If the half-life of a first-order reaction is 2.50 minutes, the rate constant is 0.277 min-1. A first-order reaction is a reaction in which the rate of conversion of reactants into products is directly proportional to the concentration of the reactants.
The rate constant of a first-order reaction if the half-life is 2.50 minutes is given by the formula k = 0.693/t1/2. It is possible to estimate the time needed for a chemical reaction to take place by determining the rate constant, which is a numerical value that describes the rate at which reactants are turned into products.
A first-order reaction is a reaction in which the rate of conversion of reactants into products is directly proportional to the concentration of the reactants. The half-life of a first-order reaction is the time it takes for the concentration of a reactant to be reduced to half of its initial value.
The rate constant of a first-order reaction can be calculated using the half-life of the reaction, which can be calculated using the formula t1/2 = ln2/k, where t1/2 is the half-life and k is the rate constant. The rate constant of a first-order reaction is given by the formula k = 0.693/t1/2, where t1/2 is the half-life of the reaction.
If the half-life of a first-order reaction is 2.50 minutes, the rate constant can be calculated as follows:k = 0.693/2.50 = 0.277 min-1. Therefore, the rate constant of a first-order reaction with a half-life of 2.50 minutes is 0.277 min-1.
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Given the production rules below, is the plus operator (+) left-associative, right-associative, or neither? You need to provide a sample sentence and a parse tree of it that supports your answer.
S → T + S | T
T → 1 | 2 | 3
Given the production rules below, is the plus operator (+) left-associative, right-associative, or neither a parse tree of it is in the explanation part below.
In the provided production rules, the addition operator (+) is left-associative.
Consider the statement "1 + 2 + 3" to show this.
This sentence's parse tree is as follows:
The addition operator's left-associativity is shown in this parse tree. The operands 1 and 2 are combined by the leftmost plus operator, and the resultant total is merged with the operand 3 by another plus operator. This depicts the assessment of the statement "1 + 2 + 3" from left to right.
If the plus operator were right-associative, the parse tree would be different, with the rightmost plus operator first combining operands 2 and 3, and then combining the resultant sum with operand 1.
Thus, the parse tree is attached below as image.
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it would be easier to pull the evacuated magdeburg hemispheres apart if they were
It would be easier to pull the evacuated Magdeburg hemispheres apart if they were smaller in diameter or had less surface area in contact with each other.
The Magdeburg hemispheres experiment involves two hemispheres that are joined together and evacuated, creating a vacuum seal between them. Due to the atmospheric pressure pushing down on the hemispheres, it becomes difficult to pull them apart.
If the hemispheres were smaller in diameter, there would be less surface area in contact with each other, which means less atmospheric pressure acting on the surfaces.
This would make it easier to pull the hemispheres apart. Additionally, if the hemispheres had less air evacuated from them, there would be less vacuum force holding them together, which would also make it easier to separate them.
The Magdeburg hemispheres experiment is used to demonstrate the effects of atmospheric pressure and the concept of a vacuum, so any changes to the setup could alter the results and make them less reliable.
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Which statement is true according to Newton's second law of motion?
Answer:
When a net force acts on a body it produces acceleration in body the magnitude of tries acceleration is directly proportional to the net force acting and inversely proportional to the mass of the body
Mathematical form
F=ma
Explanation:
I hope it will help you
A race car sets out on a 100.0 km race. At the halfway marker, the pit crew notes that the driver has averaged only 80.0 km/h. What speed must the driver maintain for the second half of the race in order to average 100.0 km/h overall?
The driver has to maintain the speed of 133.3 km/h for second half of the race in order to average 100km/h.
What does "average velocity" and "speed" mean?In order to calculate average velocity, divide the change in position or displacement (x) by the time intervals (t) during which the displacement takes place. Depending on the displacement's sign, the average velocity can either be positive or negative. Meters per second (m/s or ms-1) is the SI measure for average velocity. By dividing the entire distance the body has traveled by the amount of time it took to cross that distance, the average speed formula can be calculated.
