Answer:
Available energy = 35 x 10⁶ J
Explanation:
Given:
Amount of energy (Q) = 21 gj = 21 x 10⁹ J
Temperature T1 = 600 k
Temperature T0 = 27 + 273 = 300k
Find:
Available energy
Computation:
Available energy = Q[1/T0 - 1/T1]
Available energy = 21 x 10⁹ J[1/300 - 1/600]
Available energy = 35 x 10⁶ J
During heavy lifting, a disk between spinal vertebrae is subjected to a 5000-N compressional force. (a) What pressure is created, assuming that the disk has a uniform circular cross section 2.00 cm in radius? (b) What deformation is produced if the disk is 0.800 cm thick and has a Young's modulus of 1.5×109 N/m2?
Answer:
[tex]3978873.58\ \text{Pa}[/tex]
[tex]0.00002122\ \text{m}[/tex]
Explanation:
F = Force = 5000 N
r = Radius of circular cross section = 2 cm
l = Length of disk = 0.8 cm
A = Area = [tex]\pi r^2[/tex]
Y = Young's modulus = [tex]1.5\times 10^9\ \text{N/m}^2[/tex]
Pressure is given by
[tex]P=\dfrac{F}{A}\\\Rightarrow P=\dfrac{5000}{\pi (2\times 10^{-2})^2}\\\Rightarrow P=3978873.58\ \text{Pa}[/tex]
The pressure on the cross section is [tex]3978873.58\ \text{Pa}[/tex]
The change in length of the cross section is given by
[tex]\Delta L=\dfrac{PL}{Y}\\\Rightarrow \Delta L=\dfrac{3978873.58\times 0.8\times 10^{-2}}{1.5\times 10^9}\\\Rightarrow \Delta L=0.00002122\ \text{m}[/tex]
The deformation produced is [tex]0.00002122\ \text{m}[/tex]
A cylindrical wire of radius 2 mm carries a current of 3.0 A. The potential difference between points on the wire that are 44 m apart is 3.8 V.
Required:
a. What is the electric field in the wire?
b. What is the resistivity of the material of which the wire is made?
Answer:
a. E = 86.36 x 10⁻³ V/m = 86.36 mV/m
b. ρ = 3.6 x 10⁻⁷ Ωm
Explanation:
a.
The electric field in terms of the voltage is given by the following formula:
E = V/d
where,
E = Electric Field in the Wire = ?
V = Potential Difference = 3.8 V
d = distance between the points = 44 m
Therefore,
E = 3.8 V/44 m
E = 86.36 x 10⁻³ V/m = 86.36 mV/m
b.
Now, from Ohm's Law:
V = IR
R = V/I
where,
R = Resistance of wire = ?
I = Current = 3 A
Therefore,
R = 3.8 V/3 A
R = 1.27 Ω
Now, the resistance of a wire can be given as:
R = ρL/A
where,
ρ = resistivity of material = ?
L = Length = 44 m
A = Cross-sectional area = πr² = π(0.002 m)² = 1.25 x 10⁻⁵ m²
Therefore,
1.27 Ω = ρ*44 m/1.25 x 10⁻⁵ m²
(1.27 Ω)(1.25 x 10⁻⁵ m²)/44 m = ρ
ρ = 3.6 x 10⁻⁷ Ωm
A sample of an ideal gas has a volume of 0.0100 m^3, a pressure of 100 x 10^3 Pa, and a temperature of 300K. What is the number of moles in the sample of gas?
Answer:
Explanation:
pV = nrT
n = PV/RT
n = (100*10^3)(.01)/(300*0.082057)
n = 40.62 moles
Help!!! Need answer ASAP.
Answer:
Hey
Explanation:
A piano of mass 852 kg is lifted to a height of 3.5 m. How much gravitational potential energy is added to the piano? Acceleration due to gravity is g = 9.8 m/s2 O A. 102,282 J O B. 29,224J O C. 2982 J O D. 304.3J SUSM
Answer:
29223.6J
Explanation:
Given parameters:
Mass of Piano = 852kg
Height of lifting = 3.5m
Unknown:
Gravitational potential energy = ?
Solution:
The gravitational potential energy of a body can be expressed as the energy due to the position of a body;
G.P.E = mgh
m is the mass
g is the acceleration due to gravity
h is the height
Now insert the given parameters and solve;
G.P.E = 852 x 9.8 x 3.5 = 29223.6J
You are driving on the highway at a speed of 40 m/s (which is over the speed limit) when you notice a cop in front of you. To avoid a ticket, you press on the brake and slow to a speed of 30 m/s over the course of 5 seconds. What is the acceleration of the car? WORK=BRAINLIEST
What is your car's initial velocity?
