The frequency of the mass spring system would decrease by a factor of 3 if length of the spring is cut into one third.
What is frequency ?Frequency is described as the number of occurrences of a repeating event per unit of time which is also occasionally referred to as temporal frequency for clarity, and is distinct from angular frequency.
The energy equation is shown as E = hν.
where E = energy,
h = Planck's constant (6.626 x 10 -34 J · s),
and v= frequency.
The energy equation shows a direct relationship between frequency and energy because as frequency increases, energy also increases.
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please help me in this question pls
a) Yes, the force of thrust of the engine does work as it is causing the plane to accelerate and lift off the ground.
b) Yes, the kinetic energy of the plane increases as it takes off and gains speed.
c) Yes, the gravitational potential energy of the plane increases as it gains height.
d) Yes, the force of thrust of the engine changes the mechanical energy of the plane.
What is Kinetic energy?The kinetic energy of an object is the form of energy that it possesses due to its motion which is also defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
The work done by the engine's thrust increases the plane's kinetic energy and gravitational potential energy, thereby changing its mechanical energy.
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Two cars stuck in a traffic jam and each sounds its horn at a frequency of 625 Hz. A bicyclist between the two cars, 4.50 m from each horn, is find that she is at a point of constructive interference. How far backward must she move to reach the nearest point of destructive interference? As a speed of sound use the speed of 343 m/s.
The bicyclist needs to move backward by a distance of 0.2744 m to reach the nearest point of destructive interference.
What is the distance for the nearest point of destructive interference?The wavelength of the sound wave produced by the horns can be calculated as;
λ = v/f
λ = 343/625
λ = 0.5488 m
let the integer multiple of the wavelength = d
d = mλ
d = 4.50 + x
where;
x is the distance that the bicyclist is from the point of constructive interference towards one of the horns4.50 + x = mλ
4.50 + x = m(0.5488)
let the odd multiple of half the wavelength = d'
d' = (2n + 1)(λ/2)
d' = 4.50 - y
where;
y is the distance that the bicyclist is from the point of destructive interference towards one of the horns.4.50 - y = (2n + 1)(λ/2)
4.50 - y = (2n + 1)(0.2744)
mλ = 2n(λ/2) + (λ/2) + 4.50 - y
x - y = (2n + 1)(λ/2) - 4.50
x - y = (2n + 1)(0.2744) - 4.50
Let n = 0
x - y = (0 + 1)(0.2744) - 4.50
y = 4.50 - 0.2744
y = 4.2256
The distance is cakculated as;
4.50 - y = 0.2744 m
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5. You are driving at a constant speed of 35.0 m/s
when you pass a traffic officer on a motorcycle
hidden behind a billboard. One second after your
car passes the billboard, the traffic officer sets out
from the billboard to catch you, accelerating at a
constant rate of 3.0 m/s². How long does it take the
traffic officer to overtake your car?
The traffic cop needs 23.3 seconds to pass the automobile.
What is the acceleration of a car moving in a straight line at a constant speed?When your velocity (not speed) changes, you are accelerating. A automobile moving at a steady 100 km/h in a straight line has no acceleration. Average acceleration is equal to (change in velocity) / (duration). The car's acceleration is zero because its change in velocity is also zero.
[tex]d1 = v1*t1 = 35.0 m/s * 1 s = 35.0 m[/tex]
[tex]d = d1 = 35.0 m[/tex]
[tex]d2 = v2*t + (1/2)at^2[/tex]
[tex]d2 = (1/2)at^2[/tex]
[tex]v2*t + (1/2)at^2 = (1/2)at^2[/tex]
[tex]v2*t = (1/2)at^2[/tex]
Solving for t, we get:
[tex]t = (2v2/a) = (235.0 m/s)/3.0 m/s^2 = 23.3 s[/tex] (rounded to 2 decimal places)
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if it took her 2.7 seconds to lift the lawnmower, how much power did she output
Answer:
N/A
Explanation:
The following formula can be used to compute the power output of a person lifting a lawnmower:
Work (W) / Time (t) = Power (P).
Where:
Work (W) is defined as the force used to lift the lawnmower multiplied by the distance traveled (i.e., work done against gravity).
Time (t) is the amount of time it takes to lift the lawnmower.
To determine the power output, however, we would need to know the force used to lift the lawnmower as well as the distance it was lifted. We won't be able to provide an accurate power output value without this information.
Using the Left Hand Rule, if motion is toward you and the field is up, which way is the current?
