Answer:
There are several advantages to the high specific heat capacity of water. Some of the key advantages are:
1.Water can store a large amount of heat energy without undergoing significant temperature changes. This means that water can help to regulate the temperature of the Earth and other bodies of water, providing a stable environment for life to thrive.
2.The high specific heat capacity of water allows it to act as a buffer against temperature changes. For example, when the temperature outside is very hot, water bodies such as oceans and lakes can absorb some of the heat energy, preventing the temperature from getting too high. Similarly, when the temperature outside is very cold, water bodies can release some of their stored heat energy, helping to keep the temperature from dropping too low.
3.The high specific heat capacity of water also makes it a useful heat transfer medium. Water can be heated and then used to transfer heat to other objects, such as in a radiator or a steam engine. This allows water to be used in a variety of industrial and domestic applications.
Technetium‑99m, an important radionuclide in medicine, has a half‑life of 6.0 hours. What percentage of a sample of technetium‑99m will remain undecayed after each of the given times?
After specific periods, 12.5g of a technetium-99m sample will still be intact.
What is radionuclide used for?Radionuclide scan is used for disease identification, classification, and tracking. The radionuclide is injected into the vein after being consumed in very small amounts. Various radionuclides are transported to various organs via human blood. Examples of radionuclides include strontium-90, cesium-137, and radium-226. Some are produced artificially, either on purpose or as consequences from nuclear reactions, while others are found produced naturally in nature.
Briefing:Consider the fact that first order kinetics governs radioactive decay. So, keep in mind
ln [A]t=−kt + ln[A]₀ and by extension,
t[tex]\frac{1}{2}[/tex]=1n(2)/k
Now, let's derive the rate constant,
k=1n(2)/t[tex]\frac{1}{2}[/tex]
=0.116h⁻¹
Given
t=6h,
1n=Aτ/A₀
Aτ=12.5g
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how does the presence of an active galactic nucleus in a starburst galaxy affect the starburst process?
The availability of the a galactic nucleus inside a galaxy experiencing starbursts can slow or stop the starburst process.
Why did Coles and Woolworths stop selling Starburst?Due to "increasing financial concerns," Mars Wrigley quietly pulls Starburst candies from grocery shelves throughout Australia. An popular Australian lollipop brand got dropped by a US confectionery business after one social media user noticed her favorite delicacy was inexplicably gone while looking for it.
What are Starburst called now?22 years after being renamed, Starburst will become Opal Fruit, according to a statement from the candy's manufacturer, Mars. Stores including Poundland, B&M, Home Bargains, Iceland, Savers, and others will sell the goods for fans to purchase.
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how are distant (young) galaxies different from the galaxies that we see in the universe today? what is the evidence that star formation began when the universe was only a few hundred million years old?
Less brilliant and gas-rich galaxies could be found in the distance, distant (young) galaxies different from the galaxies that we see in the universe today.
All of space, time, and its objects, such as planets, stars, galaxies, and other types of matter and energy, are collectively referred to as the universe. The prevailing cosmological explanation for the universe's formation is the Big Bang theory. The universe has been expanding ever since the Big Bang, which occurred 13.7870.020 billion years ago, according to this theory. It is feasible to measure the size of the observable universe, which is around 93 billion light-years in diameter at the moment, even if the total spatial extent of the universe is unknown. Some of the earliest geocentric views of the cosmos, which centered on Earth, were developed by Greek and Indian philosophers. The Sun was positioned at the center of the Solar System by Nicolaus Copernicus in the heliocentric model, which was developed in response to increasingly precise astronomical measurements throughout time. When developing the law of universal gravitation, Isaac Newton built upon the research of Copernicus, Johannes Kepler's planetary motion equations, and Tycho Brahe's observations.
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What is the acceleration of a motorcycle moving north when the speed goes from 0-80 mi/hr in 8 seconds?