What is your car's final velocity?
How long does it take the car to slow down?
Write the equation you will use to solve this problem.
What is the acceleration of your vehicle?
+ 2.0 m/s^2
- 2.0 m/s^2
+ 8.0 m/s^2
- 6.0 m/s^2
Explanation:
U = 40m/s
V = 30m/s
T = 5 sec
A = ?
[tex]a = \frac{u - v}{t}[/tex]
[tex]a = \frac{40 - 30}{5}[/tex]
[tex]a = \frac{10}{5}[/tex]
[tex]a = 2[/tex]
since it's decreasing in speed, The acceleration will be " - 2.0ms^-2 " or " - 2.0m/s^2 "
If you liked this answer, feel free to follow me for more!
Btw don't mind me answering twice. I want the free points and maybe another brainliest? lol.
A nonmechanical water meter could utilize the Hall effect by applying a magnetic field across a metal pipe and measuring the Hall voltage produced.What is the average fluid velocity in m/s for a 4.25 cm diameter pipe, if a 0.575 T field across it creates a 60.0 mV Hall voltage?
Answer:
The velocity is [tex]v =2.455 \ m/s[/tex]
Explanation:
From the question we are told that
The diameter of the pipe is [tex]d = 4.25 \ cm = 0.0425 \ m[/tex]
The magnetic field is [tex]B = 0.575 \ T[/tex]
The hall voltage is [tex]V_H = 60.0 mV = 60 *10^{-3} \ V[/tex]
Generally the average fluid velocity is mathematically represented as
[tex]v = \frac{V}{ B * d }[/tex]
=> [tex]v = \frac{60*10^{-3}}{ 0.575 * 0.0425 }[/tex]
=> [tex]v =2.455 \ m/s[/tex]
On Earth, we experience lunar and solar eclipses. what types of eclipses (if any) would an inhabitant of the moon experience? Explain.
Answer:
However, those astronauts would experience a second spectacle: A solar eclipse caused by the Earth – the Sun disappearing behind the dark disc of the Earth. When Earth inhabitants witness a lunar eclipse, Moon inhabitants would, simultaneously be witnessing a solar eclipse.
A vertical spring gun is used to launch balls into the air. If the spring is compressed by 4.9 cm, the ball of mass 5.5 g is launched to a maximum height 50.2 cm. How much should the spring be compressed to send the ball twice as high?
We know, by conservation of energy :
[tex]\dfrac{kx^2}{2}=mgh[/tex]
Therefore,
[tex]\dfrac{x_1^2}{x_2^2}=\dfrac{h_1}{h_2}[/tex]
Putting given values, we get :
[tex]\dfrac{x_1^2}{x_2^2}=\dfrac{h_1}{h_2}\\\\\dfrac{4.9^2}{x_2^2}=\dfrac{50.2}{2\times 50.2}\\\\x_2^2=2\times 4.9^2\\\\x_2 = 4.9\times \sqrt{2}\\\\x_2=6.93\ cm[/tex]
Therefore, the spring be compressed to 6.93 cm to send the ball twice as high.
Hence, this is the required solution.
Which environment is least likely to support protists
A soil
B open ocean
C shallow pod
D organisms blood
Answer:
A: Soil
Explanation:
Protists need a moist environment to survive, and shallow ponds, oceans, and blood is all moist. So, the answer would be the soil, because that is the least moist environment out of these options.
Bani wants to know that when a cold wooden spoon is dipped in a cup of hot milk, it transfers heat to its other end by the process of -
Conduction
Convection
Radiation
None of these
Answer:
Conduction is the movement of heat through a substance by the collision of molecules. ... This process continues until heat energy from the warmer object spreads throughout the cooler object, like the heat from the milk spreading throughout the wooden spoon dipped in it. Hence, Option Conduction is correct.
What is the electric force between two point charges when 91 = -4e, 92 = +3 e,
and r= 0.05 m?
e = 1.6 x 10-1C, k = 9.00 x 10°Nom/C2)
Kouch
A. -1.1 * 10-24 N
B. 1.1 * 10-24 N
C. 5,5 x 10-25 N
D. -5.5 x 10-25 N
Answer:option B
Explanation:
A solid concrete block weighs 169 N and is resting on the ground. Its dimensions are
0.400m×0.200m×0.100m
A number of identical blocks are stacked on top of this one. What is the smallest number of whole blocks (including the one on the ground) that can be stacked so that their weight creates a pressure of at least two atmospheres on the ground beneath the first block?
