The half-life period of the radioactive source is approximately 693.15 days.
The activity of a radioactive source is known to follow an exponential decay law given by:
A(t) = A(0) × (1/2)[tex]^{t/T}[/tex]
where,
A(t) = activity at time t
A(0) = initial activity
T = half-life period and (1/2)[tex]^{t/T}[/tex] is the fraction of the original activity remaining after time t.
We are given that the activity of the source has decayed to 1/10 of 1% of its initial activity, which is equivalent to 0.001 times the initial activity. This means that:
A(t) = 0.001 ) × A(0)
We are also given that this has occurred in 100 days, so:
t = 100
Substituting these values in the equation, we get:
0.001 × A(0) = A(0) × (1/2)¹⁰⁰/[tex]^T[/tex]
Simplifying and solving for T, we get:
T = -100 / In(1/2) × log(0.001))
T ≈ 693.15 days
Therefore, the half-life period of the radioactive source is approximately 693.15 days.
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The half-life of a radioactive source that decayed to 1/10 of 1% of its initial activity in 100 days is approximately 14.61 days.
Explanation:The given problem can be solved using the formula for radioactive decay, which is N = N0 * (1/2)^(t/h), where N is the final quantity, N0 is the initial quantity, t is time passed, and h is the half-life time. Here, the radioactive source has decayed to 1/10 of 1% of its initial activity, meaning N = 0.001 * N0. The time passed is 100 days. Plugging these values into the formula we have: 0.001 = (1/2)^(100/h). Solving for h, the half-life time, gives us a half-life of approximately 14.61 days.
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3) Vector A is 2.8 cm at 60° above the positive x-axis. Vector B is 1.90 cm at 60° below the
positive x-axis. Use components to find the following:
a) A + B
b) A -B
c) B-A
a) A + B: 3.9 cm, 0°
b) A - B: 0.9 cm, 60°
c) B - A: 0.9 cm, 240°
A proton is accelerated from rest through a potential difference of 91 V. Calculate the final speed of this proton.
Answer: v = 4.17 x 10^5 m/s
Explanation:
The potential difference (ΔV) is given as 91 V. The charge of the proton is given by q = 1.6 x 10^-19 C.The mass of the proton is given by m = 1.67 x 10^-27 kg. The acceleration due to gravity is given by g = 9.81 m/s^2. The final speed of the proton can be calculated as follows:
The potential energy gained by the proton (ΔU) can be calculated using the formula:
ΔU = qΔV
where
q = charge of the proton
ΔV = potential difference
Substituting the given values, we get:
ΔU = (1.6 x 10^-19 C) x (91 V) = 1.456 x 10^-17 J
The kinetic energy gained by the proton (K) can be calculated using the formula:
K = (1/2)mv^2
where
m = mass of the proton
v = final speed of the proton
The kinetic energy gained by the proton is equal to the potential energy gained by the proton. Therefore, we have:
K = ΔU = 1.456 x 10^-17 J
Substituting the given values, we get:
1.456 x 10^-17 J = (1/2) x (1.67 x 10^-27 kg) x v^2
Simplifying the equation, we get:
v^2 = (2 x 1.456 x 10^-17 J) / (1.67 x 10^-27 kg)
v^2 = 1.743 x 10^10 m^2/s^2
Taking the square root of both sides, we get:
v = 4.17 x 10^5 m/s
Therefore, the final speed of the proton is 4.17 x 10^5 m/s.
When a proton is accelerated from rest through a potential difference of 91 V then final speed of this proton is
A proton is a stable subatomic particle with a +1 e (elementary charge) positive electric charge. It has a little lower mass than a neutron and a mass that is 1,836 times that of an electron (the proton-to-electron mass ratio). Protons and neutrons, each with a mass of around one atomic mass unit, are referred to collectively as "nucleons" (particles found in atomic nuclei).
Potential energy of the proton gets converted into kinetic energy.
i.e. 1/2 mv² = qV
Where m is mass of the proton, v is velocity of the proton and q is charge on proton, V is potential difference.
