1.) 450 cm =____m

2.) 24 miles =____cm

3.) 16.7 gallons =____liters

The net forces on the box acting perpendicular and parallel to the floor are

∑ F[perp] = F[normal] - 325 N + (475 N) sin(-35°) = 0

∑ F[perp] = (475 N) cos(-35°) - F[friction] = ma

where m is the mass of the box and a is its acceleration.

Solve for F[normal] :

F[normal] = 325 N + (475 N) sin(35°) ≈ 597 N

Then the frictional force has magnitude

F[friction] = 0.55 F[normal] ≈ 329 N

and so

60.5 N ≈ (325 N) a/g

(note that sin(-35°) = -sin(35°), cos(-35°) = cos(35°), and mg = 325 N so m = (325 N)/g)

Solve for a :

a = (60.5 N) / (325 N) g ≈ 1.82 m/s²

(a) Assuming this acceleration is constant, starting from rest, the box achieves a final velocity v such that

v² = 2a∆x

v² = 2 (1.82 m/s²) (5.80 m)

⇒   v ≈ 4.60 m/s

which happens in time t such that

v = at

4.60 m/s = (1.82 m/s²) t

⇒   t ≈ 0.177 s

(b) Let µ be the coefficient of static friction. The box just begins to slide if the magnitude of the parallel component of the applied force matches the magnitude of friction, i.e.

∑ F[para] = (475 N) cos(-35°) - F[friction] = 0

We have

F[friction] = µ F[normal] = (597 N) µ

so that

(597 N) µ = (475 N) cos(35°)

⇒   µ ≈ 0.651

The medium for an ocean wave is the ocean water which involves movement on the water body.

This is defined as a substance or material that carries the wave. In the case of ocean waves, the medium is referred to the ocean water.

The medium is not transferred when a water wave moves on a lake as energy is transported but the water molecules aren't which is why lakes have water present in them.

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(a) The magnitude of the average force acting on the car to bring it to rest is 120,000 N.

(b) The horizontal (vx) and vertical (vy) components of this velocity is 9.66 m/s and 2.59 m/s respectively.

The magnitude of the force acting on the car is calculated as follows;

F = mv / t

where;

F = ( 1200 kg x 10 m/s ) / ( 0.1 s )

F = 120,000 N

The horizontal and vertical component of the velocity of the car is calculated as follows;

Vx = V cosθ

Vy = V sinθ

where;

Vx = 10 m/s  x  cos (15) = 9.66 m/s

Vy = 10 m/s x sin (15) = 2.59 m/s

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The position of the image relative to the mirror v = 20cm, position of the image behind the mirror.

Since object is always placed in front of the mirror

Hence, object distance will be negative

Object distance (u) = - 100cm

Focus of a convex mirror is behind the mirror

Hence focal length will be positive

Focal length (f)= + 25cm

Find position of the image

Let the image distance = v

Using formula,

\(\frac{1}{v}\) +\(\frac{1}{u}\) = \(\frac{1}{f}\)

\(\frac{1}{v}\) = \(\frac{1}{f} - \frac{1}{u}\)

\(\frac{1}{v} = \frac{1}{25} - \frac{1}{-100}\)

\(\frac{1}{v} = \frac{1}{25} + \frac{1}{100}\)

\(\frac{1}{v} = \frac{4 + 1}{100}\)

\(\frac{1}{v} = \frac{5}{100}\)

v = \(\frac{100}{5}\)

v = 20cm

Since v is positive

Hence, image is 20cm behind the mirror

Nature of image is Virtual and erect.

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Answer:

4.  wavelength (λ)

5.  slit distance (d)

Explanation:

I assume you did a double-slit experiment?  If so, then:

The number of bands observed on the screen depends on the wavelength (λ) and the slit distance (d), while the screen distance (L) does not directly affect the number of bands.

Wavelength (λ): The number of bands is directly proportional to the wavelength. When the wavelength increases, the fringe separation on the screen increases, resulting in a greater number of bands.

Slit distance (d): The number of bands is inversely proportional to the slit spacing (distance). When the slit spacing increases, the fringe separation on the screen decreases, resulting in a smaller number of bands.

Screen distance (L): The screen distance does not directly affect the number of bands. It primarily affects the size and overall pattern of the interference fringes but does not change the number of bands.

Summary:

Wavelength (λ) is directly proportional to the number of bands.

Slit distance (d) is inversely proportional to the number of bands.

Screen distance (L) does not directly affect the number of bands.

A. The frequency of the motion is 0.0078 Hz. B. the amplitude of the motion is 7.90 m. and C. the total mechanical energy of the motion is 14.56 J.

