Explain why the mean and standard deviation are not appropriate for particle size distributions

Solution:

Ms = 1.99 × 1030 kg− mass of Sun;

Me = 5.98 × 1024kg− mass of Earth;

Mm = 7.35 × 1022kg − mass of Moon;

rSM = 1.50 × 1011m − distance to the Moon from the Sun;

rEM = 3.85 × 108m − distance to the Moon from the Earth;

The gravitational force that acts on the Moon by the Earth (Law of Gravity):

[tex]F_{e} = G \frac {M_{e} * M_{m} } {r^{2}_{EM}} = 6.67 x 10^{-11} N * (\frac {m} {kg})^{2}*\frac {5.98 * 10^{24} kg * 7.35 * 10^{22} kg} {(3.85 x 10^{8}m)^{2}} = 1.98 * 10^{20} N[/tex]

The gravitational force that acts on the Moon by the Sun (Law of Gravity):

[tex]F_{S} = G \frac {M_{s} * M_{m} } {r^{2}_{EM}} = 6.67 x 10^{-11} N * (\frac {m} {kg})^{2}*\frac {1.99 * 10^{30} kg * 7.35 * 10^{22} kg} {(1.50 x 10^{11}m)^{2}} = 4.34 * 10^{20} N[/tex]

Net gravitational force on the moon:

[tex]F = F_{e} + F_{s} [/tex]

Pythagorean theorem for a right triangle ABC:

[tex]F = \sqrt {F^{2}_{S} + F^{2}_{e}} = \sqrt {(1.98 * 10^{20}N)^{2} + (4.34 * 10^{20} N)^{2}} = 4.77 * 10^{20}N[/tex]

Answer: Answer: magnitude of the net gravitational force on the moon is 4.77 × [tex]10^{20} [/tex]N.

The net gravitational force on the moon due to the earth and sun can be calculated using Newton's Law of Universal Gravitation. We apply this law to both the earth-moon and sun-moon systems, and the net force is the vector sum of these two forces.

The net gravitational force exerted on the moon by the sun and the earth can be calculated using Newton's law of gravitation, which states that the force between two objects is proportional to the product of their masses divided by the square of the distance between them. We use this law twice: once for the earth-moon system and once for the sun-moon system.

For the Earth-Moon system: F_EM = (G * mass of earth * mass of moon) / (distance from earth to moon)². Given the values in the problem, this amounts to F_EM = (6.67 * 10⁻¹¹ N.m²/kg² * 5.98 * 10²⁴ kg * 7.35 * 10²² kg) / (3.85 * 10⁸ m)².

For the Sun-Moon system: F_SM = (G * mass of sun * mass of moon) / (distance from sun to moon)². Again, substituting the given values we have F_SM = (6.67 * 10⁻¹¹ N.m²/kg² * 1.99 * 10³⁰ kg * 7.35 * 10²² kg) / (1.5 * 10¹¹ m)².

The net gravitational force on the moon is given by the vector sum of these two forces, which form a right angle, due to the geometry of the situation. Hence, the net force is the hypotenuse of a right triangle with sides F_EM and F_SM, and can be calculated using Pythagoras' Theorem: Net Force = √(F_EM² + F_SM²).

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The power used to mow the lawn, with a force of 110 N applied to move the lawnmower at 0.80 m/s, is calculated using the formula P = F × v and results in 88 Watts.

To calculate the power used to mow the lawn, we use the formula for power, which is the rate of doing work. Power (P) is equal to the work done (W) divided by the time taken (t), or P = W/t. In this case, work done can also be described as the force applied (F) times the distance moved (d) in the direction of the force, but since the problem doesn't provide the distance and only provides the speed at which the lawnmower is moving, we can use another formula for power: P = F × v where v is velocity.

Given that the force (F) is 110 N and the velocity (v) is 0.80 m/s, we can find the power with P = 110 N × 0.80 m/s giving us:

P = 88 Watts.

This is the power used by the person to mow the lawn while applying a constant horizontal force to move the lawnmower at a constant speed.

We must remember that the total net force equation at constant velocity is:

F – Ff = 0

of

F - µN = 0

An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. The magnetic field disappears when the current is turned off. Electromagnets usually consist of insulated wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in the hole in the center of the coil. The wire turns are often wound around a magnetic core made from a ferromagnetic or ferrimagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet.

The main advantage of an electromagnet over a permanent magnet is that the magnetic field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a continuous supply of current to maintain the magnetic field.

