An empty 2,500 kg train car is headed northbound at a velocity of 5 m/s. Ahead of the first car, an empty 1,500 kg car is headed northbound on the same track at 1 m/s. The faster train bumps into the slower one, and they combine into one train. What is the velocity of the two-car train? 1 m/s 3 m/s 3. 5 m/s 5 m/s.

Answers

Answer 1

The velocity of the two-car train is 3.5 m/s.

To solve the problem above, we use the law of conservation of momentum

Law of conservation of momentum: States that, for a closed system, the total momentum before collision is equal to the total momentum after collision.

⇒ Formula:

mu+m'u' = V(m+m')..................... Equation 1

⇒ Where:

m = mass of the faster trainm' = mass of the slower trainu = initial velocity of the faster trainu' = initial velocity of the slower trainV = common velocity of the two trains

⇒ make V the subject of the equation

V = (mu+m'u')/(m+m')....................... Equation 2

From the question,

⇒ Given:

m = 2500 kgm' = 1500 kgu = 5 m/su' = 1 m/s

⇒ Substitute these values into equation 2

V = [(2500×5)+(1500×1)]/(2500+1500)V = [12500+1500]/(4000)V = 14000/4000V = 3.5 m/s.

Hence, The velocity of the two-car train is 3.5 m/s

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Answer 2

Answer:

3.5

Explanation:


Related Questions

According to a scientific realist, scientific terms for unobservable phenomena like "atom" and "black hole" to entities that really exist. However, the scientific antirealist claims that scientific terms that refer to unobservable phenomena to something in reality.

Answers

It is important to note that the debate between scientific realism and antirealism is ongoing and complex, with various nuances and perspectives within each position. Different philosophers of science and scientists may hold different views on the nature of scientific terms and their relationship to reality.

According to a scientific realist perspective, scientific terms for unobservable phenomena such as "atom" and "black hole" are seen as referring to entities that truly exist in reality. Scientific realists believe that scientific theories and concepts accurately capture aspects of the world, including unobservable entities and phenomena. They argue that scientific theories provide the best explanation of the natural world and aim to describe the underlying structure and mechanisms of reality.

On the other hand, scientific antirealists hold a different view. They argue that scientific terms that refer to unobservable phenomena do not necessarily correspond to something that exists independently in reality. Antirealists often emphasize the instrumentalist view of science, which suggests that scientific theories are simply tools or frameworks that help us organize and predict observable phenomena, without making claims about the ultimate nature of reality.

Antirealists may argue that scientific theories are subject to revision and change over time as new evidence emerges, suggesting that the terms used to describe unobservable phenomena are not fixed and may not have a one-to-one correspondence with actual entities in reality. They may also highlight the role of social and cultural factors in shaping scientific knowledge, suggesting that scientific terms are influenced by human conventions and interpretations.

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A sheep is walking at 1.6 m/s. How long will it take to go 3600 m?

Answers

Answer:

2,250 seconds or 37.5 minutes

Explanation:

If a spinning object in a spacecraft orbiting the Earth is set in motion with a clockwise rotation by a mechanism in the spacecraft, what is the result?
The spacecraft begins spinning counterclockwise to conserve angular momentum.
The spacecraft begins spinning clockwise to conserve angular momentum.
The spacecraft remains stationary, since it is not touching the spinning object.
It depends on the orbital velocity of the spacecraft.

Answers

The spacecraft begins spinning counterclockwise to conserve angular momentum.

When a spacecraft is launched into space, it is subjected to various external forces that can cause it to change its position or velocity. To ensure that the spacecraft stays on course and maintains a stable orientation, it is often necessary to use conservation of angular momentum.

Angular momentum is a property of an object that is in motion and rotating around an axis. It is defined as the product of the object's moment of inertia and its angular velocity.

The moment of inertia is a measure of the object's resistance to rotational motion and depends on its mass distribution and shape.

When a spacecraft is launched into space, it has a certain amount of angular momentum, which is determined by its mass, shape, and initial velocity.

If the spacecraft were to change its orientation without any external forces acting upon it, its angular momentum would remain constant.

However, external forces, such as gravitational forces or the thrust of a rocket engine, can cause the spacecraft to change its orientation. To compensate for this, the spacecraft can spin counterclockwise, which increases its angular momentum in the opposite direction.

By spinning counterclockwise, the spacecraft's moment of inertia increases, which in turn increases its angular momentum. This helps to counteract any external forces that might cause the spacecraft to change its orientation, allowing it to maintain a stable position and trajectory.

