Answer:
0.174 plasma
[tex]$5.85 \times 10^{-4}$[/tex] flame
Explanation:
Given :
Energy :
[tex]$\Delta E=3.371 \times 10^{-19} $[/tex] J per atom
[tex]$g^*=2$[/tex] (degenraci of excited state)
g = 1 (degenraci of excited state)
Boltzmann Distribution
[tex]$\frac{N^*}{N}=\frac{g^*}{g}e^{-\frac{\Delta E}{kT}}$[/tex]
where,
[tex]$N^*$[/tex] = atoms in excited state
N = atoms in lower energy level
k = [tex]$1.38 \times 10^{-23}$[/tex] J/K
Therefore,
Relative population in plasma
T = 10,000 K
[tex]$\frac{N^*}{N}=\frac{g^*}{g}e^{-\frac{\Delta E}{kT}}$[/tex]
[tex]$\frac{N^*}{N}=\frac{2}{1}e^{-\frac{-3.37\times 10^{-19}}{1.38 \times 10^{-23} \times 10000}}$[/tex]
[tex]$\frac{N^*}{N}=2 \times e^{-2.44275}$[/tex]
[tex]$\frac{N^*}{N}=2 \times 0.8692$[/tex]
[tex]$\frac{N^*}{N}=0.1738$[/tex]
Relative population in flame
T = 3000
[tex]$\frac{N^*}{N}=\frac{g^*}{g}e^{-\frac{\Delta E}{kT}}$[/tex]
[tex]$\frac{N^*}{N}=\frac{2}{1}e^{-\frac{-3.371\times 10^{-19}}{1.38 \times 10^{-23} \times 3000}}$[/tex]
[tex]$\frac{N^*}{N}=2 \times e^{-8.1425}$[/tex]
[tex]$\frac{N^*}{N}=2 \times 2.9090 \times 10^{-4}$[/tex]
[tex]$\frac{N^*}{N}=5.85 \times 10^{-4}$[/tex]
On the Earth's surface, how much does a 100kg mass weigh? 1
Answer:
100kg
Explanation:
100kg=100kg
:P
Answer: 50 because thats the mass weight
Explanation: Its the obviouse answer.
state the Newton 2nd law of motion and also prove that F= ma
Explanation:
F = ma is the formula of Newton's Second Law of Motion. Newton's Second Law of Motion is defined as Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.
...
Water is to be heated from 10°C to 80°C as it flows through a 2-cm-internal-diameter, 13-m-long tube. The tube is equipped with an electric resistance heater, which provides uniform heating throughout the surface of the tube. The outer surface of the heater is well insulated, so that in steady operation all the heat generated in the heater is transferred to the water in the tube. If the system is to provide hot water at a rate of 5 L/min, determine the power rating of the resistance heater. Also, estimate the inner surface temperature of the pipe at the exit.