Electromagnets are widely used as components of other electrical devices, such as motors, generators, relays, loudspeakers, hard disks, MRI machines, scientific instruments, and magnetic separation equipment. Electromagnets are also employed in industry for picking up and moving heavy iron objects such as scrap iron and steel.[2]

Electromagnets are temporary magnets powered by electric current with versatile applications in different fields.

**An electromagnet** is a piece of wire that generates a magnetic field when an electric current passes through it. Unlike permanent magnets, **electromagnets** can be turned on and off by controlling the flow of electricity. They are widely used in various applications such as electric motors, generators, MRI machines, and even in scrapyard cranes.

Answer : The distance of the image from the lens is, -42 cm

The height of the image is, 35 cm

Solution :

First we have to calculate the image distance.

Formula used :

[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]

where,

f = focal length = 7 cm

p = object distance = 6 cm

q = image distance = ?

Now put all the given values in the above formula, we get the distance of the image from the lens.

[tex]\frac{1}{7cm}=\frac{1}{6cm}+\frac{1}{q}[/tex]

[tex]q=-42cm[/tex]

Therefore, the distance of the image from the lens is, 42 cm and the negative sign indicates that the image is virtual.

Now we have to calculate the height of the image.

Formula used :

[tex]\frac{h}{h'}=\frac{p}{q}[/tex]

where,

h = height of object = 5 cm

h' = height of image = ?

Now put all the given values in this formula, we get the height of the image.

[tex]\frac{5cm}{h'}=\frac{6cm}{-42cm}=-35cm[/tex]

Therefore, the height of the image is, 35 cm and the negative sign indicates that the image is inverted.

A. The distance of the image from the lens is –42 cm.

B. The height of the image is 35 cm

The image distance is defined as the distance of the image from the lens. Thus, it can be obtained as follow:

1/v = 1/u – 1/f (convex lens

v = (uf) / (u –f)

v = (6 × 7) / (6 – 7)

v = 42 / – 1

v = –42 cm

The height of the image is the height of the image as displayed by the lens. It can be obtained as follow:

v / u = Hᵢ / Hₒ

–42 / 6 = Hᵢ / 5

–7 = Hᵢ / 5

Cross multiply

Hᵢ = –7 × 5

Hᵢ = –35 cm

NOTE: The negative sign indicates that the image is a virtual image.

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The statement “When you jump start a vehicle, if the stalled vehicle started, then you remove the cables in the same order in which they were connected”, is false.

Go through these steps before you even connect the cables:

1.     Both batteries should have the same polarity and same voltage.

2.     Never let the vehicles touch each other and your cars should be near enough to connect the cables.

3.     Turn off the lights, accessories, and ignition switch in both cars. Put the vehicles in neutral mode and make sure the parking brake is set. Also wear safety glasses.

4.     Never smoke. An explosion is possible if sparks and ear a battery.

5.     Don’t try to it the battery if the weak battery is frozen because it can explode.

6.     Be sure to be able to identify the positive and negative terminals of both batteries. You need to have enough room to clamp to the cable terminals.

In a ray diagram, the three rays usually originate from the same point on the object. Following predefined ray-tracing rules, these rays pass through or reflect off a lens or mirror, converging or diverging to form an image. The point where these rays intersect represents the location of the image.

In a ray diagram, the three rays typically start from the same point on the object. This point on the object is the source from which the rays emanate. As the rays travel towards the lens or mirror involved, they will follow particular paths based on a set of simple ray-tracing rules. For example, one ray might pass through the focal point on its way to the lens and exit the lens parallel to the optical axis. These rays will then converge or diverge to form an image, depending on the lens or mirror set-up.

It is important to note that although three rays are often drawn for clarity and verification, only two are necessary to locate a point in the image. The point at which these rays intersect on the other side of the lens or mirror is where the image of the point from which they originated is located. Following these ray-tracing rules correctly will provide an accurate representation of how light behaves in the given optical system, illustrating the fundamental principles of geometric optics.

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Final answer:

The period of oscillation of a mass on a spring is the same on both Earth and the Moon, as it is independent of gravity.

Explanation:

The question asks where the period of oscillation of a mass on a spring is the greatest, either on Earth or on the Moon. The period of a spring-mass system, according to the formula T = 2π√(m/k), where T is the period, m is the mass, k is the spring constant, and π (pi) is approximately 3.14159, is independent of gravity. Hence, the gravitational differences between the Earth and the Moon do not affect the period directly. However, external forces like gravity can influence the amplitude of the oscillation, not the period itself. Therefore, the period of oscillation will be the same on both the Earth and the Moon, assuming no other factors are changed.

