Answer:
The specific heat of the substance is 393.939 joules per kilogram-degree Celsius.
Explanation:
We notice that the student is mixing a substance with a high temperature and another substance with a low temperature, where the first release heat to the latter one until thermal equilibrium is reached. By the First Law of Thermodynamics and assuming that the entire system has no energy interactions with the surroundings, we get the following model:
[tex]\Delta U_{x}+\Delta U_{w} = 0[/tex] (1)
Where [tex]\Delta U_{x}[/tex] and [tex]\Delta U_{w}[/tex] are the changes in internal energy for the unknown substance and water, measured in joules.
By definition of internal energy, we expand the equation above now:
[tex]m_{x}\cdot c_{x}\cdot (T_{o,x}-T_{f,x})+m_{w}\cdot c_{w}\cdot (T_{o,w}-T_{f,w}) = 0[/tex] (2)
Where:
[tex]m_{x}[/tex], [tex]m_{w}[/tex] - Masses of the unknown substance and water, measured in kilograms.
[tex]c_{x}[/tex], [tex]c_{w}[/tex] - Specific heats of the unknown substance and water, measured in joules per kilogram-degree Celsius.
[tex]T_{o,x}[/tex], [tex]T_{f,x}[/tex] - Initial and final temperatures of the unknown substance, measured in degrees Celsius.
[tex]T_{o,w}[/tex], [tex]T_{f,w}[/tex] - Initial and final temperatures of water, measured in degrees Celsius.
Then, we clear the specific heat of the unknown substance:
[tex]c_{x} = \frac{m_{w}\cdot c_{w}\cdot (T_{f,w}-T_{o,w})}{m_{x}\cdot (T_{o,x}-T_{f,x})}[/tex]
If we know that [tex]m_{w} = m_{x} = 0.075\,kg[/tex], [tex]c_{w} = 4186\,\frac{J}{kg\cdot^{\circ}C}[/tex], [tex]T_{f,w} = T_{f,x} = 31.15\,^{\circ}C[/tex], [tex]T_{o,x} = 96.5\,^{\circ}C[/tex] and [tex]T_{o,w} = 25\,^{\circ}C[/tex], then the heat capacity of the unknown substance is:
[tex]c_{x} = \frac{(0.075\,kg)\cdot \left(4186\,\frac{J}{kg\cdot ^{\circ}C} \right)\cdot (31.15\,^{\circ}C-25\,^{\circ}C)}{(0.075\,kg)\cdot (96.5\,^{\circ}C-31.15^{\circ}C)}[/tex]
[tex]c_{x} = 393.939\,\frac{J}{kg\cdot ^{\circ}C}[/tex]
The specific heat of the substance is 393.939 joules per kilogram-degree Celsius.
The wavelengths corresponding to the harmonics of an organ pipe that is open at one end and closed at the other can be found by saying that the length of the pipe must be equal to:___________.
A. an integer number of wavelengths.
B. an odd number of half-wavelengths.
C. an integer number of half-wavelengths.
D. an odd number of quarter-wavelengths.
Answer:
The answer is "Option D"
Explanation:
Its ranges referring to the harmonic currents of its organ pipe which are open at one end and shut at another side could be noticed saying whether a strange amount of quarter-wavelengths should equal the length of its pipe. It's also the fourth wavelengths principle to have enough space and consume a minimum of 25% of our design frequency, as we're going to be taking 40 Hz.
plz help asap.
1. Describe the methods by which an electric potential develops in primary cells and dry cells.
2. Describe the methods by which an electric potential develops in generators and thermocouples.
3. Identify the scenarios below as to whether they would increase or decrease the resistance of an electric current through a body.
a. Increase the length of the conductor
b. Utilize a conductor with a larger cross-section
c. Cool the conductor to lower its temperature
4. If 0.8 Wh of electrical energy is lost as heat, how much heat energy (in Btu) is produced?
5. How many kilowatt-hours of energy would be used by a 40 W bulb that runs for 10 hours every day during the course of one year?
Not my answer but nevertheless
Answer:
Electric potential develops in primary/dry cells through a chemical reaction between the cell plates of the cell. free electrons move from the zinc plate to the copper plate through a conducting material.
Electric potential develops in Generators via magnetic induction i.e. the movement of a conducting rod through the magnetic field between the poles of the horseshoe magnets produces Electric potential in Generators.
