The specific heat capacity of a material is defined as the amount of heat energy required to raise the temperature of 1 gram of the material by 1 degree Celsius. In this case, we are given that the specific heat .
What is specific heat capacity ?To calculate the amount of thermal energy required to increase the temperature of a 20g sample of copper from 20°C to 50°C, we can use the following formula:Q = m x c x ΔT
where Q is the thermal energy in Joules, m is the mass of the sample in grams, c is the specific heat capacity of the material in J/g°C, and ΔT is the change in temperature in degrees Celsius.Substituting the given values, we get:
Q = 20g x 0.385 J/g°C x (50°C - 20°C)
Q = 20g x 0.385 J/g°C x 30°C
Q = 231 Joules
Therefore, the amount of thermal energy required to increase the temperature of a 20g sample of copper from 20°C to 50°C is 231 Joules. Hence, the answer is D) 231.To know more about specific heat capacity , check out :
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the earliest known measurement of the circumference of the earth used is called___
The earliest known measurement of the circumference of the earth used is called ; Eratosthenes' Method.
What is the measurement ?The measurement is the process of determining the size, amount, or degree of something. Measurement can involve counting, weighing, or measuring physical characteristics such as length or volume. It can also involve observing or assessing behavior, or determining the amount or degree of something that cannot be physically measured, such as intelligence or happiness. Measurement is an important tool in many fields, including science, economics, engineering, and industry. Measurements are often used to compare different items or to track changes over time.
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The earliest known measurement of the circumference of the earth used is called ; Eratosthenes' Method.
What is the measurement ?The measurement is the process of determining the size, amount, or degree of something. Measurement can involve counting, weighing, or measuring physical characteristics such as length or volume.
It can also involve observing or assessing behavior, or determining the amount or degree of something that cannot be physically measured, such as intelligence or happiness.
Measurement is an important tool in many fields, including science, economics, engineering, and industry. Measurements are often used to compare different items or to track changes over time.
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Which motor performs more work in the same amount of time- a 10 kW motor or a 20 kW motor? How much more work can it do?
Answer:
20kw twice the work
Explanation:
Find the magnitude of the electrostatic force experienced by the positive charge.
The magnitude of the electrostatic force experienced by the positive charge is equal to the magnitude of the Coulomb force, which is given by F = k*|q1|*|q2|/r², where k is the Coulomb constant, q1 and q2 are the charges
What is the Coulomb ?The Coulomb (symbol: C) is a unit of electric charge that is named after the French physicist Charles-Augustin de Coulomb. This unit is used to measure the magnitude of electric charge, electric potential, and electric field strength. It is equal to the charge of one electron, which is equal to 1.602 x 10-19 Coulombs of charge. The Coulomb is a fundamental unit in electrical engineering and physics and is used to calculate the force between two charged particles. It is also used to measure electrical capacitance and electric dipole moments.
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two coherent sources of radio waves, a and b, are 5.00 meters apart. each source emits waves with wavelength 6.00 meters. consider points along the line connecting the two sources.
At points along the line connecting the two sources, the two sources of radio waves interfere with each other. This interference can result in constructive or destructive interference, depending on the relative phase of the waves at the point of interest.
If the two waves have the same phase, they will reinforce each other, resulting in constructive interference and a maximum in the total amplitude of the waves. If the two waves have a phase difference of 180 degrees, they will cancel each other out, resulting in destructive interference and a minimum in the total amplitude of the waves.
The phase difference between the two waves at a given point along the line connecting the two sources can be calculated using the difference in the path lengths from the two sources to the point. The path difference is given by:
d = (2n + 1) λ/2
where n is an integer, λ is the wavelength of the radio waves, and d is the path difference. For constructive interference, the path difference must be an integer multiple of λ, while for destructive interference, it must be an odd multiple of λ/2.
So, considering the two sources of radio waves a and b are 5.00 meters apart and each source emits waves with wavelength 6.00 meters, the path difference between the two waves at a given point along the line connecting the two sources can be calculated as d = 5.00 meters. Based on the equation above, this corresponds to a phase difference of approximately 150 degrees, resulting in destructive interference at that point.
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How does the proportion of hydrogen and helium in the universe support the big bang theory?.
According to extensive spectroscopic studies, it became clear that the hydrogen: helium ratio is proven to be 3:1. Along with the scarcity of other elements gives clues that supports Big Bang.
