What are the 4 ways to solve an equation?.

Answer:

Explanation:

ME = GPE + KE

At the top of building all the mechanical energy is GPE because the ball isn't moving yet.  Just before it hits the ground, all the mechanical energy is KE because the GPE has decreased to 0 (h = 0 at ground level).

a.  Total E (top of bldg.) = mgh = (5 kg)(9.8 m/s²)(22 m) = 1078 J

b.  Total E (at ground) = 1/2mv² = 1/2(5 kg)(18 m/s)² = 810 m/s

c.  The energies are not the same because some of the energy is converted to thermal energy as they ball falls due to friction.

To calculate the standard uncertainty of the Young's modulus, in units kN/m2, you need to use the formula for the standard deviation of a sample, which is the square root of the variance.

The variance is calculated by taking the sum of the squared differences between each value and the mean, and then dividing by the number of values in the sample. Therefore, you need to first calculate the mean value of the Young's modulus, and then use the formula to calculate the standard deviation. Once you have the standard deviation, you can multiply it by the appropriate conversion factor to get the standard uncertainty in units kN/m2.

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Answer:

[tex]\huge\boxed{\sf t = 0.9 \ s}[/tex]

Explanation:

Mass = m = 1.2 kg

Initial Velocity = [tex]V_i[/tex] = 2.0 m/s

Final Velocity = [tex]V_f[/tex] = 5.0 m/s

Force = F = 4.0 N

Time = t = ?

[tex]\displaystyle F=\frac{m(V_f-V_i)}{t}[/tex]

Put the given data in the above formula

[tex]\displaystyle 4=\frac{1.2(5-2)}{t} \\\\4=\frac{1.2(3)}{t} \\\\4=\frac{3.6}{t} \\\\Multiply \ t\ to \ both \ sides\\\\4t = 3.6\\\\Divide \ both \ sides \ by \ 4\\\\t=3.6/4\\\\t = 0.9 \ s \\\\\rule[225]{225}{2}[/tex]

Answer:

0.9s

Explanation:

This question tests on the concept of the Kinematics Equations.

Given information from the question,

we can use the equation:

v = u + at

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

We also need the equation: F = ma,

where F is the force applied, m is the mass the object, and a is acceleration.

We first find the acceleration of the object.

F = ma,

4N = (1.2kg) × a

a = 4 ÷ 1.2 =

[tex]3 \frac{1}{3} \frac{m}{ {s}^{2} } [/tex]

Now with the acceleration, we can find the time taken for the acceleration to take effect.

v = u + at,

[tex]5 = 2 + (3 \frac{1}{3} )t \\3 \frac{1}{3} t = 3 \\ t = 3 \div 3 \frac{1}{3} = 0.9s[/tex]

Therefore time taken = 0.9s

When a new evidence is contradicts part of a theory will cause the theory rejected or incorrect.

Theory is a condition of an estimation from the researcher that did not prove the fact about but it is estimated to be true. In research, theory is a key to the flow of a research. The research itself are done by:

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Using the work done relation, the value of force is 25 Newton.

When a force is applied along a displacement, "work" in physics refers to the energy that is transported to or away from an object. The following situations include work: relocating a table. a door being pulled and pushed. Walking. raising a stone.

The work W that a force F traveling across a distance x exerts on an object is calculated using the formula W=Fs. If the object is moving in the opposite direction from how we expect it to, we add a minus sign.

Work done is equal to displacement times force.

50J = force × 2

f=50/2

Force = 25 Newton.

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According to the problem it takes 3 seconds to reach a speed of 29. 4m/s.

Speed is the rate of change in the position of an object over a given period of time. It is a scalar quantity, meaning it is a magnitude with no direction. Speed is the magnitude of the velocity vector. It is measured in units such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph). Speed is determined by the formula speed = distance/time.

The equation for calculating the time it takes for an object to reach a certain velocity given an initial velocity of zero is t = (vf - vi) / a,where an is the acceleration, vi is the starting velocity, and vf is the final velocity.

In this case, vf = 29.4 m/s, vi = 0 m/s, and a = 9.8 m/s^2.

t = (29.4 - 0) / 9.8

t = 3 seconds

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Sound intensity is described as sound per unit area perpendicular to the path of the sound waves and which is represented by I and calculated as [tex]I =\dfrac{P}{A}[/tex] , where, P = sound power and A = area.

The term "sound intensity," also known as "acoustic intensity," refers to the amount of energy carried by sound waves per unit area in a direction perpendicular to that area. Watts per square metre (W/m2) is the SI unit of intensity, which also includes sound intensity. The noise measurement of sound intensity in the air at a listener's location as a sound energy quantity is one use.

Sound pressure and sound intensity are not the same physical quantities. Sound pressure, which is correlated with sound intensity, can affect human hearing. Consumer audio electronics refer to level differences as "intensity" differences, but sound intensity is a precisely defined quantity that cannot be detected by a straightforward microphone.

