Two skaters stand facing each other. One skater's mass is 60 kg, and the other's mass is 72 kg. If the skaters push away from each other without spinning, what happens?

Answer:

The centripetal acceleration of the rock can be calculated using the formula:

a = v^2 / r

where v is the tangential velocity and r is the radius of the circle.

Substituting the given values, we get:

a = (12.56 m/s)^2 / 1m = 157.93 m/s^2

Rounding to the hundreds place, the centripetal acceleration of the rock is approximately 157.93 m/s^2.

The physical quantity which is equal to the rate of change of momentum is force.

Force is defined as any interaction that, when unopposed, will change the motion of an object. The rate of change of momentum of an object is equal to the force acting on the object, as described by Newton's second law of motion.

This law states that the force acting on an object is equal to its mass multiplied by its acceleration, or F = ma. By rearranging this equation, we get a = F/m, which tells us that the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. Thus, force is the physical quantity that is equal to the rate of change of momentum.

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Kepler's third law states that the square of the period of a planet's orbit around the sun is proportional to the cube of its average distance from the sun.

Kepler's third law, also known as the law of harmonies, is a mathematical relationship that describes the motion of planets around the sun. It states that the ratio of the cube of a planet's average distance from the sun to the square of its orbital period is constant for all planets in the solar system.

Mathematically, this can be expressed as T^2 = k*R^3, where T is the orbital period of the planet, R is its average distance from the sun, and k is a constant of proportionality. Kepler's third law is an important tool for astronomers to study and understand the dynamics of the solar system.

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The amount of strength that is applied to the rope in a pulley to raise the object is called tension.

Basically use a rope to pull an object by the means of pulley system.

When we raise an object to a certain height a strength forces developed in the rope that is called tension in the rope.

We use the pulley and rope system in order to distribute the weight of an object evenly on all the pulleys in the system.

When lifted directly vertically the tension in the string is equal to the weight of the object that it is lifting.

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Answer:  

C) Plane 1 has more kinetic energy and plane 2 has more potential energy.

Explanation:

he potential energy of an object is determined by its height above a reference level and its mass, while the kinetic energy of an object is determined by its mass and speed.

In this scenario, plane 1 has a higher speed than plane 2, but it is flying at a lower height. On the other hand, plane 2 is flying at a higher height, but it has a lower speed. Since the planes have different heights, they have different potential energies.

Therefore, the correct statement is: C) Plane 1 has more kinetic energy and plane 2 has more potential energy.

Answer:  

C) Plane 1 has more kinetic energy and plane 2 has more potential energy.

Explanation:

he potential energy of an object is determined by its height above a reference level and its mass, while the kinetic energy of an object is determined by its mass and speed.

In this scenario, plane 1 has a higher speed than plane 2, but it is flying at a lower height. On the other hand, plane 2 is flying at a higher height, but it has a lower speed. Since the planes have different heights, they have different potential energies.

Therefore, the correct statement is: C) Plane 1 has more kinetic energy and plane 2 has more potential energy

The increase in efficiency for each degree Fahrenheit rise in temperature is approximately 0.0167, or 1.67%.

To find the increase in the efficiency for each degree Fahrenheit rise in temperature, we first need to convert the temperature change from Celsius to Fahrenheit. We can use the formula:

°F = (9/5) * °C + 32

where °F is the temperature in Fahrenheit and °C is the temperature in Celsius.

Next, we need to calculate the increase in efficiency for a 1-degree Celsius rise in temperature. Let's call this increase "x". We know from the problem statement that the efficiency increases by 3 percent for each degree Celsius rise in temperature, so we can write:

x = 3%

x = 0.03

Now, to find the increase in efficiency for a 1-degree Fahrenheit rise in temperature, we can use the chain rule of differentiation to convert the rate of change in Celsius to the rate of change in Fahrenheit. The chain rule states that:

(dy/dx)_a = (dy/dt)_a / (dx/dt)_a

where (dy/dx)_a is the rate of change of y with respect to x at a particular point a, (dy/dt)_a is the rate of change of y with respect to t at point a, and (dx/dt)_a is the rate of change of x with respect to t at point a.

In this case, we want to find the rate of change of efficiency (y) with respect to temperature in Fahrenheit (x). We know the rate of change of efficiency with respect to temperature in Celsius (t), which is x, and we can use the formula for converting Celsius to Fahrenheit to find the rate of change of temperature in Fahrenheit with respect to time, which is:

(dx/dt)_a = (9/5)

So applying the chain rule, we get:

(dy/dx)_a = (dy/dt)_a / (dx/dt)_a

= 0.03 / (9/5)

= 0.0167

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A circuit breaker is identified as either an overload condition or a short-circuit condition.

