A 20 kg box is released on a 28 degree incline and accelerates down the incline at 0.26 m/s^2.
A. Find the friction force impeding its motion.
B. Determine the coefficient of kinetic friction.

Given the following information:Mass of the system, m = 20 kg.Damping coefficient, b = 6 Ns/m.Force, F = 90 N.Frequency of applied force, f = ?Applied force angular frequency, w = 6 rad/s.Forced vibration equation:F(t) = F0 sin(wt)where F0 = 90 N and w = 6 rad/s.Under the action of the force F, the mass m will oscillate.The equation of motion for the mass-spring-damper system is given by:$$\mathrm{m\frac{d^{2}x}{dt^{2}}} + \mathrm{b\frac{dx}{dt}} + \mathrm{kx = F_{0}sin(\omega t)}$$where k is the spring constant.x(0) = 0 and x'(0) = 0.As we have the damping coefficient (b), we can calculate the damping ratio (ζ) and natural frequency (ωn) of the system.Damping ratio:$$\mathrm{\zeta = \frac{b}{2\sqrt{km}}}$$where k is the spring constant and m is the mass of the system.Natural frequency:$$\mathrm{\omega_{n} = \sqrt{\frac{k}{m}}}$$where k is the spring constant and m is the mass of the system.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$At resonance, the amplitude of the system will be maximum when forced by a sinusoidal force of frequency equal to the resonant frequency.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$$$\mathrm{\omega_{d} = \sqrt{(6.57)^{2}-(-2.88)^{2}} = 6.98 rad/s}$$Hence, the frequency of applied force at which resonance will occur is 6.98 rad/s.

The frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.

To determine the frequency of the applied force at which resonance will occur, resonance happens when the frequency of the applied force matches the natural frequency of the system. The natural frequency can be determined using the formula:

ωn = √(K / M),

where ωn is the natural frequency, K is the spring constant, and M is the mass of the system.

Substituting the given values of K = 400 N/m and M = 20 kg into the equation, we can calculate the natural frequency ωn.

ωn = √(400 N/m / 20 kg) = √(20 rad/s²) = 2√5 rad/s.

Therefore, the frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.

The correct question is given as,

M= 20kg

Fo = 90 N

ω = 6 rad/s

K = 400 N/m

C = 125 Ns/m

Determine the frequency of applied force at which resonance will occur?

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The correct answer is Option (A). A small solar system body.

Asteroids are small, rocky objects that orbit the Sun. Although asteroids orbit the Sun like planets, they are much smaller than planets.

There are lots of asteroids in our solar system. Most of them live in the main asteroid belt—a region between the orbits of Mars and Jupiter.

An asteroid, comet, or other object that orbits the Sun but is too small to be classified as a planet or dwarf planet is referred to as a small solar system body. These objects are typically rocky or icy remnants from the early formation of the solar system and can range in size from tiny grains to larger objects several hundred kilometers in diameter. They are distinct from space junk, which refers to human-made debris in space, and planetesimals, which are larger objects that can potentially form planets through accretion. Satellites, on the other hand, are objects that orbit around a larger celestial body, such as a planet or dwarf planet.

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Answer:

I think its C or A

Explanation:

Answer:

The  recoil velocity of the cannon is 2.38 m/s.

Explanation:

Given;

mass of cannonball, m₁ = 8 kg

mass of stationary cannon, m₂ = 1000 kg

initial velocity of the cannonball, u₁ = 300 m/s

initial velocity of the cannon, u₂ = 0

Let the recoil velocity of the cannon, = v

Apply the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = v(m₁ + m₂)

8(300) + 1000(0) = v(8 + 1000)

2400 = v(1008)

v = 2400/1008

v = 2.38 m/s

Therefore, the  recoil velocity of the cannon is 2.38 m/s.

The consequences of different speeds of light in different media include mirages, rainbows, and the brilliant colors of diamonds. Therefore, the correct option is D) all of the above.