Given,
mass of the proton m = 1.6 × 10⁻²⁷ kg
charge on proton q =1.6 × 10⁻¹⁹ C
P.D. V = 91 V
putting values in equation,
1/2× 1.6 × 10⁻²⁷ kg × v² = 1.6 × 10⁻¹⁹ C × 91 V
0.8 × 10⁻²⁷ v² = 145 × 10⁻¹⁹ C
v = 1.34 × 10⁵ m/s
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 1.What did Ruskin write about Nocturne in Black and Gold: Falling Rocket?
2. How did Whistler defend his work in court? ( You need to mention the two paintings he brought with him to court.)
3. What was the outcome of the trial?
4. Why do you think the lawsuit was important in the history of art?
Answer:
Ruskin wrote a scathing review of James McNeill Whistler's painting Nocturne in Black and Gold: Falling Rocket, describing it as "flinging a pot of paint in the public's face." He criticized the painting for not being representative enough and lacking in artistic skill.Whistler defended his work in court by stating that he was not interested in creating a realistic depiction of the subject, but rather capturing the mood and atmosphere of the scene. He brought two other paintings, Nocturne in Blue and Silver and Harmony in Blue and Gold, to demonstrate his artistic style and prove that his intention was not to deceive the public.The outcome of the trial was a victory for Whistler, but he was only awarded a farthing in damages. The judge ruled that Ruskin's review did damage Whistler's reputation but only to a very small extent.The lawsuit was important in the history of art because it highlighted the changing attitudes towards art in the 19th century. Whistler's defense challenged the traditional idea of what art should be, which was based on realism and technical mastery. It paved the way for the emergence of modern art, which emphasized imagination and individual expression.Additionally, the trial drew attention to the importance of art criticism and the power of critics to influence public perception of art.
Consider the circuit in the diagram below.
Circuit diagram showing a battery on the left leg, with the positive terminal towards the top. Across the top leg of the circuit, a switch is positioned to the left of center in the open or off position. On the right leg of the circuit, there is a capacitor. On the bottom leg of the circuit, there is a lightbulb to the right of center. Running vertically through the center of the circuit, there is another branch connecting the top leg and bottom leg. In the center of this leg, there is a switch in the open or off position.
If the switch at the top is moved to the closed or on position, what would best describe the flow of the conventional current?
The electricity would flow from the positive terminal of the battery in a clockwise direction.
The electricity would flow from the negative terminal of the battery in a counterclockwise direction.
The electricity would flow from the bottom of the capacitor around in a clockwise direction.
The electricity would flow from the top of the capacitor around in a counterclockwise direction.
If the switch at the top is moved to the closed or on position, the best description of the flow of conventional current would be " The electricity would flow from the positive terminal of the battery in a clockwise direction." The correct option is A.
This is because in a circuit, the conventional current flows from the positive terminal of the battery to the negative terminal of the battery. In this circuit, the positive terminal of the battery is connected to the top leg of the circuit, and the negative terminal is connected to the bottom leg of the circuit. When the switch at the top is closed, the current would flow from the positive terminal of the battery, through the switch, and down through the top leg of the circuit in a clockwise direction.
Option B is not true because the conventional current flows from the positive terminal to the negative terminal of the battery, not the other way around.
Option C is not true because the current would not flow through the capacitor until it is charged. At the moment the switch is closed, the capacitor is uncharged and acts like an open circuit, so the current would not flow through it.
Option D is not true because the current would flow from the positive terminal of the battery, through the switch, and down through the top leg of the circuit in a clockwise direction. It would not flow around the capacitor in a counterclockwise direction.
Hence, the correct answer is option A.
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Ice of mass 14.6 kg at 0°C is placed in an ice chest. The ice chest has 3.5 cm thick walls of thermal conductivity 0.01 W/m x K and a surface area of 1.21 m^2. Express your answers with appropriate mks units.
(a) How much heat must be absorbed by the ice during the melting process?
(b) If the outer surface of the ice chest is at 36° C, how long will it take for the ice to melt?