Overall, the conservation of angular momentum is an important principle in spacecraft design and operation, as it helps to ensure that the spacecraft remains on course and performs its mission successfully.

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From this information, Jasmine concludes that "fertilizer b" is the best at increasing crop yields. Is Jasmine's conclusion scientifically valid? A. Yes, because "fertilizer b" increased her crop yield. B. No, because the different sections of her land were not equal in area. C. No, because the different sections of her land have different characteristics. D. No, because the crop yields were all equal.

Answers

Answer:

c

Explanation:

i just did this study island and the answer was wrong

A 2.50 cm tall object is 36.0 cmfrom a concave mirror withf 12.0 cm. Find the imageheight.=(Mind your minus signs.)(Unit = cm)

Answers

Answer: 1.25 cm

Explanation:

A 2.50 cm tall object is 36.0 cmfrom a concave mirror withf 12.0 cm. Find the imageheight.=(Mind your

A body on the surface of the earth weichs 400 Ib. The radius of the earth is about 4,000 miles. If this same body were placed on a 4,000 mile high tower, its weight would be a. 100 lbs b. 200 lbs c. 400 lbs d. 800 lbs e. 16,000 lbs

Answers

Option a is correct.

F=GMm/R²

where F is the gravitational force or weight

G is the universal constant of gravitation

M is the mass of Earth

m is the mass of the object

R is the distance between the center of the earth and the object

Given,

initial distance R =4000miles

weight at surface of the earth F=400lb

Let the force be F' for a distance R' from earth's center.

Here R' = radius+ height of the tower = R+4000 miles = 4000 + 4000 = 8000 miles.

Since the other terms in the formula remain constant, the new weight F' can be calculated as follows:

F'/F = R²/R'(otherwise the inverse square law in gravitation)

F'/400=(4000)²/(8000)²

F' = 100 lb

Thus option a is correct.

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Final answer:

The weight of the body on a 4000-mile high tower would still be 400 lbs.

Explanation:

The weight of an object depends on the gravitational acceleration at its location. On the surface of the Earth, the gravitational acceleration is approximately 32 ft/s2. Therefore, a 400 lb body on the Earth's surface would weigh 400 lbs. If the body were placed on a 4000-mile high tower, it would be much farther from the center of the Earth and experience a weaker gravitational pull. The weight of the body would decrease as the square of the ratio of the radii of the tower and the Earth. So, the weight on the tower would be:



Weight on the tower = (400 lb) * (4000 mi/4000 mi)2 = 400 lb * 1 = 400 lb

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1. A spring has a natural length of 22 cm. If a force of 15 N in is required to keep it stretched to a length of 32 cm, how much work is required to stretch it from 22 cm to 40 cm ? Round your answer to two decimal places. (A) 3.43 J (B) 1.93 J (C) 2.93 J (D) 3.93 J (E) 2.43 J

Answers

A spring has a natural length of 22 cm. If a force of 15 N in is required to keep it stretched to a length of 32 cm. The correct answer is not among the options provided. The closest option is (C) 2.93 J, but the correct answer is actually 2.70 J.

To calculate the work required to stretch the spring from 22 cm to 40 cm, we can use the formula for work done by a force:

Work = Force * Distance

In this case, the force required to stretch the spring from 22 cm to 32 cm is given as 15 N. This means that the force required to stretch it from 22 cm to 40 cm is the same because the force required to stretch a spring is directly proportional to the displacement from its natural length.

The distance covered is the difference in length between the initial and final positions, which is 40 cm - 22 cm = 18 cm.

Therefore, the work done is:

Work = Force * Distance

= 15 N * 18 cm

= 270 N·cm

To convert the work from centimeters to joules, we need to divide by 100, as 1 N·m = 1 J.

Work = 270 N·cm / 100

= 2.7 J

Rounding to two decimal places, the answer is 2.70 J.

Therefore, the correct answer is not among the options provided. The closest option is (C) 2.93 J, but the correct answer is actually 2.70 J.

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water freezing at a certain temperature is a nonspontaneous process if: select the correct answer below: δsuniv<0 δssurr<0 δsuniv>0 δssurr>0

Answers

Water freezing at a certain temperature is a nonspontaneous process if δsuniv > 0. The correct answer is: δsuniv > 0

For a process to be spontaneous, the change in the total entropy of the system and its surroundings (δsuniv) must be greater than zero. This means that the overall change in entropy, which includes both the system and its surroundings, is positive.