When light travels through different media, its speed can change. This change in speed leads to various optical phenomena and consequences. Mirages occur due to the bending of light as it passes through air layers with different refractive indices, caused by temperature gradients. This bending creates the illusion of objects appearing in locations where they are not actually present, such as seeing water on a hot road. Rainbows are formed when sunlight is refracted, reflected, and dispersed by water droplets in the atmosphere. The different speeds of light in the droplets cause the light to separate into its constituent colors, resulting in the formation of a colorful circular arc.

The brilliant colors of diamonds and other gemstones are due to the phenomenon called dispersion. Different wavelengths of light have different speeds when passing through the gemstone, causing them to separate and produce a range of colors. Therefore, all of the given options (mirages, rainbows, and the brilliant colors of diamonds) are consequences of different speeds of light in different media.

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The two products or technologies that supply Africans with most of their domestic energy are biomass (specifically firewood and charcoal) and fossil fuels (primarily coal and oil).

In Africa, a significant portion of domestic energy needs is met through the use of biomass and fossil fuels. Biomass, such as firewood and charcoal, is widely used for cooking, heating, and lighting purposes, particularly in rural areas. Firewood is obtained from trees and woody vegetation, while charcoal is produced by burning wood in a controlled manner.

Fossil fuels, including coal and oil, are also significant sources of domestic energy in Africa. These fuels are used for electricity generation, heating, cooking, and transportation in both urban and rural areas. Coal-fired power plants, diesel generators, and the burning of oil for various purposes contribute to the reliance on fossil fuels for domestic energy supply.

It's worth noting that Africa is a diverse continent with varying energy sources and availability across different regions and countries. The reliance on biomass and fossil fuels for domestic energy can differ depending on factors such as urbanization, infrastructure development, access to electricity, and availability of renewable energy resources.

The two primary sources of domestic energy for Africans are biomass, specifically firewood and charcoal, and fossil fuels, primarily coal and oil. These sources play a crucial role in meeting energy needs for cooking, heating, lighting, and other domestic purposes across the continent.

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A nodal voltage source is a type of voltage source that is connected directly between two nodes in a circuit, rather than being connected in series with a circuit element.

Nodal analysis is a circuit analysis technique that uses Kirchhoff's Current Law (KCL) to determine the voltage at each node in a circuit. When a voltage source is connected between two nodes, it can be included in nodal analysis as a source term in the equation for the corresponding node.

The voltage value of the source is simply included as a known value in the equation. This technique can be used to analyze complex circuits with multiple voltage sources and circuit elements.

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Answer:

When substances made of iron are exposed to oxygen and moisture (water), rusting takes place. Rusting removes a layer of material from the surface and makes the substance weak. Rusting is a chemical change.

Answer:

B) Iron rusts in water

Explanation:

Physical property is defined as the property of a substance which becomes evident during physical changes. Example: Melting point  , electrical conductivity, malleability,

Chemical property is defined as the property of a substance which becomes evident during chemical changes. Example: Reactivity with other substances

Rust is hydrated ferric oxide .

Corrosion of iron is called as rusting. Rust is hydrated ferric oxide .

Thus rusting of iron is a chemical property.

Answer:

When you have two materials with the same index of refraction, it means that if they are touched by a ray of light it won't have a chance, and its form would prevail.

Explanation:

The reason behind this is that in the first place. When light passes through an object of certain refraction it is modified from its natural state, allowing it to change in color to the human eye or many other effects in other perceptive elements. However, when the same light passes through two objects with the same refraction due to their physical characteristics, it doesn't change because once it comes out of the first one it will suffer the same effect from the last one. For it to change the refraction would have to be higher or lower. Then it would be modified. The reason is because the dimensions are not modified. Because at some point the ray of light has to come out of the first one to enter the second one.