Answer:
0.003 mi/s²
Explanation:
a = (Vf - Vi) / t
Vi = 0 (started from rest)
First you have to convert MPH into miles/sec (the problem did not state that you have to convert to meters/sec)
(80 miles/hr)/(3600 sec/hr) = 0.022 mi/sec
a = (0.022 mi/sec - 0)/8 sec = 0.003 mi/s²
what would you have to do and/or what equipment would you need to have, in order to live in jupiter safely?
Jupiter is a gas giant with no solid surface so it needs airships floating houses or spacecraft to live on.
Jupiter is the fifth planet from the Sun and the largest planet in the solar system. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth the mass of the Sun.
Jupiter's magnetic field traps charged particles from the Sun and Mars's volcanic moon Io. These particles create intense radiation belts. The radiation belt around Io's orbit is powerful enough to kill an unprotected human within minutes. It's easy to see with your eyes if you know when and where to look.
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if a car is traveling westward and slowing down, what is the direction of the force on the car that causes it to slow down?
If the car is traveling westward and slowing down, then the direction of the force on the car that causes it to slow down must act to eastward direction.
If the car is slowing down, a force must be pulling in the direction opposite to its velocity. In the given situation the car is moving westward and slowing down, so force that will slow it down will act towards eastward i.e. acceleration will be in eastward direction and negative because direction of acceleration is opposite to its motion.
what is acceleration:
Acceleration is the rate at which velocity changes with time, in terms of both speed and direction. A point or an object moving in a straight line is accelerated if it speeds up or slows down.
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The planet Earth orbits around the Sun and also spins on its own axis.
- Calculate the angular momentum, in kilogram meters squared per second, of the Earth in its orbit around the Sun.
- Calculate the angular momentum, in kilogram meters squared per second, of the Earth spining on its axis.
- How many times larger is the angular momentum of the Earth in its orbit than the angular momentum of the Earth spinning on its axis?\
In Newtonian physics, an object's mass and velocity are combined to form momentum, more precisely linear momentum or translational momentum. It is a mechanically accepted amount.
The angular momentum can be found by the formula:
L = m · v · r
Where:
mass of Earth = m = 10²⁴ ×5.972 kg
v = velocity of Earth around the Sun = 2.978×10⁴ m/s
r = distance from Sun = 1.496×10¹¹ m
Now, apply the formula:
L = 5.972×10²⁴ · 2.978×10⁴ · 1.496×10¹¹
= 2.661×10⁴⁰ kg·m²/s
The angular momentum of Earth in its motion around the Sun is 2.661×10⁴⁰ kg·m²/s.
It is a mechanically accepted amount. It has both a magnitude and a direction, making it a vector quantity. If an item has a mass of m and a velocity of v (also a vector quantity), then it has momentum of p.
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Why is there no such thing as an ideal machine? A. Machines never have friction. B. Machines are always breaking. C. No machine is 100% efficient. D. The work input always equals the work output.
There is no such thing as an ideal machine because no machine is 100 % efficient.
Hence option D is the correct option.
For a machine to be ideal, machine should follow many criteria the machine should be frictionless and the work input must always be equal to the work output.
In reality, no machine is an ideal machine as every machine involves friction. There is no machine without friction. Friction is a necessity in our life. Without friction, we can not survive. Friction helps us to walk and even stop. Friction is like oxygen, it has vital importance in our life. Hence no machine is friction-free and friction causes wear and tear in machines. Similarly, no machine is 100 % efficient. There is always some energy loss in the process, so work input is never equal to the work output.
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Chevrolet Corvette Sting Ray developed 360 horsepower and hada displacement of 327 cubic inches. Express this displacement inliters (L) by using only the conversions 1 L = 1000 cm3 and1 in. = 2.54 cm.
The displacement in litres is 5.36 L.
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects.