Electric potential develops in thermocouples via heat transfer ; A heat source is applied to the connecting end of the thermocouple strips and this will cause the production electric charges ( potential ) at the free ends
3) Identifying effect of each scenerio
a) The resistance of an electric current will increase when the length of the conductor increases
b) The resistance of an electric current through a body will decrease when the conductor has a larger cross-section
c) The resistance of an electric current through a body will decrease when the temperature of the conductor is cooled
4) The amount of heat lost as heat in Btu = 2.73 Btu
amount of heat lost = 0.8 Wh
convert to Btu = 0.8 Wh / 0.293 = 2.73 Btu ( note : 1 Btu = 0.293 Wh )
5) The amount of of energy used by a 40 W bulb for 365 days = 146 kWh
Power of bulb = 40 W
Run time = 10 hours * 365 days
∴ amount of energy used = 3650 * 40 = 146 * 10^3 Wh = 146 kWh
find the vector parallel to the resultant of the vector A=i +4j-2k and B=3i-5j+k
Answer:
2008
Explanation:
2000+3+5======2008
Answer:
[tex]8\hat i-2\hat j-2\hat k[/tex]
Explanation:
Vectors in 3D
Given a vector
[tex]\vec P = P_x\hat i+P_y\hat j+P_z\hat k[/tex]
A vector [tex]\vec Q[/tex] parallel to [tex]\vec P[/tex] is:
[tex]\vec Q = k.\vec P[/tex]
Where k is any constant different from zero.
We are given the vectors:
[tex]\vec A = \hat i+4\hat j-2\hat k[/tex]
[tex]\vec B = 3\hat i-5\hat j+\hat k[/tex]
It's not specified what the 'resultant' is about, we'll assume it's the result of the sum of both vectors, thus:
[tex]\vec A +\vec B = \hat i+4\hat j-2\hat k + 3\hat i-5\hat j+\hat k[/tex]
Adding each component separately:
[tex]\vec A +\vec B = 4\hat i-\hat j-\hat k[/tex]
To find a vector parallel to the sum, we select k=2:
[tex]2(\vec A +\vec B )= 8\hat i-2\hat j-2\hat k[/tex]
Thus one vector parallel to the resultant of both vectors is:
[tex]\mathbf{8\hat i-2\hat j-2\hat k}[/tex]
Two cylinders each with a 60 cm diameter, thatare closed at one end, open at the other, are joined to form asingle cylinder, then the air inside is removed.
How much force does the atmosphere exert onthe flat end of each cylinder?
Suppose one cylinder is bolted to a sturdy ceiling. How many 90 kg football players would need to hang from the lower cylinder to pull the two cylinders apart
Answer:
a
The force is [tex]F = 2864561.4 \ N[/tex]
b
The number is [tex]N = 3248 \ players[/tex]
Explanation:
From the question we are told that
The of each cylinder is [tex]d = 60 \ cm = 6 \ m[/tex]
The mass of the players is [tex]m = 90 \ kg[/tex]
Generally the cross-sectional area of the cylinder is mathematically represented as
[tex]A = \pi * \frac{d^2}{4}[/tex]
=> [tex]A = 28.3 \ m^2[/tex]
Generally force exerted on the flat end of each cylinder is mathematically represented as
[tex]F = A * P[/tex]
Here P is the atmospheric pressure with value [tex]P = 101300 \ Pa[/tex]
So
[tex]F = 28.3 * 101300[/tex]
=> [tex]F = 2864561.4 \ N[/tex]
Generally the weight of a single football player is
[tex]W = m * g[/tex]
=> [tex]W = 90 * 9.8[/tex]
=> [tex]W = 882\ N[/tex]
Generally the number of player required to pull the two cylinders apart is mathematically represented as
[tex]N = \frac{ F }{W}[/tex]
=> [tex]N = \frac{ 2864561.4 }{882}[/tex]
=> [tex]N = 3248 \ players[/tex]
The voltage provided by the battery of a circuit was 12 V, if the total
resistance in the circuit was 6 ohms, calculate the total current present.
options:
72 A
2A
0.5 A
7.2 A
Answer:
2 Amps
which agrees with the second option in the list of answers
Explanation:
Use Ohm's law:
V = R * I
which with the information given to us becomes:
12 = 6 * I
then solving for I we get:
I = 12 V / 6 Ω = 2 Amps
Sb +
Cl2 →
SbCl3
Balance chemical equation
Answer:
Cl2 + Sb → SbCl3
Cl2 + Sb → SbCl5
Cl2 + Sb → SbCl
Cl2 + Sb → SbCl2
Cl2 + Sb → SbCl3 + SbCl5
Explanation: Hope it will help
To balance the chemical equation Sb + Cl₂ → SbCl₃ on further simplification The final balanced chemical equation is Sb + 3Cl₂ → SbCl₃.
