Answer:
The velocity of the car when it hits the ground is approximately 55.574 meters per second.
Explanation:
According to this expression, the car goes straight into the cliff and goes down due to gravity, whose situation is described by the Principle of Energy Conservation and supposing that all non-conservative forces are negligible:
[tex]U_{g,1}+K_{1} = U_{g,2}+K_{2}[/tex] (1)
Where:
[tex]U_{g,1}[/tex], [tex]U_{g,2}[/tex] - Gravitational potential energies of the car at the top and the bottom, measured in joules.
[tex]K_{1}[/tex], [tex]K_{2}[/tex] - Translational kinetic energies of the car at the top and the bottom, measured in joules.
By definitions of gravitational potential and translational kinetic energies, we expand and simplify the equation above:
[tex]\frac{1}{2}\cdot m\cdot v_{2}^{2} = \frac{1}{2}\cdot m \cdot v_{1}^{2}+m\cdot g \cdot (z_{1}-z_{2})[/tex] (2)
[tex]v_{2}^{2} = v_{1}^{2}+2\cdot g\cdot (z_{1}-z_{2})[/tex]
[tex]v_{2} = \sqrt{v_{1}^{2}+2\cdot g\cdot (z_{1}-z_{2})}[/tex]
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]v_{1}[/tex], [tex]v_{2}[/tex] - Velocity of the car at the top and the bottom, measured in meters per second.
[tex]g[/tex] - Gravitaitional acceleration, measured in meters per square second.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Height of the car at the top and at the bottom, measured in meters.
If we know that [tex]v_{1} = 50\,\frac{m}{s}[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]z_{1} = 30\,m[/tex] and [tex]z_{2} = 0\,m[/tex], then the velocity of the car when it hits the ground is:
[tex]v_{2} = \sqrt{\left(50\,\frac{m}{s} \right)^{2}+2\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (30\,m-0\,m)}[/tex]
[tex]v_{2}\approx 55.574\,\frac{m}{s}[/tex]
The velocity of the car when it hits the ground is approximately 55.574 meters per second.
Was the Big Bang a loud explosion? Why?
Answer:
bc it was a universal explosion and It started the future
Explanation:
FACTS
Answer:
i wouldn't believe so.
Explanation:
because there was no room or air for the sound to move through. this is because of immense heat and the amount of hyperactive neutrons, electrons and protons clouding everywhere. This would mean that even if there was sound it would a. not travel far or b. go in a completely different direction than expected.
The coulombic force between two ions is reduced to ______ of its original strength when the distance between them is quadrupled.
Answer:
1/16Explanation:
According to the coulombs law, the force existing vetween the ions is expressed as;
F = kQq/r² .... 1
Q and q are the ions
r is the distance between the ions
If the distance between the ion is quadrupled, then;
F2 = kQq/(4r)²
F2 = kQq/16r² ... 2
Divide equation 2 by 1;
F2/F = kQq/16r² ÷ kQq/r²
F2/F = kQq/16r² × r²/kQq
F2/F = 1/16
F2 = 1/16 F
Therefore the coulombic force between two ions is reduced to 1/16 of its original strength when the distance between them is quadrupled.
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
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:
Question 25
The drawings below show four objects that are acted upon by different forces The direction of the forces are represented by the arrows, and the units of the forces are in newtons (N) Based on Newton's law of
inertia, which object is moving at a steady speed, assuming that all four objects are moving on a frictionless surface?
Answer:
The one with equal forces on both sides, D is your answer
Explanation:
A, 5 and 10 No
B 13 and 8 no
C 5 and 8 no
D 6 and 6 YES
Object 4 have steady speed. Object 4 have same force on both the sides of object. Same force is applied on both the sides.
What is steady speed?Uniform or constant velocity describes a body's motion when there is no acceleration. A body's velocity is its rate of movement in a specific direction.
When running steadily, your exhaustion should be caused by the length of the run, not by your speed. A steady-state run pace, according to the McMillan Running website, is halfway between your current 30k and half-marathon pace. This speed should allow you to run for 25 to 75 minutes.