Horsepower = 360
Displacement 327 inches³
1 L = 1000 cm³
1 inch = 2.54 cm
Displacement in litres is =
First find displacement in cubic centimetre =
= d = 327 inch³ X (2.54 cm / 1m)³
= d = 327 X 2.54
= d = 5358.57 cm³
We know that, 1 L = 1000 cm³,
Thus,
The displacement in Litres is =
= d = 5358.57 cm³ X (1L / 1000 cm³)
= d = 5.36 L
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a guitar string has its length shortened to 3/4 of its intial length. if the original frequency was 256 hz what will the final frequency be
frequency is inversely proportional to the length. So, the magnitude of the final frequency is 341 Hz
What is Frequency ?
Frequency can be defined as the number of complete revolution per second made by a vibrating body.
Given that a guitar string has its length shortened to 3/4 of its initial length. if the original frequency was 256 Hz, what will the final frequency be ?
Experiment shows that frequency is inversely proportional to the length of the string. That is, F [tex]\alpha[/tex] 1/L
F = V/L
V = FL
Since the speed of the sound is the same, we can say
F1L1 = F2L2
Where
F1 = 256 HzL1 = LF2 = ?L2 = 3L/4Substitute all the parameters
256L = 3L/4 × F2
The L cancels out
256 = 3/4 × F2
F2 = 4/3 × 256
F2 = 1024/3
F2 = 341.3 Hz
Therefore, the final frequency will be 341.3 Hz
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explain how the difference between the observed lapse rate and the adiabatic lapse rate causes air parcels to move toward or away from their original location
The observed lapse rate refers to the decrease in temperature with increasing tropospheric altitude. This is the temperature of the environment at different altitudes. It does not imply air movement. Adiabatic cooling relates only to rising air cooling by expansion.
The ambient Leakage Rate is the rate at which the air temperature increases. Our surroundings change as we rise into the atmosphere. Dry adiabaticity is when an unsaturated air mass expands and cools as it rises through the atmosphere or heats and compresses as it descends.
So the rising air cools slowly as it rises. The wet adiabatic decay rate is generally less negative than the dry adiabatic decay rate. If the environmental decay rate is greater than the dry adiabatic decay rate, the atmosphere is said to be absolutely unstable. This means that the rising air mass will always cool more slowly than its surroundings even if it is not saturated.
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discuss whether any work is being done by each of the following agents and, if so, whether the work is posi- tive or negative. (a) a chicken scratching the ground (b) a person studying (c) a crane lifting a bucket of concrete (d) the gravitational force on the bucket in part (c) (e) the leg muscles of a person in the act of sitting down
(a) The act of a chicken scratching the ground is doing positive work.
(b) A person studying does no work.
(c) A crane lifting a bucket of concrete does positive work.
(d) The gravitational force on the bucket in part (c) does negative work.
(e) When a person sits down, their leg muscles are said to be doing negative work.
We are aware of the work equation as being the result of force and displacement.
(a) The work done will be positive as the chicken is scratching the ground. Here, the displacement is along the direction of force.
(b) As there is no displacement, work done is zero, learning the language of physics is not work.
(c) The crane uses the bucket to perform positive work, and the displacement in this case is in the force's direction.
(d) The force of gravity pulls the bucket downward. In this case, the work completed will be negative because the forces acting on the bucket are in opposition to one another.
(e) Since the muscle's applied force are opposite to the displacement, negative work will be done.
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A long -jumper had a take-off of 9.5m/s. What is the maximum possible horizontal distance the man can jump
Answer:
4.5125m
Explanation:
Initial Velocity(U)=9.5m/s
Maximum Horizontal Distance (i.e maximum height) = ?
V^2=U^2-2gH (negative because the motion is against gravity i.e g is negative)
where V=0m/s and g=10m/s^20^2=9.5^2-(2×10×H)
0=90.25-20H
20H=90.25
H=90.25/20=4.5125m
i need the answer for this question it’s physics
Answer: 2 m/s. v = Δx/Δt = (12 m)/(6 s)
a car is moving at a constant tangential speed of 50.0 m/s and takes one lap around a circular track in a time of 74.4 s. what is the magnitude of the acceleration of the car?
