Answer: I hope this helps
Explanation:
The law is named after Amedeo Avogadro who, in 1812, hypothesized that two given samples of an ideal gas, of the same volume and at the same temperature and pressure, contain the same number of molecules.n 1811 Avogadro put forward a hypothesis that was neglected by his contemporaries for years. Eventually proven correct, this hypothesis became known as Avogadro's law, a fundamental law of gases.On this day in 1776, Amedeo Avogadro, an Italian scientist known as one of the founders of physical chemistry, was born. Avogadro studied the properties of electricity and liquids, but his best known work was with gases. It was known by 1809 that all gases, when heated equally, expand by the same amount.
Here is a example of the classical conditioning process. A kid was drinking a Sprite soda. When he wasn’t looking, a bee crawled into the can. He took another drink and was stung by a bee on the inside of his cheek. He was startled and in pain! For years afterward, Sprite soda made him feel anxious.
Identify from this example the unconditioned stimulus, unconditioned response, conditioned stimulus, and conditioned response.
Answer:
The unconditioned stimulus (UCS) in this illustration of classical conditioning is a bee sting. The child's discomfort and startle response are examples of the unconditioned response (UCR).
The Sprite drink is the conditioned stimulus (CS). The Sprite soda did not initially elicit any specific reactions (it was neutral). However, since the child had a bee sting while drinking soda, the discomfort and bee sting are now connected to the beverage, specifically Sprite.
The child's fear of the Sprite soda is the conditioned reaction (CR). The child now has anxiety whenever he sees or consumes sprite soda as a result of the link between the bee sting and the soda.
Explanation:
see above
A small toy car of mass 3.00kg runs into another toy car of mass 2.00kg at rest. They stick together and slide 2.0 meters along the rough floor m = 0.25. how fast was the first car going when it hit the ground car? Is this collision elastic or inelastic?
Answer:
Explanation:To determine the speed of the first car when it hit the second car, we can use the conservation of momentum. The momentum of the first car before the collision is equal to its mass multiplied by its velocity, and the momentum of the two cars after the collision is also equal to their combined mass multiplied by their combined velocity.
The momentum of the first car before the collision is 3.00kg * v1 = m1 * v1
The momentum of the two cars after the collision is (3.00kg + 2.00kg) * v2 = (m1 + m2) * v2
From the conservation of momentum, we can set these two equations equal to each other and solve for v1:
m1 * v1 = (m1 + m2) * v2
v1 = (m1 + m2) * v2 / m1
v1 = (3.00kg + 2.00kg) * v2 / 3.00kg
v1 = 5.00kg * v2 / 3.00kg
v1 = (5/3) * v2
The combined velocity of the two cars after collision is v2 = 2.0m / (2.0s) = 1.0m/s
Therefore, the first car was going at (5/3) * 1.0m/s = 1.67m/s.
To determine if this collision is elastic or inelastic, we need to calculate the coefficient of restitution (e).
e = (initial velocity of first car - final velocity of first car) / (initial velocity of first car)
The initial velocity of the first car was 1.67m/s and final velocity of the first car is 0 m/s (since it stops after the collision).
e = (1.67m/s - 0m/s ) / (1.67m/s)
e = 1.0
The coefficient of restitution is 1.0, which means the collision is perfectly elastic. This means that the kinetic energy is conserved in the collision.
explain the difference between electricity and electrical energy
Explanation:
Electrical energy is caused by moving electric charges called electrons. Electricity is a type of energy that comes from electrical energy.
The speed of a moving bullet can be determined by allowing the bullet to pass through
two rotating paper disks mounted a distance
97 cm apart on the same axle. From the
angular displacement 12.9◦
of the two bullet holes in the disks and the rotational speed
1319 rev/min of the disks, we can determine
the speed of the bullet.
What is the speed of the bullet?
Answer in units of m/s.