Therefore, Object 4 have steady speed. Object 4 have same force on both the sides of object. Same force is applied on both the sides.
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Two blocks of masses 1.0 kg and 2.0 kg, respectively, are pushed by a constant applied force F across a horizontal frictionless table with constant acceleration such that the blocks remain in contact with each other, as shown above. The 1.0 kg block pushes the 2.0 kg block with a force of 2.0 N. The acceleration of the two blocks is
0
1.0 m/s2
1.5 m/s2
2.0 m/s2
3.0 m/s2
Answer:
1.0 m/s^2
Explanation: happy to help :)
Answer: [tex]1\ m/s^2[/tex]
Explanation:
Given
Masses of the block are [tex]m_1=1\ kg[/tex] and
[tex]m_2=2\ kg[/tex]
Force applied by [tex]1\ kg[/tex] block on [tex]2\ kg[/tex] block is [tex]2\ N[/tex]
From the free body diagram of [tex]2\ kg[/tex] block, the net force on
[tex]\therefore m_2a=2\\\\\Rightarrow 2\times a=2\\\\\Rightarrow a=\dfrac{2}{2}\\\\\Rightarrow a=1\ m/s^2[/tex]
Thus, the acceleration of two blocks is [tex]1\ m/s^2[/tex]
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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?
compute the velocity of light in calcium fluoride which has dielectric constant of 2.056 .
Answer:
idl low presure but de 2.518 has a 6 divide 8 equal di. ko alam?I need help understanding this question, so I know the arrow is traveling 80 meters per second, but it was launched from a starting point of 32 meters. I know for a fact an arrow does not have any thrust left at around 3 seconds of being in the air.
I just need someone to explain the questions and provide an answer to each.
Answer:
a) h(g) = 358,53 m
b) t = 8,16 s
c) t(t) = 16,71 s
Explanation:
Equations for vertical shooting are:
Vf = V₀ - g * t ; h = V₀*t - (1/2)*g*t² ; Vf² = V₀² - 2*g*h
And at maximum heigt Vf = 0 then
0 = V₀ - g * t
t = V₀/g V₀ = 80 m/s and g = 9,8 m/s²
t = 80 / 9,8 (s)
t = 8,16 s
Then 8,16 s is the time to get maximum height
If we plug t = 8,16 (s) in equation h = V₀*t - (1/2)*g*t²
we get: h (max) = (80)*8,16 - 0,5*9,8*(8,16)² (m)
h (max) = 652,8 - 326,27 m
h (max) = 326,53 m
Then relative to ground that height becomes
h(g) = 326,53 + 32
h(g) = 358,53 m
In order to get the time the arrow is in the air we proceed as follows:
a) for the arrow to be at the launched point will take the same time that from the launched point to the maximum height, and after that we have to find out the time the arrow takes from 32 m down to the ground level
Then
t(t) = 8,16 + 8,16 + tₓ (2)
Where tₓ is the time from 32 m height to ground
h = V₀*tₓ - (1/2)*g*tₓ² but since the arrow now is going down then we change the sign of the second term on the right side of the equation
32 = (80)*tₓ + 0,5 * 9,8 * tₓ² Note that when the arrow is at 32 m height the speed is again V₀ = 80 m/s
32 = 80*tₓ + 4,9*tₓ²
A second-degree equation for tₓ, solving it
4,9*tₓ² + 80*tₓ - 32 = 0
t₁,₂ = -80 ± √ 6400 + 627,2 / 9,8
t₁,₂ =( - 80 ± 83,8 ) / 9,8
there is not a negative time therefore we dismiss such solution and
t₁ = 3,8 / 9,8
t₁ = 0,39 s
And
t(t) = 8,16 + 8,16 + 0,39 s
t(t) = 16,71 s
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
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
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Which of the following is not an example of work being done on an object?