Answer:
Explanation:
cross sectional area = .4 x .2 = .08 m²
Let n be the number of blocks required to make pressure = 2 atm
169 x n / .08 = 2 x 10⁵ N / m²
169 x n = .16 x 10⁵
n = 94.67
or 95 blocks .
An eraser is thrown upward with an initial velocity of 5.0m/s. The eraser’s velocity after 7.0 second is
Answer:
-63.6m/s
Explanation:
Given parameters:
Initial velocity = 5m/s
Time of flight = 7s
Unknown:
Velocity of the eraser after 7s = ?
Solution:
To solve this problem, we have to use the right motion equation which is given below;
v = u - gt
v is the final velocity
u is the initial velocity
g is the acceleration due to gravity = 9.8m/s²
t is the time taken;
Now insert the parameters and solve for v;
v = 5 - (9.8 x 7)
v = -63.6m/s
Find the change in thermal energy of a 25kg severed clown doll head that heats up from 25°C to 35°C, and has the specific heat of 1,700 J/(kg°C).
Answer:
Q = 425 kJ
Explanation:
Given that,
Mass, m = 25 kg
The clown doll head that heats up from 25°C to 35°C
The specific heat is 1700 J/kg°C
We need to find the internal energy of it. The heat required to raise the temperature is given by the formula as follows :
[tex]Q=mc\Delta T\\\\Q=25\times 1700\times (35-25)\\\\Q=425000\ J\\\\Q=425\ kJ[/tex]
So, 425 kJ of thermal energy is severed.
Which statement explains how it is possible to carry books to school without changing the kinetic or potential energy of the books or doing any work?
a. by moving the book without acceleration and keeping the height of the book constant
b. by moving the book with acceleration and keeping the height of the book constant
c. by moving the book without acceleration and changing the height of the book
d. by moving the book with acceleration and changing the height of the book
Answer:
a. by moving the book without acceleration and keeping the height of the book constant
Explanation:
FOR CONSTANT KINETIC ENERGY:
The kinetic energy of a body depends upon its speed according to its formula:
ΔK.E = (1/2)mΔv²
So, for Δv = 0 m/s
ΔK.E = 0 J
So, for keeping kinetic energy constant, the books must be moved at constant speed without acceleration.
FOR CONSTANT POTENTIAL ENERGY:
The potential energy of a body depends upon its height according to its formula:
ΔP.E = mgΔh
So, for Δh = 0 m/s
ΔP.E = 0 J
So, for keeping potential energy constant, the books must be moved at constant height.
So, the correct option is:
a. by moving the book without acceleration and keeping the height of the book constant
carrier concentration for n type
Answer:
Consider an n-type silicon semiconductor at T = 300°K in which Nd = 1016 cm-3 and Na = 0. The intrinsic carrier concentration is assumed to be ni = 1.5 x 1010 cm-3. - Comment Nd >> ni, so that the thermal-equilibrium majority carrier electron concentration is essentially equal to the donor impurity concentration.
Explanation:
HELP ASAP!
What happens to a circuit's resistance (R), voltage (V), and current (I) when you increase the length of the wire in the circuit?
Answer:
B R is constant V increases /increases
If one increase the length of the wire in the circuit, then, R increases, V decreases, I decreases. The correct option is D.
The resistance (R) of a wire increases as its length is increased in a circuit. This is because longer wires have more resistance because resistance increases with length.
Ohm's Law states that the current (I) in the circuit will drop if the resistance (R) rises while the voltage (V) stays constant. This is due to the inverse proportionality between current and resistance.
Thus, the correct option is D.
For more details regarding Ohm's law, visit:
https://brainly.com/question/1247379
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1000 kg car takes travels on a circular track having radius 100 m with speed 10 m/s. What is the direction of the acceleration of the car? *
A- outside track, and normal to track
B- towards the center and normal to the track
C- up
D- down
Answer:
B.
Explanation:
What resistance should be added in series with a 3.0-H inductor to complete an LR circuit with a time constant of 4.0 ms? A)0.75 k Ω Β) 12 Ω C) 0.75 Ω D) 2.5 Ω
Answer:
O.75KΩ
Explanation:
We measure the time constant τ, using the formula τ = L/R,
t is in seconds, then we have R to be the value of the resistor which is measured in ohms and also L is the value of the inductor which is measured in Henries.