A. Left
B. Right
C. Toward you
D. Away from you
A uniform, aluminum beam 9.00 m
long, weighting 300 N
, rests symmetrically on two supports 5.00 m
apart. A boy weighing 600 N
starts at point A
and walks toward the right. (Figure 1) How far beyond the support can the boy walk without tipping?
The boy weighing 600 N can walk at most 4.1 m beyond point A without tipping the beam.
What is center of mass?It is the weighted average position of all the system's or object's constituent pieces. It is the average position of all the parts of the system or object, weighted according to their mass. In other words, the center of mass is the point where an applied force will result in pure translation of the object, without any rotation.
To avoid tipping, the center of mass of the beam and the boy together must remain over the area between the two supports. Let's first find the center of mass of the beam.
The weight of the beam is 300 N and it is uniform, so its center of mass will be located at the midpoint, or 4.5 m from either support.
Next, we need to find the center of mass of the boy-beam system as the boy walks along the beam. Let's assume the boy moves a distance d to the right of point A before tipping occurs. The weight of the boy is 600 N and we can approximate his weight as acting at the center of his body, which we'll assume is 0.9 m from the left end of the beam. The combined center of mass of the boy-beam system will be at a distance (4.5 m + 0.9 m + d) from the left end of the beam.
For the system to remain stable, this combined center of mass must remain between the two supports, which are 5.00 m apart. Therefore, we can write:
4.5 m ≤ 4.5 m + 0.9 m + d ≤ 9.5 m
Solving for d, we get:
d ≤ 4.1 m
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find a recent (less than 5 years old) article addressing some aspect of
environmental science that we have covered so far this year.
"Greenland ice sheet melting at alarming rate of 8,300 tonnes per second" is a recent article addressing some aspect of environmental science that we have covered so far this year.
This article, published in The Guardian in January 2021, addresses the melting of the Greenland ice sheet, which is a topic covered in environmental science. The article highlights a new study that found the ice sheet is melting at a rate of 8,300 tonnes per second, which is seven times faster than in the 1990s.
The melting of the Greenland ice sheet contributes significantly to rising sea levels and could have disastrous consequences for coastal communities worldwide. The article discusses the causes and potential consequences of this rapid melting, as well as the urgent need for action to mitigate climate change and its effects. This topic relates to the study of climate change, the cryosphere, and the impacts of human activity on the environment.
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A block of wood weighing 15 N rest on top of the table. How mush force is exerted by the table on the blockso that it will remainat rest. Explain your answer
Why is it called “static” electricity?
A. Charges can easily flow
B. Charges are not trapped in place
C. Charges cannot easily flow
D. Charges are free to move around
It is called static electricity because Charges cannot easily flow, hence option C is the answer.
Static electricity is called "static" because the charges are not free to move around easily. They tend to build up on the surface of an insulator and remain in place, rather than flowing like current in a conductor.
This buildup of charge can occur due to friction, induction, or any other mechanisms in the conductor. Therefore, option C is the correct option that says "Charges cannot easily flow".
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The critical angle for total internal re
ection at a liquid-air interface is
42.5.
(a) If a ray of light traveling in the liquid has an angle of incidence at the
interface of 35.0, what angle does the refracted ray in the air make
with the normal?
(b) If a ray of light traveling in air has an angle of incidence at the
interface of 35.0, what angle does the refracted ray in the liquid make
with the normal?
A wave has a frequency of 11 Hz and a wavelength of 9 meters
what is the speed of the wave
The speed of the wave is 99 meters per second.
What is Wave?
A wave is a disturbance or variation that travels through a medium or space, transferring energy without the net movement of matter. Waves can occur in various forms, such as mechanical waves that require a medium for propagation (e.g., sound waves, water waves) or electromagnetic waves that can travel through a vacuum (e.g., light waves, radio waves).
The speed of a wave can be calculated using the formula:
speed (v) = frequency (f) x wavelength (λ)
Given that the frequency (f) is 11 Hz and the wavelength (λ) is 9 meters, we can plug these values into the formula to calculate the speed of the wave:
v = 11 Hz x 9 meters
v = 99 meters per second
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What barriers do you currently face that interfere with your personal performance? What are your plans to address these barriers?
I need some examples, help me Guys, please
Personally, the barriers I face that interfere with my performance are:
Lack of motivationLack of resourcesPhysical health issuesPersonal and environmental distractionThese can all be addressed by
Setting clear goalsSeeking support when necessaryDeveloping healthy habitsManaging distractionsMore details on the barriers and how to address themPeople can face various barriers that can interfere with their personal performance. Some of the common barriers that people face include:
Lack of motivation or direction: People may struggle with finding motivation or a clear direction for their goals, which can hinder their personal performance.