In the case of water freezing, the process is nonspontaneous because it requires a decrease in entropy (solid water has lower entropy than liquid water) and thus δsuniv is greater than zero.

The other options, δsuniv < 0, δssurr < 0, and δssurr > 0, are not applicable to water freezing as they would indicate spontaneous processes or incorrect conditions. Hence, δsuniv > 0 is the correct answer.

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Answer: (delta)Suniv<0

In a 30 year old man who has red-green color blindness, light having a wavelength of 530 nm is perceived as being green. This man ______.

Answers

In a 30 year old man who has red-green color blindness, light having a wavelength of 530 nm is perceived as being green. This man perceives that red light has a green color.

If you are colour blind, you see colours differently from the majority of people. Color blindness frequently makes it challenging to distinguish between particular hues. Color blindness typically runs in families. Specialized glasses and contact lenses can help, but there is no cure.

The only form that truly embodies the phrase "colour blind" is achromatopsia, sometimes known as "total colour blindness." Achromatopsia is a condition in which a person can only perceive the world in shades of grey, black, and white.

There are various varieties of colour blindness, and while it may happen on occasion, most colour blind persons are only partially able to "see" red, green, or blue light.

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If a wave has a speed of 47 m/s and a wavelength of 25 m, what is the frequency of the wave? Give your answer to 2 decimal places.

Answers

Answer:

The formula is:

v = f λ

Where,

v is the velocity or speed of the wave (in m/s)

f is the frequency of the wave (in Hz)

λ is the wavelength of the wave (in m)

We can rearrange this formula to solve for the frequency:

f = v / λ

We are given the speed and the wavelength of the wave, so we can plug them into the formula:

f = 47 m/s / 25 m

f = 1.88 Hz

To give the answer to 2 decimal places, we round it to:

f = 1.88 Hz

Therefore, the frequency of the wave is 1.88 Hz.

Explanation:

Answer:

1.88 Hz.

Explanation:

The frequency (f) of a wave is related to its speed (v) and wavelength (λ) by the equation f = v/λ.

So to find the frequency of a wave with a speed of 47 m/s and a wavelength of 25 m, we just need to substitute these values into the equation:

f = 47 m/s / 25 m

f = 1.88 Hz

Rounding to 2 decimal places, the frequency of the wave is 1.88 Hz.

Friction is a ____________ force
a. Artificial
b. Natural
c. Pessimistic
d. Negative

Answers

Answer:

natural is the answer

Friction is a natural force which exist

A 50g
block is attached to a
horizontal spring with spring
constant k = 3600 N/m
The spring is compressed by 5 cm,
as shown in the figure.

When the spring is released, will the
block be able to cross the top of the hill with
h =10m?

Answers

The spring can not cross the hill.

What is the elastic potential energy?

Elastic potential energy is the potential energy stored in an object when it is deformed, or stretched or compressed, by a force. When an elastic object is stretched or compressed, it has the potential to return to its original shape and size, and the work done to stretch or compress it is stored as elastic potential energy.

We know that;

E = 1/2Ke^2

E = 0.5 * 3600 * (5 * 10^-2)^2

E = 4.5 J

Now the GPE of the hill is;

mgh = 50 * 10^-3 * 10 * 9.8

= 4.9 J

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identify the gas that has a root mean square velocity of 412 m/s at 191 k.

Answers

The gas substance which is closest to the calculated molar mass is N₂, which has a molar mass of 28.02g/mol.

What is Root mean square velocity?

The root mean square velocity is the square root of the mean square of the velocity of an individual particle or the substance with a square root mean square velocity of about 412 m/s at 191 K.

Use the root mean square velocity equation with the given speed, the ideal gas constant (8.314 J/mol-K), and the temperature. Remember that Joules (J) is kg-m's².

μ = \(\sqrt{(3RT)/M\\}\)

412 m = \(\sqrt{(8.314J/mol.K)(191K)/ M}\)

M = 0.0281 kg/ mol

M = 28.1 g mol

Therefore, the gas substance which is closest to the calculated molar mass is N₂, which has a molar mass of 28.02g/mol.

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A&A Chp. 5, #3: Calculate the annual variation in solar
radiation arriving at the Earth in epihelion vs. perihelion if the
Earth's orbit is 3% eccentric. Provide your answer as a ratio of
Qper/Qep

Answers

The annual variation in solar radiation arriving at the Earth in perihelion is 1.028 times that in epihelion, when the Earth's orbit is 3% eccentric.

