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Mechanical energy changes when a roller coaster starts at a height of 40 meters and reaches a height of 20 meters. The potential energy decreases, while the kinetic energy increases.

When a roller coaster starts at a height of 40 meters and reaches a height of 20 meters, mechanical energy changes. In physics, mechanical energy is the sum of potential and kinetic energy that is present in the objects. When an object is moved, it gains or loses energy, thus the mechanical energy changes. There are two forms of mechanical energy, namely kinetic energy and potential energy. Kinetic energy is the energy that a moving object possesses due to its motion, while potential energy is the energy that an object possesses due to its position or shape.
In the case of a roller coaster, when it starts at a height of 40 meters, it has potential energy that is equal to its mass multiplied by the acceleration due to gravity multiplied by its height. As it moves down the track, the potential energy gets converted into kinetic energy, which is the energy of motion. When the roller coaster reaches a height of 20 meters, it has a lower potential energy compared to when it started. The difference in potential energy is equal to the amount of work done by the force of gravity in bringing the roller coaster down from a height of 40 meters to a height of 20 meters. At the same time, the roller coaster has a higher kinetic energy than when it started, as it gained speed during the descent.
Therefore, in summary, mechanical energy changes when a roller coaster starts at a height of 40 meters and reaches a height of 20 meters. The potential energy decreases, while the kinetic energy increases.

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2.5 mL of Thallium-201 should be injected to administer a recommended dose of 3.0 mCi.

Thallium-201 is a radioisotope that is used in brain scans to detect brain cancer. It is used in nuclear medicine as a radiopharmaceutical. The recommended dose for Thallium-201 is 3.0 mCi. If a vial of Thallium-201 contains 60. mCi in 50. mL, we can determine the number of milliliters that should be injected by using proportionality.A proportion can be used to compare two ratios and solve for an unknown value. For example, if x is the unknown value we are trying to solve for and a/b and c/d are two ratios that are equal, we can write a proportion:

a/b = c/d.

Cross-multiplying gives us the equation

ad = bc.

This formula can be used to solve for the unknown value x. For this problem, we can use a proportion to solve for the number of milliliters that should be injected. Let x be the number of milliliters that should be injected. Then we have the following ratio:

3.0 mCi / x mL = 60. mCi / 50. mL

To solve for x, we can cross-multiply:

3.0 mCi * 50. mL = 60. mCi * x mL150. mCi mL = 60. mCi x mCx = (150. mCi mL) / (60. mCi) x = 2.5 mL

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Hello,

✔ We have Ek = 1/2m x v²

In order to come to a complete stop, the cyclist must convert all his kinetic energy into thermal energy. Given that the braking force opposes movement, the work is therefore resistant, i.e.  W = -10 214.4 J.

Standard atmospheric pressure is the average pressure exerted by the Earth's atmosphere at sea level under normal conditions. It is defined as 101.325 kPa or 1 atm and serves as a reference point for scientific measurements and comparisons related to atmospheric pressure.

Standard atmospheric pressure is the average pressure exerted by the Earth's atmosphere at sea level under normal conditions. It is defined as 101.325 kilopascals (kPa) or 1 atmosphere (atm). This pressure is used as a reference point for various scientific measurements and is crucial in fields such as meteorology, physics, and engineering.

Atmospheric pressure is caused by the weight of the air above a given point on the Earth's surface. The air is composed of molecules, mainly nitrogen (approximately 78%) and oxygen (approximately 21%), along with other trace gases. These molecules are in constant motion and exert a force on the surfaces they come into contact with, including the Earth's surface.

The standard atmospheric pressure of 101.325 kPa is equivalent to the pressure exerted by a column of mercury 760 millimeters (mm) in height in a barometer at sea level. This measurement was established as a reference point for atmospheric pressure, providing a consistent value for scientific calculations and comparisons.

It is important to note that atmospheric pressure can vary with altitude and weather conditions. As altitude increases, the atmospheric pressure decreases because the column of air above becomes thinner. In areas of high or low pressure systems associated with weather patterns, the atmospheric pressure deviates from the standard value.

The standard atmospheric pressure is a valuable reference in many applications. For instance, it is used as a standard for measuring gas pressure in laboratories and industrial processes. It is also used in meteorology to calculate and compare pressure systems and to study atmospheric phenomena such as wind patterns and weather changes.

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Final Answer:

If there is lower air pressure being "pushed" onto the surface of the water, then the water molecules do not need as much energy to overcome the force of atmospheric pressure pushing on the surface, and they can more easily escape and become a vapor. When the vapor pressure of the liquid is equal to the air pressure surrounding the liquid, it will boil. If you lower the air pressure, you will lower the temperature that water will boil at.