Lack of resources: People may face financial or other resource constraints that limit their ability to pursue their goals or develop their skills.
Physical or mental health issues: Physical or mental health issues can impact a person's ability to perform at their best, affecting their energy levels, focus, and overall well-being.
Personal or environmental distractions: People may be distracted by personal or environmental factors such as noise, social media, or family obligations that can interfere with their ability to focus on their goals.
To address these barriers, there are various plans that people can take, such as:
Setting clear goals: By setting specific and measurable goals, people can have a clearer sense of direction and motivation for their personal performance.
Seeking support: People can seek support from friends, family, or professionals to help them overcome resource or health-related barriers.
Developing healthy habits: Practicing healthy habits such as exercise, mindfulness, and good sleep hygiene can improve physical and mental health and increase energy and focus.
Managing distractions: People can create an environment that is conducive to their personal performance by minimizing distractions, prioritizing their time, and creating routines that support their goals.
Overall, addressing these barriers requires a combination of self-reflection, planning, and taking action to overcome obstacles and achieve personal growth and success.
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a. How did the residents of donora initially respond?
The Pennsylvanian towns of Donora were struck by a smog at the end of October 1948 that forever altered the way environmental protection was practiced in the country.
During this, 20 people were confirmed dead, according to conservative estimates, while 5900 more people, or 43% of Donora's population, were adversely affected by the smog.
A firetruck and an ambulance from Donora's first responders started responding to calls. These rescue cars had to be led by a man walking in front carrying a torch due to the darkness. Later, when this technique was rendered impossible, firefighters started going door to door to give residents of Donora oxygen. Doctors advised anyone with long-term medical concerns to leave, but as the fog grew thicker, the routes became impassable.
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A weather balloon used by meteorologists is made of a flexible bag that allows the gas inside freely expand. If a weather balloon containing 25.0 m^3 of helium gas  is released from sea level, what is the volume of gas when the balloon reaches a height of 2100 m, where the pressure is 0.82×10^5 PA? Assume the temperature is unchanged. 
The volume of the helium gas in the weather balloon, when it reaches a height of 2100 m, is 30.85 m^3.
To solve this problem, we can use the ideal gas law, which states that the product of the pressure (P), volume (V), and temperature (T) of an ideal gas is proportional to the number of particles of the gas (n) and the universal gas constant (R). Since the temperature is assumed to be constant, we can write:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume of the helium gas, and P2 and V2 are the pressure and volume at a height of 2100 m.
At sea level, the pressure is approximately 1.01×10^5 Pa, so we have:
P1 = 1.01×10^5 Pa
V1 = 25.0 m^3
At a height of 2100 m, the pressure is 0.82×10^5 Pa, so we can solve for V2:
P1V1 = P2V2
V2 = (P1*V1)/P2
V2 = (1.01×10^5 Pa * 25.0 m^3) / (0.82×10^5 Pa)
V2 = 30.85 m^3
Therefore, the volume of the helium gas in the weather balloon when it reaches a height of 2100 m is approximately 30.85 m^3.
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Mathias is going to do some informational interviewing. What is one of the main benefits of doing these interviews?
O A.
OB.
O C.
O D.
A.He will gain insight about a new career opportunity.
B.He will likely be offered a position with a company.
C.He will be able to ask questions about job openings.
D.He will find out how much money everyone earns.
Answer:
A
Explanation:
One of the main benefits of informational interviewing is that it allows the person conducting the interviews to gain insights and information about a particular career or industry.
5. How did your calculated final temperature compare with the actual temperature of the
air-metal mixture? Why or how did you make the prediction that you did?
To calculate the final temperature of an air-metal mixture, we need to use the principle of heat transfer.
The heat transfer equation states that the heat gained by the metal is equal to the heat lost by the air. This equation can be written as:
mcΔT = mairCpΔT
How to make prediction the of the final temperature?To make a prediction of the final temperature, we need to consider factors such as the thermal conductivity of the metal and air, the specific heat capacities of the materials, and the heat transfer coefficients at the metal-air interface. Additionally, the shape and size of the metal object and the surrounding environment can affect the final temperature.