Let's start by balancing the antimony (Sb) atoms:
On the left side, we have 1 Sb atom, and on the right side, we also have 1 Sb atom. The antimony is already balanced.
Next, let's balance the chlorine (Cl) atoms:
On the left side, we have 2 Cl atoms, and on the right side, we have 3 Cl atoms. To balance the chlorine, we need to multiply the Cl₂ on the left side by 3:
Sb + 3Cl₂ → SbCl₃
Now, the chlorine atoms are balanced.
The final balanced chemical equation is:
Sb + 3Cl₂ → SbCl₃
To know more about balanced chemicals equation:
https://brainly.com/question/34199830
#SPJ6
The sharper the sound is the smaller the frequency of a vibrating body true or false
You throw a baseball (mass 0.145 kg) vertically upward. It leaves your hand moving at 12.0 m/s. Air resistance can be neglected.
A. At what height above your hand does the ball have half as much upward velocity?
B. At what height above your hand does the ball have half as much kinetic energy as when it left your hand?
Answer:
Explanation:
A ) initial velocity u = 12 m /s
final velocity v = 6 m /s
height = h
acceleration = - g = - 9.8 m /s²
v² = u² - 2gh
6² = 12² - 2 x 9.8 x h
h = 5.51 m
B )
Let the final velocity when energy becomes half be V at height H
kinetic energy at height h = 1/2 m V²
Given ,
.5 x 1 / 2 m x 12² = 1/2 m x V²
V² = 12² / 2
V = 8.486 m /s
V² = u² - 2 gH
8.486² = 12² - 2 x 9.8 x H
H = 3.67 m .
One of the major differences between our common Physics models of energy change and realistic models of them is:
a
In the Physics models, the acceleration due to gravity is rounded to a non-exact but easier to use number
b
In the Physics models, the velocities are only calculated at set intervals of time, instead of continuously
c
In the Physics models, the objects are assumed to have simplified shapes in order to make motion by acceleration easier to calculate
d
In the Physics models, we do not take into account the energy change by the friction of moving components
Answer:
d
In the Physics models, we do not take into account the energy change by the friction of moving components
Answer:
In the Physics models, we do not take into account the energy change by the friction of moving components
The glowing dot represents the transmission of a nerve impulse along the nerves that make up the neural pathway. A nerve impulse is an electrical signal that travels from one nerve cell to another.
Which part of the brain processes this signal?
Answer:
The answer is "Cerebral Cortex"
Explanation:
The neurotransmitter diffuses across the short distance of the synapse and ties to a receptor protein of the objective neuron. At the point when the sub-atomic sign ties to the receptor, the cell film of the objective neuron changes its electrical state and another evaluated expected starts. On the off chance that that evaluated potential is sufficiently able to arrive at limit, the subsequent neuron produces an activity potential at its axon hillock. The objective of this neuron is another neuron in the thalamus of the mind, the piece of the CNS that goes about as a transfer for tactile data.
At another neurotransmitter, synapse is delivered and ties to its receptor. The thalamus at that point sends the sensory information to the cerebral cortex, the furthest layer of dark issue in the brain, where cognizant view of that water temperature starts.
A region of the cortex is particular for imparting signs down to the spinal cord for development. The upper engine neuron is in this area, called the precentral gyrus of the frontal cortex, which has an axon that broadens right down the spinal cord. At the degree of the spinal cord at which this axon makes a neurotransmitter, a reviewed potential happens in the cell membrane of a lower engine neuron.
What is causing the boat to move toward the shore?
A
The moving water applies a force on the boat, which results in the boat pushing
back on the water, propelling the boat forward.
B
The moving wind applies a force on the boat, which results in the boat pushing
back on the wind, propelling the boat forward.
с
The boy applies a force on the oars, which results in the water pushing back on
the oars, propelling the boat forward.
D
The boy applies a force on the oars, which results in gravity pushing back on the
oars, propelling the boat forward.
Answer:c
Explanation:because when u push the oar back u go forward
Answer:
It's C. Because this is a Newton's 2nd Law about force and acceleration and he's putting force on the oars which is making the boat goe forward due to the water and the movements.