The quantity that describes how tightly packed matter is inside of an object is: a) density

The density of an object is the relation that exist between the mass and the space that the object occupies. The general formula of the density is:

ρ = m/v

Where:

For example if we want to know which is the density of a body that has a mass of 100g and a volume of 150 cm³, applying the density formula we get:

ρ = 100 g/150 cm³

ρ = 0.666 g/cm³

It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

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Answer:

2.38 T

Explanation:

Since the number of coils and the change in time are both 1, I set it up as 3.57=1.50(x) and then solved for x to be 2.38 T.

Answer:

B. It can be answered using measurements.

Explanation:

Scientific inquiry can be defined as the various ways, techniques and approach used by scientists to study the world and provide a detailed description (information) based on the empirical evidence derived from the investigation.

Measurements can be defined as a technique which typically involves the process of identifying and determining the dimensions, quality and quantity of a physical object.

Hence, the statement which best describes a characteristic of a question that can be answered through scientific inquiry is that, it can be answered using measurements. Using scientific inquiry to answer questions entails using measurements to propose specific and evidential explanations, as well as back up theories associated with the question.

Size exclusion chromatography is the method by which scientists determine the molecular size (not the weight), of a particular substance.

Size-exclusion chromatography (SEC), also known as molecular sieve chromatography, is a chromatographic method in which molecules in solution are separated by their size, and in some cases molecular weight. It is usually applied to large molecules or macromolecular complexes such as proteins and industrial polymers.

Typically, when an aqueous solution is used to transport the sample through the column, the technique is known as gel-filtration chromatography, versus the name gel permeation chromatography, which is used when an organic solvent is used as a mobile phase. The chromatography column is packed with fine, porous beads which are commonly composed of dextran, agarose, or polyacrylamide polymers. The pore sizes of these beads are used to estimate the dimensions of macromolecules.

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The distance the from the bottom of the container at which the hole

should be depends on pressure head of the water.

Response:

First part:

The distance the water will shoot out horizontally is given from the formula which is derived ;

\(H - h = \mathbf{\dfrac{1}{2} \cdot g \cdot t^2}\)

\(t = \mathbf{\sqrt{\dfrac{2 \cdot (H-h)}{g} }}\)

\(Horizontal \ velocity, \ v = \mathbf{\sqrt{2 \cdot g \cdot h}}\)

Which gives;

Where;

H = The height of the cylinder

h =

\(Horizontal \ velocity, \ v = \sqrt{2 \cdot g \cdot h}\)

\(Horizontal \ distance, \ x = v \cdot t = \sqrt{2 \cdot g \cdot h} \cdot t = \mathbf{\sqrt{2 \cdot g \cdot h} \cdot \sqrt{\dfrac{2 \cdot (H-h)}{g} }}\)

\(Horizontal \ distance, \ x = \sqrt{2 \cdot g \cdot h} \cdot \sqrt{\dfrac{2 \cdot (H-h)}{g} }= \mathbf{2 \sqrt{h \cdot (H - h)}}\)

x² = 4·h·H - 4·h²

\(Maximum \ x^2 \ is \ at \ h = -\dfrac{4 \cdot H}{2 \cdot (-4)} = \dfrac{H}{2}\)

\(\dfrac{H}{2}\) = \(\dfrac{29.8 \, cm}{2}\) =  14.9 cm. from the top is \(\dfrac{H}{2}\) = 14.9 cm from the bottom

Therefore;

If the water is to shoot as far as possible, the distance from the the

bottom of the container, at which the hole should be is punched is half

way from the bottom of the container which is 14.9 cm. from the bottom.