To complete the race in 1 hr => 100 km/hr in a 100 km
Driver is going 80 km/hr at half way marker (50m).
Time taken to cover 50m = 50 km * (1 hr/80 km) = 5/8 hour.
Total time to complete the race on average 100 km/hr is 1 hr.
Hence, time required to cover second half of the race => 1 hr - 5/8 hr
=> 3/8 hr
v= 50km/(3/8 hr) = 50*(8/3) = 133.3 km/h
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I NEED THE RIGHT ANSWER ASAP NO LINKS !!!
This is a Science question
Answer:
B is the correct answer
Explanation:
12 - (-7)
NB: Negative times negative gives positive
12 + 7
Hope it helps. Brainliest please.
Two people are carrying a uniform 974.0 N log through the forest. Bubba is 1.2 m from one end of the log (x), and his partner is 1.3 m from the other end (y). The log is 5.0 m long (z). What weight is Bubba supporting?
Bubba is supporting 194.8 N of the log's weight.
Weight in physics is the force that gravity applies to an object. Weight has both a magnitude and a direction, making it a vector quantity. The weight of an item is equal to the gravitational force exerted on it, which is defined by its mass and gravitational acceleration.
Given that,
Weight of the log = 974.0 N
Distance from one end to x = 1.2m
Therefore,
Weight from one end to x = (weight of the log/length of the log) x distance from one end to x.
= (974.0 / 5.0) x 1.2
= 194.8 N
Therefore, Bubba is supporting 194.8 N of the log's weight.
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a coin is fixed in place 11 cm from the axis of a rotating turntable. the angular speed of the turntable is increased and when it reaches 36 rev/min the coin slides off. what is the coefficient of static friction between the coin and the turntable? group of answer choices 0.56 0.11 0.32 0.16
Answer:
Coefficient of static friction = 0.547
Explanation:
The maximum resistive force offered by the body(coin)against the applied force(turntable) to continue its state of motion is called Coefficient Of Static Friction
When given
The angular velocity which is 51.1rpm
We are going to calculate velocity of coin
= r*w(angular velocity) = 0.108*(51.1*2π/60) = 0.58
Coefficient=F/N
F= coefficient* N = coefficient*m*g
F= mv^2/r which is centripetal force
Therefore, mv^2/r = coefficient*m*g
coefficient = mv^2/mgr = v^2/rg
Where g,gravity = 9.81
Substitute into the equation coefficient = 0.58^2/9.81*0.108
= 0.547
what is the magnitude of velocity for a 1500 kg car possessing 4500 kgm/s of momentum?
define equilibrium position, displacement and amplitude as they relate to a wave
The equilibrium position is the undisturbed state of a medium, displacement is the change in position of a particle due to the wave, and amplitude is the maximum displacement of a particle from its equilibrium position, indicating the energy carried by the wave.
The equilibrium position, displacement, and amplitude are essential terms related to wave motion. Let's define each term as it relates to a wave:
1. Equilibrium position: The equilibrium position is the undisturbed or rest position of a medium or a particle when no wave is passing through it. In other words, it is the point at which the medium is not experiencing any net force, and no energy is being transmitted through it. When a wave propagates through the medium, the particles oscillate about this equilibrium position.
2. Displacement: Displacement refers to the change in the position of a particle in a medium as it oscillates due to the wave passing through it. It is the distance between the current position of the particle and its equilibrium position. Displacement can be measured both horizontally and vertically, depending on the type of wave (transverse or longitudinal).
3. Amplitude: Amplitude is the maximum displacement of a particle from its equilibrium position as it oscillates due to the wave passing through it. It is a measure of the wave's energy, as a wave with a larger amplitude carries more energy than a wave with a smaller amplitude. The amplitude can be observed as the height of a crest or the depth of a trough in a transverse wave, or as the maximum compression or rarefaction in a longitudinal wave.
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Two horses have hooves of about the same area. Horse A has a much bigger mass than horse B. How would the pressure that they produce on the ground be different?