Answer: 0.0541
Explanation:
If the car took a time of 74.4 seconds to complete one lap around a circular track, the circumference of the track is 50.0 m/s * 74.4 s = <<50.0*74.4=3720>>3720 m.
The radius of the circular track is half the circumference, so it is 3720/2 = <<3720/2=1860>>1860 m.
The acceleration of a body moving in a circle with constant speed is given by the formula a = v^2/r, where a is the acceleration, v is the speed, and r is the radius of the circle.
Therefore, the magnitude of the acceleration of the car is 50.0^2/1860 = <<50.0^2/1860=0.0541>>0.0541 m/s^2
what characterized the sound of the second wave of hip-hop, as characterized in the work of run-dmc and the beastie boys?
The characterized the sound of the second wave of hip-hop, as characterized in the work of run-dmc and the beastie boys is that it is second wave.
S-waves (secondary waves or shear waves) are a swaying, rolling motion that rocks the ground back and forth perpendicular to the direction of the wave and lasts more slowly.
Wave – A secondary body wave that vibrates the ground perpendicular to the direction of wave propagation. They travel about 1.7 times faster than P waves. S-waves cannot travel through liquids such as water, lava, and the outer core of the Earth because liquids cannot withstand shear stress.59.903
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1) how does a white dwarf differ from a neutron star? how does each form? what keeps each from collapsing under its own weight?
An electron degenerate object is a white dwarf, whereas a neutron star is a neutron degenerate object. A white dwarf is less compact and has a larger radius than a neutron star.
A white dwarf is very dense, its mass is comparable to that of the Sun.
A white dwarf would collapse into a denser entity known as a neutron star if it reached the Chandrasekhar limit and nuclear reactions were to stop. This would happen if nuclear reactions continued to occur.
White dwarf stars are prevented from collapsing by the fact that electrons are fermions, while neutron stars are prevented from collapsing by the fact that electrons are fermions.
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planet dreidel has a radius that is twice as large as the radius of earth and dreidel has three times the mass that earth has. harry weights 1200 n on earth, and is taken to the surface of planet dreidel, how much would harry weigh on the new planet?
Harry's weight is 1200 N on earth, then Harry's weight on the planet Dreidel is 355 N.
The force of gravity or the weight of an object on a planet is affected by the gravitational acceleration on that planet.
R[tex]__e[/tex] = R
R[tex]__p[/tex] = 2R
ρ[tex]__p[/tex] = 1/3 ρ[tex]__e[/tex]
w[tex]__e[/tex] = 1200 N
Determine the ratio of the mass of the earth to the mass of the planet through the relationship:
ρ = m/V → m = ρV
So:
[tex]\frac{me}{mp} = \frac{ p_e V_e}{p_pV_p}[/tex] (1)
Where is the volume of the planet. If both the earth and the planet are considered a ball, then it has the shape:
V = 4/3πR³
So, if we substitute the form above into the equation, we will get:
[tex]\frac{me}{mp} = \frac{p_eR_e^3}{p_pR_p^3} \\\\\frac{me}{mp} = \frac{p_eR_e^3}{1/3p_p(2R)^3}\\\\\frac{me}{mp} = \frac{3}{8}[/tex] (2)
The weight of an object is expressed as:
[tex]w =G\frac{mM}{r^2}[/tex]
If we take the comparison of the object's weight when it is on the earth's surface from the planet's surface it meets the:
[tex]\frac{w_e}{w_p} = \frac{me}{mp} (\frac{R_p +R}{R_e} )^2\\\\\frac{1200}{w_p} = \frac{3}{8} (\frac{2R +R}{R} )^2\\\\\frac{1200}{w_p} = \frac{3}{8} (\frac{9}{1} )^2\\\\w_p= \frac{1200 (8)}{3 (9)} \\\\w_p= \frac{9600}{27} = 355 N[/tex]
Hence Harry's weight on the new planet is 355 N.