Explanation:
If a body having mass 40kg started moving initially with rest and it takes a velocity of 20m/sec in time 4 seconds. Find the value of force
[tex]{\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}} \\ \\[/tex]
[tex]\:\:\:\:\bullet\:\:\:\sf{Mass \ of \ the \ body \ (m) = 40 \ kg}[/tex]
[tex]\:\:\:\:\bullet\:\:\:\sf{Final \ velocity \ of \ the \ body \ (v) = 20 \ m/s}[/tex]
[tex]\:\:\:\:\bullet\:\:\:\sf{Initial \ velocity \ of \ the \ body \ (u) = 0}[/tex]
[tex]\\[/tex]
[tex]{\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}} \\ \\[/tex]
[tex]\:\:\:\:\bullet\:\:\:\sf{Force \ exerted \ by \ the \ body \ ( F)}[/tex]
[tex]\\[/tex]
[tex]{\mathfrak{\underline{\purple{\:\:\: Solution:-\:\:\:}}}} \\ \\[/tex]
☯ Using 1st equation of motion
[tex]\\[/tex]
[tex]\dashrightarrow\:\: \sf{v = u + at}[/tex]
[tex]\\[/tex]
[tex]\dashrightarrow\:\: \sf{20 = 0 + a(4)}[/tex]
[tex]\\[/tex]
[tex]\dashrightarrow\:\: \sf{20 = 4a}[/tex]
[tex]\\[/tex]
[tex]\dashrightarrow\:\: \sf{\dfrac{\cancel{20}}{\cancel{4}} = a}[/tex]
[tex]\\[/tex]
[tex]\dashrightarrow\:\: \sf{a = 5}[/tex]
[tex]\\[/tex]
☯ Now, Finding the force exerted
[tex]\\[/tex]
[tex]\dashrightarrow\:\: \sf{F = ma}[/tex]
[tex]\\[/tex]
[tex]\dashrightarrow\:\: \sf{F = 40 \times 5}[/tex]
[tex]\\[/tex]
[tex]\dashrightarrow\:\: \sf{F = 200 \ N}[/tex]
[tex]\\[/tex]
☯ Hence, [tex]\\[/tex]
[tex]\:\:\:\:\star\:\:\:\sf{The \ force \ exerted \ by \ the \ body \ is \ 200N}[/tex]
Which of the following statements are true of cancer types? Check all that apply. --
- Cancer is named according to the color the cells turn.
- Skin cancer is considered a very common type of cancer.
- Cancer is often named according to what body type it affects.
- Skin cancer is the least common type of cancer.
the answer is cancer is often named according to what body type it affects
Answer:
B,C
Explanation:
skin cancer is considered a very common type of cancer. Cancer is often named accordingly to a body type it affects.
A fluid of density rho = 900 kg/m3 flows along a pipe of constant diameter from point A to point B. Gauge pressure at point A is equal to zero, and absolute pressure at point B is 30% lower than pressure at point A. What is the height difference, Δh, between points A and B?
a. Δh = 8.09 m with point A above point B.
b. Δh = 344 m with point B above point A.
c. Δh = 303 m with point B above point A.
d. Δh = 3.44 m with point A above point B.
The height difference between points A and B is : ( B ) Δh = 3.44 m with point B above point A.
Given data :
fluid density = 900 kg/m³
Diameter of pipe = constant
Gauge pressure at Point A = 0
Gauge pressure at point B = 30% lower
Determine the height difference between points A and Bfirst step : determine absolute pressure
Pa (absolute pressure )= gauge pressure + atmospheric pressure
= 0 + patm
Therefore : Pa = Patm
Also;
Pressure at point B ( Pb ) = Pa - 30%Pa
= 0.7 Patm
Hence ; Pa - Pb = 0.3 Patm ----- ( 1 )
Final step : Determine the height difference
we will apply the formula below from equation ( 1 )
p *g * Δh = 0.3 * 1.013 * 10⁵ ( note : Patm = 1.013 * 10⁵ )
900 * 9.81 * Δh = 0.3 * 1.013 * 10⁵
therefore :
Δh = ( 0.3 * 1.013 * 10⁵ ) / ( 900 * 9.81 )
= 3.44 m
Hence we can conclude that The height difference between points A and B is Δh = 3.44 m with point B above point A.
Learn more about height difference in fluids : https://brainly.com/question/17200230
7. DRAW A PICTURE TO SHOW WORK.
Brandon buys a new Seadoo. He goes 12
km north from the beach. He jumps
wakes for 6 km to the east. Then chases
a boat 12 km south. He then turns and
goes 3 km to the West. What distance
did he cover? What was his
displacement?
A solid CUBE has a side of 4cm and is 192 grams in mass. What is the density?