The pressure will be different because of the difference in the masses of horse A and horse B.
Horse A will have greater pressure due to much bigger mass.
Who do horses have hooves?In order for a horse to survive and operate, its hooves are necessary. Throughout a horse's lifetime, its hooves expand. Each foot of a horse has a single, solid hoof. The size of this might vary according on the breed, size, and running and jumping prowess of the horse.
Scholars have long disagreed on how animals—whose predecessors were dog-sized creatures with three or four toes—came to have only one hoof. According to a recent research, when horses grew bigger, one big toe was shown to be more resistant to bone stress than several smaller toes.
Thus, horse A will have greater pressure due to much bigger mass.
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A uniform rod with mass 6M and length 2L is rotating freely around an axis.
(1)
(2)
A) What is the angular velocity at position 1?
B) What is the velocity of the center of mass at position 2, given the angle theta relative to position 1?
(1) The angular velocity at position 1 of a uniform rod rotating freely around an axis can be determined.
(2) The velocity of the center of mass at position 2.
(1) To determine the angular velocity at position 1, we need to consider the conservation of angular momentum. Since the rod is rotating freely, there are no external torques acting on it.
The initial angular momentum is zero, and at position 1, the angular momentum is given by L = Iω, where I is the moment of inertia of the rod and ω is the angular velocity. By substituting the values of mass and length of the rod into the formula for moment of inertia, we can solve for ω.
(2) To calculate the velocity of the center of mass at position 2, relative to position 1 and at an angle theta, we can use the concept of angular velocity and linear velocity. The linear velocity of the center of mass is given by v = ωr, where ω is the angular velocity and r is the distance between the center of mass and the axis of rotation. By considering the given angle theta and the length of the rod, we can determine the distance r.
Substituting the value of ω calculated in part (1) into the formula, we can find the velocity of the center of mass at position 2, relative to position 1 and at angle theta.
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A coiled spring would be useful in illustrating a __________________ wave.
a. surface
b. body
c. shear
d. compressional
picture
A coiled spring would be useful in illustrating a d. compressional wave. A compressional wave, also known as a longitudinal wave, is a type of wave where the disturbance or oscillation occurs parallel to the direction of wave propagation.
A coiled spring can be used to demonstrate this type of wave by compressing and expanding the coils of the spring. As the coils are compressed, they represent the regions of compression in the compressional wave. When the coils expand, they illustrate the regions of rarefaction. The coiled spring visually represents the alternating pattern of compression and rarefaction characteristic of compressional waves. A compressional wave, also known as a longitudinal wave, is a type of wave where the disturbance or oscillation occurs parallel to the direction of wave propagation. In a compressional wave, particles within the medium oscillate back and forth in the same direction as the wave is traveling.
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Inez uses hairspray on her hair each morning before going to school. The spray spreads out before reaching her hair partly because of the electrostatic charge on the hairspray droplets. If two drops of hairspray repel each other with a force of 9 x 10^-9 N at a distance of 0.07 cm ( 7 x 10^ -4 m), what is the charge on each of the equally charged drops of hairspray?
Please show the steps as well. Written out, if possible.
The charge on each of the equally charged drops of hairspray willl be 7 × 10 ⁻¹³ C
What is Columb's law?The force of attraction between two charges, according to Coulomb's law, is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Similar charges repel each other, whereas charges that are opposed attract each other.
Given data;
Electric force,F = 9 × 10 ⁻⁹ N
Distance between charges,d = 7 × 10⁻⁴ m
Chrge,q₁ = q₂ =q C
From Columb's law;
\(\rm F = K \frac{q_1q_2}{d^2} \\\\ 9 \times 10^{-9} = 9 \times 10^9 \frac{q^2}{(7 \times 10^{-4})^2} \\\\ q^2 = 4.9 \times 10^{-25} \\\\ q = 7 \times 10^{-13} \ C\)
Hence the charge on each of the equally charged drops of hairspray willl be 7 × 10 ⁻¹³ C
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Calculate acceleration if net force acting on an object is 140N and mass
is 15 kg
Answer:
9.33333333 m / s2
Explanation:
140 N divided by 15 kg
As a freely falling object picks up downward speed, what happens to the power supplied by the gravitational force?.