Before big bang all the atoms and molecules were dissociated and ionized. because the temperature was very higher. After Big Bang happened, the temperature falls down rapidly, and all ions fused to form atoms and molecules. Since the process was much faster protons and neutrons collided to form deuterium, Collision between deuterium and protons and neutrons occurred resulting in tritium and helium. A small amount of lithium was also formed. Formation of heavier atoms have not occurred because the process was rapid.
Almost all the matter were formed during this small time. Because of the rapid process hydrogen formed more constituting the 74% and helium next constituted 23-24%. All other elements were gradually formed during stellar evolutions. But still now the constitution of nuclear matter remains the same.
So the unchanging ratio supports the Big Bang theory.
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When heating this reaction mixture at reflux, the reaction temperature will be maintained at approximatelyA. 25CB. 65CC. 100CD. 125C
The reaction temperature will be maintained at approximately 100°C when heating the reaction mixture at reflux.
What is Reflux?Reflux is a common technique in organic chemistry where a reaction mixture is heated at a temperature near its boiling point, with the vapor generated by the reaction being condensed and returned to the reaction flask. This maintains the temperature of the reaction mixture at a constant value, typically near the boiling point of the solvent used in the reaction.
In general, the temperature of a reflux reaction will depend on the boiling point of the solvent used. If the solvent has a boiling point of 100°C, for example, then the reaction temperature will be maintained at approximately 100°C when the reaction mixture is heated at reflux.
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What is kinetic-molecular theory in solids?
Kinetic molecular theory states that gas particles are in constant motion and exhibit perfectly elastic collisions.
The assumption that matter is made up of microscopic particles that are always in motion is the foundation of the kinetic-molecular theory, a theory that describes the states of matter.
However, the theory is most simply understood when it is applied to gases, therefore this is where our in-depth study will start. The theory especially pertains to the ideal gas model of a gas. An ideal gas is a hypothetical gas whose behaviour exactly matches all of the kinetic-molecular theory's presumptions. Although they are not perfect in actuality, gases come extremely close to being perfect in most real-world situations.
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In the diagram, R1= 40.0 ohms,
Answer:
58.7Ω
Explanation:
You want the equivalent resistance of 40Ω in series with the parallel combination of 25.4Ω and 70.8Ω.
Parallel resistorsThe equivalent resistance of two parallel resistors, r1 and r2 is ...
req = 1/(1/r1 +1/r2)
For the two given parallel resistors, that is ...
1/(1/25.4 +1/70.8) ≈ 18.69 . . . . ohms
Equivalent resistanceThe circuit has a 40Ω resistor in series with this, so the equivalen resistance is ...
40 +18.69 = 58.69Ω ≈ 58.7Ω
__
Additional comment
Since the given resistor values are expressed to 0.1 ohms, we have rounded the answer to the same precision. The exact value is 141158/2405 as shown in the calculator display—assuming the given values are exact.
What is spring-mass-damper system formula?
The formula of a spring-mass-damper system is given by md2x/dt2 + cdx/dt + kx = F(t).
The spring-mass-damper system is a common model used in physics and engineering to describe the behavior of various mechanical systems, such as a car suspension system or a building during an earthquake. The equation of motion for a spring-mass-damper system is typically given by:
md2x/dt2 + cdx/dt + kx = F(t)
where m is the mass of the object attached to the spring and damper, x is the displacement of the mass from its equilibrium position, t is time, c is the damping coefficient, k is the spring constant, and F(t) is an external force applied to the system at time t.
The term md2x/dt2 represents the acceleration of the mass, while cdx/dt represents the damping force (i.e. resistance to motion) caused by the damper, and kx represents the force exerted by the spring. The external force F(t) can be any force applied to the system, such as an oscillating force or a constant force.
The solution to this differential equation depends on the initial conditions (i.e. the initial position and velocity of the mass) and the specific values of the parameters m, c, and k. The behavior of the system can be analyzed using various techniques, such as finding the natural frequency of the system or using numerical simulations to model the motion over time.
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Light and Sound Waves Quick Check
How are mechanical waves defined? (1 point)
1. They are waves that require some form of matter as a medium.
2. They are waves that involve matter, rather than energy, moving from one place to another.
3. They are waves that are generated by humans, rather than naturally.
4. They are waves that are able to pass through a vacuum.
Mechanical waves can be defined as one whereby 1. They are waves that require some form of matter as a medium.