Frequency is a measurement of how often something occurs over a period of time. It is typically measured in hertz (Hz) or cycles per second.

a) The frequency of the motion can be calculated using the equation:
frequency = 1 / (2π * √(k/m))
where k is the spring constant, and m is the mass of the block.
Substituting in the given values, we get:
frequency = 1 / (2π * √(1980 N/m / 4.70 kg))
= 1 / (2π * √(420.42 N/kg))
= 1 / (2π * 20.52 N/kg)
= 1 / (127.71 N/kg)
= 0.0078 Hz
Therefore, the frequency of the motion is 0.0078 Hz.

b) The amplitude of the motion can be calculated using the equation:
amplitude = (2π * √(k/m)) * x
where x is the displacement from equilibrium, k is the spring constant, and m is the mass of the block.
Substituting in the given values, we get:
amplitude = (2π * √(1980 N/m / 4.70 kg)) * 0.062 m
= (2π * 20.52 N/kg) * 0.062 m
= 127.71 N/kg * 0.062 m
= 7.90 m
Therefore, the amplitude of the motion is 7.90 m.

c) The total mechanical energy of the motion can be calculated using the equation:
E = ½ mv² + ½ kx²
where m is the mass of the block, v is the initial velocity, k is the spring constant, and x is the displacement from equilibrium.
Substituting in the given values, we get:
E = ½ (4.70 kg) (1.80 m/s)² + ½ (1980 N/m) (0.062 m)²
= 8.39 J + 6.17 J
= 14.56 J
Therefore, the total mechanical energy of the motion is 14.56 J.

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The interaction of an attracting or repulsive force between two charged bodies is referred to as an electric force.

This force is comparable to other forces in that it strikes and affects a specific item, and it is simple to illustrate using Newton's law of motion. One of the forces acting on other bodies is the electric force.

Electric force is the interaction of any two charged bodies that is either repellant or attracting. Similar to any force, Newton's laws of motion describe how it affects the target body and how it does so. The list of additional forces that apply to objects includes the electric force.

The electrostatic force between the two electrons is one of repulsion since electrons are negatively charged and items with like charges repel one another.

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Answer:

No, they don't have the same velocity

Explanation:

Given that one person pushes the car 2 m/s east, and the other pushes the car 1.5 m/s east.

As velocity is a vector quantity, so, to have equal velocity, both magnitude as well as the direction must be equal.

For the first person:

Magnitute of the velocity = 2 m/s.

The direction of the velocity: Towards east.

For the second person:

Magnitute of the velocity = 1.5 m/s.

The direction of the velocity: Towards east.

As both the person have the same direction but the different magnitude of the velocity, so, they don't have the same velocity.

The Romans could have made the statue out of lodestone, or placed a core of lodestone inside. Then the frame of the statue would have had to be made of iron in order to have equal net forces around the statue.

Lodestones led to a magnetic compass.

Lodestone is a form of magnetite that exhibits distinctive magnetic qualities. This quality led to the use of lodestones as an early form of compass, as they could be used to show the way north.

As is often the case with scientific phenomena that are difficult to explain, gemstones have historically been associated with magical or alchemical events, and many people who practice magic use gemstones in their work. Magnets and objects with magnetic qualities continue to be popular in alternative medicine and magical practices.

Magnetite is a form of iron oxide. When a rock has a certain crystal structure and chemical composition, it has the potential to become a magnet. If a stone is magnetized, it will be attracted to the earth's magnetic poles, and when it is suspended in the air, it will slowly point towards the poles. It will also attract iron, as observed by the Chinese in the fourth century AD.

Seafarers used lodestones in their navigation; the Chinese seem to have been the first to discover the properties of magnetite in a navigational context.

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Acceleration will increase as the angle of incline does, and as a result, force will as well.

The gravitational force acting on the cart increases as the slope of the incline increases, causing it to accelerate more quickly.The ramp's steepness will cause an increase in inclination. As a result, the acceleration increases as the inclination angle increases. This acceleration causes the object to descend with greater speed.

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As the possible origin for the Kuiper belt is believed to be from the remnants of the early solar system, specifically the outer regions where gas giants like Jupiter and Saturn formed.

These planets grew, they gravitationally scattered smaller objects like comets and asteroids outward towards the Kuiper belt, where they eventually settled into orbit.

A possible origin for the Kuiper belt is that it formed from the remnants of the solar nebula, the cloud of gas and dust from which our solar system originated. These leftover materials coalesced into a vast collection of icy bodies beyond Neptune's orbit, creating the Kuiper belt.

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Sound travels at approximately 343 meters (or 1,125 feet) per second in dry air at room temperature.

To determine how far away lightning is when thunder sounds 10 seconds after the lightning flash, we can use the speed of sound.

Distance = Speed × Time

Distance = 343 m/s × 10 s

Distance = 3,430 meters

Therefore, if thunder sounds 10 seconds after the lightning flash, the lightning is approximately 3,430 meters (or 3.43 kilometers) away.