Pushing on a rock that will not move
Paddeling a canoe down a river
Lifting a bag of groceries
Throwing a ball across a field
Answer:
Lifting a bag of groceries
Answer:
paddeling a canoe down a river :D or throwing a ball across a field
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]
A wave travels at 175 m/s along the x-axis.If the period of the periodic vibrations of the wave is 3.00 milliseconds,then what is the wavelength of the wave?
A) 25.5 cm
B) 35.6 cm
C) 42.9 cm
D) 49.5 cm
E) 52.5 cm
Answer:
E) 52.5 cmExplanation:
Step one:
given data
period T= 3 milliseconds= 0.003
velocity v= 175m/s
wave lenght λ=?
Step two:
we know that f=1/T
the expression relating period and wave lenght is
v=λ/T
λ=v*T
λ=175*0.002
λ=0.525m
to cm= 0.525*100
=52.5cm
The wavelength of the wave is E) 52.5 cm
What is the flow sensitivity of a biosensor?
Answer:
Sensitivity of biosensor
The biosensor showed good linear correlation in the wide detection range of 0.001–2000 ng/mL with good sensitivity. In addition, it retained its biosensing property for seven days with high reproducibility
Explanation:
There is a bell at the top of a tower that is 45 m high. The bell weighs 190 N. The bell has ____________ energy.
Answer:
The bell has 8,550 Joule energy.
Explanation:
Gravitational Potential Energy
Gravitational potential energy is the energy stored in an object because of its height in a gravitational field.
It can be calculated with the equation:
U=m.g.h
Where:
m = mass of the object
h = height
g = acceleration of gravity, or [tex]9.8 m/s^2[/tex]
Since the weight of an object of mass m can be calculated as:
W = m.g
The gravitational potential energy is:
U = W.h
The bell of weight W=190 N at the top of a tower is h=45 m high. Thus its energy is:
U = 190 N . 45 m
U = 8,550 Joule
The bell has 8,550 Joule energy.
If a ball has kinetic energy of 1000 joules and a speed of 5m/s, what is its mass?
Answer:
m = 80[kg]
Explanation:
The kinetic energy can be calculated by means of the following equation.
[tex]E_{k}=\frac{1}{2}*m*v^{2}[/tex]
where:
m = mass [kg]
v = velocity = 5 [m/s]
Ek = kinetic energy = 1000 [J]
Now replacing:
[tex]1000 = \frac{1}{2} *m*5^{2}\\2000 = 25*m\\m=80[kg][/tex]
The mass of a ball will be "80 kg".
Kinetic energy:According to the question,
Kinetic energy, [tex]E_k[/tex] = 1000 Joules
Velocity, V = 5 m/s
As we know the formula,
→ Kinetic energy = [tex]\frac{1}{2}[/tex] × mass × (velocity)²
→ [tex]E_k = \frac{1}{2}[/tex] × m × v²
By substituting the values,
[tex]1000= \frac{1}{2}\times m\times (5)^2[/tex]
[tex]1000\times 2=25\times m[/tex]
[tex]2000=25\times m[/tex]
[tex]m = \frac{2000}{25}[/tex]
[tex]= 80[/tex] kg
Thus the above answer is correct.
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A (10.0+A) g ice cube at -15.0oC is placed in (125 B) g of water at 48.0oC. Find the final temperature of the system when equilibrium is reached.
Specific heat of ice: 2.090 J/g K
Specific heat of water: 4.186 J/gK
Latent heat of fusion for water: 333 J/g
Answer: Final temperature is 34.15°C.
Explanation: When two objects have different temperature, they will exchange heat energy until there is no more net energy transfer between them. At that state, the objects are in thermal equilibrium.