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A laboratory measurement finds 200 μg of hemoglobin per μL of blood. Hemoglobin, the blood protein that transports oxygen, has a molecular weight of 64 kDa or 64,000 u , where 1 dalton ( Da ) = 1 atomic mass unit ( u ) = 1.66×10^−24g . Estimate the number of hemoglobin proteins in one red blood cell. Express your answer in hemoglobin per red blood cell.
One red blood cell contains an estimated 251 molecules of haemoglobin, according to our estimation.
What size does a red blood cell typically have?The average red blood cell has a diameter of 6 to 8 micrometres, according to the American Society of Haematology, and a volume of 113-268 μm³ or 113-268x10⁻¹² L.
Let's first change the haemoglobin concentration from grammes per litre to grammes per litre so that it has the same units as the molecular weight:
200 μg/μL x 1 g/1000 μg x 10⁶ μL/L = 0.2 g/L
Next, let's translate hemoglobin's molecular weight from kDa to grammes per molecule:
64 kDa x 1000 Da/kDa x 1.66x10⁻²⁴ g/Da = 1.06x10⁻²⁰ g/molecule
Using Avogadro's number, we can now determine how many haemoglobin molecules are present in a single litre of blood ([tex]6.022*10^{23}[/tex] molecules/mol): 0.2 g/L x 1 mol/1.06x10⁻²⁰ g x [tex]6.022*10^{23}[/tex] molecules/mol = 1.13x10¹⁵ molecules/L.
Divide the total number of molecules in 1 litre of blood by the volume of red blood cells to get the amount of haemoglobin molecules per red blood cell. The typical red blood cell count range, according to the American Society of Haematology, is between 4.5-5.5 million cells/L, which translates to 4.5-5.5x10¹² cells/L.
When we divide the quantity of red blood cells in 1 L by the quantity of haemoglobin molecules, we get:
1.13x10¹⁵ molecules/L / 4.5x10¹² cells/L = 251 Red blood cell haemoglobin molecules, rounded to the closest integer.
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A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later. Determine the distance the ball was thrown.
The distance the ball was thrown is 52.22m by A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later.
How to calculate distance?Every motion under constant acceleration is projectile motion
Angle above horizontal Ф = 35°, initial speed v1 = 25m/s , time 2.55s
Substituting value in the below equation
x=x₁ + (v₁*cosθ)(t)+1/2 *a*t²
a= 0 as acceleration in horizontal direction is zero
x= 25*cos(35)*2.55
x=52.22 m
Projectile motion is a form of motion in which object influenced when it is launched into the gravitational force from the surface of Earth along a curved path.
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An incandescent lamp is written: 12 V, 2 A. What is the resistance of the filament of this lamp in working condition?
Answer:
The resistance is 6 ohms
Explanation:
V = 12V
I = 2A
Use ohm's law:
R = V / I
R = 12V / 2A
R = 6 ohms
By how much would a windmill power increase in [%] if the wind speed increased 3%?
a. 33 b. 9 c. 13 d. 5 e. 21
The power will increase by about 9.27% (when rounded to two decimal places).
Therefore, the correct answer choice is (b) 9.
How do we calculate?The power generated by a windmill is proportional to the cube of the wind speed and which means that if the wind speed increases by 3%, the power generated will increase by:
(1.03)^3 −1 = 0.0927
In physics, power is described as the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt.
So the power will increase by about 9.27%
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Many chemical reactions release energy. Suppose that at the beginning of a reaction, an electron and proton are separated by 0.115 nm , and their final separation is 0.105 nm . How much electric potential energy was lost in this reaction (in units of eV)?
The electric potential energy lost in this reaction is approximately 2.81 eV.
What is potential energy?
To calculate the electric potential energy lost in this reaction, we first need to calculate the difference in electric potential energy between the initial and final states. We can use the following formula to calculate electric potential energy:
E = kq1q2/r
where E is the electric potential energy, k is Coulomb's constant (8.99 x [tex]10^{9}[/tex] N*m²/C²), q1 and q2 are the charges of the two particles, and r is the separation distance between them.
In this case, we have an electron and a proton, which have charges of -1.602 x [tex]10^{-19}[/tex] C and +1.602 x [tex]10^{-19}[/tex] C, respectively. The initial separation distance is 0.115 nm, which is 1.15 x [tex]10^{-10}[/tex] m, and the final separation distance is 0.105 nm, which is 1.05 x [tex]10^{-10}[/tex] m.