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Answer:

Sound waves are examples of A. or longitudinal waves

Horse latitudes and doldrums are the two global wind currents that rise or sink slowly. Winds are created by the earth's rotation, convection, and atmospheric pressure differences.

There are three main global wind currents in the earth's atmosphere, the polar easterlies, the mid-latitude westerlies, and the trade winds that blow from the east in the tropics.These winds are created by the differences in atmospheric pressure between the equator and the poles and the earth's rotation. They are responsible for weather changes around the globe, including tropical storms, hurricanes, and tornadoes.The horse latitudes are two belts of dry and calm air around 30 degrees north and south of the equator.

The area is named after the sailors who threw their horses overboard to conserve drinking water on long journeys across the Atlantic. Because of the lack of winds in this region, sailing ships often became trapped, hence the name. The area between the equator and the horse latitudes is known as the tropics. The trade winds are easterly winds that blow from the east in the tropics.Doldrums are known for their heat and humidity. In conclusion, the horse latitudes and doldrums are two global wind currents that rise or sink slowly.

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Answer:

Explanation:

a ) The motion is one dimensional , so motion is along x - axis , starting from origin ( 0 , 0 )

b ) Initial velocity is 18.5 m /s when boat is situated at origin . When he displaces by 250 m along x axis and his position is ( 250 , 0 ) along x axis , his velocity becomes 36 m /s . Both his velocity and acceleration is along x - axis.

c ) Initial velocity vi = 18.5 m /s

final velocity vf = 36 m/s

Displacement x  = 250 m

Acceleration a = ?

Most appropriate formula is given below .

vf² = vi² + 2 a x

2ax = vf² - vi²

x =  ( vf² - vi² ) / 2 a

d )

Putting the given values

36² - 18.5² / 2 x 250

= 1296 - 342.25 / 500

= 1.9 m /s².

f ) Time interval t = ?

Required formula

vf = vi + at

t = (vf - vi ) / a

Putting the values

t = (30 - 18.5) / 1.9

= 6.05 second .

Answer:

Explanation:

57.8 m/s

Answer:

7.8 m/s

Explanation:

Let m1 be the mass of the rocket, m2 - the mass of burned fuel.

V1 - velocity of the rocket after the fuel has burned,

V2 - average velocity of burned fuel.

According to the law of conservation of linear momentum  :

0 = m1V1 - m2V2

V1 = V2*m2 / m1

V1 = 625*0.05/4 = 7.8125 m/s

So, the velocity of the rocket is 7.8 m/s.

Hope this helps, have a nice day :D

To assign a value to the variable "gradage" that is 4 more than the value of the variable "matricage," you can use the statement "gradage = matricage + 4."

In programming, the assignment operator (=) is used to assign a value to a variable. In this case, we want to assign a value to the variable "gradage" based on the value of the variable "matricage." To add 4 to the value of "matricage," we use the addition operator (+). By writing "gradage = matricage + 4," .

We are instructing the program to calculate the sum of "matricage" and 4, and then assign the result to the variable "gradage." This way, "gradage" will hold a value that is 4 more than the original value of "matricage."

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Answer:

The relationship between the wave's amplitude and frequency is such that it is inversely proportional to the frequency. The amplitude decreases as the frequency increases. The amplitude increases as the frequency decreases. The higher the energy of a wave, the higher the amplitude. The lower the energy, the lower the amplitude. Energy has no effect on wavelength, speed, or frequency, only the amplitude.

Explanation:

We will see that the given statement is true.

It is the amount of work needed to move a unit charge from a reference point (usually Earth) to a given point against an electric field. This is a scalar potential

A field that acts on charged objects, applying a force that is the charge of the object times the magnitude of the electric field. This is a vectorial field.

So the electric potential is a scalar that only depends on the position, while the electric field needs to have a direction (because it is a field, and because the direction of the force depends on the direction of the field).

Thus the statement is correct, the electric potential is a scalar potential, so it has a sign and magnitude, while the electric field is vectorial, so it has magnitude and direction.

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Answer:

the answer is A and B, decrease in distance and decrease in mass

From the given velocity and time of motion,  the object is not accelerating.

The acceleration of the object is determined from the change in velocity and change in time of motion as shown below;

a = Δv/Δt

where;

a = (8 - 8)/(4 - 2) = 0 m/s²

Thus, we can conclude that from the given velocity and time of motion,  the object is not accelerating.

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There is no acceleration in the horizontal direction because the speed in that direction is constant. So it stays at zero.

Answer: Moisture and food (bread)

Explanation:

Mould grows best in humid, damp air/wet conditions.

Since the bread is moist it will provide humidity for the mould as well as food.

A container with a cover would not be a favoring condition as mould needs oxygen to grow and survive.

(A) The image you see of yourself in the shiny tablespoon is inverted.