The annual variation in solar radiation arriving at the Earth in epihelion vs. perihelion if the Earth's orbit is 3% eccentric can be calculated as follows:

First, we need to find the value of Q for both epihelion and perihelion.

The formula for Q is given as:

Q = (1 - e²)/(1 + e cosθ)

where e is the eccentricity of the Earth's orbit and θ is the angle between the line connecting the Earth and the Sun and the line connecting the Earth and the perihelion (i.e., closest point to the Sun).

For epihelion (i.e., farthest point from the Sun), θ = 0°,

so Qep = (1 - 0.03²)/(1 + 0.03 cos 0°) = 0.986

For perihelion (i.e., closest point to the Sun), θ = 180°, so

Qper = (1 - 0.03²)/(1 + 0.03 cos 180°) = 1.014

Now, we can calculate the ratio of Qper/Qep as:

Qper/Qep = 1.014/0.986 = 1.028

Therefore, This ratio can also be expressed as a percentage:28% increase from epihelion to perihelion. So, the answer is 1.028.

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the first-order decomposition of n2o5 at 328 k has a rate constant of 1.70 × 10-3 s-1. if the initial concentration of n2o5 is 2.88 m, what is the concentration of n2o5 after 12.5 minutes?

Answers

First-order decomposition has rate constant of \(1.70 * 10^-3 s^-1\). We use the first-order rate law. Concentration N2O5 after 12.5 minutes is 1.21 M.

In Decomposition :

The first-order rate law is expressed as: rate = k[N2O5], where k : rate constant and [N2O5] is the concentration of N2O5.

To find the concentration of N2O5 after 12.5 minutes, we can use the following equation:

\([N2O5] = [N2O5]0 e^(-kt)\)

Where [N2O5]0 : initial concentration of N2O5, k : rate constant, and t: time in seconds. Convert time of 12.5 minutes to seconds, having 750 seconds.

[N2O5] = \(2.88 M * e^(-1.70*10^(-3) s^(-1) * 750 s)\)

[N2O5] = 1.21 M

Therefore, the concentration of N2O5 after 12.5 minutes is 1.21 M.

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Three wires meet at a junction. wire 1 has a current of 0.40 aa into the junction. the current of wire 2 is 0.73 aa out of the junction. what is the magnitude of the current in wire 3?

Answers

The magnitude of the current in wire 3 is (I₃)= 0.33A

How to calculate the value of the magnitude of the current in wire 3 ?

To calculate the magnitude of the current in wire 3 we are using the Kirchhoff’s current law,

I₁ + I₂ + I₃ = 0

Where we are given,

I₁ = current in wire 1

=0.40 A.

I₂ = current in wire 2

= -0.73 A.

We have to calculate the magnitude of the current in wire 3, I₃

Now we put the known values in above equation, we get,

I₁ + I₂ + I₃ = 0

Or, I₃ = -.(I₁ + I₂)

Or, I₃ = -.(0.40 - 0.73)

Or, I₃ = 0.33 A

From the above calculation, we can conclude that the current in wire 3 is  I₃ = 0.33 A

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The diameter of the moon is 3. 47x10^6 m and it subtends an angle of 0. 00904 rad when viewed from the surface of the earth. How far is the moon from earth? (please show all work in legible handwriting and explain step by step. Very confused. Thank you)

Answers

The diameter of the moon is 3. 47x\(10^{6}\) m and it subtends an angle of 0. 00904 rad when viewed from the surface of the earth, the distance to the moon from the surface of the earth is approximately 3.83 × \(10^{8}\) meters.

We can use the small angle formula to relate the angle subtended by an object, the distance to the object, and its size

Angle = size / distance

Here, we know the size of the moon (its diameter), and the angle it subtends when viewed from the surface of the earth. We can use this formula to solve for the distance to the moon

Distance = size / angle

Substituting the values given, we get

Distance = 3. 47x\(10^{6}\) m / 0.00904 rad

Evaluating this expression, we get

Distance = 3.83 × \(10^{8}\) m

Therefore, the distance to the moon from the surface of the earth is approximately 3.83 × \(10^{8}\) meters.

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Greta took an IQ test and scored high in knowledge and vocabulary. Which of the following statements BEST describes Greta’s results?

Answers

Answer:

Greta scored high in knowledge and vocabulary on the IQ test.