Explanation:

The boiling point of a liquid depends on the balance between the vapor pressure of the liquid and the external pressure, which is typically atmospheric pressure. When the external pressure is reduced, such as at higher altitudes or in a vacuum, the liquid molecules require less energy to escape the surface and become vapor. This is because there is less force pushing down on the liquid's surface, allowing for easier vaporization.

At lower air pressure, the water molecules can overcome the diminished force of atmospheric pressure more readily, requiring less heat energy to transition from liquid to vapor. When the vapor pressure of the liquid equals the surrounding air pressure, the liquid will start to boil.

Boiling point and vapor pressure are fundamental concepts in thermodynamics and phase transitions. Understanding how pressure affects the boiling point of liquids is crucial in various scientific and engineering applications, such as cooking, chemical processes, and high-altitude cooking.

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The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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earth energy budget is the relationship between how much energy the earth receive from the sun and energy the earth radiates out.

Energy is described as the quantitative property that is displaced to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.

The term earth's energy budget is also described as the  balance between of the amount of energy, that gets to the earth. from the Sun and the energy that leaves Earth and returns to the universe.

The earth's energy budget was mainly three types as shown:

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Answer:

we measure sound intensity in Decibels.

Answer:

Explanation:

We measure  sound power or sound pressure in decibels.

They  were named in honour of Alexander Graham Bell,( the inventor of both the telephone and the audiometer).

According to newton gravitational law any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them:

Where m1 and m2 are the masses of the objects, r is the distance between the objects and G is the gravitational constant. Therefore, the answer is:

a. Weight of the objects and distance between the two objects

We have that for the Question, it can be said that

From the question we are told

From,

\(tan\theta = \frac{h}{2}\)

differentiate with respect to h

\(sec^2\theta * \frac{do}{dz} = \frac{1}{2} * \frac{dh}{dz}\\\\\frac{dh}{dz} = 2 sec^\theta * \frac{d\theta}{dz}\\\\\theta = \frac{\pi}{6} and \frac{d\theta}{dz} = 0.1rad/min\\\\\frac{dh}{dz} = 2sec^2 (\frac{\pi}{6}) * (0.1)\\\\= 0.266miles/min\)

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Answer:

1 kg lead to earth is greater attraction as mass of earth is much more than 1kg lead.

Explanation:

Objects with more mass have more gravity. Gravity also gets weaker with distance. So, the closer objects are to each other, the stronger their gravitational pull is. Earth's gravity comes from all its mass

The answer for the experiment is obtained by the principle of Newton's law of cooling. The initial temperature of the Room is taken as 32°C.

The ice cubes are mixed with room-temperature water, the ice starts to melt and the water becomes cold. This is because the ice and water have two different temperatures and when they are mixed there is an exchange of heat is taken place. When the ice cubes mixed with water the room temperature is decreases from 32°C. After stirring the mixture because of the heat released, the temperature increases.

When the ice-water mixture is stirred, the heat energy is evolved which melts the ice in the mixture, and therefore the temperature increases gradually. And stirring of water for every 5 minutes leads ice cubes to melt completely to form water and the level of water increases in the final stage. This was given by Newton's law of cooling.

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The magnitude of the third charge is determined as -1.37 μc.

The magnitude of the charge on q3 is calculated as follows;

F = q12 + q23 + q13

F = kq₁q₂/r₂ + kq₂q₃/r² + kq₁q₃/r²

4.2 = (9 x 10⁹ x 2 x 10⁻⁶ x 3 x 10⁻⁶)/(0.1²) + (9 x 10⁹ x 3 x 10⁻⁶q₃)/(0.2²) + (9 x 10⁹ x 2 x 10⁻⁶ x q₃)/0.3²)

4.2 = 5.4 + 675,000q₃ + 200,000q₃

-1.2 = 875,000q₃

q₃ = -1.2/875000

q₃ = -1.37 x 10⁻⁶ C

q₃ = -1.37 μC

Thus, the magnitude of the third charge is determined as -1.37 μc.

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Answer:

18m

Explanation:

v=frequency × wavelenght

wavelength=v/f

wavelength=360÷20

=18m

Answer:

18m

Explanation:

wave speed / frequency = wavelength

360 / 20 = 18

Answer:

Above is correct

Usually, we use sampling when a population is hard to study, for some reason.