What is mechanical wave?An oscillation of matter known as a mechanical wave is what is responsible for the transmission of energy via a medium. The transmission medium sets a restriction on how far a wave can travel. In this instance, there is almost little translational motion and the oscillating material rotates around a fixed point.
A mechanical wave is one whose energy cannot be transmitted via a vacuum. To transfer their energy from one place to another, mechanical waves need a medium. A mechanical wave is something like a sound wave.
Therefore, option 1 is correct.
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Answer:
1.
Explanation:
i did test
Three objects having the same mass begin at the same height, and all move down the same vertical distance h. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of of a string.
The work completed should be comparable in all three circumstances.
The body's work is equal to mgH. (Gravitational potential energy).
Gravity and the normal force are both at work on a body descending a frictionless inclined plane. It won't make a difference to the gravitational potential energy.
The purpose of distance calculationWe can find out an object's actual size by knowing how far away it is. The area an object occupies in space above us can be measured. Once we know how far away it is, we can calculate its true size.
What is a distance?Length is an item's general motion in a purposeless fashion. Distance can be thought of as the amount of space a thing has traveled since it first appeared.
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why did newton conclude that gravity has to be mutual and universal?
Newton concluded that gravity had to be mutual and universal because of his laws of motion. According to these laws, every action must have an equal and opposite reaction.
So, when an object attracts another object, the second object must also attract the first. This attraction must exist between all objects in the universe, thus making gravity mutual and universal.
Sir Isaac Newton's laws of motion, which were published in 1687, describe the motion of all objects in the universe.
The first law states that an object will remain at rest or move in a straight line unless an external force acts on it. The second law states that an object will accelerate when an external force acts on it.
From this, Newton concluded that if one object attracted another, then the second object must also be attracted to the first.
Therefore, Newton concluded that gravity was a mutual and universal force that acted between all objects in the universe.
He reasoned that since this force was mutual and acted on all objects, it must be the same force that kept the planets in orbit around the Sun.
This idea of universal gravity was revolutionary and changed the way people thought about the universe.
By demonstrating that all objects in the universe were subject to the same force, Newton showed that the universe was interconnected in a way that had never been seen before.
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early february is halfway between what two seasonal events. t/f
True.
Early February is halfway between the winter solstice and the spring equinox in the Northern Hemisphere.
What is Winter Solstice & Spring Equinox?The winter solstice occurs around December 21st or 22nd and marks the shortest day and longest night of the year. The spring equinox occurs around March 20th or 21st and marks the start of spring, when the day and night are roughly equal in length. Halfway between these two events is approximately February 10th, marking the gradual shift from winter to spring.
The winter solstice marks the point when the sun is at its farthest point from the equator and the Northern Hemisphere is tilted away from the sun, causing the shortest day and longest night of the year. On the other hand, the spring equinox marks the point when the sun is directly over the equator and the day and night are approximately equal in length.
Halfway between the winter solstice and the spring equinox is a time when the days start to get noticeably longer and the sun rises higher in the sky, signaling the end of winter and the beginning of spring. This is a gradual transition and not a sudden change. In early February, the sun rises earlier and sets later, and the length of daylight continues to increase until the spring equinox.
In the Northern Hemisphere, early February is a time when the weather starts to warm up and the first signs of spring become visible, such as the emergence of buds on trees and the first crocus flowers in gardens. However, it is still winter and the weather can be cold and wintry.
In the Southern Hemisphere, early February is the height of summer, with warm temperatures and longer daylight hours. This is the opposite of the Northern Hemisphere, where it is the height of winter.
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what term is used to describe published studies that describe original experiments in science?
Since it focuses on measuring, analyzing, and testing hypotheses, primary literature descriptions of original study produced by the are occasionally referred to as empirical research.
What does scientific experimental evidence entail?Observations made under controlled circumstances as opposed to through other forms of empirical study constitute experimental evidence. Researchers can deduce causes for a behavior they are studying thanks to experimental energy .
Which two sorts of experimental investigations are there?True experiments and quasi-experimental designs are the two broad categories into which experimental research can be divided. Both designs call for the manipulation of the treatment; but, whereas real experiments also call for randomization, quasi-experiments do not.
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4. A roller coaster car of mass m = 200 kg is released from rest at the top of a 60
Im high hill (position A), and rolls with negligible friction down the hill,
through a circular loop of radius 20 m (positions B, C, and D), and along a
horizontal track (to position E).