Answer:
f = 1219/min = 1219 / 60 / sec = 20.32 / sec
T = 1/f = 1 / 20.32 = .04922 sec period of 1 revolution
t = 12.9 / 360 * .04922 = .001764 sec time to pass between disks
V = S / t = .97 m / .001764 = 550 m/sec
A 75-kg base runner begins his slide into second base when he is moving at a speed of 5.0 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base.
a) How much mechanical energy is lost due to friction acting on the runner? how many J?
b) How far does he slide? how many m?
(a) The mechanical energy lost due to friction force acting on the runner is 936.4 J.
(b) The distance travelled by the runner as he slides is 1.82 m.
What is the acceleration of the runner?The acceleration of the runner is calculated by applying Newton's second law of motion as shown below.
ma = μmg
a = μg
where;
μ is the coefficient of frictiong is acceleration due to gravitya = ( 0.7 x 9.8 m/s² )
a = 6.86 m/s²
The distance travelled by the runner is calculated as;
v² = u² - 2as
where;
v is the final velocity of the runner = 0u is the initial velocity of the runners is the distance travelled by the runnera is the acceleration of the runner0 = u² - 2as
s = u² / 2a
s = ( 5² ) / ( 2 x 6.86 )
s = 1.82 m
The mechanical energy lost due to friction force is calculated as;
W = Fs
W = mas
W = ( 75 kg x 6.86 m/s² x 1.82 m )
W = 936.4 J
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Dr. Burke performs an experiment to determine how plants grow in a variety of temperature and moisture conditions. He runs five trials with five different groups of the same species of plant. The table below shows the results from his experiment. Plant Group Temperature Moisture Average Plant Growth Group 1 high high 2 in Group 2 moderate moderate 6 in Group 3 low low 0 in Group 4 high moderate 3 in Group 5 moderate high 4 in After finishing the experiment, Dr. Burke explains that heat and moisture have no effect on plant growth. Based on the evidence shown in the table, is his explanation valid?
No, his explanation is not valid. The data from the experiment shows that both temperature and moisture do have an effect on plant growth.
What is the temperature?
An object's temperature serves as a gauge for its heat or coldness. Temperature is usually measured in degrees on the Celsius or Fahrenheit scales. At a temperature of 0 degrees Celsius (or 32 degrees Fahrenheit), water freezes. At 100 degrees Celsius (or 212 degrees Fahrenheit), water boils. Temperature can affect how quickly things happen, such as the speed at which a chemical reaction takes place. Temperature also affects how people and other living things feel and behave.
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If you charge a rod by running it through some material like fur, and then bring it near a stream of water that has no charge, the water will show some attraction to the rod. This is because _____.
of electrostatic induction
of friction and contact
electricity is conducted through water
none of the above
The attraction of the water is because of electrostatic induction. Option A
What is static electricity?We know that it is possible for static electricity to be induced on a body. In the first case, the charge that we have obtained is one that we have gotten by the purpose of friction. That is the running of one material against the other.
In the second case, we can see that there is a transfer of charge from one material to the other without the materials actually touching. This is charging by induction.
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Calculate the distance (in km) between a moonlet ( m = 6.3 x1014 kg ) and an alien planet ( M = 1.04 x1026 kg ) if the force of gravity acting on the moonlet, due to the planet, is 5.2 x1016 N.