Circuit breakers are safety devices that protect electrical systems from overloading or short-circuiting. An overload occurs when the amount of current flowing through a circuit is more than the maximum current-carrying capacity of the wires, which can cause them to overheat and start a fire. A short circuit occurs when there is a direct connection between two conductors of a circuit, causing an excessive amount of current to flow and potentially causing damage to the equipment or electrical system. Circuit breakers are designed to trip and interrupt the flow of current in the event of an overload or short circuit to prevent damage or fire.

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The correct option is D. all of the given frequencies except for 900 Hz are resonant frequencies of the pipe.

f = (n/2L) * v

In this case, the fundamental frequency (n=1) is 200 Hz, so we can solve for the speed of sound:

v = f * 2L / n = 200 * 2L / 1 = 400L

Now we can calculate the frequencies of the first few overtones:

n=2: f = 2 * 200 = 400 Hz

n=3: f = 3 * 200 = 600 Hz

n=4: f = 4 * 200 = 800 Hz

n=5: f = 5 * 200 = 1000 Hz

So all of the given frequencies except for 900 Hz (option D) are resonant frequencies of the pipe.

Frequency is a fundamental concept in physics that describes the number of cycles or oscillations of a wave or periodic motion per unit of time. It is defined as the reciprocal of the period, which is the time required for one complete cycle or oscillation. Frequency is measured in units of Hertz (Hz), which represents the number of cycles per second. For example, if a wave completes 10 cycles in one second, its frequency is 10 Hz.

Frequency plays a crucial role in many areas of physics, including optics, acoustics, and electromagnetism. In optics, frequency is related to the color of light, with higher frequencies corresponding to shorter wavelengths and therefore bluer colors. In acoustics, frequency determines the pitch of a sound, with higher frequencies producing higher-pitched sounds. In electromagnetism, frequency is related to the energy and wavelength of electromagnetic radiation, such as radio waves, microwaves, and X-rays.

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To convert watts to joules, we can use Formula: Energy (joules) = Power (watts) x Time (seconds)

Watts and joules are both units of energy, but they measure different things. Watts are a unit of power, which is the rate at which energy is transferred or used, while joules are a unit of energy itself. To convert watts to joules, you need to know the time over which the power is being used.

The formula for converting watts to joules is:

Energy (joules) = Power (watts) x Time (seconds)

For example, if you have a 100-watt light bulb that is turned on for 5 seconds, the amount of energy used by the light bulb can be calculated as:

Energy (joules) = 100 watts x 5 seconds = 500 joules

In other words, the light bulb used 500 joules of energy during the 5 seconds it was turned on.

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33600 J/K is the latent heat of fusion of ice. The amount of heat needed to transform a unit mass of ice from a solid state into a liquid state is known as the latent heat of fusion of ice.

We have some data:

Into an insulated cup is added 100g of water at 25°C.

The water is added to 50g of ice that is at 0°C.

Until the water reaches a temperature of 0°C, it is swirled.

18g of ice have not yet melted.

Water has a specific heat capacity of 4.2J/g'C.

Mass of water mg = 100 g

Water's initial temperature T1w = 25 degree C

Water's final temperature T2w = 0 degree C

Initial mass of ice m1 = 50 g

Final mass of ice m2 = 18 g

Ice that melted = Change in mass = 50 - 18 = 32 g

L is ice's latent heat of fusion

Heat lost by water = water ice received to melt 32 g

mw * C * change in T = change in mL

L = (100 * 4.2 * 25)/32

L = 328 J/g = 330 J/g

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The equivalent resistance between points A and B in the circuit is 9.844 Ω.

A resistor is an electronic component designed to provide resistance to the flow of electric current in an electronic circuit. Resistors are passive components, meaning they do not amplify or switch the current, but instead they regulate the flow of current by impeding the flow of electrons.

To find the equivalent resistance between points A and B in the circuit, we can use a combination of series and parallel resistors.

First, we can combine resistors R1 and R2 in parallel to get an equivalent resistance:

1/R_eq = 1/R1 + 1/R2

1/R_eq = 1/5 + 1/7

1/R_eq = 0.4 + 0.1429

1/R_eq = 0.5429

R_eq = 1/0.5429

R_eq = 1.844 Ω (rounded to 3 decimal places)

The two resulting resistors, R3 and R_eq, are in series with each other, so we can add their resistances to get the total equivalent resistance:

R_total = R3 + R_eq

R_total = 8.00 Ω + 1.844 Ω

R_total = 9.844 Ω

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Answer:

Explanation:

The farther a celestial object (a mass in space) is from another, the less of a gravitational force that they have on each other.