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when a mass m hangs from a vertical wire of length l, waves travel on this wire with a speed v.A. what will be the speed of these waves if we triple M without stretching the wire?
B. what will be the speed of these waves if we replace the wire with an identical one, except twice as long?
C. What will be the speed of these waves if we replace the wire with one of the same length, but two times as heavy
D. what will be the speed of these waves if we stretch the wire to thrice its original length
E. What will be the speed of these waves (in terms of V) if we increase M by a factor of 18.0, which stretches the wire to double its origina length?
A. The speed of the waves will remain unchanged if the mass is tripled without stretching the wire.
B. The speed of the waves will be halved if the wire is replaced with an identical one, except twice as long. This is because the waves will have to travel twice the distance in the same amount of time.
C. The speed of the waves will remain unchanged if the wire is replaced with one of the same lengths, but two times as heavy.
D. The speed of the waves will be halved if the wire is stretched to thrice its original length. This is because the waves will have to travel thrice the distance in the same amount of time.
E. The speed of the waves will be halved if the mass is increased by a factor of 18.0 and the wire is stretched to double its original length. This is because the waves will have to travel twice the distance in the same amount of time. The speed of the waves will thus be V/2.
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During laboratory investigation, students determined a large block of iron to have a density of 7.75 g/mL. If the block were to be cut in half, what would be the density of the smaller block?a. 7.75 g/mLb. 15.5 g/mLc. 3.88 g/mLd. 5.58 g/mL
If the density of the whole block is 7.75 g/mL, then the density of half of it is also 7.75 g/mL. (a)
The density of any substance is the same ... mass/volume ... no matter how big or small the sample is.
If the substance is pure, then its density is always the same. It doesn't matter whether your sample is a tiny drop in the middle of your finger-nail or a super-tanker full of it.
rank the objects from least to greatest mass, according to the stars that produce each. a. neutron star b. black hole c. white dwarf group of answer choices
Rank the objects from least to greatest mass, according to the stars that produce each:
White DwarfNeutron StarBlack holeA property of a body that is a measure of inertia is usually viewed as a measure of the amount of matter contained in the body that causes it to have weight in a gravitational field. Mass is a dimensionless quantity that describes the amount of matter in a particle or object.
The mass of an object is a measure of its inertial properties or the amount of matter it contains. The weight of an object is a measure of the force exerted on it by gravity, or the force required to support it. Mass can best be understood as the amount of matter present in an object or body. Everything around us has mass.
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calculate δs∘rxn for this balanced chemical equation. 2no(g)+o2(g)→2no2(g)
The δs∘rxn for the reaction 2NO(g)+O₂(g) → 2NO₂(g) is -146 J/K.
Entropy is a scientific concept and observable physical feature that is typically associated with a state of chaos, unpredictability, or uncertainty.
The unpredictability or chaos of the system would be gauged by entropy. As unpredictability rises, so does entropy. It has a state function as well as a wide range of attributes. The unit is present J⁻¹ K mol⁻¹ .
ΔS°rxn = 2 mol × S°(2NO(g) - S°O₂(g) - 1mol S°O₂
ΔS°rxn = 2 mol × 240 J/mol.K - 2 mol × 210 J/mol.K-1 mol ×205.2 J/mol.K
ΔS°rxn = -146.8 J/K
Therefore, the δs∘rxn for the reaction 2NO(g)+O₂(g)→2NO₂(g) would be -146 J/K.
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the belt of constellations through which all the planets move is called the ________.
The belt of constellations through which all the planets move is called the Zodiac. The zodiac belt runs along the plane of the ecliptic.