The heat absorbed by the melting ice is Q = 4,875,600 J.
How to solvea, Given mass (m) = 14.6 kg, then the heat absorbed by the melting ice is Q = 4,875,600 J.
This can be determined using Q = 14.6 kg × 334,000 J/kg.
b. By utilizing the equation P = (0.01 W/m × K × 1.21 m^2 × 36 K) / 0.035 m, we can determine that P equals 12.396 watts.
To discover how long it will take for the ice to melt, we can use another formula: t = Q / P.
With the given value of Q as 4,875,600 joules and P is equal to 12.396 watts, we find that t evaluates to roughly 393,292 seconds.
In order to transform this result into hours, simply divide by 3600 which leads us to t ≈ 109.25 hours.
Therefore, it is predicted that the ice will melt in approximately 109.25 hours.
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You are pushing a 30-kg wooden crate across the floor. The force of sliding friction on the crate is 90 N. How much force must you exert on the crate to keep it moving with a constant velocity.
To keep the crate moving with a constant velocity, the force you need to exert on it is the force of kinetic friction, which in this case is 90 N. This is the minimum force required to overcome the force of sliding friction and maintain a constant velocity.
When an object is moving across a surface, there is a force of friction that opposes its motion. This is known as the force of kinetic friction. In the case of the wooden crate being pushed across the floor, the force of sliding friction is 90 N.
In order to keep the crate moving at a constant velocity, the force being applied to it must be equal and opposite to the force of sliding friction. This is because if the applied force is less than the force of sliding friction, the crate will slow down and eventually come to a stop. If the applied force is greater than the force of sliding friction, the crate will accelerate.
The force you need to exert on the crate is:
Force = Force of kinetic friction = 90 N
Note that the mass of the crate is not needed to calculate the force you need to exert, only the force of sliding friction acting on it.
Therefore, the force you must apply to the crate in order to maintain its constant velocity is the force of kinetic friction, which in this instance is 90 N. This is the bare minimum force necessary to overcome sliding friction and preserve constant speed.
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A work done of 50 μJ happen to a charge that is 6 nC. Calculate the voltage.
How do scientists believe elements were originally formed?
Question 3 options:
Under high pressure in the ocean
Through the cooling of lava in volcanoes
Through fusion in stars
Through chemical burning reactions
Answer:
Scientists believe that elements were originally formed through fusion in stars.
Explanation:
Because lighter elements combine to form heavier ones under high temperatures and pressures, this process is known as nuclear fusion and occurs within stars' cores. When a star exhausts its fuel, it undergoes a supernova explosion that releases heavier elements into space, which can then be incorporated into new stars, planets, and other celestial bodies.
The specific heat values for solid gold and solid iron are listed below:
J/8°C
gold
= 0.129
J/8°C
iron
= 0.449
If a 10g sample of gold and a 10g sample of iron were exposed to the same heat source for 1 minute, which sample would have a higher final
temperature? Why?
O The gold sample contains fewer atoms, therefore its final temperature is higher
O The gold sample contains fewer atoms, therefore its final temperature is lower
O The gold sample contains more atoms, therefore its final temperature is higher
O The gold sample contains more atoms, therefore its final temperature is lower
The gold sample contains fewer atoms, therefore its final temperature is higher
Does iron have a higher specific heat capacity than gold?The specific heat capacity of a substance is defined as the amount of heat energy required to raise the temperature of one gram of the substance by one degree Celsius.
The specific heat capacity of gold is 0.129 J/g°C, while the specific heat capacity of iron is 0.449 J/g°C. This means that it takes less heat energy to raise the temperature of one gram of iron by one degree Celsius compared to gold . Therefore, iron can absorb more heat energy before it reaches the same temperature as gold .
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How do i solve E=MC^2
Answer:
Calculating E = mc^2 for any object tells you how much energy would result if the entire object disappeared. Weigh the object you will perform the calculation for with a mass balance scale. Record its mass. Convert the mass to kg, if necessary. To convert from g to kg, for example, divide by 1,000. Square the speed of light.