According to Dr. Hayne, the spacecraft mission that was the first to explore the planets in the outer solar system is Mariner 9.

On May 30, 1971, Mariner 9 lifted off from Cape Canaveral, Florida. A little over five months later, it entered orbit around Mars, thereby becoming the first spacecraft ever to orbit a planet other than our own Earth. During the initial stages of planetary exploration, it was customary for both these superpowers to launch pairs of spacecraft. The idea behind such an implementation was to ensure that one served as the backup for the other even if one of them failed in their objective completely. In 1965, the U.S. enjoyed its first success with respect to Mars as Mariner 4 flew by Mars, capturing the first close-up images of the planet. Considering this success came hot on the heels of its twin Mariner 3’s failure, the idea of launching in pairs seemed a good one. By 1969, NASA had furthered its accomplishments as Mariners 6 and 7 flew over Mars days within each other, with Mariner 7 even capturing an image of Phobos, one of Mars’s two natural satellites.

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As you accelerate upward in an elevator, the force exerted on you that has the greatest magnitude is the apparent weight, which is the normal force exerted by the elevator floor on your feet.

The apparent weight is equal in magnitude and opposite in direction to the force of gravity, and it increases as the elevator accelerates upward. This is because the force of gravity remains constant, but the elevator floor exerts an additional force on your feet to accelerate your body along with the elevator. Therefore, the apparent weight, or the normal force, is the greatest force exerted on you as you accelerate upward in an elevator.

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Magnetic fields B are vectors; that is in addition to their strength magnitude, we must also specify their direction.

Direction is characterized as the course that anything follows, the route that must be taken to go to a particular location, the direction in which something is beginning to take shape or the direction you are facing.

Instructions explain how to perform an action or the proper sequence. You are provided instructions for many of your assignments and assessments. It's critical to comprehend the motivation behind the instructions. Before starting anything, it's also crucial to read ALL of the instructions.

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The work done is 1,944 J, when a weight lifter lifts 130 kg from 1.5 m to 2.0 m above the ground

Work done is a term used to describe the amount of effort that has been expended on a particular task or project. It can refer to the amount of time and energy that has been put into something, or the amount of progress that has been made. It can also refer to the results of that work, such as the completion of a task or the production of a product. Work done is typically measured in terms of hours worked, milestones achieved, or the amount of output produced.

when a weight lifter lifts 130 kg from 1.5 m to 2.0 m above the ground, the work done is

Work = [tex]force\times distance[/tex]

Work = [tex]mass\times gravity \times height[/tex]

Work = [tex]130 kg\times 9.8 m/s^2 \times 0.5 m[/tex]

Work = 1,944 J

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To convert Pascal (Pa) to Kilopascal (kPa), you can use the following formula:1 kPa = 1000 Pa and 1 Pa = 0.001 kPa

Pascal's theory refers to the scientific contributions of Blaise Pascal, a French mathematician, physicist, and philosopher who lived in the 17th century. Pascal's work made significant contributions to several areas of science, including mathematics, physics, and hydrodynamics.

One of Pascal's most famous contributions to science is his work on hydrostatics, the study of fluids at rest. He discovered that the pressure exerted by a fluid at rest is the same in all directions, a principle known as Pascal's law. This law has important applications in many fields, including hydraulic systems, which rely on the transfer of pressure through fluids to power machines.

Pascal also made contributions to the study of probability theory, including the development of a mathematical theory of probability and the use of probability to solve problems in gambling. He also made important contributions to the development of the mechanical calculator, a precursor to modern computers.

Therefore, to convert Pa to kPa, you can divide the value in Pa by 1000. For example, if you have a pressure of 5000 Pa and want to convert it to kPa, you can divide 5000 by 1000 to get:

5000 Pa / 1000 = 5 kPa

So, 5000 Pa is equivalent to 5 kPa.

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Answer:

Approximately 500,000 N.

Explanation:

We can start by using the equation for the efficiency of a screw:

efficiency = load / effort

where load is the force being exerted on the nut by the spring, and effort is the force being exerted on the end of the spanner. Solving for effort, we get:

effort = load / efficiency

Substituting the given values, we get:

effort = 1000 N / 0.3 = 3333.33 N

Next, we can use the equation for the mechanical advantage of a screw:

mechanical advantage = length of effort arm / pitch

where the length of the effort arm is the length of the spanner, and the pitch is the distance traveled by the screw for one complete turn. Substituting the given values, we get:

mechanical advantage = 15 cm / 0.1 cm = 150

Finally, we can use the formula for the relationship between force, effort, and mechanical advantage:

force = effort × mechanical advantage

Substituting the values we found, we get:

force = 3333.33 N × 150 = 499999.5 N

Therefore, the force being exerted on the end of the spanner is approximately 500,000 N.