Second part:

The horizontal distance from the side of the container the water will land is therefore;

\(x_{max} = 2 \times \sqrt{14.9 \times (29.8 - 14.9)} = 2 \times \sqrt{14.9^2} = \mathbf{29.8}\)

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Answer:

this was 2 weeks ago, but im pretty sure the correct answers are:

B=c

C=d

D=b

hope this helps and is correct :)

Answer:

a) v₂ = 4.2 m/s

b) v₂ = 5 m/s

Explanation:

a)

We will use the law of conservation of momentum here:

\(m_1u_1+m_2u_2=m_1v_1+m_2v_2\)

where,

m₁ = m₂ = mass of bowling pin = 1.8 kg

u₁ = speed of first pin before collsion = 5 m/s

u₂ = speed of second pin before collsion = 0 m/s

v₁ = speed of first pin after collsion = 0.8 m/s

v₂ = speed of second after before collsion = ?

Therefore,

\((1.8\ kg)(5\ m/s)+(1.8\ kg)(0\ m/s)=(1.8\ kg)(0.8\ m/s)+(1.8\ kg)(v_2)\\v_2 = 5\ m/s - 0.8\ m/s\)

v₂ = 4.2 m/s

b)

We will use the law of conservation of momentum here:

\(m_1u_1+m_2u_2=m_1v_1+m_2v_2\)

where,

m₁ = m₂ = mass of bowling pin = 1.8 kg

u₁ = speed of first pin before collsion = 5 m/s

u₂ = speed of second pin before collsion = 0 m/s

v₁ = speed of first pin after collsion = 0 m/s

v₂ = speed of second after before collsion = ?

Therefore,

\((1.8\ kg)(5\ m/s)+(1.8\ kg)(0\ m/s)=(1.8\ kg)(0\ m/s)+(1.8\ kg)(v_2)\)

v₂ = 5 m/s

The current sensitivity of the first coil is  0.5 times that of the second coil. The voltage sensitivity of the first coil is 2.5 times that of the second coil.

Current sensitivity can be determined as how much a galvanometer will deflect on flowing some current through it. Voltage sensitivity can be determined by how much the galvanometer will show deflection when a potential difference is developed across its ends.

Current sensitivity is directly proportional to the number of turns while voltage sensitivity is the ratio of the number of turns of the coil to the resistance.

The number of turns in the first coil, n₁ = 50

The number of turns in the second coil, n₂= 100

The current sensitivity:

\(\frac{CS_1}{CS_2}= \frac{50}{100}\)

C.S₁ = 0.5 C.S₂

The current sensitivity of the first coil is  0.5 times that of the second coil.

Given the resistance of the first coil = 10 ohm

The resistance of the second coil = 50 ohm

The voltage sensitivity of coils:

\(\frac{V.S_1}{V.S_2} =\frac{50/10}{100/50}\)

V.S₁ = 2.5 V.S₂

The voltage sensitivity of the first coil is 2.5 times that of the second coil.

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The resistance of wire W2 can be determined by using the formula for resistance, which depends on the resistivity, length, and cross-sectional area of the wire.

Since wire W1 and W2 are made from the same metal, their resistivity is the same. Considering the given length and cross-sectional area, the resistance of W2 is 8Ω.

The resistance of a wire can be calculated using the formula:

R = (ρ * l) / A

where R is the resistance, ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.

Since wire W1 and W2 are made from the same metal, they have the same resistivity, denoted as ρ. Therefore, the resistivity is constant for both wires.

For wire W2, the length is given as l2 and the cross-sectional area is 2A. Substituting these values into the resistance formula:

R2 = (ρ * l2) / (2A) = (1/2) * [(ρ * l2) / A]

Since we know the resistance of W1 is 16Ω, we can substitute this value into the resistance formula for W1:

16Ω = (ρ * l) / A

Simplifying, we have:

ρ * l = 16Ω * A

Substituting this into the expression for R2:

R2 = (1/2) * [(ρ * l2) / A] = (1/2) * [(16Ω * A) / A] = 8Ω

Therefore, the resistance of wire W2 is 8Ω.

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Explanation:

An isolated system cannot exchange any heat, work, or matter with the surroundings, while an open system can exchange energy and matter.