A
b = 60m
r = 20m
B
D
C
a. What is the velocity of the car at position B?
The velocity of the car at position B would be 34.7 m/s.
What is potential energy?The energy of the body due to its position in relative to earth is called potential energy.
Given is that a roller coaster car of mass m = 200 kg is released from rest at the top of a 60m high hill (position A), and rolls with negligible friction down the hill, through a circular loop of radius 20 m (positions B, C, and D), and along a horizontal track (to position E).
From the energy conservation, we can write -
mgh = 1/2 mv²
60 x 10 x 200 = 1/2 x 200 x v²
v² = 1200
v = √1200
v = 34.7 m/s
Therefore, the velocity of the car at position B would be 34.7 m/s.
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What is the difference between precession and nutation in terms of the earth's rotation?
Precession is the change in direction of axis without change in tilt. Whereas nutation is the rocking, swaying, or nodding motion in the axis of rotation.
What is the difference between precession and nutation?Precession and nutation are due to gravity of nearer Earth and farther Sun on the Earth that varies with changing distance. The inclination 5 deg of orbital plane of Moon to the Earth's orbital plane and the inclination of equatorial bulge of the Earth at 23.4 deg to ecliptic are also contributors.
Period of long-term precession motion is about 260 centuries. In this motion, poles trace small circle of radius almost 2530 km, about normal to ecliptic. The short-term nutation (nodding) of polar axis is having compounded period of almost 18.6 years from oscillations with smaller periods up to as low as some days.
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4. Find someone in the class that has a wire hoop with a different number of loops in it. When you put your magnet near their hoop, does it rotate at the same rate, at a greater rate, or at a lower rate? Explain why you think this is relative to their number of loops.
When you put your magnet near a wire hoop with a different number of loops, the rate of rotation will depend on the number of loops in the wire hoop.
How does wire hoop experiment work?The greater the number of loops, the greater the induced current and the stronger the magnetic field. This results in a greater torque on the wire hoop and a faster rate of rotation. On the other hand, a wire hoop with a smaller number of loops will have a weaker induced current and magnetic field, resulting in a slower rate of rotation.
Therefore, the rate of rotation of the wire hoop will depend on the number of loops in the wire hoop, with more loops resulting in a greater rate of rotation and fewer loops resulting in a slower rate of rotation.
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12. Viking 1, the first spacecraft to land on Mars, traveled 7.00x10 km in 303 d. Calculate its average
speed in kilometers per second
Answer:
Viking 1 had reached a top speed of over 4 kilometers per second, or almost 9000 miles per hour. This is a fair bit over 10 times the speed of sound (in air), making it well over supersonic speeds.
A 0. 36-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 48 n/m. The block is initially displaced 5 cm from the equilibrium point and then released to set up a simple harmonic motion. A frictional force of 0. 3 n exists between the block and surface. What is the speed of the block when it passes through the equilibrium point after being released from the 5-cm displacement point?.
The block moves at a speed of 40 m/s2 when it reaches the equilibrium point after being freed from the 5-cm displacement point.
What time of year is spring?Indian culture considers the months of March and April to be the start of spring, with an average high temperature of about 32 °C. Ugadi, the springtime celebration of some Indians, is notably popular in the state of Karnataka.
What makes springs crucial to physics?Springs play a crucial role in many complex physical systems because they provide as straightforward models for them. As you continue studying physics, you will see SHM repeatedly as it describes how things that behave like springs behave. the spring constant being denoted by k.
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what theory was written by copernicus, and it placed the sun in the middle of the solar system?
Copernicus proposed the heliocentric theory of the solar system, in which the sun is positioned at the system's centre.
In his heliocentric theory, Copernicus predicted the arrangement of all known planets and calculated their average orbital periods around the sun.He was also effective in explaining the everyday motions of heavenly bodies, such as the sun's rising and setting, with this idea.He said that the sun is fixed and situated at the centre of the solar system under this hypothesis.This model provided a mathematical explanation for the apparent daily motion of the stars and planets, and it also allowed for better predictions of their positions in the sky.
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A feather and a coin dropped in a vacuum fall with the equal
a) Momentum
b) Acceleration
c) Kinetic energy
d) Forces
In a vacuum, a feather and a coin will fall with equal acceleration, but not with equal forces, momentum, or kinetic energy.