Since t = L/R
We make R subject of the formula
R = L/τ
= 3/4x10-3
= 0.00075
= 0.75 KΩ
So we have it that the first Option (A) is the correct answer to the question
The resistance to be added is required.
The resistance added should be A. [tex]0.75\ \text{k}\Omega[/tex]
L = Inductance = 3 H
[tex]\tau[/tex] = Time constant = 4 ms
R = Resistance
Time constant is given by
[tex]\tau=\dfrac{L}{R}\\\Rightarrow R=\dfrac{L}{\tau}\\\Rightarrow R=\dfrac{3}{4\times 10^{-3}}=750\ \Omega=0.75\ \text{k}\Omega[/tex]
The resistance added should be [tex]0.75\ \text{k}\Omega[/tex]
Learn more:
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A wire carries a current of 11.4 A in a direction that makes an angle of 11.4° with a magnetic field of magnitude 11.4 à 10-3 T. The magnitude of the force on 11.4 cm of this wire is:____.a) 11.4 * 10^-3 N
b) 0.130 N
c) 1.48 * 10^-2 N
d) 2.93 * 10^-3 N
Answer:
(d) 2.93 x 10⁻³ N
Explanation:
Given;
current in the wire, I = 11.4 A
angle of inclination, θ = 11.4⁰
magnetic field on the wire, B = 11. 4 x 10⁻³
length of the wire, L = 11.4 cm = 0.114 m
The magnitude of magnetic force on the wire is given by;
F = BILsinθ
F = (11.4 x 10⁻³)(11.4)(0.114)(sin 11.4°)
F = 0.00293 N
F = 2.93 x 10⁻³ N
Therefore, the correct option is "D"
An inductor is connected to a 26.5 Hz power supply that produces a 41.2 V rms voltage. What minimum inductance is needed to keep the maximum current in the circuit below 126 mA?
Answer:
The minimum inductance needed is 2.78 H
Explanation:
Given;
frequency of the AC, f = 26.5 Hz
the root mean square voltage in the circuit, [tex]V_{rms}[/tex] = 41.2 V
the maximum current in the circuit, I₀ = 126 mA
The root mean square current is given by;
[tex]I_{rms} = \frac{I_o}{\sqrt{2} } \\\\I_{rms} = \frac{126*10^{-3}}{\sqrt{2} }\\\\I_{rms} =0.0891 \ A[/tex]
The inductive reactance is given by;
[tex]X_l = \frac{V_{rms}}{I_{rms}} \\\\X_l= \frac{41.2}{0.0891}\\\\X_l = 462.4 \ ohms[/tex]
The minimum inductance needed is given by;
[tex]X_l = \omega L\\\\X_l = 2\pi fL\\\\L = \frac{X_l}{2\pi f}\\\\L = \frac{462.4}{2\pi *26.5}\\\\L = 2.78 \ H[/tex]
Therefore, the minimum inductance needed is 2.78 H
Use the information below for the next five questions:
An open organ pipe emits B (494 Hz) when the temperature is 14°C. The speed of sound in air is v≈(331 + 0.60T)m/s, where T is the temperature in °C
Determine the length of the pipe.
What is the wavelength of the fundamental standing wave in the pipe?
What is frequency of the fundamental standing wave in the pipe?
What is the frequency in the traveling sound wave produced in the outside air?
What is the wavelength in the traveling sound wave produced in the outside air?
How far from the mouthpiece of the flute should the hole be that must be uncovered to play D above middle C at 294 Hz? The speed of sound in air is 343 m/s.
Answer: Please see answer in explanation column.
Explanation:
Given that
v≈(331 + 0.60T)m/s
where Temperature, T = 14°C
v≈(331 + 0.60 x 14)m/s
v =331+ 8.4 = 339.4m/s
In our solvings, note that
f= frequency
λ=wavelength
L = length
v= speed of sound
a) Length of the pipe is calculated using the fundamental frequency formulae that
f=v/2L
Length = v/ 2f
= 339.4m/s/ 2 x 494Hz ( s^-1)= 0.3435m
b) wavelength of the fundamental standing wave in the pipe
L = nλ/2,
λ = 2L/ n
λ( wavelength )= 2 x 0.3435/ 1
= 0.687m
c) frequency of the fundamental standing wave in the pipe
F = v/ λ
= 339.4m/s/0.687m=
494.03s^-1 = 494 Hz
d) the frequency in the traveling sound wave produced in the outside air.