As a freely falling object picks up downward speed. What happens to the power supplied by the gravitational force? The power will increase because (Power=work/time; work=f(d); and F x d/t; FV).
What Is Gravity?Greatness is the estimation or supreme esteem of an amount. A size is spoken to by a positive, genuine number.Some illustrations of the drive of gravity incorporate: The drive that holds the gasses within the sun. The drive that causes a ball you toss within the discuss to come down once more. The drive causes a car to coast downhill once you aren't venturing on the gas. The drive that causes a glass you drop to drop to the floor.Forces are the way that vitality is exchanged from one protest to another when they connected, but powers are not the vitality itself. Gravity may be a constrain, so it fair gives one way for objects to trade and change vitality to diverse states.As a freely falling object picks up downward speed. What happens to the power supplied by the gravitational force? The power will increase because (Power=work/time; work=f(d); and F x d/t; FV).
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The fastest helicopter, the Westland Lynx, can travel 3.33 km in the forward direction in just 30.0 s. What is the average velocity of this helicopter? Express your answer in both m/s and km/hr.
Answer:
The value in m/s \(v_{a} = 111 \ m/s \)
The value in km/h \(v_{a} = 400\ km/h \)
Explanation:
Generally the average velocity of the helicopter is mathematically represented as
\(v_{a} = \frac{\Delta D}{ t}\)
substituting \(3.33 km = 33.3*10^3\ for\ \Delta D\) and 30.0 s for t
We have
\(v_{a} = \frac{33.3 *10^{3}}{ 30}\)
=> \(v_{a} = 111 \ m/s \)
Now converting to km/h
\(v_{a} = 111 * \frac{3600 *\frac{s}{h} }{1*10^{-3} *\frac{km}{m}} \)
=> \(v_{a} = 400\ km/h \)
Which best explains how the coating works?
Glare appears on a computer screen when light from
the surroundings reflects off of the screen's surface.
Some computer screens have a special coating to
reduce glare.
O The coating absorbs light that shines on it and
prevents the light from reflecting.
O The surface of the coating is rough, so light that
shines on it gets scattered in many directions.
O The coating bends light that passes through it and
prevents the light from reaching the user's eyes.
O The surface of the coating allows light from the room
to pass through but blocks the light from the screen.
My
Answer: Glare appears on a computer screen when light from the surroundings reflects off of the screen's surface. Some computer screens have a special coating to reduce glare. Which best explains how the coating works? The surface of the coating is rough, so light that shines on it gets scattered in many directions.
HOPE THIS HELPS IF NOT SORRY
The surface of the coating is rough, so light that shines on it gets scattered in many directions best explains how the coating works.
What is coating?A coating is a protective layer that is put to the surface of an item, The coating can be applied for ornament and jewelry.
Paints are a type of coating that protect the surface of the material and also used for its decoration as well as also used in corrosion prevention.
When any light is to fall on any rough surface in that condition, the light get scattered in many directions.
The surface of the coating is rough, so light that shines on it gets scattered in many directions best explains how the coating works.
Hence, option B is correct.
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A 70.0 kg person leaps from a bridge in with a bungee cord attached and falls 120 meters. If the bungee cord stretches 2.5 meters during the stopping process, what’s its force constant (k)?
The force constant of the bungee cord when a person of mass 70 kg leaps on a bridge with it is 219.52 N/m.
What is force constant?The force constant or spring constant is a measure of the stiffness of a spring. It is the force per unit deformation of the spring. Its SI unit is N/m.
To calculate the force constant of the bungee cord, we use the formula below.