The Zodiac is the belt of constellations that all the planets pass through. The sun and moon are also always within this belt. The ecliptic occurs when they appear to move ordinarily along on the particular path through the sky. On the path of the ecliptic, those are 13 astronomical constellations:
CapricornusAquariusPiscesAriesTaurusGemini CancerLeo VirgoLibraScorpiusSagittariusOphiuchus.In the fifth century B.C., astronomers identified the 12 astronomical constellations as zodiac signs without Ophiuchus. Ophiuchus did not fit into the ancient calendar of 12 lunar months. As a result, the astronomers omitted Ophiuchus for practical reasons.
Astronomy studies the constellations of the zodiac. So, the constellations of the zodiac are not astrology, which is concerned with personal characteristics (zodiac signs differ with zodiac constellations). In the past, they assisted in the creation of calendars and served to track the time period and the seasons for ancient people. They are still applied today for scientific observations and maritime navigation. For example, they serve as excellent reference points for amateur astronomers when trying to find planets.
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a 60.-kilogram car travels clockwise in a horizontal circle of radius 10. meters at 5.0 meters per second. towards which letter will the car move if it hits ice at the bottom of the circle?
If the vehicle strikes ice at the circle's base, 150N will cause it to move.
What does a kilogram mean?The International Bureau of Weights and Measures defines it as the mass of a certain international prototype constructed of platinum-iridium and stored there. Initially, it was specified as being equal to the mass of one liter (10-3 cubic meters) of pure water. A mass of 1 kilogram weighs roughly 2.20 pounds at the surface of the Earth (lb).
What does 1 kilogram represent?The metric system's fundamental unit of mass is the kilogram (kg). The mass of 1,000 cubic centimeters of water is very nearly equal to one kilogram, although it was initially intended to be exactly equal. The precise definition of a pound is 0.45359237 kg.
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1.5 m/s is a typical walking speed. At what temperature (in degrees Celsius) would nitrogen molecules have an rms speed of 1.5 m/s?
At -272.997°C the nitrogen molecules will have an rms speed of 1.5 m/s
The speed of gas molecules is the speed experienced by gas particles based on their average speed. Molecular velocity is a representation of the overall value of the speed of gas molecules moving in a vessel.
Given that
The molecular mass of nitrogen is m = 28(1.66x 10⁻²⁷ kg) = 4.6 x 10⁻²⁶ kg
The speed rms formula is
vrms = √[(3kT)/m]
So, the temperature
T = (v)²(m)/(3k)
T = (1.50 m/s)²(4.6 x 10⁻²⁶ kg)/(3(1.38 x 10⁻²³K)
T = (2.25 m/s) (4.6 x 10⁻²⁶ kg)/(4.14 x 10⁻²³K)
T = 10,35 x 10⁻²⁶/4.14 x 10⁻²³K
T = 2,5 x 10⁻³
T = 00025 K.
T = 2.5 mK
in °C
T = -272.997°C
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A braking force of 6000 N was applied to a 1000-kg automobile bringing it to a complete stop in 75 m.
–How much work was done in stopping the automobile?
–How did the kinetic energy of the automobile change?
–What relationship could be used to find the initial velocity of the automobile before the brakes were applied?
–Calculate the initial velocity of the automobile before the brakes were applied.
a) The work done is 450 kJ
b) The kinetic energy gets lesser with time
c) The relation is v^2 = u^2 - 2as
d) The initial velocity is 30 m/s
What is the work done?We know that the work that is done is the product of the force and the distance that is moved by a body. We know that work is said to be done when the force that is applied moves a distance in the direction of the force.
1) Work done = Force * distance
= 6000 N * 75 m
= 450 kJ
2) The kinetic energy of the automobile would decrease with time.
3) To obtain the initial velocity we have to use the relation;
v^2 = u^2 - 2as
v = final velocity
u = initial velocity
a = acceleration
s = distance covered
Given that;
F = ma
a = F/m
a = 6000 N / 1000-kg
a = 6 m/s^2
The we have;
0^2 = u^2 - (2 * 6 * 75)
u^2 = (2 * 6 * 75)
u = √ (2 * 6 * 75)
u = √900
u = 30 m/s
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A woman of mass 53 kg jumps off the bow of
a 62 kg canoe that is intially at rest.