The rock was launched in the upward direction with an initial velocity of 8.58 m/s.The speed of the rock 4.5 seconds after launch is  35.52 m/s.

Given:

Time after launch (t) = 2.1 s

Rising rate (v) = 12 m/s

(a) By using the equation of motion v = u + at

where,

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

v = u + at

12= u + (9.8) × 2.1 s

u = 12 - (9.8 m/s² × 2.1 s)

u = 12 - 20.58

u = -8.58 m/s

The negative sign indicates that the rock was launched in the upward direction with an initial velocity of 8.58 m/s.

(b) To calculate the speed 4.5 seconds after launch,

v = u + at

v = -8.58 + (9.8) × 4.5 s

v = 35.52 m/s

The speed of the rock 4.5 seconds after launch is  35.52 m/s.

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To find the total distance traveled by the particle, we need to consider both the forward and backward movements. The distance traveled during the forward motion is given by the integral of the absolute value of the velocity function from t=0 to t=6. the total distance traveled by the particle from time t=0 to t=6 is 64 units.

Given that the velocity function is v(t) = 12t - 3t^2, we can calculate the total distance traveled as follows: ∫[0 to 6] |v(t)| dt. To determine the intervals where the particle moves forward or backward, we need to find the points where the velocity function changes sign. In this case, the velocity function changes sign at t=0 and t=4. At t=0, the particle starts moving, and at t=4, the particle changes direction. Now, let's calculate the total distance traveled: For t=0 to t=4 (forward motion): ∫[0 to 4] (12t - 3t^2) dt = [6t^2 - t^3] [0 to 4] = 6(4^2) - 4^3 = 96 - 64 = 32. For t=4 to t=6 (backward motion): ∫[4 to 6] -(12t - 3t^2) dt = [-6t^2 + t^3] [4 to 6] = -6(6^2) + 6^3 - (-6(4^2) + 4^3) = -216 + 216 + 96 - 64 = -32. The total distance traveled is the sum of the distances traveled in both directions: Total distance = |32| + |-32| = 32 + 32 = 64. Therefore, the total distance traveled by the particle from time t=0 to t=6 is 64 units.

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Answer:

A formula I am pretty sure

Answer: 19 meters.

Explanation:

We want to find the total displacement between t = 2s and t = 4s.

To do it, we can integrate our function, first write our velocity equation.

for t ≤ 3s, we have a linear equation, let's write it:

A linear relationship can be written as:

y = a*t + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Now we can see that our line passes through the points (1, 0) and (0, -2)

then the slope is:

a = (0 -(-2)/(1 - 0) = 2/1 = 2

and knowing that when t = 0s, v(0s) = -2m/s, then our equation is:

v(t) = (2m/s^2)*t - 2m/s for t ≤ 3s

now, for t ≥3s the equation is constant, v(t) = 4m/s.

then we have

v(t) = (2m/s^2)*t - 2m/s -------if t ≤ 3s

v(t) = 4m/s ----- if t ≥ 3s

Now we integrate over time to get the position:

for t ≤ 3s we have:

p(t) = (1/2)*(2m/s^2)*t^2 - 2m/s*t + C

where C is a constant of integration, as we are calculating the displacement  this constant actually does not matter, so we can use C = 0m

p(t) = (1m/s^2)*t^2 - 2m/s*t  for t ≤ 3s

and p(3s) =  (1m/s^2)*3s^2 - 2m/s*3s = 9m - 6m = 3m is the initial position of the other part of the function.

for t ≥ 3s we have:

p(t) = 4m/s*t + p(3s) = 4m/s*t + 3m

then the position equation is:

p(t) = (1m/s^2)*t^2 - 2m/s*t  ---- t ≤ 3s

p(t) = 4m/s*t + 3m --- if t ≥ 3s

Now the displacement will be:

p(4s) - p(2s) where for each time, you need to use the correct function:

p(4s) = 4m/s*4s + 3m = 16m + 3m = 19m

p(2s) =  (1m/s^2)*2s^2 - 2m/s*2s = 4m - 4m = 0m

p(4s) - p(2s) = 19m - 0m = 19m

The butterfly displacement x from t=2 to 4s is 19 meters.