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High torque transmission is possible with gear couplings. They are therefore utilized in heavy-duty applications.

Generally speaking, torque seems to be a twisting of turning force and tends to create rotation along an axis, which could be a fixed point or the center of mass. The capacity of a spinning object, such as a gear or perhaps a shaft, can overcome turning resistance is another way to conceptualize torque.

When an engine strains itself, torque—a twisting force that refers to the rotational force—measures the amount of that bending force that is accessible. Everyday activities like turning a door, opening a drink bottle, to use a wrench, or peddling a bicycle all involve some kind of torque.

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Three formulas of newton's law of motion are:- a) v = u + at, b) S = ut +0.5at² c) v² = u² + 2as

Newton's first law of motion defines the relation between final velocity(v) of an object after some time(t), if the initial velocity of the object is u and acceleration is a.

v = u + at

Newton's second law of motion is used to determine the distance(S) travelled by an object in accelerated motion for time(t), having an initial velocity u.

S = ut +0.5at²

Newton's third law gives the relationship between, final, initial velocities, acceleration(a), and the distance(s) travelled by the object.

v² = u² + 2as

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Light waves can pass through matter, but sound waves cannot, depending on the characteristics of the waves, sound waves can either be absorbed or transmitted when they travel through materials.

One of the most essential things to understand about both light and sound is that they are both waves of energy. Light and sound waves both move as waves and are manifestations of energy, but they differ greatly in key respects.

Light waves travel in a transverse direction, whereas sound waves travel in a longitudinal direction. In a vacuum, light waves can move.

Due to the need for a physical medium, sound waves cannot propagate in a vacuum.

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Mineralogically, barite is a sulfate, bornite is a sulfide, cuprite is an oxide, magnesite is a carbonate.

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Among the mineral groups, barite is a sulfide mineral, bornite is a sulfide mineral, cuprite is an oxide mineral, and magnesite is a carbonate mineral.

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Yes, the gravity is always 9. 8 N. Every mass acts as a gravitational force or pull on every other mass. The mass of the objects in play determines how strong this pull is.

The moon orbits the Earth while the planets revolve around the sun thanks to gravity. Therefore, gravity is defined as, A body is drawn toward the center of the earth or any other mass-containing physical body by the force of gravity.

After learning what gravity is, explain how gravity is crucial to the continuation of life on Earth. The atmosphere is held in place and gives us the air we need to breathe to survive because of the gravitational attraction of the planet and the sun. Additionally, it shields us from the light.

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Answer:

The sum of the exterior angles must always be 360 deg.

Consider an equilateral triangle   3 * 120 = 360

For a square   4 * 90 = 360

For a pentagon  5 * 72 = 360

So for a 20-gon each interior angle = 180 - 18 = 162 with an exterior angle of 18

One must rotate 18 * 20 to get the full 360 deg so the side is back where it started

Since each interior angle = 162 deg one has

20 * 162 = 3240 deg for the sum of the interior angles

Answer:100

Explanation:100 times is 100

Latency and bandwidth are both dependent on each other and have an inverse relationship

Bandwidth is the amount of data a connection can handle, and latency refers to the delay that affects how quickly data reaches your device. They are very different, but related in one important way. This means that low bandwidth can result in high latency. The difference between bandwidth and delay depends on what you are measuring. Bandwidth considers the amount of data transferred, and latency indicates how long it takes to transfer data. Collectively, these two terms are called throughput and describe the amount of data transferred over a period of time.

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Mass and energy of an object are related to each other .

In the theory of special relativity, mass and energy are closely related through the famous equation E = [tex]mc^{2}[/tex] , where E is the energy, m is the mass, and c is the speed of light.

This equation shows that energy and mass are interchangeable and can be converted into each other. So, in that sense, mass does depend on energy and vice versa.

In everyday life, however, the effects of special relativity are not significant and the mass of an object remains constant regardless of its energy. For example, a car at rest and the same car in motion at a high speed, both have the same mass, but they have different kinetic energy.

So, in general, mass and energy are related, but the relationship is only significant when dealing with objects that are moving at velocities close to the speed of light.

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"According to Newton's third law, there is an equal and opposite reaction to every action." For instance, a rocket goes upward after receiving reaction force from an ejecting jet, and a bullet fired from a pistol receives force from the gun that causes it to move forward. The bullet pushes the weapon rearward with an equivalent amount of force.

A body's forces of action and reaction are never equal. The explanation for this is because action and response always occur in pairs, are of equal size, and always point in the opposite direction.They cannot counteract one another since they act on distinct bodies.

The force that the first object applies to the second during an interaction between two objects is referred to as the action. The force applied by the second body to the first body is known as the response force. Action and reaction are therefore opposite and of equal magnitude.