So, the initial electric potential energy is:
E_initial = kq_electronq_proton/r_initial
= (8.99 x [tex]10^{9}[/tex] N*m²/C²) * (-1.602 x [tex]10^{-19}[/tex] C) * (1.602 x [tex]10^{-19}[/tex] C) / (1.15 x [tex]10^{-10}[/tex] m)
= -1.44 x [tex]10^{-18}[/tex] J
And the final electric potential energy is:
E_final = kq_electronq_proton/r_final
= (8.99 x [tex]10^{9}[/tex] N*m²/C²) * (-1.602 x [tex]10^{-19}[/tex] C) * (1.602 x [tex]10^{-19}[/tex] C) / (1.05 x [tex]10^{-10}[/tex] m)
= -1.89 x [tex]10^{-18}[/tex] J
The electric potential energy lost in this reaction is:
ΔE = E_final - E_initial
= (-1.89 x [tex]10^{-18}[/tex] J) - (-1.44 x [tex]10^{-18}[/tex] J)
= -0.45 x [tex]10^{-18}[/tex] J
To express the electric potential energy lost in units of eV, we can use the following conversion factor:
1 eV = 1.602 x [tex]10^{-19}[/tex] J
So, the electric potential energy lost in this reaction is:
ΔE = (-0.45 x [tex]10^{-18}[/tex] J) / (1.602 x [tex]10^{-19}[/tex] J/eV)
= -2.81 eV
Therefore, the electric potential energy lost in this reaction is approximately 2.81 eV.
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Under a pressure of 862 Pa, a gas has a volume of 752 L. The pressure is increased, without changing the temperature, until the volume is 624 L. What is the new pressure?
Claims that if temperature is kept constant, the end result of both volume and pressure is constant. The new level is 1036 Pa, which is how this can be expressed.
How does pressure work?So either a strong force or a strong force applied over a short area can cause a lot of pressure. When we stand up compared to when we are walking, more of our feet are in proximity to the earth. Pressure would be lower if there was more surface area in contact.
Describe a force?An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. There are both living things and non-living objects in the concept of a force.
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A water wave travels a distance of 30m in 15s. What is the wave's speed in m/s?
substitute d = 30 into formula
v = 15 d = v x t
30 = 15t
30/15 or 30 over 15 fraction :)
simplify
=
2
answer = 2
I hope this helps, this is what I know, I'm sorry if it's wrong :(
URGENT PLEASE HELP SOLVE THANK YOU SO MUCH
centers of two small particles charged particles are separated by a distance of 1.2x10-4 meter. The charges on the particle are 8x10^-19 and 4.8*10^-19, respectively. what is the the magnitude of the electrostatic force between these two particles?
Answer:
the magnitude of the electrostatic force between these two charged particles is 4.32 x 10^-28 N.
Explanation:
F = k * (q1 * q2) / r^2
where:
F is the electrostatic force
k is the Coulomb's constant (9 x 10^9 Nm^2/C^2)
q1 and q2 are the charges of the particles
r is the distance between the particles
Plugging in the given values:
q1 = 8 x 10^-19 C
q2 = 4.8 x 10^-19 C
r = 1.2 x 10^-4 m
k = 9 x 10^9 Nm^2/C^2
we can calculate the electrostatic force:
F = (9 x 10^9 Nm^2/C^2) * (8 x 10^-19 C) * (4.8 x 10^-19 C) / (1.2 x 10^-4 m)^2
F = 4.32 x 10^-28 N
The electrostatic force between these two particles is therefore calculated to be **1.44x10⁻¹⁴ N**1 using Coulomb's equation of electrostatic force.
COULOMB LAW BE DEFINED?With a force proportional to the product of the charges and inversely proportional to the square of the distance between them, Coulomb's law states that like charges repel and opposite charges attract. There is a formula that may be used to calculate the force between two point charges. Charles-Augustin de Coulomb created Coulomb's law in 1785
The electrostatic force between two charges is inversely proportional to the square of the distance between them and directly proportional to the product of their magnitudes1.
The centers of the two tiny charged particles in this example are separated by a distance of **1.2x10⁻⁴ meter**, with charges of **8x10⁻¹⁹** and **4.8*10⁻¹⁹**, respectively.
F is the electrostatic force
k is the Coulomb's constant (9 x 10⁹ Nm²C²)
q1 and q2 are the charges of the particles
r is the distance between the particles
Plugging in the given values:
q1 = 8 x 10⁻¹⁹ C
q2 = 4.8 x 10⁻¹⁹C
r = 1.2 x 10⁻⁴ m
k = 9 x 10₉ Nm²/C²
we can calculate the electrostatic force:
F = (9 x 10⁹Nm²/C²) * (8 x 10⁻¹⁹ C) * (4.8 x 10⁻¹⁹ C) / (1.2 x 10⁻⁴ m)²
The electrostatic force between these two particles is therefore calculated to be **1.44x10⁻¹⁴N**1 using Coulomb's equation of electrostatic force.