The distance (in Km) between the moonlet and the alien planet, given that the force of gravity acting on the moonlet due to the planet is 5.2×10¹⁶ N, is 9167.4 Km
How do I determine the distance between the moonlet and the alien planet?We can obtain the distance between the moonlet and the alien planet by using the following formula:
F = GM₁M₂ / r²
Where
F is the force of gravityG is the gravitational constant M₁ and M₂ are the masses of the objects r is the distance apartThe following data were obtained from the question:
Mass of moonlet (M₁) = 6.3×10¹⁴ KgMass of alien planet (M₂) = 1.04×10²⁶ KgForce of gravity (F) = 5.2×10¹⁶ N Gravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²Distance (r) = ?F = GM₁M₂ / r²
5.2×10¹⁶ = (6.67×10¯¹¹ × 6.3×10¹⁴ × 1.04×10²⁶) / r²
Cross multiply
5.2×10¹⁶ × r² = 6.67×10¯¹¹ × 6.3×10¹⁴ × 1.04×10²⁶
Divide both sides by 5.2×10¹⁶
r² = (6.67×10¯¹¹ × 6.3×10¹⁴ × 1.04×10²⁶) / 5.2×10¹⁶
Take the square root of both sides
r = √[(6.67×10¯¹¹ × 6.3×10¹⁴ × 1.04×10²⁶) / 5.2×10¹⁶]
r = 9167442.4 m
Divide by 1000 to express in Km
r = 9167442.4 / 1000
r = 9167.4 Km
Thus, we can conclude that the distance between them is 9167.4 Km
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Which statement is true about the theory of plate tectonics and the theory of continental drift?
A) The theory of plate tectonics proves the theory of continental drift completely wrong.
B) The theory of plate tectonics tells exactly where the continents were before Pangaea divided.
C) The theory of plate tectonics gives the method by which continents can move as part of plates.
D) The theory of plate tectonics does not explain how continental movements could occur.
The statement that is true about the theory of plate tectonics and the theory of continental drift C. The theory of plate tectonics gives the method by which continents can move as part of plates .
What is theory of plate tectonics and the theory of continental drift ?According to the scientific hypothesis of plate tectonics, the underground movements of the Earth create the primary landforms. By explaining a wide range of phenomena, including as mountain-building events, volcanoes, and earthquakes, the theory, which became firmly established in the 1960s, revolutionized the earth sciences.
The scientist Alfred Wegener is most closely connected with the concept of continental drift. Wegener wrote a paper outlining his notion that the continents were "drifting" across the Earth, occasionally crashing through oceans and into one another, in the early 20th century.
According to tectonic theory, the Earth's surface is dynamic and can move up to 1-2 inches every year. The numerous tectonic plates constantly move and interact. The outer layer of the Earth is altered by this motion. The result is earthquakes, volcanoes, and mountains.
Therefore, option C is correct.
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A pilot light is typically wired in series with a/an____ to indicate whether the fan is moving air
A. auxiliary contact
B. thermostat
C. flow switch
D. thermal overload
to indicate whether the fan is moving air.
A pilot light is typically wired in series with a thermostat to indicate whether the fan is moving air
Who is a pilot?We know that the pilot is such a person that have been trained so as to be able to fly the air plane. This is the individual that can be able to control a plane and there are tools that the pilot would have to use to do his job.
Now we know that the pilot light is one of the tools that the pilot can use to be able to use in the discharge of his job when he is flying the air craft that is moving and it has to be in series with the thermostat.
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Tidal effects in the Earth-Moon system are causing the Moon’s orbital period to increase
at a current rate of about 35 ms per century. Assuming the Moon’s orbit around the Earth
is circular, to what rate of change in the Earth-Moon distance does this correspond? Hint :
Differentiate Kepler’s third law.
The rate of change in the Earth-Moon distance does this correspond to 1.1977e-9 m/s.
What is the difference between Kepler's laws?
The difference between Kepler and Newton laws is that Kepler law describes planetary motion around the Sun, whereas Newton laws describe an object's motion and its relationship to the force acting on it.
T= sqrt ((4 × pie^2 × r^3)/GM)
= 2 × 3.1416 × (r^3/GM)^0.5
T = 2 × 3.1416 × (r^3)^0.5 (1/(6.67e-11 × 5.97e24))^0.5
T = 3.1487e-7 (r^3)^0.5
dT/dr = 3.1487e-7 × (0.5) × (3 r^2) × (r^3)^-0.5
dT/dr = 3.1487e-7 × (0.5) × (3) × (r)^0.5
dT/dr = 3.1487e-7 × (0.5) × (3) × (384400e3)^0.5
dT/dr = 0.009260069 s/m
dr = 35e-3/0.009260069
dr = 3.77967 meters per century
v = dr/t
= 3.779669/(100 × 365.25 × 24 × 60 × 60)
= 1.1977e-9 m/s
Thus, The rate of change in the Earth-Moon distance does this correspond to 1.1977e-9 m/s.