According to the kinetic molecular theory, the temperature of a material is proportional to the total kinetic energy of its particles. The average kinetic energy for 1.00 mol he atoms at 300 K is 3741.3 J mol⁻¹.

The average energy possessed by the gas particles which are in motion is defined as the average kinetic energy. The average kinetic energy of the gas molecules is proportional to the absolute temperature of the gas.

The equation of average kinetic energy for one mole of any gas is:

Average kinetic energy = 3/2 nRT

3/2 × 1 × 8.314 × 300

= 3741.3 J mol⁻¹

Thus the average kinetic energy for 1.00 mol He atoms is 3741.3 J mol⁻¹.

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Answer:

Explanation:

if we were to have 30 milliamps we would have .03 amps

when converting from milliamps to amps we are basically multiplying by 10^-3. you could also just remember that in order to convert from milliamps to amps you just need to move the decimal 3 places to the left

Convection is heat transfer through fluids. Examples: boiling water, sea breeze, hot air balloon, atmospheric convection, heating a room.

Convection is a course of intensity move that happens in liquids, like fluids and gases. It includes the development of hot and cold liquids because of contrasts in their densities. At the point when a liquid is warmed, it turns out to be less thick and ascends, while colder, denser liquid sinks. This makes a roundabout movement that moves heat starting with one piece of the liquid then onto the next.

The following are five instances of convection:

Bubbling water in a pot: The warmed water at the lower part of the pot rises and is supplanted by cooler water, making a course design.

Ocean breeze: During the day, land warms up quicker than water, making air over the land rise and cooler air from the ocean to move in, making an ocean breeze.

Sight-seeing balloon: The warmed air inside the inflatable ascents, making the inflatable light and making it lift off the ground.

Climatic convection: Daylight warms the World's surface, making warm air rise and cooler air to sink, bringing about the arrangement of mists and weather conditions.

Warming a room: A radiator warms the air around it, making it rise and making a course design that circulates the warm air all through the room.

In synopsis, convection is a course of intensity move that happens in liquids, where hotter, less thick liquids rise and are supplanted by cooler, denser liquids. This makes a roundabout movement that moves heat starting with one piece of the liquid then onto the next, and should be visible in regular models like bubbling water, climatic convection, and warming a room.

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Answer: closely compacted in substance.

Explanation:

You can disregard the weight of the rope and assume that the rope does not stretch. Use 9.81m/s2 as the gravitational acceleration value.

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. It is a vector quantity to accelerate (in that they have magnitude and direction). The direction of the net force acting on an object determines the direction of its acceleration. According to Newton's Second Law, an object's acceleration is the result of two factors working together: the object's mass, which varies depending on the materials it is made of, and the net balance of all external forces acting on it. The magnitude of an object's acceleration is inversely proportional to the object's mass.

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Answer:

All of the planets travel around the Sun in the same direction, counterclockwise as seen from above the Sun's north pole, because they were formed from the same rotating disk of gas and dust that surrounded the young Sun about 4.6 billion years ago. This rotating disk of gas and dust, called the solar nebula, was slowly rotating in the same direction as the Sun's rotation. The planets formed from this disk by a process called accretion, where the particles in the disk collided and stuck together to form larger and larger bodies. Because the disk was already rotating in one direction, the planets formed from it also inherited the same direction of rotation, which is counterclockwise as seen from above the Sun's north pole.

The planets lie on a fairly flat plane, known as the ecliptic plane, because the solar nebula from which they formed was also a flat, rotating disk. As particles in the disk collided and stuck together to form larger bodies, their orbits would be constrained to lie roughly in the same plane as the disk, due to the conservation of angular momentum. This is because the angular momentum of a system remains constant unless acted upon by an external force, so any rotation in the system would cause the particles to flatten into a disk. This is also why most of the other objects in the Solar System, such as asteroids, dwarf planets, and comets, also lie on or near the ecliptic plane. The only notable exceptions are some comets, which have highly elliptical orbits that can take them far out of the plane of the Solar System.

Explanation:

The work required is greater for accelerating the car from 20 to 30 m/s than from 10 to 20 m/s.

The effort is greater when the car is accelerated from 20 to 30 m/s than from 10 to 20 m/s due to the change in kinetic energy. This is due to the fact that an object's kinetic energy grows as a function of velocity, hence as velocity rises, so does the amount of work needed to produce a given increase in kinetic energy.