This is the same as the frequency in the open organ pipe = 494Hz
e)The wavelength of the travelling sound wave produced in the outside air is the same as the wavelength calculated in b above = 0.687m
f) To play D above middle c . the distance is given by
L =v/ 2 f
= 343/ 2 x 294
=0.583m
In the video your blood is compared to a __________________ that delivers oxygen to your body and picks up CO2 to be released out when you breath.
Answer:
Delivery truck
Explanation:
Which has a greater buoyant force on it, a 35.0-cm3 piece of wood floating with part of its volume above water or a 35.0-cm3 piece of submerged iron?
The iron has, because it's displacing more water than the wood is.
Two tiny conducting spheres are identical and carry charges of -20μC and +50μC. They are separeted by a distance of 2.50cm. (a) what is the magnitude of the force that each sphere each sphere experience, and is the force attractive or repulsive ? (b) The spheres are brought into contact and then separated toa distance of 2.50cm. Determine the magnitude of the force that each sphere now experiences, and state whether the force is attractive or repulsive.
Answer:
[tex]14400\ \text{N}[/tex], Attractive
[tex]3240\ \text{N}[/tex], Repulsive
Explanation:
[tex]q_1[/tex] = -20 μC
[tex]q_2[/tex] = 50 μC
r = Distance between the charges = 2.5 cm
k = Coulomb constant = [tex]9\times 10^9\ \text{Nm}^2/\text{C}^2[/tex]
Electrical force is given by
[tex]F=\dfrac{kq_1q_2}{r^2}\\\Rightarrow F=\dfrac{9\times 10^9\times (-20\times 10^{-6})\times (50\times 10^{-6})}{(2.5\times10^{-2})^2}\\\Rightarrow F=-14400\ \text{N}[/tex]
The magnitude of force each sphere will experience is [tex]14400\ \text{N}[/tex]
Since the charges have opposite charges they will attract each other.
Now the charges are brought into contact with each other so the resultant charge will be
[tex]q=\dfrac{q_1+q_2}{2}\\\Rightarrow q=\dfrac{-20+50}{2}\\\Rightarrow q=15\ \mu\text{C}[/tex]
[tex]F=\dfrac{kq^2}{r^2}\\\Rightarrow F=\dfrac{9\times 10^9\times (15\times 10^{-6})^2}{(2.5\times 10^{-2})^2}\\\Rightarrow F=3240\ \text{N}[/tex]
The magntude of the force the spheres experience will be [tex]3240\ \text{N}[/tex]
The spheres have the same charge now so they will repel each other.
A ball filled with an unknown material starts from rest at the top of a 2 m high incline that makes a 28o with respect to the horizontal. The ball rolls without slipping down the incline and at the bottom has a speed of 4.9 m/s. How many revolutions does the ball rotate through as it rolls down the incline
Answer:
Searching in google I found the total mass and the radius of the ball (m = 1.5 kg and r = 10 cm) which are needed to solve the problem!
The ball rotates 6.78 revolutions.
Explanation:
Searching in google I found the total mass and the radius of the ball (m = 1.5 kg and r = 10 cm) which are needed to solve the problem!
At the bottom the ball has the following angular speed:
[tex] \omega_{f} = \frac{v_{f}}{r} = \frac{4.9 m/s}{0.10 m} = 49 rad/s [/tex]
Now, we need to find the distance traveled by the ball (L) by using θ=28° and h(height) = 2 m:
[tex] sin(\theta) = \frac{h}{L} \rightarrow L = \frac{h}{sin(\theta)} = \frac{2 m}{sin(28)} = 4.26 m [/tex]
To find the revolutions we need the time, which can be found using the following equation:
[tex] v_{f} = v_{0} + at [/tex]
[tex] t = \frac{v_{f} - v_{0}}{a} [/tex] (1)
So first, we need to find the acceleration:
[tex] v_{f}^{2} = v_{0}^{2} + 2aL \rightarrow a = \frac{v_{f}^{2} - v_{0}^{2}}{2L} [/tex] (2)
By entering equation (2) into (1) we have:
[tex] t = \frac{v_{f} - v_{0}}{\frac{v_{f}^{2} - v_{0}^{2}}{2L}} [/tex]
Since it starts from rest (v₀ = 0):
[tex] t = \frac{2L}{v_{f}} = \frac{2*4.26 m}{4.9 m/s} = 1.74 s [/tex]
Finally, we can find the revolutions:
[tex] \theta_{f} = \frac{1}{2} \omega_{f}*t = \frac{1}{2}*49 rad/s*1.74 s = 42.63 rad*\frac{1 rev}{2\pi rad} = 6.78 rev [/tex]
Therefore, the ball rotates 6.78 revolutions.