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How many centimeters are in a kilometer? Step by step explanation
100,000 centimeters or 10⁵ centimeters are in a kilometer.
What is unit of length?Any arbitrarily selected and widely used reference standard for length measurement is referred to as a unit of length. The metric system, which is adopted by every nation on earth, is the most widely utilized in modern times.
We know that:
1 kilometer = 1000 meters.
And 1 meter = 100 centimeters.
So, 1 kilometer = 1000 meters
1 kilometer = 1000 × 100 centimeters
1 kilometer = 100,000 centimeters
1 kilometer = 10⁵ centimeters.
Hence, 100,000 centimeters or 10⁵ centimeters are in a kilometer.
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You weigh 610 n. what would you weigh if the earth were six times as massive as it is and its radius were three times its present value? answer in units of n.
Answer:
F1 = G M1 M2 R^2 force between objects M1 and M2
F2 = G M1 * 6 M2 / (3 * R)^2
F2 = 6 / 9 * F1
F2 = 2/3 * 610 n = 407 n
A glass Capillary tube of diameter 2.0mm
is dipped into pool of water How high
in the tube ?
( take contact angle betwen glass of water
as oº, surface fension of pater as 0.073 ~m²"
& density of water as
a
1000kgm ³)
3×10Nm¹ and the contact angle with the tubes as 45⁰
Answer:
To calculate the height of the water in the capillary tube, we can use the equation h = 2πσcosθ/ρg, where h is the height of the water in the tube, σ is the surface tension of the water, θ is the contact angle between the glass and the water, ρ is the density of the water, and g is the acceleration due to gravity. Plugging in the given values, we get h = 2π(0.073)cos(45°)/(1000)(9.8), which is equal to 0.0092 meters.
Which is the correct answer
The correct product of the above nuclear reaction is 221/87 Fr (option C).
What is a nuclear reaction?A nuclear reaction is the process such as the fission of an atomic nucleus, or the fusion of one or more atomic nuclei and/or subatomic particles in which the number of protons and/or neutrons in a nucleus changes.
In a nuclear reaction, the reaction products may contain a different element or a different isotope of the same element.
Alpha decay is a specific type of nuclear reaction in which an alpha particle made up of helium-4 atom (consisting of two protons and two neutrons), is emitted.
According to this question, the nuclear reaction (alpha decay) of an atom with mass number 225 and atomic number 89 is given. To find the mass number and atomic number of the product, we subtract 4 and 2 respectively.
225 - 4 = 22189 - 2 = 87Therefore, option C is correct.
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A wire of resistance R connected in series with 1.5V cell is found to be carrying a current of 0.05A. If the wire is now connected i parallel with an identical wire, find the new current in the circuit
Answer:Assuming, The new circuit is like the circuit attached below, the current in the new circuit will be 0.1 Ampere.
Explanation: Given, We have Potential Difference of 1.5V, Current of 0.05A.
Now, we know V = I x R ,where V is potential difference, I is current and R is resistance in the circuit.
∴ Putting the values ⇒ 1.5V = 0.05A x R
⇒R = 1.5/0.05
∴R = 30 Ω
Now, It is said that A same identical wire is connected in parallel with the previous wire.
∴ New R will be ⇒ [tex]\frac{1}{R(new)}[/tex] = [tex]\frac{1}{r} + \frac{1}{r}[/tex]
=[1/30] + [1/30]
=1/15
∴ 1/R(new) = 15 Ω
Now, New Current in the circuit will be:
⇒ V= IR
⇒1.5V = I x 15
⇒I = 0.1 A
Therefore, Answer will be 0.1 ampere.
the product of an object's instantaneous momentum and acceleration is what quantity?