Explanation:
1. Which type of subatomic particle is not found in the nucleus?(1 point)
a. proton
b. quark
c. electron
d. neutron
Answer:
(c) electron - they are found in the outer "shells" of atoms
PLEASE HELP!
The figure shows wire 1 in cross section; the wire is long and straight, carries a current of 4.20 mA out of the page, and is at distance d₁ = 2.58 cm from a surface. Wire 2. which is parallel to wire 1 and also long, is at horizontal distance d-5.05 cm from wire 1 and carries a current of 6.88 mA into the page. What is the x component of the magnetic force per unit length on wire 2 due to wire 1?
Answer: I think The correct Answer is 41.5pN/m
What two things can be considered to be substances?
Answer:Classification of Matter According To Composition
When you think about classifying matter, you likely think of the three states of matter: solid, liquid, and gas. But, thinking back to the donut metaphor, we can also classify matter according to what it is made of (aka its chemical composition)! So, what makes up matter? Well, on a molecular level, all matter is made up of atoms that can form elements, compounds, and molecules! Even with all these different components, matter can be split into two broad categories based on its composition: pure substances and mixtures. We will spend most of our time on pure substances, but briefly cover mixtures! So, let’s dive into pure substances!
We will go into more detail on all the components of matter, but for a more thorough review, check out Atomic Structure!
Definition of Pure Substances
A simple way to think about pure substances is as something that is made up of only one type of matter that always has the same properties, such as melting point, boiling point, density, etc.
Pure substances are matter that has a fixed chemical composition and properties that do not change.
Can you guess what are pure substances in your day-to-day life? I bet you may have salt (NaCl) and tin cans (Sn) in your pantry! These are perfect examples of pure substances because salt is made up of purely NaCl molecules, and tin is made up of only tin atoms.
But wait, you may have noticed a difference between salt and tin and asked how exactly salt is only made up of one type of matter when it’s two different atoms bonded together?
Pure substances can be further divided into two classes: elements and compounds.
Pure Substance Examples
We are going to spend some time looking at elements and compounds separately and some common examples of each!
Elements
If you think elements sound familiar, you are correctly thinking of the 118 organized in the periodic table. Tin is an example of an element!
Explanation:
What is the primary difference between outlaw motorcycle gangs and social motorcycle groups?
O A.
OB.
O C.
O D.
being a structured group with roles
having a group leader
their group activities and behavior
having group rules
Answer:
The primary difference between outlaw motorcycle gangs and social motorcycle groups is their group activities and behavior. Outlaw motorcycle gangs are typically involved in criminal activities, such as drug trafficking, extortion, and violence. They often have a hierarchical structure and strict rules for membership and behavior. In contrast, social motorcycle groups are primarily focused on riding motorcycles and socializing with other riders. They do not engage in criminal activities and do not have a strict hierarchy or rules for membership. While both types of groups may have some level of structure, such as having a group leader or group rules, the main difference lies in their group activities and behavior.
A ball swings in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point on its way up, its total acceleration is (-22.5i + 20.2j) m/s2 . For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball.
(a) The vector diagram of the acceleration is attached.
(b) -13.5 m/s²
(c) speed is 2.95 m/s and velocity is (1.79 i + 2.95 j) m/s.
How to calculate magnitude, speed and velocity?(b) At the highest point, the velocity of the ball is horizontal and the acceleration is vertical. So, radial acceleration:
radial acceleration = ar = a sin(θ) = (-22.5 m/s²) sin(36.9°) ≈ -13.5 m/s²
(c) The speed of the ball using the conservation of energy equation:
mgh + (1/2)mv² = constant
where m = mass of the ball,
g = acceleration due to gravity,
h = height of the ball above the lowest point, and
v = speed of the ball.