Formula:
K = 2mgh/e²............. Equation 1Where:
K = Force contant of the bungee cordm = Mass of the persong = Acceleration due to gravityh = Height at which the person falle = extensionFrom the question,
Given:
m = 70 kgg = 9.8 m/s²h = 120 me = 2.5 mSubstitute these values into equation 1
K = (2×70×9.8/2.5²)K = 219.52 N/mHence, the force constant of the bungee cord is 219.52 N/m.
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A Bugatti Chiron travels 116 m/s for 10 seconds. How far did it travel? A. 116 m B. 11.6m C. 0.086m D. 1.160m
Answer:
V= 1,160 mExplanation:
formula:V= V* T
remplazamos:V= 116m /s * 10s
V= 1,160 m
espro que etayude#yoarenpdiin scientific notation, we would express the result of (0.0035 * 200000) as
Answer:
I think it's 7 × 10²
Explanation:
0.0035 time 200000 is 700 and 700 in scientific notation is 7 × 10²
Though i'm not certain if that is correct
A ray of light is incident at an angle of 53. 8 ◦ on the surface of a piece of crown glass whose index of refraction is 1. 52. What is the angle of refraction?
The angle of refraction for the incident light ray is approximately 34.1 degree
To determine the angle of refraction of a ray of light incident on a piece of crown glass with an index of refraction of 1.52, we can use Snell's law.
Given that the angle of incidence is 53.8 degrees and the index of refraction is 1.52, we can calculate the angle of refraction as follows:
n1 * sin(θ1) = n2 * sin(θ2)
Where n1 is the index of refraction of the medium the light is coming from (assumed to be air, so n1 = 1), θ1 is the angle of incidence, n2 is the index of refraction of the medium the light is entering (crown glass, n2 = 1.52), and θ2 is the angle of refraction.
Plugging in the given values:
1 * sin(53.8) = 1.52 * sin(θ2)
Rearranging the equation to solve for θ2:
sin(θ2) = (1 * sin(53.8)) / 1.52
θ2 = arcsin((1 * sin(53.8)) / 1.52)
Using a calculator, we find that θ2 is approximately 34.1 degrees.
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when a person is standing on a scale, the magnitude of what force is displayed by the scale? group of answer choices the force of the scale acting on the person minus the acceleration of the person multiplied by the person's mass. the person's weight. the mass of the person multiplied by their acceleration. the normal force of the scale acting on the person.
A typical force applied towards the aspects in an equal and opposing force being applied to the individual. Therefore, the scale's display of force equals its magnitude.
How does science define force?Within science, each word "power" has a particular definition. At this level, calling a force a pushed or a pull is quite appropriate. An object neither "has in it" nor "contains" a power.
What exactly are force and also its unit?Force is a necessary attribute that alters or has the potential to alter an object's state of motion or motion as well as its form. Newton is the SI unit of force.
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If a paper airplane has a forward velocity of 2 m/s, but air resistance has a velocity of 1 m/s acting against the paper airplane, then what is the resultant forward velocity of the paper airplane?
Answer:
F_{resultant} = 1 [m/s]
Explanation:
These types of problems can be solved by means of relative velocities, where vectors (forces or velocities) are necessarily handled, these velocities depending on the velocity are added or subtracted.
Forces to the right are taken as positive and negative to the left.
\(F_{velocity}-F_{air}=F_{resultant}\\2-1 = F_{resultant}\\\\F_{resultant} = 1 [m/s]\)
A proton is located at x = 1.0 nm, y=0 nm and an electron is located at x=0 nm, y=4.0 nm. Find the attractive Coulombic force between them.
The attractive Coulombic force between the proton and electron is approximately 2.3 x 10^-8 N.
To calculate this force, we can use Coulomb's law: F = (kq1q2)/r^2, where F is the force, k is Coulomb's constant, q1 and q2 are the charges of the two particles, and r is the distance between them. Plugging in the values, we get F = (9x10^9 Nm^2/C^2)(1.6x10^-19 C)*(-1.6x10^-19 C)/(4x10^-18 m^2) = -2.3x10^-8 N. The negative sign indicates that the force is attractive.