Explanation:
In differential form, this is Newton's second law; the rate of change of the momentum of a particle is equal to the instantaneous force F acting on it, hence the net force is equal to the mass of the particle times its acceleration.
1. Helium gas is cooled from 20 °C to 10 °C by expanding from 40 atm to 1 atm. If there is 1.4 mol of helium,
(a) What is the final volume of helium?
(b) What is the change in internal energy?
By expanding from 40 atm to 1 atm, helium gas is cooled from 20 °C to 10 °C. If there is 1.4 mol of helium;(a) The final volume of helium is 28.7 L.(b) The change in internal energy is -453.8 kJ.
What is the volume?Volume is a measure of the amount of three-dimensional space an object takes up. It is measured in units of cubic units, such as cubic meters, cubic centimeters, or cubic inches. Volume is often used to measure the size of liquids, solids, and other substances. It is also used to calculate the amount of space an object occupies, such as a room, box, or container. Volume is a useful tool to calculate the amount of an ingredient in a recipe or mixture, or to measure the capacity of a storage container.
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Part A
Compute the x and y components of vector A.
Express your answers in meters to three siginificant figures. Enter your answers separated by
A comma
The component of vector A in the x direction will be -11.01 meters. and in the y direction will be 9.18 meters.
What is meant by vectors?A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are examples of vectors in nature.
What are examples of vectors?Vector quantities can also include things like movement, acceleration, force, momentum, weight, the speed of light, a gravitational field, current, and more.
component of vector A in x direction = A cos theta
= 12 cos(53)
= -11.01 meters
component of vector A in y direction = A sin theta
= 12 sin (53)
= 9.18 meters
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2. A student attempts to fire a small steel sphere (mass= 250 g) into a cup from a spring-loaded cannon affixed to a table.
The cup is located 74.7 cm from the table's edge. If compressing the spring by 2.2 cm results in the sphere travelling
82.2 cm, by what distance should the spring be compressed to project the sphere into the cup?
From conservation of energy, the distance the spring should be compressed is 2 cm
What is Work ?The work done on an object is the product of force and distance in the direction of the force.
Given that a student attempts to fire a small steel sphere (mass = 250 g) into a cup from a spring-loaded cannon affixed to a table.
The cup is located 74.7 cm from the table's edge.
If compressing the spring by 2.2 cm results in the sphere travelling 82.2 cm, then,
the elastic potential energy = work done on the object
1/2ke² = Fs
Where F = mg = 0.25 × 9.8
F = 2.45 N
1/2 × k × (2.2/100)² = 2.45 × 82.2/100
0.000242K = 2.0139
k = 2.0139/0.000242
k = 8321.9 N/m
The distance the spring should be compressed in order to project the sphere into the cup can be known by using the same formula since k is the same elastic constant.
1/2ke² = Fs
1/2 × 8321.9 × (e)² = 2.45 × 74.7/100
4161e² = 1.83015
e² = 1.83015/4161
e² = 0.00044
e = √0.00044
e = 0.02 m
e = 2 cm
Therefore, the spring should be compressed by 2 cm in order to project the sphere into the cup.
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a small, 250 g cart is moving at 1.60 m/s on a frictionless track when it collides with a larger, 3.00 kg cart at rest. after the collision, the small cart recoils at 0.840 m/s .
what is the speed of the large cart after the collision?1
m(small cart) = 250 g = 0.25 Kg
vi(small cart) = 1.60 m/s
m(large cart) = 3.00 kg
vi(large cart) = 0 m/s
vf(large cart) = ?
The speed of the larger cart after the collision is 0.084 m/s.
The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on the system. In this case, the momentum of the two carts before the collision is equal to the momentum of the two carts after the collision. We can use this principle to find the speed of the larger cart after the collision.
Let's call the speed of the larger cart after the collision "v".
