, mercury, an electric current, and a tool to measure resistance

Consumer packaged goods companies have significant diversification in their product mixes.

Diversification refers to the practice of offering a wide range of products across various product lines or categories.

Consumer packaged goods firms want to reach a wider audience and target certain market segments, thus they diversify their product portfolios to do so. This tactic enables businesses to seize possibilities in numerous markets while reducing the dangers related to depending too heavily on a single product or product line.

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Thermal system is used on some electric and hybrid vehicles to cool the power electronics and charger modules.

What is thermal system?

An isolated system has no interaction with the rest of the physical universe, a closed system can only exchange heat and work, and an open system can also exchange mass. In thermodynamics, a system is the portion of the physical universe that the observer chooses to analyse separately from the rest.

A thermal system, on the other hand, is a complex assembly of coupled components, some of which are thermal, that exhibits a common structured behavior  for instance, a refrigerator consists of pipes, a compressor, an electric motor, heat exchangers, valves, insulation, a casing, doors, a lamp, and other components that interact to achieve the internal goal of producing cold.

The interior space or the refrigerant are thermodynamic systems, whereas a refrigerator is a thermal system. While large thermal systems, like a refrigerated store, are constructed on the job site, small thermal systems, like a refrigerator, typically come fully installed from the manufacturer (although a straightforward split-air-conditioning system needs installation). Thermal systems often require services such as fuel supply, flue stack, water intake and exit, air intake and exit, and electrical supply (for power or at least for control).

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It will take 2.857 minutes (or about 2 minutes and 51 seconds) for the fish to reach a temperature of 60 °C.

To determine the time it will take for the fish to reach a temperature of 60 °C, we can use the principle of heat conduction and the concept of temperature difference.

We know that the rate of heating by conduction is proportional to the temperature difference between the body and its surroundings. Therefore, we can write the following equation:

(T - Ts) = k * t

where T is the temperature of the fish, Ts is the temperature of the surroundings (boiling water), k is the proportionality constant, and t is the time.

Given that the initial temperature of the fish is 20 °C and it takes 5 minutes to reach 30 °C, we can substitute these values into the equation:

(30 - 100) = k * 5

-70 = 5k

Solving for k, we find k = -14.

Now we can use this value of k to find the time it will take for the fish to reach 60 °C:

(60 - 100) = -14 * t

-40 = -14t

Dividing both sides by -14, we get t = 2.857 minutes.

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Answer:

Explanation:

height of one floor = 3.01 m

height of 96 floor h = 96 x 3.01 = 288.96 m

time of fall t = 12.6 s

h = 1/2 g x t²

288.96 = 1/2 x g x 12.6²

g = 3.64 m /s²

v = u + gt

v = 0 + 3.64 x 12 .6

= 45.86 m /s

velocity of impact = 45.86 m /s .

The frequency of the second harmonic of a note with a fundamental frequency of 200 Hz is 400 Hz, and the frequency of the third harmonic is 600 Hz.

To calculate the harmonics of a note, you will need to know the fundamental frequency of the note. The frequency of the second harmonic is twice the fundamental frequency, and the frequency of the third harmonic is three times the fundamental frequency. For example, if the fundamental frequency is 200 Hz, then the frequency of the second harmonic is 400 Hz and the frequency of the third harmonic is 600 Hz.

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The charge contained in a section of the line of length 2.50 cm is 8.87 × 10⁻¹⁰ C.

The formula for electric field intensity of a line charge is given by:E= λ/2πε₀rwhere,λ is the linear charge density of the line.ε₀ is the permittivity of free space.r is the perpendicular distance of the point from the line charge.

Electric field intensity, E = 810 N/CandDistance, r = 0.385 mUsing the above formula, we can find the value of linear charge density of the line.λ = 2πε₀Erλ = 2 × π × 8.85 × 10⁻¹² × 810 × 0.385λ = 3.55 × 10⁻⁸ C/mLength of the section of the line, L = 2.5 cm = 0.025 mWe need to find the charge present in a section of the line of length 2.50 cm.Since the linear charge density of the line is 3.55 × 10⁻⁸ C/m,Charge in a section of the line of length 0.025 m = λLq = λLq = 3.55 × 10⁻⁸ × 0.025q = 8.87 × 10⁻¹⁰ C

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Answer:

Escape velocity is defined as the velocity which will take a body to go the infinite distance away above the surface of the earth when projected upwards.

Hope this helps...

Good luck on your assignment....

Answer:

 E_g = m 392 J,      Ek = m 392

Explanation:

Mechanical energy is a very important concept since if the system does not have friction it remains constant

the potential energy of a system is

          E_g = U = m g (y2 - i)

          E_g = m 9.8 (40 -0)

          E_g = m 392 J

The kinetic energy for this system assuming it started from rest

          E_k = K = ½ m v2

how mechanical energy is conserved

         E_g = E_k

         Ek = m 392

The car will have traveled through an angle of 27.5 radians when the magnitude of its total acceleration is 2.2 m/s^2.