Answer:

B on EDGE2k21

Explanation:

trust me bih

The ship that will speed up faster if they fire their rockets at the same time is; The one with the lower mass

We are told that;

There are two spaceships

Each spaceship has different masses

Each spaceship has rocket engines of identical force.

We know that formula for force is;

F = ma

Thus, if force is constant, the higher the mass, the lesser the acceleration and also the lesser the speed. Thus, the lower the mass the faster the speed.

This means the spaceship that will speed up faster will be the one with lesser mass.

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The speed of the meteoroid is calculated by using the Pythagorean theorem and considering its horizontal and vertical speeds as vectors. Plugging in the given values, the meteoroid's speed is approx 21.72 km/s.

To calculate the speed of the meteoroid, we can use the concept of vectors and Pythagorean theorem. The meteoroid has a horizontal speed (eastward movement) and a vertical speed (downward movement). The total speed is the magnitude of the resultant vector. This can be calculated using Pythagorean theorem as follows:

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Speed = sqrt[(Horizontal speed)^2 + (Vertical speed)^2]

Plugging in the given values:

Speed = sqrt[(18.3 km/s)^2 + (11.5 km/s)^2]

After calculating, we found that the speed is approx 21.72 km/s.

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If air resistance can be neglected, the acceleration will be the same for both the thrown ball and dropped ball which is 9.8 m/s² as only gravity is working on it.

Air resistance can be defined as a force that is caused by air. The air strikes the front of an object, leading to decelerating its motion. The lesser the face area of a body, the lesser air striking the body, and the lesser the overall air resistance.

Air resistance opposes motion that occurs between air and another object. The object can exploit as it passes through the air because of air resistance. Gravity and air resistance are the only two forces of nature that shift on anything on Earth.

Air resistance force exerts in the opposite direction to an object moving in the air. Air resistance is a frictional force so the faster the body’s motion, the more will be air resistance.

In the absence of air resistance, only force due to gravity will act on an object and the gravitational acceleration will be the same for both upward and downward directions.

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Answer:

velocity = 0.5 m/s Towards South

Explanation:

As we know that velocity is the ratio of displacement and time

so here it is given that object displaced by total displacement of d = 30 m

also we know that time taken is 60 seconds

now we know the formula as

[tex]v = \frac{displacement}{time}[/tex]

now plug in the values in it

[tex]v = \frac{30}{60}[/tex]

[tex]v = 0.5 m/s[/tex] Towards South

So the average velocity must be 0.5 m/s Towards South

16.6 is the answer. Not 17.0 do not round.

The electric field strength at a distance 2d from a charge Q is one-fourth the electric field strength at a distance d, due to the inverse square nature of the electric field with respect to distance.

The question pertains to the concept of the electric field created by point charges in physics. To determine the electric field strength E at a distance d and at a distance 2d from a charge Q, we use Coulomb's law, which relates the electric field E to the charge Q and the distance r from the charge as E = kQ/r², where k is Coulomb's constant (approximately 8.99 × 10⁹ Nm²/C²).

For the charge Q generating a field strength E at a distance d, the electric field at distance d is simply E. However, at a distance 2d, since the distance from the charge is doubled, the electric field strength is reduced by a factor of four (since it's inversely proportional to the square of the distance). Therefore, the electric field strength at 2d is E/4.

Example Calculation: If the original distance is 2.00 × 10⁻² m and charge is 5.00 × 10⁻¹ C, the electric field at distance d can be calculated using the formula provided. If E is known initially at distance d, to find the field at 2d, simply divide that E by 4.

Final answer:

The electric field strength at a distance 2d from a charge Q is one-fourth the electric field strength at a distance d, according to the equation E = kQ/r², where E is electric field strength, k is Coulomb's constant, Q is the charge, and r is the distance.

Explanation:

The question deals with determining the electric field strength at distances d and 2d from a charge Q. The electric field strength created by a point charge is given by the equation E = kQ/r², where k is Coulomb's constant, Q is the charge, and r is the distance from the charge.

At a distance d, the electric field strength is E. To find the electric field strength at 2d, we simply plug in the new distance into the equation, which results in E = kQ/(2d)². Because 2d is simply twice the original distance, the denominator becomes four times as large, resulting in an electric field strength at 2d that is ¼ of what it was at d. Therefore, the electric field strength at 2d will be E/4.

Answer:

Explanation:

Torque is defined as the product of force and the perpendicular distance.

If we take a screw driver of small length then we need to apply a large force to open or tighten the screw.

If a screw driver of long arm, then we need to apply small force to open or tighten the screw.

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