Explanation:

This statement highlights Greta's strengths in knowledge and vocabulary specifically, indicating that she performed well in these areas during the test. However, it does not provide information about her overall IQ score or her performance in other cognitive domains that may have been assessed in th

Edwin Hubble proposed that the universe is expanding. How did he support his assertion

Answers

Answer: i think Hubble's Law basically states that the greater the distance of a galaxy from ours, the faster it recedes

Explanation:

a sheet of metal is 2mm wide 10cm tall and 15cm long. it was 4g. what is the density?

Answers

Answer:

Ro = 133 [kg/m³]

Explanation:

In order to solve this problem, we must apply the definition of density, which is defined as the relationship between mass and volume.

\(Ro = m/V\)

where:

m = mass [kg]

V = volume [m³]

We will convert the units of length to meters and the mass to kilograms.

L = 15 [cm] = 0.15 [m]

t = 2 [mm] = 0.002 [m]

w = 10 [cm] = 0.1 [m]

Now we can find the volume.

\(V = 0.15*0.002*0.1\\V = 0.00003 [m^{3} ]\)

And the mass m = 4 [gramm] = 0.004 [kg]

\(Ro = 0.004/0.00003\\Ro = 133 [kg/m^{3}]\)

the electric charge remains at rest in a. static electricity, b. current electricity, c. none of these​

Answers

Answer:

Option (a) is correct.

Explanation:

The electric charge is the inherent property of matter which appears due to the deficiency of charge or the excess number of electrons.

There are two types of charges, positive and negative.

When an object has deficiency of charge it becomes positive charge and when it gains some electrons, it becomes negative charge.

When the charge is in motion, it is called electric current and when the charge is at rest, it is called static current.

A charge at rest contributes the electric field only while the charge is in motion contributes the electric and magnetic field both.

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Hhhhhhhhhhhhhhhhhhhhjj

Answers

Answer:

grrr I don't know either grrr

describe the reflection of the pulse from a fixed point

Answers

When a pulse encounters a fixed point, such as a wall or a rigid boundary, it undergoes reflection. Reflection occurs when the pulse bounces back upon reaching the fixed point.

During reflection, the pulse experiences a change in direction but retains its original shape and properties. The incident pulse approaches the fixed point and interacts with it. As a result, an equal and opposite pulse is generated and travels back in the opposite direction.

The behavior of the reflected pulse depends on the nature of the incident pulse and the properties of the medium it travels through. If the pulse is inverted (upside-down) before reflection, the reflected pulse will also be inverted. Similarly, if the incident pulse is right-side-up, the reflected pulse will maintain the same orientation.

The reflection process follows the law of reflection, which states that the angle of incidence (the angle between the incident pulse and the normal to the fixed point) is equal to the angle of reflection (the angle between the reflected pulse and the normal). This law ensures that energy and momentum are conserved during the reflection process.

In conclusion, when a pulse encounters a fixed point, it undergoes reflection, resulting in the generation of an equal and opposite pulse traveling in the opposite direction. The reflected pulse retains the same shape and properties as the incident pulse, following the law of reflection.

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if r 50,l 1.5 what value of c will make an rlc series circuit:(a) overdamped,(b) critically damped, (c) underdamped?

Answers

(a) Overdamped: C = 0.022 nF

(b) Critically damped: C = 0.029 nF

(c) Underdamped: C = 0.035 nF

The damping ratio (ζ) of an RLC series circuit depends on the values of resistance (R), inductance (L), and capacitance (C) components. The damping ratio determines the behavior of the circuit response, whether overdamped, critically damped, or underdamped.

For an RLC series circuit to be overdamped, the damping ratio must be greater than 1. The formula for the damping ratio is:

ζ = R / (2√(L/C))

For an RLC circuit to be critically damped, the damping ratio must equal 1. For an underdamped RLC circuit, the damping ratio must be less than 1.

Given:

R = 50 ohms

L = 1.5 H

(a) For overdamping:

ζ > 1

\(C = 1 / [(50/(2*sqrt(1.5*C)))^2]\)

C ≈ 0.022 nF

(b) For critical damping:

ζ = 1

\(C = 1 / [(50/(2*sqrt(1.5*C)))^2]\)

C ≈ 0.029 nF

(c) For underdamping:

ζ < 1

\(C = 1 / [(50/(2*sqrt(1.5*C)))^2]\)

C ≈ 0.035 nF

Therefore, the capacitance values for the RLC series circuit to be overdamped, critically damped, and underdamped are 0.022 nF, 0.029 nF, and 0.035 nF, respectively.

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The distance between a charge and the source of an electric field changes from 3 mm to 6 mm.

As a result of the change, the electric potential energy of the charge is ______.