(B) The image you see of yourself in the shiny tablespoon is reduced.

(C) The image you see of yourself in the shiny tablespoon is virtual.

A) When you look at the front side of the spoon, the light rays reflecting off your face or any other object get reflected by the curved surface of the spoon. This reflection follows the laws of reflection, resulting in an inverted image. Therefore, the image you see of yourself in the spoon is inverted.

B)  In this case, the shiny tablespoon acts as a concave mirror. Concave mirrors can produce reduced images depending on the position of the object relative to the mirror's focal point. When the object is held at arm's length, the image formed in the spoon is smaller in size compared to the actual object. Hence, the image you see of yourself in the spoon is reduced.

C) A virtual image is formed when the light rays do not physically converge at the location of the image. In the case of a spoon, the reflected rays from the curved surface do not intersect to form a real image that can be projected onto a screen. Instead, your eyes perceive the apparent image formed by the reflected rays, which is known as a virtual image. Therefore, the image you see of yourself in the spoon is virtual.

Option (A) inverted, (B) reduced, and (C) virtual are the correct answers.

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Answer:

\(P=40 \ W\)

Conceptual:

\(\boxed{\left\begin{array}{ccc}\text{\underline{Equations for Work:}}\\W=F \Delta rcos(\theta) \ \text{(Constant} \ \vec F) \\W= \int\limits^{r_2}_{r_1} {Fcos(\theta)} \, dr \ \text{(Varible} \ \vec F) \end{array}\right }\)

The angle "θ" is the angle between the force applied and the direction of displacement.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Formula for Power:}}\\\\P=\frac{W}{t} \end{array}\right}\)

Explanation:

Given that an engine does 400 J of work in 10 seconds. Find the power of the engine.

\(W=400 \ J\\t=10 \ s\)

Plug these values into the formula for power.

\(P=\frac{W}{t} \\\\\Longrightarrow P=\frac{400}{10}\\\\\therefore \boxed{P=40 \ W}\)

Thus, the engines power is calculated.

Among the successive ionization reactions of phosphoric acid (H₃PO₄), the equilibrium reaction that will have the largest Ka value is the first ionization reaction.

The first ionization of phosphoric acid can be represented by the equation:

H₃PO₄ + H₂O ⇌ H₃O⁺ + H₂PO₄⁻

In this reaction, one hydrogen ion (H⁺) is released, forming the hydronium ion (H₃O⁺) and the hydrogen phosphate ion (H₂PO₄⁻). The Ka value represents the acid dissociation constant, which indicates the extent of ionization of an acid in water. A higher Ka value indicates a greater degree of acid strength.

In the case of phosphoric acid, the first ionization reaction has the largest Ka value because it is the initial and most significant ionization step.

As the subsequent ionization reactions proceed, the remaining hydrogen atoms become increasingly difficult to remove due to the decreasing strength of the acid.

Therefore, the first ionization reaction of phosphoric acid has the highest Ka value among its successive ionization reactions.

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The average distance of the object from the Sun is 4.88 x 10¹¹ m.

The average distance from the sun is calculated as follows;

(T² / a³) = (4π² / GM)

Where;

a = (GMT² / 4π²)^(1/3)

a = [(6.67 x 10⁻¹¹ x 1.989 x 10³⁰ x  (5.91 x 3.15 x 10⁷)² / (4π²)]^(1/3)

a = 4.88 x 10¹¹ m

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The ratio of angular velocity of the ball at end of the plane to its angular velocity (passing the center point C of the inclined plane) will be equivalent to "sqrt (5/2)."

The principle of conservation of energy can be applied here to determine the required ratio. As the ball rolls down the inclined plane, the potential energy it possessed at the top is transformed into kinetic energy as well as rotational energy.

Now, let's assume the ball has a mass 'm', a radius 'r', and an inertial moment of '\(I = (2/5)mr^{2}\)' (for a solid sphere). Let 'h' represent the height of the inclined plane's top and 'θ' represent the angle that the plane makes with the horizontal.

By applying the principle of conservation of energy, we get:

\(mgh = (1/2)I\omega^2 + (1/2)mv^2\)

where, \(mgh\) = potential energy of the ball at the top of the plane ('g' denoting acceleration due to gravity), \((1/2)I\omega^2\) = rotational kinetic energy ('ω' being the angular velocity), and \((1/2)mv^2\) denoting the translational kinetic energy ('v' is the linear velocity) of the ball.

On simplifying the equation, we get:

\(\omega f/\omega c = \sqrt{5r/h}\)

where \(\omega f\)= angular velocity of the ball at end of the plane, and \(\omega c\)  = angular velocity of the ball as it passes the center point C of the plane.

"sqrt (5/2)" is the correct option since it matches the expression obtained earlier, i.e., \(\omega f/\omega c = \sqrt{5r/h}\).

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