In summary, the attractive Coulombic force between the proton and electron is -2.3 x 10^-8 N, which is found using Coulomb's law and the charges and distances given in the problem.
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What duty cycle should transformer-rectifier units have (at least) for CAC-A?
Made from graphite, copper coated, and operated on direct type current.
Should be three phase units with at least a 60% duty cycle
No--trash containers are not fabricated to the quality of a nuclear power plant
Transformer-Rectifier units for CAC-A (Constant Current Arc Welding) should have a minimum of 60% duty cycle, with at least three-phase units.
Constant Current Arc Welding is also known as "stick welding." The acronym CAC stands for "constant current," which means the power source must be able to produce a constant output current, regardless of the resistance of the welding arc.
To create the appropriate current for the welding, a transformer-rectifier is used. A transformer-rectifier unit comprises of a transformer and a rectifier. The transformer converts high voltage, low current AC electricity from the power source to low voltage, high current AC electricity, which is then supplied to the rectifier. The rectifier transforms the AC input into a direct current (DC) output that the welding equipment requires.
The duty cycle is defined as the amount of time during which the machine can operate without overheating. The transformer-rectifier should have a 60% duty cycle or higher because welding generates a lot of heat and needs a lot of power. If the duty cycle is too low, the unit will shut down too often and be unable to perform effectively.
A 60% duty cycle ensures that the welding machine can run continuously for six minutes out of every ten minutes. It is recommended that you choose a transformer-rectifier with a duty cycle that meets your requirements, as a higher duty cycle would allow you to weld for longer periods of time before requiring a cool down period.
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Neils thinks that a comb carrying a charge of static electricity will be able to dissipate its
charge quickly in humid air.
To test this hypothesis, Neils charges a comb by running it through his hair 20 times. He then takes the comb into a room set to 80% humidity and waits 30 seconds. Next, Neils brings the
comb in close proximity to 100 small, identical scraps of paper and counts how many scraps are
attracted to the comb.
To continue testing his hypothesis, what control experiment should Neils run?
A. He should repeat the experiment with more scraps of paper.
B. He should repeat the experiment using a larger comb.
C. He should repeat the experiment with an uncharged comb.
D.
He should repeat the experiment, but only wait 20 seconds before testing the comb's
attractive effects.
To continue testing his hypothesis, Neil should repeat the experiment, but only wait 20 seconds before testing the comb's attractive effects.
In a controlled experiment, all other factors are held constant with the exception of one. One or more other groups are studied with all conditions being the same as the control group and each other except for one variable. Typically, a collection of data is considered to be the control group, which is often the normal or usual state.
Comparing a control group to an experimental group is a popular form of controlled experiment. The factor being examined is the only difference between the two groups' variables.
A controlled experiment has the benefit of making it simpler to determine whether the results are meaningful.
Imagine you want to know if the type of soil influences how long it takes a seed to germinate and you choose to conduct a controlled experiment to find out. Five similar pots might be used, each filled with a different kind of soil, and each with identical bean seeds. The pots could then be placed in a sunny window, watered equally, and the time it takes for the seeds in each pot to sprout could be recorded.
This is a controlled experiment because the only variable that will change is the kind of soil you use. You are in charge of these options.
Here in given case Neil's goal is to find out how quickly charge dissipate in humid air. So he should try his hypothesis by varying wait time.
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If you start with a sample containing 10^10 nuclei that have half-life 2.5 hours, what is the activity of the sample after 5 hours?
The activity of the sample after 5 hours is 2.5 * 10^9 dps or 2.5 * 10^9 Bq
The activity of a radioactive sample refers to the rate at which its nuclei decay, and it is typically measured in units of disintegrations per second (dps) or becquerels (Bq).
To determine the activity of the sample after 5 hours, we need to consider the concept of half-life. The half-life of a radioactive substance is the time it takes for half of the nuclei in a sample to decay.
Given that the half-life of the nuclei in the sample is 2.5 hours, we can calculate the number of half-lives that occur within the 5-hour period.