The kinetic energy of an object determines how much labour is necessary to accelerate it from one velocity to another.

The equation: gives the kinetic energy of an item

K = (1/2)mv^2

where

m is the mass of the object

v is its velocity.

We have to find the at which velocity a car required more work to accelerate a car from 10 to 20 m/s or from 20 to 30 m/s we can find it by comparison,

To determine the change in kinetic energy, we may compute the car's kinetic energy at each velocity and then subtract the beginning kinetic energy from the final kinetic energy.

Let's take mass of that the car is 1000 kg.

Case1:  accelerating the car from 10 m/s to 20 m/s:

Initial kinetic energy [tex]= (1/2)mv^2[/tex]

Initial kinetic energy [tex]= (1/2)(1000 kg)(10 m/s)^2[/tex]

Initial kinetic energy [tex]= 50,000 J[/tex]

Final kinetic energy [tex]= (1/2)mv^2[/tex]

Final kinetic energy  [tex]= (1/2)(1000 kg)(20 m/s)^2[/tex]

Final kinetic energy  [tex]= 200,000 J[/tex]

Change in kinetic energy = 200,000  - 50,000

Change in kinetic energy = 150,000 J

Case2: accelerating the car from 20 m/s to 30 m/s:

Initial kinetic energy [tex]= (1/2)mv^2[/tex]

Initial kinetic energy [tex]= (1/2)(1000 kg)(20 m/s)^2[/tex]

Initial kinetic energy [tex]= 200,000 J[/tex]

Final kinetic energy [tex]= (1/2)mv^2[/tex]

Final kinetic energy [tex]= (1/2)(1000 kg)(30 m/s)^2[/tex]

Final kinetic energy [tex]= 450,000 J[/tex]

Change in kinetic energy = 450,000  - 200,000

Change in kinetic energy = 250,000 J

We can see that accelerating the automobile from 10 to 20 m/s results in less effort than accelerating it from 20 to 30 m/s due to the change in kinetic energy.

The automobile must thus put in more effort to accelerate from a greater velocity than from a lower one.

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The required heat of vaporization is calculated when the pressure and temperature are given using the Clausius-Clapeyron equation.

The mathematical equation of Clausius-Clapeyron is given as,

ln(P₁/P₂) = -ΔHvap/R (1/T₂ - 1/T₁)

where,

P₁, P₂ are the vapour pressures at two temperatures T₁, T₂

ΔHvap is enthalpy of vapourization

R is gas constant

When the temperature reaches a certain level, known as the critical temperature, the heat of vaporisation entirely disappears.

Latent heat of condensation grows as pressure rises, while latent heat of vapourization decreases.

By substituting the required values in the above equation, we get the heat of vaporization value.

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The statement saying that when wax freezes it absorbs energy is false.

When the wax freezes utilizes energy into the surrounding because it is an exothermic process.

As the particles present in the wax settles and entropy of the system of the wax decreases they tend to lose energy and attained the state in which they will have the least potential energy.

In the process of the freezing of wax both these things take place and it results in the energy being released. So, the statement saying that energy is absorbed during the freezing of wax is false.

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The Biot-Savart law is a fundamental law in electromagnetism that describes the magnetic field produced by a current-carrying wire.

When a current flows through a wire, a magnetic field is generated around the wire. The Biot-Savart law allows us to calculate the magnetic field at any point in space due to a current-carrying wire.

A finite solenoid is a coil of wire wound in a helix shape that has a finite length. The Biot-Savart law can be used to calculate the magnetic field produced by a finite solenoid. The magnetic field of a finite solenoid is similar to that of an infinite solenoid, but with additional end effects.

The formula for the magnetic field produced by a finite solenoid is complex and involves integrating over the length of the solenoid. The magnetic field depends on various factors such as the number of turns in the solenoid, the current flowing through it, and the radius and length of the solenoid. The Biot-Savart law is a crucial tool for understanding and analyzing the behavior of magnetic fields produced by current-carrying wires and is used in various applications in physics and engineering.

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The tension in the cable is equal to the gravitational force on the elevator.

When an elevator is moving upward at a constant speed, it means that its acceleration is zero. According to Newton's second law of motion, the net force acting on an object is equal to its mass times its acceleration. Since the acceleration is zero, the net force on the elevator must be zero.

In this scenario, there are only two forces acting on the elevator: its weight (which is equal to the gravitational force acting on it) and the tension in the cable. The tension in the cable is upward, while the weight is downward. Therefore, for the net force to be zero, the tension in the cable must be equal in magnitude to the weight of the elevator.

Therefore, the tension in the cable is equal to the gravitational force on the elevator.

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