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The movement of a projectile through a resisting medium, like as air, is referred to as a ballistic issue. The projectile's launch, flight, behaviour, and effects are all studied by the mechanics subfield known as ballistics.

The science or art of creating and speeding projectiles to create a desired performance, particularly projectiles like bullets, unguided bombs, rockets, or the like. A weapons engineer or armorer—often referred to as a "ballistician"—creates cartridges using the scientific principles of ballistics. The term "rocket" refers to any missile, spacecraft, aircraft, or other kind of vehicle that runs on rocket power. The name "ballistics" is derived from the Greek verb meaning "to throw." An object is a projectile if it is propelled into the air by the use of force.

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The electron can move from the third shell to the fourth shell in a sodium atom as a result of electron transitions. These transitions are triggered by the absorption or emission of energy, such as in the form of photons.

Photons are the smallest unit of electromagnetic radiation. They are a particle of light that are produced when an atom is excited, and are responsible for most of the light we see around us. Photons travel at the speed of light, and can be described in terms of frequency and wavelength. Photons have no mass and no charge, but they do have momentum and energy. They are also the primary carriers of the electromagnetic force. Photons play an important role in quantum mechanics and are the mediators of all electromagnetic interactions. Photons are also the only particles that can travel through a vacuum, and are the only way to directly measure the properties of the electromagnetic field.

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The Moon travels 2288 miles per hour as it orbits around the Earth with an orbital period of 27 days.

Orbital velocity is known as the speed needed to stay in orbit.

The Moon is an celestial body that orbits around our planet Earth and is Earth's only natural satellite.

The Moon orbits around the Earth at a speed of 2,288 miles per hour  which is 3,683 kilometers per hour or can be 1.022 km/s. The orbital period is 27 days. During this time of the motion it travels a distance of 1,423,000 miles  which is 2,290,000 kilometers around the Earth in a fixed orbit.

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The thing that happens to the sum of the ball’s kinetic energy and potential energy as the ball rolls from point A to point E is option C. The sum remains the same.

The total mechanical energy of an object is the sum of its kinetic energy (energy of motion) and its potential energy (energy of position or stored energy). According to the law of conservation of energy, the total mechanical energy of an object remains constant in an isolated system, as long as no external forces (like friction, air resistance) are acting on it.

The image attached is a curved path, and the ball is rolling from point A to point E. As the ball moves down the incline, it gains kinetic energy, and potential energy is lost, but the total energy remains constant.

When it reaches point B, it has the maximum kinetic energy and minimum potential energy, and as it continues on the path, its potential energy increases, and kinetic energy decreases. At point E, it has the minimum kinetic energy and maximum potential energy. However, the total energy remains the same.

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Radius is considered as r in this formula. The gravitational force which try pulls two objects with masses m1 and m2 apart over a certain distance is represented by the equation F = G*m1*m2/r^2. G, which represents the universal gravitational constant.

The product of each object's individual mass determines the gravitational force between them. The square of one object's mass determines how much gravity will pull on the other. If their mass is raised by a factor of two, the gravitational force between the two objects is quadrupled.

The formula F = GMm /r^2 describes the dimensions of G as the gravitational force that pulls two objects with point masses of m1 and m2 toward one another, and r represents the distance between them.

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A rock of ma m = 0. 52 kg i attached to a male string of length L = 0. 79 m, the magnitude of the tension at which the string breaks is 1576.2 N. The rock travels 227.3 m high after the string breaks.

a) To determine the magnitude of the tension at which the string breaks:

L = 0.79 m

v = 4.8 m/s

= 480 cm/s.

= 79 cm.

So,

F = (0.52 kg)(480 cm/s)²/(79 cm)

= 1576.2 N

b) To determine how high the rock travels after the string breaks, we need to use the conservation of energy principle:

KE = (1/2)(0.52 kg)(480 cm/s)²

= 117,964.8 J

KE = (1/2)mv²

= (1/2)T(L)

= (1/2)(1576.2 N)(79 cm)

= 62,360.1 J.

KE = PE

117,964.8 J = (0.52 kg)(9.81 m/s²)h

h = 227.3 m

Thus, the rock travels 227.3 m high after the string breaks.

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h = v 0 y 2 2 g ,This equation, which only depends on the vertical component of the initial velocity, specifies the maximum height of a projectile above its launch site.

Calculate the ball's greatest height using the vertical motion model, h = -16t2 + vt + s, where v is the initial velocity in feet/second and s is the height in feet.

We can see that for the longest-range punts 2 = 90 degrees and, consequently, = 45 degrees because the sine function has an input angle of 90 degrees that results in its highest output value, 1. In other terms, a projectile moves the farthest.

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The answers are:

A:  The impulse applied to the ball is -6.75 kg m/s.