What is kinetic energy?The drag force created by the air causes the feather to descend more slowly than the coin when there is air present. Both objects will descend with the same acceleration owing to gravity if there is no air present since there will be no air resistance.
Because the acceleration caused by gravity is constant, all objects in free fall will experience the same acceleration, which is around 9.8 m/s2, regardless of their mass. This implies that in a vacuum, the feather and the coin will descend at the same pace.
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What is a very long solid nonconducting cylinder of radius
A very long solid nonconducting cylinder of radius is a three dimensional object that is cylindrical in shape and has a very large length in comparison to its radius.
The cylinder is made of a nonconducting material which means that it does not conduct electricity. This type of cylinder can be used in a variety of applications such as insulating materials or structural support.. The radius of the cylinder refers to the distance from the center of the cylinder to its outer edge. The larger the radius: the greater the volume of the cylinder.
This means that a larger radius cylinder would be more useful in applications where a greater amount of material is required.
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How big is the Sun's radius compared to Earth?
The Sun is tons large than the Earth, with a radius of about 695,700 kilometers, while the earth has a radius of around 6,371 kilometers.
Because of this, the Sun's radius is greater than one hundred times larger than the earth's. The size difference between the Sun and the earth is quite massive.
In fact, if you have been to compare the sizes of the 2 items visually, the sun might appear as a huge, sparkling ball in the sky, while the earth might be just a tiny dot in contrast.
The sun's gigantic size performs a crucial position in the formation and renovation of our sun machine. Its gravity is chargeable for keeping all the planets in orbit, inclusive of the earth.
Additionally, the sun's excessive warmth and radiation provide the electricity important for existence to exist in the world. Standard, the sun's radius is an awful lot larger than earth's, and this size distinction has essential implications for the structure and behavior of our solar gadget.
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what is theory of change lewin?
The theory of change Lewin is a framework used to analyze and understand how a certain change can be achieved in a given situation.
The theory of change Lewin was developed by Kurt Lewin, a social psychologist who studied how to bring about change in organizations and communities. The theory explains that any change process involves three main stages: unfreezing, changing, and refreezing.
Unfreezing is when people become aware that change is necessary and are willing to let go of old habits and beliefs. Changing is the actual implementation of new behaviors and practices. Refreezing is when the new behaviors become the norm and are reinforced to ensure sustainability.
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During a race, the 48 kg runner accelerates from 5.1 m/s to 8.7 m/s to take the lead. What is the runner's change
in momentum?
Answer: the runner's change in momentum is 172.8 kg·m/s.
Explanation:
To find the change in momentum of the runner, we can use the equation:
change in momentum = mass x change in velocity
The mass of the runner is given as 48 kg, and the change in velocity can be calculated as:
change in velocity = final velocity - initial velocity
change in velocity = 8.7 m/s - 5.1 m/s
change in velocity = 3.6 m/s
Therefore, the change in momentum of the runner is:
change in momentum = mass x change in velocity
change in momentum = 48 kg x 3.6 m/s
change in momentum = 172.8 kg·m/s
So the runner's change in momentum is 172.8 kg·m/s.
rank the types of radiation in order of their energy, from least to greatest.
The types of radiation, ranked in order of their energy from least to greatest are:
Radio WavesMicrowavesInfrared RadiationVisible LightUltraviolet RadiationX-raysGamma RaysWhat is radiation?It's important to note that these types of radiation form a continuous spectrum, with the boundaries between each type of radiation being somewhat arbitrary. The amount of energy in a particular type of radiation depends on its frequency or wavelength. In general, radiation with higher frequency or shorter wavelength has more energy than radiation with lower frequency or longer wavelength.
Radiation refers to the emission of energy as electromagnetic waves or as moving subatomic particles, especially high-energy particles that cause ionization.