Sampling is a technique commonly employed in research and statistics when it is impractical or impossible to study an entire population directly. It involves selecting a subset, or sample, from the population and using the information gathered from the sample to make inferences about the entire population. This is done with the assumption that the sample is representative of the population and that the findings from the sample can be generalized to the larger population.

There are several reasons why a population might be difficult to study comprehensively. One reason is the size of the population. For example, if the population of interest is the entire world or a country, it would be practically impossible to study each individual in the population due to logistical constraints and limited resources. In such cases, sampling allows researchers to gather information from a smaller, manageable subset of the population.

Another reason for using sampling is when the population is dispersed or geographically scattered. If the population is spread out across a wide area, it can be challenging and costly to reach and collect data from every individual. Sampling allows researchers to select representative individuals or clusters from different regions, making data collection more feasible.

Additionally, there are cases where the population is inaccessible or hard to reach due to privacy concerns or ethical considerations. For example, if the population consists of individuals with certain medical conditions or sensitive personal information, it may be challenging to obtain consent or access to the entire population. In such cases, researchers can use sampling methods to obtain data from a subset of individuals who are willing to participate and meet the necessary criteria.

In summary, sampling is a valuable tool when studying populations that are hard to access, too large, or dispersed. It allows researchers to gather relevant data from a representative subset of the population and make valid inferences about the larger population, despite the challenges posed by studying the population as a whole.

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The question probable may be:

Usually, we use                  when a population is hard to study, for some reason.

Answer:

(a) The dc value is 95.5 volts

(b) The rms value is 106.1 volts

(c) The period is 0.01s

Explanation:

Given

\(V(t) = 150\sin(wt)\)

\(f = 100Hz\)

Solving (a): The dc value

\(V(t) = 150\sin(wt)\) implies that

\(V_{max} = 150\)

So, the dc value is:

\(V = \frac{2}{\pi} * V_{max}\)

\(V = \frac{2}{\pi} * 150\)

\(V = \frac{300}{\pi}\)

\(V = 95.5V\)

Solving (b): The RMS value

This is calculated as:

\(V_{rms} = \frac{1}{\sqrt 2} * V_{max}\)

So, we have:

\(V_{rms} = \frac{1}{\sqrt 2} * 150\)

\(V_{rms} = \frac{150}{\sqrt 2}\)

\(V_{rms} = 106.1V\\\)

Solving (c): The period

This is calculated as:

\(T = \frac{1}{f}\)

So, we have:

\(T = \frac{1}{100Hz}\)

\(T = 0.01s\)

Of the options listed, the only effect that can be caused by exposure to infrared light is overheating (option a).

Infrared light is a form of electromagnetic radiation that is invisible to the human eye but can be detected as heat. When exposed to high levels of infrared light, such as in close proximity to a powerful infrared source, it can lead to overheating of the body or objects. Skin cancer (option b) is not directly caused by infrared light. It is primarily associated with overexposure to ultraviolet (UV) radiation from the sun or artificial sources like tanning beds. UV radiation falls in the higher energy range of the electromagnetic spectrum, while infrared radiation has lower energy. Radiation sickness (option c) is caused by exposure to high-energy ionizing radiation, such as gamma rays or X-rays. Infrared light does not possess enough energy to cause ionization and is therefore not capable of inducing radiation sickness. Memory loss (option d) is not a known effect of exposure to infrared light. Memory loss can be attributed to various factors, such as neurological conditions, head injuries, or aging, but not specifically to infrared light exposure. In summary, while exposure to high levels of infrared light can lead to overheating, it does not cause skin cancer, radiation sickness, or memory loss.

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The vehicle has a 2000kg mass.

Take a mass's acceleration into account. Use the formula F = m a to determine the force's value. Kilogram-meter/second-squared will be used as the unit of force. The short name for this unit, which is made up of the three basic SI units, is newton.

F= ma

m= F/a

m= 50000/25

m= 2000 kg

According to Newton's Second Law of Motion, acceleration (gaining speed) occurs whenever a force acts on a mass (object). This law of motion is best demonstrated by riding a bicycle. The mass is your bicycle. The force that propels you forward on your bicycle comes from your leg muscles.

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Answer:

192.6N

Explanation:

Let's consider the forces acting on the beam:

Weight of the beam (W): It acts vertically downward and has a magnitude of W = mass * gravitational acceleration = 39.4 kg * 9.8 m/s^2.

Force exerted by the link on the beam (F_link): It acts at an angle of 90 degrees with respect to the beam and has two components: the vertical component and the horizontal component.