Number of half-lives = (Time elapsed) / (Half-life)
Number of half-lives = 5 hours / 2.5 hours = 2
This means that within the 5-hour period, two half-lives have occurred.
Since each half-life reduces the number of nuclei by half, after one half-life, the number of nuclei remaining is (1/2) * (10^10) = 5 * 10^9 nuclei.
After two half-lives, the number of nuclei remaining is (1/2) * (5 * 10^9) = 2.5 * 10^9 nuclei.
The activity of the sample is directly proportional to the number of remaining nuclei.
Therefore, After 5 hours, the sample has an activity of 2.5 * 109 dps or 2.5 * 109 Bq.
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what happens to the temperature of and energy in an object during the phase transition from liquid to gas?
During the phase transition from liquid to gas, the temperature of the object remains constant despite continuous heating. The energy supplied to the object is used to break the intermolecular forces holding the liquid molecules together rather than increasing the temperature.
During the phase transition from liquid to gas, the temperature of the object remains constant at the boiling point of the substance. This phenomenon is known as the latent heat of vaporization. As heat is supplied to the liquid, the energy is used to break the intermolecular forces between the molecules, allowing them to overcome the attractive forces and transition into the gas phase.
While the energy is being absorbed by the liquid to undergo the phase transition, the temperature does not increase. Instead, it remains constant until the entire substance has transitioned to the gas phase. This is because the energy supplied is utilized in the process of changing the state of the substance rather than increasing the kinetic energy of the individual molecules, which would result in a temperature increase.
Once the phase transition is complete, any additional energy supplied will result in an increase in temperature as the gas molecules gain kinetic energy. Thus, the phase transition from liquid to gas involves a constant temperature and a transfer of energy to break intermolecular forces rather than a change in the object's temperature.
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Convert the SI unit:
1000 meters equal to
how many km.
Answer:
1000m=1km
simple :) . . .
a 4.70 kg block hangs from a spring with spring constant 1980 n/m . the block is pulled down 6.20 cm from the equilibrium position and given an initial velocity of 1.80 m/s back toward equilibrium.a) what is the frequency of the motion (units: Hz)b) what is the amplitude (units: m)c) what is the total mechanical energy of the motion (units: J)
A. The frequency of the motion is 0.0078 Hz. B. the amplitude of the motion is 7.90 m. and C. the total mechanical energy of the motion is 14.56 J.
What is frequency?Frequency is a measurement of how often something occurs over a period of time. It is typically measured in hertz (Hz) or cycles per second.
a) The frequency of the motion can be calculated using the equation:
frequency = 1 / (2π * √(k/m))
where k is the spring constant, and m is the mass of the block.
Substituting in the given values, we get:
frequency = 1 / (2π * √(1980 N/m / 4.70 kg))
= 1 / (2π * √(420.42 N/kg))
= 1 / (2π * 20.52 N/kg)
= 1 / (127.71 N/kg)
= 0.0078 Hz
Therefore, the frequency of the motion is 0.0078 Hz.
b) The amplitude of the motion can be calculated using the equation:
amplitude = (2π * √(k/m)) * x
where x is the displacement from equilibrium, k is the spring constant, and m is the mass of the block.
Substituting in the given values, we get:
amplitude = (2π * √(1980 N/m / 4.70 kg)) * 0.062 m
= (2π * 20.52 N/kg) * 0.062 m
= 127.71 N/kg * 0.062 m
= 7.90 m
Therefore, the amplitude of the motion is 7.90 m.
c) The total mechanical energy of the motion can be calculated using the equation:
E = ½ mv² + ½ kx²
where m is the mass of the block, v is the initial velocity, k is the spring constant, and x is the displacement from equilibrium.
Substituting in the given values, we get:
E = ½ (4.70 kg) (1.80 m/s)² + ½ (1980 N/m) (0.062 m)²
= 8.39 J + 6.17 J
= 14.56 J
Therefore, the total mechanical energy of the motion is 14.56 J.
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