At the lowest point, the speed of the ball is equal to the square root of 2gh, where h is the height of the ball above the lowest point. At the point where the ball is 36.9° past the lowest point, the height of the ball above the lowest point is:
h = L(1 - cos(θ)) = 1.5(1 - cos(36.9°)) ≈ 0.665 m
Therefore, the speed of the ball is:
v = √(2gh) = √(2g(L-h)) = √(2(9.81 m/s²)(1.5 - 0.665) m) ≈ 2.95 m/s
The velocity of the ball is tangential to the circle and is perpendicular to the radial acceleration. At the point 36.9°, tangential component of the total acceleration is:
at = a cos(θ) = (20.2 m/s²) cos(36.9°) ≈ 16.1 m/s²
The angular acceleration:
α = ar / L = (-13.5 m/s²) / 1.5 m ≈ -9 m/s²
Therefore, the speed and velocity of the ball are:
speed = v ≈ 2.95 m/s
velocity = (at / α) i + v j ≈ (1.79 i + 2.95 j) m/s
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An object travels at a constant speed of 10m/ s for 10s. During the next 5s, it accelerates
uniformly to 20m/ s.
0
20
10
0
5 10 15
speed
m/ s
time / s
What is the total distance travelled by the object?
A 150m B 175m C 200m D 300
The total distance travelled by the object is 175 m.
option B.
What is the total distance travelled by the object?The total distance travelled by the object is calculated by applying the following kinematic equation as shown below;
Total distance = area rectangle + area of triangle
Total distance = (15 s - 0 s) x (10 m/s - 0 m/s) + ¹/₂(5s)((10 m/s)
Total distance = (15s)(10 m/s) + (5s )(5 m/s)
Total distance = 150 m + 25 m
Total distance = 175 m
Thus, the total distance travelled by the object is sum of all the distance covered from 0 second to 15 seconds.
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1. Single Choice
The higher the frequency of a wave, ( )
A：The smaller its speed
B：The shorter its wavelength
C：The greater its amplitude
D：The larger its period
The same collision as in Question 5 takes place, only this time the car and the truck bounce off each other completely elastically What are the final velocities of the car and truck just after the collision?
The final velocities of the car and truck just after the collision will be as per the conservation of momentum.
Momentum is defined as product of mass and velocity of the body. It is denoted by letter p and it is expressed in kg.m/s. Mathematically p = mv. it discuss the moment of the body. body having zero mass or velocity has zero momentum. The dimensions of the momentum is [M¹ L¹ T⁻¹].
According to conservation of momentum, Initial momentum will be equal to the final momentum. In the elastic collision there is no loss of energy, both energy and momentum is conserved.
if the the car is coming with velocity equal to the mass of the truck and truck is coming with mass of the car, then they have same momentum in opposite direction when they collide each other the final velocity of both car and truck becomes zero.
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A 150kg diver jumps off a diving board and hits the water at 40 m/s
What is the kinetic energy of the diver entering the water?
This is an exercise in kinetic energy, which is a form of energy associated with the movement of an object and its speed. It is important in many areas of physics, from classical mechanics to modern physics. This form of energy can be transformed into other forms of energy, such as thermal energy, sound energy or electrical energy. The formula for calculating kinetic energy is KE = m * v^2/2, where m is the mass of the object and v is its speed.
Kinetic energy is a fundamental concept in classical mechanics. It is used to analyze the movement of objects and calculate the amount of work required to stop them. When an object is in motion, it has kinetic energy, which is equal to half its mass times its speed squared. If the object collides with another object, some of its kinetic energy is transferred to the second object in the form of work or heat.
Kinetic energy is also important in modern physics. In Einstein's theory of special relativity, the mass of a moving object increases with its speed, which means that its kinetic energy also increases. In fact, the kinetic energy of a moving object is a form of energy that is included in Einstein's famous equation E=mc^2, where E is the energy, m is the mass of the object, and c is the speed of light. . This equation shows how the mass of an object and its energy are related.
Kinetic energy is also important in quantum physics. In quantum mechanics, particles have a property called momentum, which is a measure of their motion. Momentum and kinetic energy are related, and experiments in quantum physics often measure the momentum and kinetic energy of particles.