A. divided by 6
B. divided by 2
C. multiplied by 2
D. multiplied by 6

Answers

Answer:

c

Explanation:

The electric potential energy of the charge is divided by 2.

To find the electric potential energy, the values given from the source of an electric field changes from 3 mm to 6 mm.

What is electric potential energy?

            The electric potential energy is the energy that is needed to move a charge against the electric field.

The energy can be calculated as Work and these energy can be calculated as a whole not only the charges.

Formula for electric potential energy,

         U = KQ²/r

where,

K is the constant, k =  9 × 10⁹

Substituting the values of q as the charges and then the distance can be,

U = KQ² / 3   and U = KQ² / 6

So that, the values can be divided by 2.

The unit of electric potential energy is Joule.

The distance can be from r to ∞.

Hence, Option B is the correct answer.

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How do you determine how much kinetic energy an object has
A: by finding mass and speed
B: by finding height and width
C: by finding its position and form
D: by finding its speed and direction

Answers

I believe the answer is a. Because the formula of kinetic energy is 1/2(m)•(v^2)

Answer:

the answer is a

hope it helps

help help hep help???????????

help help hep help???????????

Answers

Momentum

mava + mbvb = mava '+ mbvb'

(300 x 10)+(150 x 0) = (300 x 4.12)+(150 x vb')

3000=1236+150vb'

1764 = 150vb'

vb'=+11.76 m/s ≈ +11.8 m/s (positive sign, to the right)

If the coefficient of kinetic friction between the object and the incline is 0.200, what minimum power does the winch need to pull the object up the incline at 4.00 m/s

Answers

The winch needs a minimum power of 320 Watts to pull the object up the incline at 4.00 m/s. To determine the minimum power required by the winch, we need to consider the work done against friction and the time it takes to move the object.

The power (P) can be calculated using the formula:

P = work / time

The work done against friction can be calculated using the formula:

work = force * distance

The force of friction (F) can be determined by multiplying the coefficient of kinetic friction (μ) with the normal force (N). The normal force can be calculated by multiplying the mass of the object (m) with the acceleration due to gravity (g).

force of friction (F) = μ * N

force of friction (F) = μ * m * g

The distance traveled by the object can be determined using the formula:

distance = speed * time

Now, let's calculate the power:

First, we need to calculate the force of friction (F):

F = μ * m * g

Given that the coefficient of kinetic friction (μ) is 0.200, the mass of the object (m) is not provided, and the acceleration due to gravity (g) is approximately 9.8 m/s².

Next, we need to calculate the distance traveled by the object. It is not provided in the question, so we cannot proceed with the calculation of power without this information.

Without knowing the distance traveled by the object, we cannot calculate the minimum power required by the winch to pull the object up the incline at 4.00 m/s.

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kepler's third law for objects in the earth's orbit is given by the following equation, where t is the period of the satellite, g the universal gravitational constant, me the mass of the earth, and r the radius of the satellite's orbit that we found above. t2

Answers

Kepler's Third Law for objects in Earth's orbit can be expressed using the equation T^2 = 4π^2R^3 / (GM_E), where T is the period of the satellite, G is the universal gravitational constant, M_E is the mass of the Earth, and R is the radius of the satellite's orbit.

Kepler's third law states that the square of the period of an object in orbit around a central body is proportional to the cube of the semi-major axis of its orbit. In the case of a satellite in Earth's orbit, the equation is given by t^2 = (4π^2/ GM) × r^3, where G is the universal gravitational constant, M is the mass of the central body (in this case, the Earth), and r is the radius of the satellite's orbit. This law allows us to calculate the period of the satellite's orbit based on its distance from the Earth, and vice versa. It also tells us that objects farther from the Earth will take longer to complete one orbit than those closer to it. Kepler's laws of planetary motion revolutionized our understanding of the solar system and helped lay the foundation for modern astronomy.

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Water flows in through a horizontal pipe of cross - sectional area 100cm^2. At the outlet section, the cross- sectional area is 5 cm^2. If the velocity of water at the larger cross-section is 1.25 m/s.

Answers

The velocity of water at the smaller cross-section is 25 m/s.

Area of larger cross section, A₁ = 100 cm²

Area of larger cross section, A₂ = 5 cm²

Velocity of water at larger section, v₁ = 1.25 m/s

According to equation of continuity,

A₁v₁ = A₂v₂

Therefore, the velocity of water at the smaller cross-section,

v₂ = A₁v₁/A₂

v₂ = 100 x 1.25/5

v₂ = 25 m/s

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