B:  The force applied to the ball is -15.0 kg m/s^2, or 15.0 N.

a) Impulse is defined as the change in momentum of an object and can be calculated as the product of force and time. Momentum is given by the equation:

p = m * v

where m is the mass of the object and v is its velocity. The impulse applied to the ball is equal to the change in its momentum:

Δp = m * (vf - vi)

where vi is the initial velocity of the ball (38 m/s) and vf is its final velocity (27 m/s).

Substituting the values, we get:

Δp = 1.5 kg * (27 m/s - 38 m/s)

Δp = -6.75 kg m/s

So, the impulse applied to the ball is -6.75 kg m/s.

b) Force is defined as the impulse per unit time and can be calculated as:

F = Δp / Δt

where Δt is the time for which the force was applied (0.45 sec).

Substituting the values, we get:

F = (-6.75 kg m/s) / (0.45 s)

F = -15.0 kg m/s^2

So, the force applied to the ball is -15.0 kg m/s^2, or 15.0 N.

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The dot product of the force and the displacement of the force point is used to calculate the amount of work done by force. In the case of angular motion, torque takes the place of force and angular displacement of linear displacement.

Typically, the product of r and F is used to represent torque.  τ = r × F = r F sinθ

The torque's work is equivalent to the body's change in rotational kinetic energy.

As you apply a force somewhere and move a distance, there is a connection between torque and work. Torque, however, is merely a proximate indicator of force.

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First velocity of the car with one washer attached to a pulley is v1 = 0.25 m / t1, where t1 the average times the car took to reach the 0.25 m mark.

The velocity at time interval t = 0 is represented by the symbol u. It is the speed which shows that the motion has begun. There are four different initial velocity formulas: (1) If time, acceleration, and final velocity are given, the initial velocity is expressed as u = v - at.

The final velocity, on the other hand, is a vector quantity that determines the speed and direction of a body in motion after it has reached maximum acceleration.

The velocity of a body at any given time is known as instantaneous velocity. Average velocity is defined as total displacement divided by total time and can be calculated as v = x/t, where x is the total displacement of the body and t is the time. Because displacement can never be greater than the distance travelled, average velocity is always less than or equal to average speed.

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Answer:

Approximately [tex]3.43\; {\rm m\cdot s^{-2}}[/tex], assuming that air resistance is negligible in both occasions, and that [tex]g_{\text{earth}} = 9.81\; {\rm m\cdot s^{-2}}[/tex] near the surface of the Earth.

Explanation:

Let [tex]x[/tex] denote the displacement of the marker. Let [tex]a[/tex] denote the acceleration of the marker. Let [tex]t[/tex] denote the time it takes for the marker to reach the ground.

Under the assumptions, acceleration of the marker would be constant, and the SUVAT equations would apply. Rearrange the SUVAT equation [tex]x = (1/2)\, a\, t^{2}[/tex] to find acceleration [tex]a[/tex]:

[tex]\begin{aligned}a &= \frac{2\, x}{t^{2}}\end{aligned}[/tex].

Let [tex]a_{\text{Mars}}[/tex] and [tex]t_{\text{Mars}}[/tex] denote the acceleration and time taken on Mars. Similarly, let [tex]a_{\text{Earth}}[/tex] and [tex]t_{\text{Earth}}[/tex] denote the acceleration and time taken on Earth. It is implied that the Marker travelled the same distance (same displacement, [tex]x[/tex]) both on Earth and on Mars.

Using the SUVAT equation from above:

[tex]\begin{aligned}a_{\text{Mars}} &= \frac{2\, x}{{t_{\text{Mars}}}^{2}}\end{aligned}[/tex].

[tex]\begin{aligned}a_{\text{Earth}} &= \frac{2\, x}{{t_{\text{Earth}}}^{2}}\end{aligned}[/tex].

[tex]\begin{aligned}\frac{a_{\text{Mars}}}{a_{\text{Earth}}} &= \frac{\displaystyle \frac{2\, x}{{{t_{\text{Mars}}}^{2}}}}{\displaystyle \frac{2\, x}{{{t_{\text{Earth}}}^{2}}}} \end{aligned}[/tex].

[tex]\begin{aligned}\frac{a_{\text{Mars}}}{a_{\text{Earth}}} &= \left(\frac{{t_{\text{Earth}}}}{{t_{\text{Mars}}}}\right)^{2}\end{aligned}[/tex].

[tex]\begin{aligned}a_{\text{Mars}} &= \left(\frac{{t_{\text{Earth}}}}{{t_{\text{Mars}}}}\right)^{2}\, a_{\text{Earth}} \\ &= \left(\frac{1.3\; {\rm s}}{2.2\; {\rm s}}\right)^{2}\, (9.81\; {\rm m\cdot s^{-2}}) \\ &\approx 3.43\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].