Answer:
3g/cm³
Explanation:
Given parameters:
Length of the side = 4cm;
Volume of the cube = L³ = 4³ = 64cm³
Mass of the cube = 192g
Unknown:
Density = ?
Solution:
The density of a body is its mass per unit volume;
Density = [tex]\frac{mass}{volume}[/tex]
Insert parameters and solve;
Density = [tex]\frac{192}{64}[/tex] = 3g/cm³
What is the approximate distance from the sun to the astroid belt?
Answer:
The asteroid belt lies between 2.2 and 3.2 astronomical units (AU) from our sun. ( i looked this up because nobody of the top of their head knows this)
Explanation:
which of the following is true of phototsythesis but not of cellular respiration.
A- Photosynthesis releases oxygen gas as a product
B- Photosynthesis occurs in all organisms
C- Photo synthesis is a process in which glucose i broken down
D- Photosynthesis requires glucose as a reactant
Answer:
B. Photosynthesis occurs in all organisms
Hope this helps!! :)
Pretty simple physics :) will give brainliest
pls dont just use me for points
Answer:
meter per second(m/s)
Explanation:
When weather predictions are incorrect what is the most likely cause
A: measurements of the initial conditions may have been very in accurate
B: small differences in models can lead to large differences in complex systems
C: The person predicting the weather may have had a bias
D: The elevation of different landforms I have been significantly in accurate
Answer:small differences in models can lead to large differences in complex systems
Explanation: this is the most accurate phrase
Three liquids that will not mix are poured into a cylindrical container. The volumes and densities of the liquids are 0.50 L, 2.6 g/cm³; 0.25 L, 1.0 g/cm³; and 0.40 L, 0.80 g/cm³. What is the force on the bottom of the container due to these liquids? One liter = 1 L = 1000 cm³. (Ignore the contribution due to the atmosphere.)
Answer:
The force is [tex]F = 18.33 \ N[/tex]
Explanation:
From the question we are told that
The number of liquids is n = 3
The volume of the first liquid is [tex]V_1 = 0.50 L = 0.0005 \ m^3[/tex]
The density of the first liquid is [tex]\rho_1 = 2.6 \ g/cm^3[/tex]
The volume of the second liquid is [tex]V_2 = 0.25 L = 250\ cm^3[/tex]
The density of the second liquid is [tex]\rho_2 = 1.0 \ g/cm^3[/tex]
The volume of the third liquid is [tex]V_3 = 0.40 L = 400\ cm^3[/tex]
The density of the third liquid is [tex]\rho_3 = 0.80 \ g/cm^3[/tex]
Generally the force at the bottom of the container is mathematically represented as
[tex]F = m_t * g[/tex]
Here [tex]g = 980.665 \ cm/s^2[/tex]
Here [tex]m_t[/tex] is the total mass of all the liquid which is mathematically represented as
[tex]m_t = ( V_1 * \rho_1 )+ ( V_2 * \rho_2)+ ( V_3 * \rho_3)[/tex]
=> [tex]m_t = ( 500 * 2.6)+ ( 250 * 1.0 )+ ( 400 * 0.80 )[/tex]
=> [tex]m_t = 1870 \ g[/tex]
So
[tex]F = 1870 * 980.66[/tex]
=> [tex]F = 1833843.55 \ g \cdot cm /s^2[/tex]
=> [tex]F = 1833843.55 \ g \cdot cm /s^2 = \frac{1833843.55}{1000 * 100} kg \cdot m /s^2[/tex]
=> [tex]F = 18.33 \ N[/tex]
A cannonball is fired at a 45.0° angle and an initial velocity of 670 m/s. Assume no air resistance. How high did the cannonball travel?
9935 m
11454 m
754 m
13200 m
Is a seashores diverse or uniform?
Answer:
uniformes
Explanation:
Why are u asking this
What is the initial vertical velocity of the ball?
A.
0 m/s
B.
9.81 m/s
C.
20.0 m/s
D.
60.0 m/s
An electron is released from rest in a unifor electric field and accelerates to the north at a rate of 145 m/s^2. What is the magnitude and direction of the electric field?
Answer:
E = 8.26*10⁻¹⁰ N/C, due south.
Explanation:
Assuming no other forces acting on the electron than the electrostatic force due to the electric field, we can apply Newton's 2nd law as follows:[tex]F = -eE =ma (1)[/tex]
Solving for E, we can find its magnitude as follows:[tex]E =\frac{m*a}{e} = \frac{9.1e-31 kg*145m/s2}{1.6e-19C} = 8.26e-10 N/C (1)[/tex]
The direction of the electric field is by definition the one that would take a positive test charge, so if the electron is accelerated to the north, the electric field would exactly oppose to this direction, so it is directed due south.____________ is an individual sport that helps develop your hand-eye coordination.