So, when in equilibrium, the total heat flow must be zero, i.e.:
[tex]Q_{1}+Q_{2}=0[/tex]
In our case, there will be a change in state of ice into water, so total heat flow will be:
[tex]m_{1}c_{1}(T_{f}-T_{i})+m_{2}c_{2}(T_{f}-T_{i})+mL=0[/tex]
where
m₁ is mass of ice
m₂ is mass of water
c₁ is specific heat of ice
c₂ is specific heat of water
[tex]T_{f}[/tex] is final temperature
[tex]T_{i}[/tex] is initial temperature
L is latent heat fusion
Temperature is in Kelvin so the transformation from Celsius to Kelvin:
For ice:
T = -15 + 273 = 258K
For water:
T = 48 + 273 = 321K
Solving:
[tex]21(2.09)(T_{f}-258)+158(4.186)(T_{f}-321)+21(333)=0[/tex]
[tex]43.89T_{f}-11323.62+661.4T_{f}-212305.55+6993=0[/tex]
[tex]705.3T_{f}=216636.17[/tex]
[tex]T_{f}=[/tex] 307.15K
In Celsius:
[tex]T_{f}=[/tex] 34.15°C
Final temperature of the system when in equilibrium is 34.15°C
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]
The sharper the sound is the smaller the frequency of a vibrating body true or false
What is the rms current flowing through a light bulb that uses an average power of 60.0 W when it is plugged into a wall receptacle supplying an rms voltage of 120.0 V?
Answer:
I = 0.5 A
Explanation:
Given that,
Average power of a light bulb, P = 60 W
The rms voltage supplied is 120 V
We need to find the value of rms current flowing through the light bulb. The relation between the power, voltage and current is given by :
P = VI
[tex]I=\dfrac{P}{V}\\\\I=\dfrac{60}{120}\\\\I=0.5\ A[/tex]
So, the rms value of current is 0.5 A.
45.0g of a sample placed in a graduated cylinder causes the water level to rise from
25.0mL to 40.0mL. Density of the sample is?
Answer:
3g/mL
Explanation:
The density of a substance can be calculated using the formula;
Density = mass/volume
Where;
Density = g/mL
mass = grams (g)
volume = (mL)
According to this question, 45.0g of a sample placed in a graduated cylinder causes the water level to rise from
25.0mL to 40.0mL. This means that the volume of the sample is 40mL - 25mL = 15mL
Using D = m/v
D = 45/15
D = 3g/mL
Hence, the density of the sample is 3g/mL
Please help true or false
Answer:
the answer is true.......
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.what is the efficiency of a machine that uses 102kj of enegery to do 98 kJ of work?
Answer: I got an increase of 306 kJ in internal energy.
Explanation: I used the 1st Law and the sign convention to get the answer in the screenshot.
(sorry if i'm wrong)
:(
The efficiency of the machine is 96.07%.
What is efficiency?Efficiency can be defined as the ratio of work output to work input expressed in percentage.
To calculate the efficiency of the machine, we use the formula below.
Formula:
E(%) = (Wo/Wi)100.......... Equation 1Where:
E(%) = Efficiency of the machineWi = Work input of the machineWo = Work outputFrom the question,
Given:
Wi = 102 kJWo = 98 kJSubstitute these values into equation 1
E(%) = (98/102)100E(%) = 96.07%Hence, the efficiency of the machine is 96.07%.
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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.
____________ 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:
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]
A rotating heavy wheel is used to store energy as kinetic energy. If it is designed to store 1.00 x 106 J of kinetic energy when rotating at 64 revolutions per second, find the moment of inertia (rotational inertia) of the wheel. (Hint: Start with the expression for rotational kinetic energy.)
We know, [tex]1\ rpm = \dfrac{2\pi}{60} \ rad/s[/tex] .
[tex]64\ rpm\ is = \dfrac{2\pi}{60}\times 64\ rad/s\\\\= \dfrac{32\pi}{15}\ rad/s[/tex]
We know, kinetic energy is given by :
[tex]K.E = \dfrac{I\omega^2}{2}\\\\I = \dfrac{2(K.E)}{\omega^2}\\\\I = \dfrac{2\times 10^6}{\dfrac{32}{15}\times \pi}\\\\I = 298415.52 \ kg \ m^2[/tex]
Hence, this is the required solution.
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]