Tension in the cable (T): It supports the far end of the beam and acts at an angle of 90 degrees with respect to the beam. Since the angle between the beam and the cable is 90 degrees, the tension in the cable only has a vertical component.

Let's break down the forces acting on the beam:

Vertical forces:

W (weight of the beam) - T (vertical component of tension) = 0

T = W

Horizontal forces:

F_link (horizontal component of the force exerted by the link) = ?

To find the magnitude of the horizontal component of the force exerted by the link on the beam (F_link), we need to consider the equilibrium of forces in the horizontal direction.

Since the beam is inclined at an angle of θ = 33.1 degrees with respect to the horizontal, the horizontal equilibrium equation can be written as:

F_link = W * sin(θ)

Let's substitute the given values:

W = 39.4 kg * 9.8 m/s^2

θ = 33.1 degrees

F_link ≈ (39.4 kg * 9.8 m/s^2) * sin(33.1 degrees)

Using a calculator, we find that the magnitude of the horizontal component of the force exerted by the link on the beam (F_link) is approximately 192.6 N.

The mass of the metal ball is approximately equal to 0.1 kg.

Freefall is a type of motion in which an object falls with gravitational acceleration without resistance from air, surface, or medium. In a freefall, the only force acting on an object is the force of gravity. In a freefall, the acceleration of an object is given by the formula:  `g = 9.81 \(m/s^2`\)

The final velocity of a freefalling object can be calculated using the formula: `v = g*t `Where v is the final velocity, g is the gravitational acceleration, and t is the time taken to reach the final velocity. The force acting on an object is equal to the product of the mass of the object and the acceleration acting on the object. This is known as Newton's Second Law of Motion.

The formula for calculating force is:  `F = ma`.Where F is the force acting on the object, m is the mass of the object, and a is the acceleration acting on the object.Given that the velocity of the metal ball at the moment of striking the ground was 30 m/s, and that it stopped after penetrating the sand for 0.01 s, we can calculate the mass of the metal ball using the formula for force.

We can assume that the force acting on the metal ball is equal to the average resistance force of the sand against the motion of the ball.

The formula for calculating force is: `F = ma`.

Rearranging the formula, we get: `m = F/a` .

Substituting the given values, we get:  `

m = -3010/10`

Thus, the mass of the metal ball is approximately equal to 0.1 kg.

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Answer:

\(F_2=\262.5N\)

Explanation:

Since we need to find the force that the second child must exert to keep the door from moving, that means that the door is in equilibrium, which occurs when the net torque is zero:

\(\sum \tau=0\\\tau_1-\tau_2=0(1)\)

The torque is defined as:

\(\tau=Frsin\theta\)

Where F is the applied force, r is the distance between the force and the pivot point (hinges) and \(\theta\) is the angle between F and r. Both children push perpendicular to the door, so we have \(\theta_1=\theta_2=90^\circ\). Replacing in (1) and solving for \(F_2\):

\(F_1r_1sin(\theta_1)=F_2r_2sin(\theta_2)\\F_1r_1sin(90^\circ)=F_2r_2sin(90^\circ)\\F_1r_1(1)=F_2r_2(1)\\F_2=\frac{F_1r_1}{r_2}\\F_2=\frac{175N(0.6m)}{0.4m}\\F_2=262.5N\)

Answer:

Wavelength = 9.68 meters

Explanation:

Given the following data;

Speed = 300,000,000m/s

Frequency = 31 Megahertz to Hertz = 31 * 10⁶ Hz

To find the wavelength;

Wavelength = speed/frequency

Wavelength = 300,000,000/31,000,000

Wavelength = 9.68 meters

It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.

2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.

3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.

4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.

5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.

6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".

7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).

8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).

9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.

10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.

11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).

12. Evaluating the expression, we find: t ≈ 546.

13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

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Explanation:

P=E/T

E=15N

T=2s

P=15/2

P=7.5

Answer:

the answer is because Ikg gives 1000g

The sun’s gravity is relatively strong because the force of gravity between two objects is directly proportional to their masses. Gravity between the sun and Earth pulls Earth toward the sun, but Earth never falls into the sun. Instead, it constantly revolves around the sun, making one complete revolution every 365 days.

Answer:

Jun 29, 2016 · Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1.0 s at this speed? (b) What is its speed in kilometers per million years?

Explanation:

Answer:

false.

Explanation:

Since temperature and kinetic energy of molecules are proportional, the more we increase the temperature of the solvent, the faster the solute will dissolve.

This increase of kinetic energy allows the solvent molecules to more effective break apart the solvent molecules that are held together by intermolecular forces.