It tells us that the diver has a mass of 150 kg, and that he jumps from a diving board into the water at a speed of 40 m/s.
They ask us what is the kinetic energy of the diver who enters the water?We know that the formula for kinetic energy is:
KE = m * v^2/2. We should not do the formula clearance, because we are going to calculate the kinetic energy.
We already know our data from the formula, now we substitute and solve, then
KE = (m × v²)/2
KE = (150 kg × (40 m/s)²)/2
KE = (150 kg × 1600 m²/s²)/2
KE = 120000 J
When the diver enters the water, the kinetic energy is 120,000 J.
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Answer:
The kinetic energy of the diver entering the water is 120,000 Joules.
Explanation:
The kinetic energy (KE) of an object is given by:
[tex]\sf\qquad\dashrightarrow KE = \dfrac{1}{2} * m * v^2[/tex]
where:
m is the mass of the objectv is its velocity.Plugging in the given values, we get:
[tex]\sf\qquad\dashrightarrow KE = \dfrac{1}{2} * 150\: kg * (40\: m/s)^2[/tex]
[tex]\sf\qquad\dashrightarrow KE = \dfrac{1}{2} * 150\: kg * 1600\: m^2/s^2[/tex]
[tex]\sf\qquad\dashrightarrow KE = \boxed{\bold{\:\:120,000\: J\:\:}}[/tex]
Therefore, the kinetic energy of the diver entering the water is 120,000 Joules.
In which stage is the individual willing to modify their behavior and their
environment to overcome the problem, as they are ready to change and take
the proper steps to make change happen?
OA. Maintenance
OB. Precontemplation
C. Action
D. Contemplation
SUBMIT
In C. Action stage is the individual willing to modify their behavior and environment to overcome problem, as they are ready to change and take proper steps to make change happen
Five phases of behaviour modification are identified as per phases of modification model. Precontemplation, Contemplation, Preparation, Action, and Maintenance are the phases. The person has made a commitment to change and is actively making changes to their surroundings and behaviour to address the issue in the Action stage.
In this mode, people have a strategy in place, and are generally moving in the right direction. Since it involves making significant changes to behaviour, attitudes, and lifestyle, the action stage is the most labor-intensive. In addition to having the tools and assistance they require for success, the person must be motivated and dedicated to making the change.
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A hurricane travels a distance of 20 miles in 1 hour. Determine the hurricanes velocity.
Answer:
the answer is 20mi/hr
Explanation:
Given the equation X=10m+(5m/s^2) t^2, find the change in positiin at t1=1s, t2=2s
Which of the following is most likely the caption for the illustration that was scratched out of the textbook?
A. An electrically-charged object can attract an uncharged object with magnetic properties.
B. An electrically-charged object is stronger than a magnet.
C. A dry cell battery has magnetic properties.
D. An electric circuit can only have one dry cell battery.
IMAGE DOWN BELOW OR UP
The correct statement is " A dry cell battery has magnetic properties.", The correct option is C.
A dry cell battery does generate its own magnetic field due to the flow of electric current through the battery.
The magnetic field is created by the movement of charged particles (electrons) within the battery. This magnetic field is relatively weak and is not typically strong enough to be used for practical applications outside of the battery itself.
So, the magnetic properties of the dry cell battery are important for understanding its behavior within an electrical circuit.
Therefore, The correct answer is option C.
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Most meteorites that enter the Earth's atmosphere burn up before they reach the Earth itself. When this happens, lots of energy is transferred from the meteorites' __________ energy stores very quickly. What one word completes the sentence
Most meteorites that enter the Earth's atmosphere burn up before they reach the Earth itself. When this happens, lots of energy is transferred from the meteorites' kinetic energy stores very quickly.
The kinetic energy storage of meteorites are communicated to the surrounding environment as heat, sound, and light energy.
A meteorite penetrates the atmosphere of the Earth. Friction acts on the meteorite when it reaches the Earth's atmosphere. When a meteorite enters the Earth's atmosphere, it gains kinetic energy. The meteorite catches fire due to friction. At this time, the meteorite's kinetic energy will be transformed into heat energy, sound energy, and light energy.