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What is the SI unit that is equal to 0.01 meters?
Answer:one centimeter is equal to one hundredth of a meter (1 cm = 0.01 m).
Explanation:
A wave has a frequency of 50Hz and a wavelength of 20m.
Calculate the speed of the wave in m/s.
Explanation:
f= 50Hz
wavelength= 20m
Speed of wave (v) = frequency × wavelength
= 50×20
= 1000m/s
a bird flies 3km to the west and then 4km to the south. find the resultant displacement of the bird
Answer:
We are asked to calculate for the resultant displacement.
We therefore conclude that the resultant displacement of the bird is 5 Km, 53o 5 K m , 53 o South of West.
Explanation:
have a nice day.
help what’s the answer for this
The acceleration of mass, m2 is determined as 4.2 m/s².
What is the acceleration m2?The acceleration of mass, m2 is calculated by applying Newton's second law of motion, which states that force applied to a body is proportional to the product of mass and acceleration of the body.
F(net) = ma
m2g - m1g = m2a + m1a
a = (m2g - m1g)/(m2 + m1)
where;
g is acceleration due to gravitya is the acceleration of the blocksa = (5 x 9.8 - 2 x 9.8)/(5 + 2)
a = 4.2 m/s²
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Bismuth-214 is radioactive. It has a half-life of 20 minutes. (a) The nuclide notation for bismuth-214 is 214Bi. State the composition of the nucleus of bismuth-214. ASSIGNM ASSIGN
The composition of the nucleus of bismuth-214 can be described using its nuclide notation, which consists of the element symbol, atomic number, and mass number.The element symbol for bismuth is Bi, which has an atomic number of 83, meaning that all atoms of bismuth have 83 protons in their nucleus.The mass number of bismuth-214 is 214, which means that a typical bismuth-214 nucleus contains 83 protons and 131 neutrons (since mass number = number of protons + number of neutrons).Therefore, the nucleus of bismuth-214 can be represented by the nuclide notation: ^214Bi.
Solve pls:
a) What are the maina dvantages of an epicyclicgearbox? b) Figure Q4 overleaf shows a diagram for an epicyclic gear train. Power is supplied to
wheel 3 and is delivered to a load attached to the epicyclic arm, body 2. Wheel 5 is fixed to the gear case, body 1.
i) Determine T4 if t3 = 30, t4 = 40 and t5 = 60.
a) The main advantages of an epicyclic gearbox are:
High gear ratios can be achieved in a small space, making it a compact design.It can provide a smooth and efficient transfer of power due to the multiple contact points between gears.It can be used for different applications, such as increasing torque or speed, reversing direction, and providing a neutral point.How to solve a gearbox?b) i) Using the formula for the gear ratio of an epicyclic gear train:
T4/T3 = (t2/t1) x (t5/t2) x (t4/t5)
T4/30 = (1/2) x (60/20) x (40/60)
T4 = 40 Nm
ii) From the law of gearing for an epicyclic gear train:
w21 = (t3/t2) x (t5/t4) x w31 - (t3/t2) x w2
Substituting the given values:
w21 = (30/20) x (60/40) x 200 - (30/20) x 100
w21 = 150 rad/s
iii) The fixing couple that must be applied to wheel 5 can be found from the power transmitted by the gear train:
P = w3 x T3 = w2 x T2 = w1 x T1
Substituting the given values:
9 kW = 200 rad/s x 30 Nm = w2 x T2 = w2 x 20 Nm
w2 = 450 rad/s
T2 = (9 kW) / (450 rad/s) = 20 Nm
The fixing couple that must be applied to wheel 5 is equal in magnitude and opposite in direction to T2, so it is -20 Nm.
iv) The tangential force at the pitch point between wheels 3 and 4 can be found from the formula:
Ft = (2 x Pd) / (m x z3)
where Pd is the diametral pitch, m is the module, and z3 is the number of teeth on wheel 3.
Substituting the given values:
Pd = 25.4 / 5 = 5.08 teeth/inch
z3 = t3 / m = 30 / 5 = 6 teeth
Ft = (2 x 5.08) / (5 x 6) = 0.846 N
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