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In terms of the behaviour of molecules, describe what happens during the process of evaporation
Answer: Evaporation happens when a liquid substance becomes a gas. When water is heated, it evaporates. The molecules move and vibrate so quickly that they escape into the atmosphere as molecules of water vapor
Explanation: Evaporation is simply the heating of water to turn it to gas,like when you boil water in a kettle,that process is defined as evaporation
A spring of k=500 N/m that is initially compressed 2m is used to launch a 100N load of bricks up a 2 m tall
hill. Find the speed of the bricks at the top of the hill.
a. Qualitatively complete the energy flow diagram and the energy bar graphs.
c. Determine the speed
e. What would the speed at the top of the hill be with 2m of initial compression if 15% of the energy is
dissipated through friction?
d. What is the minimum compression of the spring necessary to get to the top of the hill? (v=0 at top, no
friction)
Speed of the bricks at the top of hill is 6.26 m/s. c.)speed of the bricks at the top of hill is 14.14 m/s. d)minimum compression of spring necessary to get to the top of hill is 6.26 m. e) speed of the bricks at the top of hill with 2 m of initial compression and 15% energy dissipation is 13.04 m/s.
What is energy?The capacity or power to do work, such as the capacity to move an object by application of force is called energy.
Initial potential energy of compressed spring is:
Ep = 1/2 kx^2 = 1/2 * 500 N/m * (2 m)^2 = 1000 J
k is spring constant, x is compression of the spring, and J is unit of energy in joules.
Final potential energy of the bricks is:
Ep = mgh = 100 N * 9.81 m/s^2 * 2 m = 1962 J
Ep = Ep
1/2 kx^2 = mgh
v = sqrt(2gh) = sqrt(2 * 9.81 m/s^2 * 2 m) = 6.26 m/s
Therefore, the speed of the bricks at the top of the hill is 6.26 m/s.
c. Initial potential energy of compressed spring is: 1000 J
Ek = Ep = 1000 J
Kinetic energy of the bricks is given by:
Ek = 1/2 mv^2
1000 J = 1/2 * 100 N * v^2
v = sqrt(200 / 1) = 14.14 m/s
Therefore, the speed of the bricks at the top of the hill is 14.14 m/s.
d. As, Ep = m g h
where m is mass of the bricks, g is acceleration due to gravity, and h is height of the hill.
Ep = 100 N * 9.81 m/s^2 * 2 m = 1962 J
Ep = 1/2 kx^2 = 1962 J
1/2 * 500 N/m * x^2 = 1962 J
x = sqrt(2 * 1962 J / 500 N/m) = 6.26 m
Therefore, the minimum compression of the spring necessary to get to the top of the hill is 6.26 m.
e. If 15% of the energy is dissipated through friction, final kinetic energy of the bricks at the top of the hill will be 85% of initial potential energy of the compressed spring. Therefore,
0.85 * 1000 J = 1/2 mv^2
v = sqrt(170 / 1) = 13.04 m/s
Therefore, the speed of the bricks at the top of the hill with 2 m of initial compression and 15% energy dissipation is 13.04 m/s.
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A 0. 50-m long solenoid consists of 800 turns of copper wire wound with a 5. 0 cm radius. When the current in the solenoid is 12 a, the magnetic field at a point 1. 0 cm from the central axis of the solenoid is.
The magnetic field at a point 1.0 cm from the central axis of the solenoid is 1.6 x 10^-3 T.
The magnetic field (B) inside a solenoid can be calculated using the formula:
B = μ_0 * n * I / L
where μ_0 is the vacuum permeability (4π x 10^-7 T m/A), n is the number of turns per unit length, I is the current in the solenoid, and L is the length of the solenoid.
For the given solenoid, the number of turns per unit length can be calculated as follows:
n = 800 turns / 0.5 m
n = 1600 turns/m
At a point 1.0 cm from the central axis of the solenoid, the magnetic field can be calculated as follows:
B = μ_0 * 1600 turns/m * 12 A / (0.05 m)
B = 1.6 x 10^-3 T.
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a mass is hanging from spring and vibrating. it is replaced by a mass which is twice as large and its amplitude is increased by a factor of two. what happens to the period of the pendulum?
The period of the pendulum will increase by a factor of √2 when the mass is replaced by a mass that is twice as large, but the amplitude is increased by a factor of 2.
The period of a simple harmonic oscillator, such as a mass hanging from a spring, is given by:
T = 2π√(m/k)
where T is the period, m is the mass, and k is the spring constant.
If we replace the original mass with a new mass that is twice as large, the period will change as follows:
T' = 2π√(2m/k)
where T' is the new period.
If we also increase the amplitude of the motion by a factor of 2, this will not affect the period of the pendulum. The period depends only on the mass and the spring constant, and is independent of the amplitude of the motion.
Therefore, the new period of the pendulum will be:
T' = 2π√(2m/k)
which is equal to the original period multiplied by the square root of 2.
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