Hence kinetic word word completes the sentence.
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The highness or lowness of a sound is perceived as
a.
compression.
c.
ultrasound.
b.
wavelength.
d.
pitch.
Answer:
i think its D
Explanation:
Answer:
The highness or lowness of a sound is perceived as pitch. Pitch is a perceptual property of sound that allows us to distinguish between sounds that have the same loudness and duration, but differ in their frequency content. The pitch of a sound is determined by the frequency of the sound wave, with higher frequencies producing higher pitches and lower frequencies producing lower pitches. The pitch is what makes a sound distinguishable and is important in music, language, and communication.
Drag the answer in order from most potential energy (at the top) to least potential energy (at the bottom).
Source:
Position D on the roller coaster
A person standing on the ground
Position A on the roller coaster
B
A person in an airplane in the sky
A
Target
A person in an airplane in the sky has the greatest potential energy, while a person standing on the ground has the least potential energy.
What is gravitational potential energy?Gravitational potential energy is the energy that an object possesses due to its position above the ground.
Mathematically, the formula for gravitational potential energy is given as;
PE = mgh
Where;
m is the mass of the objectg is the acceleration due to gravityh is the height of the objectThe greater the height or distance of an object above the ground, the greater the gravitational potential energy.
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*Calculation
An intensity level change of 1 dB correspond
s to what percentage change in intensity?
Answer:
An intensity level change of 1 dB corresponds to a 10% change in intensity.
A 250 kg cart starts from rest and rolls down an inclined plane from a height of 550 m. Determine its speed at a height of 125 m above the bottom of the incline. Please round to two decimal places.
Answer:
24.85 m/s.
Explanation:
PE = mgh = 250 kg x 9.81 m/s^2 x 550 m = 1,358,725 J
PE' = mgh' = 250 kg x 9.81 m/s^2 x 125 m = 308,062.5 J
PE = KE
1,358,725 J = 0.5mv^2
Solving for v, we get:
v = sqrt(2PE/m) = sqrt(2 x 1,358,725 J / 250 kg) = 59.15 m/s (rounded to two decimal places)
PE' + KE' = PE + KE
Since the cart starts from rest at the top of the incline, KE = 0. Therefore:
PE' = KE'
mgh' = 0.5mv'^2
Solving for v', we get:
v' = sqrt(2gh') = sqrt(2 x 9.81 m/s^2 x 125 m) = 24.85 m/s (rounded to two decimal places)
Therefore, the speed of the cart at a height of 125 m above the bottom of the incline is 24.85 m/s.
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A beaver runs at a speed of 2.0 m/s with 45 J of kinetic energy. What is the beaver’s mass?
A beaver runs at a speed of 2.0 m/s with 45 J of kinetic energy, then the mass is approximately 1.74 kg, and this can be calculated by using the kinetic energy (KE) of an object that is KE = (1/2) ×m × [tex]v^2[/tex].
KE = (1/2) ×m × [tex]v^2[/tex].
where m= mass of the object, v=its velocity.
The beaver runs at a speed of 2.0 m/s with 45 J of kinetic energy. Substituting these values into the above equation
45 J = (1/2) ×m × [tex](2.0 m/s)^2[/tex]
Simplifying this equation:
45 J = (1/2) × m × 4.0[tex]m^2/s^2[/tex]
45 J = 2 m × 2 [tex]m^2/s^2[/tex]
45 J = 4 [tex]m^3/s^2[/tex]
[tex]m^3[/tex] = 45 J / 4 [tex]s^2[/tex]
[tex]m^3[/tex] = 11.25 kg×[tex]m^2/s^2[/tex]
Taking the cube root of both sides to solve for mass,
m = (11.25 kg×[tex]m^2/s^2)^(^1^/^3^)[/tex]
m = 1.74 kg (rounded to two decimal places)
Learn more about the calculation of mass here.
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