Before the collision:
momentum = m1 * v1 = (250 g) * (1.60 m/s) = 0.25 kg * 1.60 m/s
After the collision:
momentum = (0.25 kg * 0.840 m/s) + (3.00 kg * v) = 0.25 kg * 0.840 m/s + 3.00 kg * v
Setting the before and after momenta equal:
0.25 kg * 1.60 m/s = 0.25 kg * 0.840 m/s + 3.00 kg * v
Solving for v:
v = (0.25 kg * 1.60 m/s - 0.25 kg * 0.840 m/s) / 3.00 kg
v = (0.25 kg * 0.760 m/s) / 3.00 kg
v = 0.25 kg / 3.00 kg * 0.760 m/s
v = 0.084 m/s
So the speed of the larger cart after the collision is 0.084 m/s.
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If you were Jean’s physician, how would you explain to her the changes that might be occurring in her aging mother?
The changes that occur in old age include decrease in bone density that can affect the normal physiological functioning of her aging mother.
What is aging process?Aging process is the changes and stages of life that an individual naturally undergoes as they advance in age and these experiences are individualized according to lifestyle.
The various changes that occur include but not the least the following:
hearing loss, cataracts and refractive errors, back and neck pain and osteoarthritis, chronic obstructive pulmonary disease, diabetes, depression and dementia. Osteoporosis.The onset of these changes depends on the mother's lifestyle, that is, intake of adequate nutrition, exercise and proper hydration.
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A 75,000-watt radio station transmits at 88 MHz. Calculate the energy of a single photon at the transmitted frequency.
5.0x 10 -29 J/photon
5.8 x 10 -32 J/photon
5.8 x 10 -26 J/photon
The energy of the photon is obtained as 5.8 x 10 -26 J/photon. Option C
What is the energy of the photon?We have to know that the energy of the photon can be obtained from the frequency. We can define the frequency as the number of cycles that is completed per second so the time that is taken is 1 s.
Energy = hf
h = Plank's constant
f = frequency
Then;
E = 6.6 * 10^-34 * 88 * 10^6
E = 5.8 x 10 -26 J/photon
The photon that we can see is going to have a total energy of 5.8 x 10 -26 J/photon.
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Does a series connection between capacitors always result in equal amount of charge being stored in each capacitor
Answer:
Yes - If a charge of +Q is removed from one side of a battery, a charge of -Q must be removed from the other side of the battery, the charges on the intervening capacitors are likewise equal.
A refrigerator is pushed across across a horizontal floor with a force of 125 N. If the refrigerator moves 4 meters, then how much work is done to move it?
The work done to move the refrigerator is 500 J.
What do you mean by work?Work is defined as force multiplied by distance, in the direction of the force.
The work done to move the refrigerator can be calculated using the formula:
work = force x distance
Given that:
force = 125 N
distance = 4 m
We can substitute these values into the formula and solve for work:
work = 125 N x 4 m
work = 500 J (Joules)
So, the amount of work done to move the refrigerator is 500 Joules.
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How to do this exercise.
Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
T^2 = 4 * d^3 * (m1 + m2)^2 / G
What is Kepler's third law?Generally, Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. In the case of two celestial bodies orbiting their center of mass, we can use Newton's laws of motion to derive the general form of Kepler's third law.
Using Newton's second law, we can write the centripetal force acting on each body as: F = m * a = m * v^2 / r
where
m is the mass of the body a is the centripetal acceleration, v is the orbital velocity, and r is the distance from the center of mass.The gravitational force between the two bodies is given by: F = G * (m * m2) / d^2
where
G is the gravitational constant, m1 and m2 are the masses of the two bodies, and d is the center-to-center distance.Equating the two forces, we get:
m * v^2 / r = G * (m1 * m2) / d^2
Solving for the orbital velocity, we get: v = (G * (m1 + m2) / d)^1/2
Using the period-velocity relationship, T = 2 * pi * r / v, we can find the period of the orbit.