The magnitude of the total acceleration of a car moving in a circular path is given by the equation:

a = v^2 / r

where "v" is the velocity of the car, "r" is the radius of the circular path, and "a" is the total acceleration.

The tangential acceleration, "a_t", is given by the equation:

a_t = v * a / r

Combining these two equations, we get:

a^2 = a_t^2 + v^2 / r^2

Since the car starts from rest, we can assume its initial velocity, "v_0", is zero. The velocity of the car after a time "t" can be found using the equation:

v = v_0 + a_t * t

Substituting this into the equation for the total acceleration, we get:

a^2 = a_t^2 + (v_0 + a_t * t)^2 / r^2

Solving for "t", we get:

t = sqrt(r^2 * a^2 - r^2 * a_t^2) / a_t

We are given that "r" = 130 m, "a_t" = 1.4 m/s^2, and "a" = 2.2 m/s^2. Plugging these values into the equation for "t" gives us:

t = sqrt(130^2 * 2.2^2 - 130^2 * 1.4^2) / 1.4 = 4.15 s

The angle traveled by the car is given by the equation:

θ = v_0 * t + 0.5 * a_t * t^2

Since "v_0" = 0, we can simplify this equation to:

θ = 0.5 * a_t * t^2

Plugging in the value for "t" gives us:

θ = 0.5 * 1.4 * 4.15^2 = 27.5 radians

Therefore, the car will have traveled through an angle of 27.5 radians when the magnitude of its total acceleration is 2.2 m/s^2.

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Answer:

10 hours to get to Paris

The diffraction pattern of the hair appears in the horizontal direction that it does because the diffraction pattern of the hair appears in the horizontal direction due to the bending and spreading of light waves around the hair.

1. When light encounters an obstacle, such as a hair, diffraction occurs. Diffraction is the bending and spreading of light waves around the obstacle.
2. The hair acts as a single slit, allowing light to pass through the narrow gap around it.
3. As the light waves pass through this gap, they interfere with each other, causing constructive and destructive interference.
4. This interference results in a diffraction pattern that appears in the horizontal direction, which is perpendicular to the direction of the hair.
5. The pattern is characterized by a series of bright and dark bands, with the bright bands representing areas of constructive interference and the dark bands representing areas of destructive interference.
In conclusion, the diffraction pattern of the hair appears in the horizontal direction due to the bending and spreading of light waves around the hair, which causes interference patterns to form perpendicular to the direction of the hair.

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Answer:

2.00072 mm

Explanation:

So, we just have to calculate 2 mm x (1 + 0.36 x 10⁻³) = 2 mm + 0.00072 mm = 2.00072 mm

The capacitor's value alone, V = Q C, defines the voltage drop across the capacitor because the charge (Q) is constant and equal.

When the switch is shut, the capacitor's charge has not had time to build up, therefore the charge and voltage are still 0.

The voltage across the capacitor can be calculated using the formula V = Q/C. Kirchoff's first law can be used to calculate the voltages across the other components. The current flowing through a capacitor must always decrease until it reaches zero because charge cannot continuously flow through a capacitor.

Maximum voltage: Each capacitor's rating determines the maximum voltage that can be dropped across it. Some capacitors may be rated at 1.5V while others may be rated at 100V. Usually, the capacitor will be destroyed if the maximum voltage is exceeded. Current leakage: Capacitors don't always work perfectly.

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Answer:

A, 0.050 Hz

Explanation:

1) Frequency = speed divided by wavelength

time is 2* 60 = 120 seconds

distance = 6 wave lengths

speed = distance divided by time

speed = 6 wave lengths divided by 120

Hope this helps!

The fuel must be ejected at a speed of 27.9 m/s [Down] to achieve the desired course.

Let's denote the velocity of the rocket after the fuel is ejected as v_r and the velocity of the ejected fuel as v_f. The total mass of the system is M = 4739 kg + 155 kg = 4894 kg.

Before the fuel is ejected, the momentum of the system is:

p1 = M * v1 = (4739 kg + 155 kg) * 83 m/s = 408332 kg m/s [Right]

After the fuel is ejected, the momentum of the system is:

p2 = M * v2 = 4739 kg * v_r + 155 kg * v_f

The direction of the final velocity is [Right 16 Up], which means that the vertical component of the velocity is v_r * sin(16) and the horizontal component is v_r * cos(16).

Using the conservation of momentum, we have:

p1 = p2

408332 kg m/s [Right] = (4739 kg * v_r + 155 kg * v_f) * v_r * cos(16)

Solving for v_r, we get:

v_r = sqrt(408332 kg m/s [Right] / ((4739 kg * cos^2(16) + 155 kg) * cos(16)))

v_r = 88.5 m/s [Right 16 Up]

Now, we need to find the velocity of the ejected fuel v_f. Since the engine can only eject the fuel perpendicular to the motion of the rocket, the horizontal component of v_f is zero. The vertical component of v_f is equal to the vertical component of v_r:

v_f * sin(90) = v_r * sin(16)

v_f = v_r * sin(16)

v_f = 27.9 m/s [Down]

Therefore, the fuel must be ejected at a speed of 27.9 m/s [Down] to achieve the desired course.

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