I hope it helps you!
I have a pen
I have a apple
what do I have now?
Answer:
You have an apple pen. :)
Answer:
I have a pen
I have a apple
apple pen
Explanation:
a vertical solid steel post 29cm in diameter and 2.0m long is required to support a load of 8200kg, ignore the weight of the post. determine the stress in the post
Answer:
The stress is [tex]\sigma = 1.218*10^{6} \ N/m^2[/tex]
Explanation:
From the question we are told that
The diameter of the post is [tex]d = 29 \ cm = 0.29 \ m[/tex]
The length is [tex]L = 2.0 \ m[/tex]
The weight of the loading mass
Generally the radius of the post is mathematically represented as
[tex]r = \frac{0.29}{2}[/tex]
=> [tex]r = 0.145 \ m[/tex]
Generally the area of the post is
[tex]A = \pi r^2[/tex]
=> [tex]A = 3.14 * 0.145 ^2[/tex]
=> [tex]A = 0.066 \ m^2[/tex]
Generally the weight exerted by the load is mathematically represented as
[tex]F = m * g[/tex]
=> [tex]F = 8200 * 9.8[/tex]
=> [tex]F = 80360 \ N[/tex]
Generally the stress is mathematically represented as
[tex]\sigma = \frac{F}{A}[/tex]
=> [tex]\sigma = \frac{80360 }{0.066}[/tex]
=> [tex]\sigma = 1.218*10^{6} \ N/m^2[/tex]
A mass m at the end of a spring of spring constant k is undergoing simple harmonic oscillations with amplitude A.
Part (a) At what positive value of displacement x in terms of A is the potential energy 1/9 of the total mechanical energy?
Part (b) What fraction of the total mechanical energy is kinetic if the displacement is 1/2 the amplitude?
Part (c) By what factor does the maximum kinetic energy change if the amplitude is increased by a factor of 3?
Answer:
a) The potential energy of the system is 1/9 of the total mechanical energy, when [tex]x= \frac{1}{3}\cdot A[/tex].
b) The fraction of the total mechanical energy that is kinetic if the displacement is 1/2 the amplitude is 1/2.
c) The maximum kinetic energy is increased by a factor of 9.
Explanation:
a) From Mechanical Physics, we remember that the mechanical energy of mass-spring system ([tex]E[/tex]), measured in joules, is the sum of the translational kinetic energy ([tex]K[/tex]), measured in joules, and elastic potential energy ([tex]U[/tex]), measured in joules. That is:
[tex]E = K + U[/tex] (1)
By definitions of translational kinetic energy and elastic potential energy, we have the following expressions:
[tex]K = \frac{1}{2}\cdot m \cdot v^{2}[/tex] (2)
[tex]U = \frac{1}{2}\cdot k\cdot x^{2}[/tex] (3)
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]v[/tex] - Velocity of the mass, measured in meters per second.
[tex]k[/tex] - Spring constant, measured in newtons per meter.
[tex]x[/tex] - Elongation of the spring, measured in meters.
If we know that [tex]U = \frac{1}{9}\cdot E[/tex], [tex]k = k[/tex] and [tex]E = \frac{1}{2}\cdot k \cdot A^{2}[/tex], then:
[tex]\frac{1}{18}\cdot k\cdot A^{2} = \frac{1}{2}\cdot k\cdot x^{2}[/tex]
[tex]\frac{1}{9}\cdot A^{2} = x^{2}[/tex]
[tex]x= \frac{1}{3}\cdot A[/tex]
The potential energy of the system is 1/9 of the total mechanical energy, when [tex]x= \frac{1}{3}\cdot A[/tex].
b) If we know that [tex]k = k[/tex], [tex]x = \frac{1}{2}\cdot A[/tex] and [tex]E = \frac{1}{2}\cdot k \cdot A^{2}[/tex], then the equation of energy conservation associated with the system is:
[tex]\frac{1}{2}\cdot k\cdot A^{2} = \frac{1}{4}\cdot k\cdot A^{2}+K[/tex]
[tex]K = \frac{1}{4}\cdot k\cdot A^{2}[/tex]
The fraction of the total mechanical energy that is kinetic if the displacement is 1/2 the amplitude is 1/2.
c) From the Energy Conservation equation associated with the system, we know that increasing the amplitude by a factor of 3 represents an increase in the elastic potential energy by a factor of 9. Then, the maximum kinetic energy is increased by a factor of 9.