Substituting for v, we get:
T = 2 * pi * r * (d / (G * (m1 + m2)))^1/2
Squaring both sides and solving for r, we get: T^2 = 4 * pi^2 * r^3 / (G * (m1 + m2))
r = (G * (m1 + m2) * T^2) / (4 * pi^2)
so T^2 = 4 * pi^2 * (G * (m1 + m2) * T^2) / (4 * pi^2) * d^3
T^2 = 4 * d^3 * (m1 + m2)^2 / G
which is the general form of Kepler's third law.
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A mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a stretched position. The position of the mass at any time is described by x = (8.8 cm)cos[2t/(4.18 s)]. Determine the following.
(a) period of the motion
(b) frequency of the oscillations
Hz
(c) first time the mass is at the position
x = 0
(d) first time the mass is at the site of maximum compression of the spring
A. The period of the motion is 4.18 s
B. The frequency of the oscillations
Hz is 0.2393 Hz
C. The first time the mass is at the position
x = 0 is 2.09 s
D. The first time the mass is at the site of maximum compression of the spring is 6.27s
How do we determine the values?a) The period of motion is given by the time it takes for the mass to complete one full oscillation. From the equation given, x = (8.8 cm)cos[2t/(4.18 s)], we can see that the function is in the form x = A cos(ωt + φ). The period of the motion T is given by the reciprocal of the angular frequency ω, which is T = 2π/ω.
In this case, the angular frequency is given by the coefficient of t in the argument of the cosine function, 2t/(4.18 s). So,
T = 2π/(2/(4.18 s)) = 4.18 s
b) The frequency of oscillations, f, is given by the reciprocal of the period, so
f = 1/T = 1/4.18 s^-1 = 0.2393 Hz
c) To find the first time the mass is at the position x = 0, we need to find the value of t when the cosine function is equal to 1.
x = (8.8 cm)cos[2t/(4.18 s)] = 8.8cm * 1 = 8.8cm
so,
cos[2t/(4.18 s)] = 1
t = (4.18 s)/2 = 2.09 s
d) To find the first time the mass is at the site of maximum compression of the spring, we need to find the value of t when the cosine function is equal to -1.
x = (8.8 cm)cos[2t/(4.18 s)] = 8.8cm * (-1) = -8.8cm
so,
cos[2t/(4.18 s)] = -1
t = (4.18 s) + (2.09 s) = 6.27s
It should be noted that the mass will be at the site of maximum compression at t = 6.27s and t = 2.09s + 4.18s = 6.27s + 4.18s = 10.45s and so on.
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A car of mass 800 kg initially at rest is accelerated at the rate of 4ms^-2. The kinetic energy of the car after 5 seconds is ?
Answer:
Explanation:
velocity after 5 seconds is 4 x 5 = 20 m/s
KE formula = 0.5mv²
= 0.5 x 800 x 400
= 400²
= 160000 J
or, 160kJ
A spring that has a spring constant of 500 N/m is compressed a distance of 0.3 meters. How much elastic potential energy is contained in this spring?
_____ J
Answer:
Below
Explanation:
EPE = 1/2 k x^2
= 1/2 * 500 N/m * (.3)^2 = 22.5 J
A floral clock in Japan has a radius of 15.5 m. If you ride a bike around
the clock, making 16 revolutions in 4.5 min, what is your average angular speed?
The average angular speed will be the ratio of total distance to total time which is 5.77 rad/s
What is Angular Speed ?Angular speed can be defined as the total angle turned per total time taken. It is measured in rad/s
Given that a floral clock in Japan has a radius of 15.5 m. If you ride a bike around the clock, making 16 revolutions in 4.5 min, what is your average angular speed ?
The circumference C of the circle = distance covered by the bike.
C = 2πr where r = 15.5 m
C = 2 × π × 15.5
C = 97.4 m
Total distance covered = 16 revolution × 97.4
Total distance covered = 1558.23 m
Total time taken = 4.5 × 60 = 270 s
Average angular speed = 1558.23 / 270
Angular speed = 5.77 rad/s
Therefore, your average angular speed is 5.77 rad/s
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