Table Tennis
Ice Skating
Swimming
Answer:
Answer option A) Table Tennis helps develop your hand-eye coordination.
Answer:
table tennis
Explanation:
Which objects cannot be observed in detail without a microscope?
Answer:
partecls
Explanation:
because they are to small to see with plain eyes
Describe how radiant energy, light energy, and solar energy are related. ( Please ❤️ )
Answer:
L’énergie solaire récolte l’énergie radiante portée par la lumière de notre soleil en la convertissant en électricité.Biomasse des plantes. Les plantes sont capables d’exploiter et d’utiliser l’énergie lumineuse dans un processus appelé photosynthèse.
Answer:
Radiant energy, light energy, and solar energy are related because The Sun produces a lot of radiant energy that is transmitted to Earth as light. Plants convert the electromagnetic energy in sunlight into chemical energy for their food, through a process called photosynthesis. Waves of radiant electromagnetic energy can be visible or invisible.
Explanation:
Find the binding energy per nucleon for the plutonium isotope 239Pu. The mass of the neutral atom is 239.05216 u.
Answer:
The answer is "[tex]\bold{7.56 \ Me\ V}[/tex]".
Explanation:
calculating the binding energy on per nucleon:
calculating number of proton and neutrons:
proton [tex]P_u=94[/tex]
neutron[tex]= 239-94=145[/tex]
calculating mass:
proton mass [tex]\ m_P=1.007825 \ amu\\\\[/tex]
neutron mass [tex]\ m_n=1.008665 \ amu\\\\[/tex]
neutral atom mass [tex]m = 239.05216 \ amu\\\\[/tex]
mass of prtons[tex]= 94 \times 1.007825 = 94.73555 \ amu\\\\[/tex]
mass of neutrons[tex]= 145 \times 1.008665= 146.256425 \ amu\\\\[/tex]
Total nucleons mass formula:
[tex]\to m_n = (P+n)[/tex]
[tex]= 94.73555+ 146.256425\\\\= 240.991975 \ amu[/tex]
calculating the mass of defect:
[tex]\to \Delta m= m_n-m\\\\[/tex]
[tex]= 240.991975 - 239.05216\\\\= 1.939815 \ amu\\\\[/tex]
calculating the total of the binding energy:
[tex]\to BE=\Delta m\times 931.5 \ mev[/tex]
[tex]= 1.939815 \times 931.5\\\\=1806.938 \ Me \ V\\\\[/tex]
BE in per nucleon [tex]=\frac{BE}{239}= 7.56 \ Me\ V[/tex]
When the displacement of a mass on a spring in simple harmonic motion is A/2 from the equilibrium position, what fraction of the total mechanical energy is kinetic energy?
Answer:
The ratio is KE : TM = 0.75
Explanation:
from the question we are told that
The displacement of a mass on a spring in simple harmonic motion is A/2 from the equilibrium position
Generally the total mechanical energy of the mass is mathematically represented as
[tex]TM = \frac{1}{2} * k * A^2[/tex]
Here k is the spring constant , A is the total displacement of the the mass from maximum compression to maximum extension of the spring
Generally this total mechanical energy is mathematically represented as
[tex]TM = KE + PE[/tex]
=> [tex]KE = TM - PE[/tex]
Here the potential energy of the mass is mathematically represented as
[tex]PE = \frac{1}{ 2} * k * [ x ]^2[/tex]
Here x is the displacement of the mass from maximum compression or extension of the spring to equilibrium position and the value is
[tex]x = \frac{A}{2}[/tex]
So
[tex]PE = \frac{1}{ 2} * k * [ \frac{A}{2} ]^2[/tex]
So
[tex]KE = \frac{1}{2} * k * A^2 - \frac{1}{2} * k * [\frac{A}{2} ]^2[/tex]
=> [tex]KE = \frac{1}{2} * k * A^2 - \frac{1}{8} * k * A ^2[/tex]
=> [tex]KE = 0.375 * k * A^2[/tex]
So the ratio of [tex]KE : TM[/tex] is mathematically represented as
[tex]\frac{KE}{TM} = \frac{0.375 k A^2 }{0.5 k A^2}[/tex]
=> [tex]\frac{KE}{TM} = 0.75[/tex]