The spacing between two specified points is represented by the one-dimensional quantity of displacement (symbolised as d or s), commonly known as length or distance.

The total displacement between t = 2s and t = 4s.

Integrate our function, the velocity equation.

for t ≤ 3s, we have a linear equation, let's write it:

A linear relationship can be written as:

y = a x t + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

The line passes through the points (1, 0) and (0, -2)

The slope is:

a = (0 -(-2)/(1 - 0) = 2/1 = 2

When t = 0s, v(0s) = -2m/s, then our equation is:

v(t) = (2m/s²) x t - 2m/s for t ≤ 3s

now, for t ≥3s the equation is constant, v(t) = 4m/s.

v(t) = (2m/s²) x t - 2m/s -------if t ≤ 3s

v(t) = 4m/s ----- if t ≥ 3s

Now we integrate over time to get the position:

for t ≤ 3s we have:

p(t) = (1/2) x (2m/s²) x t^2 - 2m/s x t + C

where C is a constant of integration, to calculate the displacement  this constant actually does not matter,

p(t) = (1m/s²)*t^2 - 2m/s x t  for t ≤ 3s

and p(3s) =  (1m/s^2) x 3s² - 2m/s x 3s = 9m - 6m = 3m is the initial position of the other part of the function.

for t ≥ 3s we have:

p(t) = 4m/s x t + p(3s) = 4m/s x t + 3m

then the position equation is:

p(t) = (1m/s^2) x t² - 2m/s x t  ---- t ≤ 3s

p(t) = 4m/s x t + 3m --- if t ≥ 3s

Now the displacement will be:

p(4s) - p(2s) where for each time, you need to use the correct function:

p(4s) = 4m/s x 4s + 3m = 16m + 3m = 19m

p(2s) =  (1m/s²) x 2s²- 2m/s x 2s = 4m - 4m = 0m

p(4s) - p(2s) = 19m - 0m = 19m

Thus, the displacement is 19 m.

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During the day, the Sun appears to move across the sky from Earth and disappears at night. As a result of the Earth's eastward rotation, this has occurred.

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Answer and Explanation:

Given that

v_f = 5 km/s = 5,000 m/s

d = 4 m

v_i = 0 m/s

The computation is shown below:

1. The acceleration in m/s is

Here we use the motio third equation which is

\(v_f^2 = v_i^2 + 2ad\)

5000^2 = 0^2 + 2 (a) (4)

So

\(a = 3.125 \times 10^{6} m/s^2\)

2. Now acceleration in g is

\(= \frac{3.125 \times 10^{6} m/s^2}{9.81}\)

\(= 3.18 \times 10^{5}g\)

3. The long of acceleration last is

\(t = \frac{v-u}{a}\)

\(= \frac{5000 - 0}{3.125 \times 10^{6}}\)

\(= 1.6 \times 10^{-3}s\)

4.As we can see that

\(3.18 \times 10^{5}\) is smaller than the \(4.5 \times 10^{5}g\)

So, it should not be ruled out

Answer:

I. 90%

II. 60 MW

Explanation:

From the question given above, the following data were obtained:

Power input = 600 MW

Power output = 540 MW

I. Determination of the efficiency.

Power input = 600 MW

Power output = 540 MW

Efficiency =?

Efficiency = output / input × 100

Efficiency = 540 / 600 × 100

Efficiency = 90%

II. Determination of the power wasted by the pump.

Power input = 600 MW

Power output = 540 MW

Power wasted =?

Power wasted = Power input – Power output

Power wasted = 600 – 540

Power wasted = 60 MW