If her velocity is 3.5 m/s to the right, what
is the velocity of the canoe after she jumps?
Answer in units of m/sˆı.
The velocity of the canoe after the woman jumps is 2.99 m/s to the left.
What is the velocity of the canoe?The velocity of the canoe is calculated by applying the principle of conservation of linear momentum as shown below.
m₁u₁ + m₂u₂ = v (m₁ + m₂)
where;
m₁ is the mass of the canoeu₁ is the velocity of the canoe after the woman jumpsu₂ is the velocity if the woman after she jumpsv is the initial common velocity of the woman and the canoe(53)(3.5) + 62(u) = 0(53 + 62)
185.5 + 62u = 0
-62u = 185.5
u = -185.5 / 62
u = -2.99 m/s
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(a) what is the effect on the period of a pendulum if you double its length? (b) what is the effect on the period of a pendulum if you decrease its length by 5.00%?
The effect on the period of a pendulum if you double its length is the period increases by a factor of √2 and if you decrease its length of a pendulum by 5.00% the period decreases by 2.5%.
A pendulum has an initial period of 2π√L/ g and then it has some new period T2 which is 2π√L2/g
(a) Give that L2 = 2L1
So we'll substitute in 2L1 in place of L2
T2 = 2π√2L1/g = √2T1
So when doubling the length, the period increases by a factor of √2
(b) Given that length of a pendulum decreases by 5.00%
Then length of remaining pendulum = L2 = 95% L1= 0.95L1
T2= 2π√L2/g = 2π√0.95L1/g = √0.95T1 = 0.975T1
Hence it decreases by 2.5%.
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which of the following defines a function f for which f(-x)=-f(x)
b) f(x) = cos(x) is the equation the satisfies the given conditon f(-x) = f(x)
To check for every function if they satisfies the conditon f(-x ) =f(x)
for option a)
f(x) = sin(x)
f(-x) = sin(-x)
=> -sin(x)
so in this option f(x) ≠ f(-x) so this option is not correct
for option b)
f(x)=cos(x)
f(-x) = cos(-x)
=> cos(x)
so in this option f(x) = f(-x) so this option is correct
for option c)
f(x) = log(x)
f(-x) = log(-x)
=> log(1/x)
so in this option f(x) ≠ f(-x) so this option is not correct
for option d)
f(x) = [tex]e^x[/tex]
f(-x) = [tex]e^-^x[/tex]
=> [tex]\frac{1}{e^x}[/tex]
so in this option f(x) ≠ f(-x) so this option is not correct
so only option B is correct.
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Complete question:
which of the following defines a function f for which f(-x)=-f(x)
a) f(x) = sin(x)
b) f(x) = cos(x)
c) f(x) = log(x)
d) f(x) = [tex]e^x[/tex]
a car traveling at 20 m/s follows a curve in the road so that its centripetal acceleration is 5 m/s2. what is the radius of the curve?
A car traveling at 20 m/s follows a curve in the road so that its centripetal acceleration is 5 m/s. 160 m is the radius of the curve.
To find the radius of the curve, we can use the formula for centripetal acceleration:
a = v^2 / r
where a is the centripetal acceleration, v is the velocity, and r is the radius of the curve. In this case, we know that the velocity of the car is 20 m/s and the centripetal acceleration is 5 m/s2. We can solve for the radius of the curve by rearranging the formula and substituting the known values:
r = v^2 / a
= (20 m/s)^2 / 5 m/s2
= 800 m / 5 m/s2
= 160 m
Therefore, the radius of the curve is 160 m.
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. When a vehicle turns, its velocity vector is altered by an acceleration in the new direction. The acceleration of the car in its present direction of motion is referred to as a linear acceleration (or tangential acceleration in circular motions).
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