Answer:
- the power rating of the resistance heater is 24139.5 W
- the inner surface temperature of the pipe at the exit is 96.34°C
Explanation:
Given the data in the question;
Flow rate of water in the tube V" = 5L/min = 8.333 × 10⁻⁵ m³/s
The water is to be heated from 10°C to 80°C;
so Average or mean temperature [tex]T_{avg[/tex] will be;
[tex]T_{avg[/tex] = (T₁ + T₂) / 2 = (10 + 80) / 2 = 90/2 = 45°C
Now, from the Table " Properties of Water " at average temperature;
at [tex]T_{avg[/tex] = 45°C
density p = 990.1 kg/m³
specific heat [tex]C_p[/tex] = 4180 J/kg-k
thermal conductivity k = 0.637 W/m-°C
Now, we determine the mass flow;
m" = pV"
we substitute
m" = 990.1 × 8.333 × 10⁻⁵
m" = 0.08250 kg/s
we know that the power rating of the resistance heater is equal to the heat transfer rate to the water;
Q' = m"[tex]C_p[/tex]( T₂ - T₁ )
we substitute
Q' = (0.08250 × 4180 ) ( 80 - 10 )
Q' = 344.85 × 70
Q' = 24139.5 W
Hence, the power rating of the resistance heater is 24139.5 W
Next, we determine the average velocity of water in the tube;
[tex]V_{avg[/tex] = V" / [tex]A_c[/tex]
[tex]V_{avg[/tex] = V" / ( [tex]\frac{1}{4}[/tex]πD² )
given that; flows through a 2-cm-internal-diameter; D = 0.02 m
we substitute
[tex]V_{avg[/tex] = (8.333 × 10⁻⁵) / ( [tex]\frac{1}{4}[/tex]π × (0.02)² )
[tex]V_{avg[/tex] = (8.333 × 10⁻⁵) / ( 3.14159 × 10⁻⁴ )
[tex]V_{avg[/tex] = 0.265 m/s
Also, from table " saturated water property table "
At 45°C
viscosity μ = 0.596 × 10⁻³ kg/m-s
Prandtl number Pr = 3.91
Now, we determine the kinematic viscosity
v = μ / p
we substitute
v = ( 0.596 × 10⁻³ ) / 990.1
v = 6.01959 × 10⁻⁷ m²/s
so, Reynolds number in the flow region will be;
Re = ([tex]V_{avg[/tex] × D) / v
we substitute
Re = ( 0.265 × 0.02) / (6.01959 × 10⁻⁷)
Re = 8804.586
we can see that our Reynolds number ( 8804.586 ) more than 2300 and less than 10,000.
Hydraulic and thermal entry length are equal in this flow region,
such that;
[tex]L_h[/tex] = [tex]L_t[/tex]
⇒ 10 × D = 10 × 0.02 = 0.2 m
we can see that the entry length ( 0.2 m ) is smaller than the given length ( 13 m ) in the question; the flow is a turbulent flow.
So we the Nuddelt number
Nu = [tex]0.023Re^{0.8} Pr^{0.4[/tex]
Nu = 0.023 × [tex]8804.586^{0.8[/tex] × [tex]3.91^{0.4[/tex]
Nu = 56.8
Hence, the heat transfer coefficient h will be;
h = [tex]\frac{k}{D}[/tex] × Nu
we substitute
h = [tex]\frac{0.637}{0.02}[/tex] × 56.8
h = 31.85 × 56.8
h = 1809.1 W/m²-°C
Now, area of the heat transfer will be
A[tex]_s[/tex] = πDL
we substitute
A[tex]_s[/tex] = π × 0.02 × 13
A[tex]_s[/tex] = 0.8168 m²
Finally we determine the inner temperature of the pipe at exit. using the relation;
Q' = hA[tex]_s[/tex]( T₃ - T₂ )
we substitute
24139.5 = 1809.1 × 0.8168( T₃ - 10 )
24139.5 = 1477.67288( T₃ - 80 )
24139.5 = 1477.67288T₃ - 118213.8304
24139.5 + 118213.8304 = 1477.67288T₃
1477.67288T₃ = 142353.3304
T₃ = 142353.3304 / 1477.67288T
T₃ = 96.34°C
Therefore, the inner surface temperature of the pipe at the exit is 96.34°C
Explain how to make aluminum magnetic
Answer:
Use some Glue.. . . Aluminium is not magnetic, so your magnet can't sticl to aluminium without using Glue. You cannot get a magnet to stick to aluminum, no matter how hard you try. Aluminum is diamagnetic, which means it repels a magnetic field.
Explanation:
Hope It Help
brainliest please
a problem solving method that involves trying all possible solutions until one works is using_____.
Answer:
trial and error.
Explanation:
a problem solving method that involves trying all possible solutions until one works is using trail and error.
What is urea? plz help me
Answer:
It is a colorless crystalline compound which is the main nitrogenous breakdown product of protein metabolism in mammals and is excreted in urine.
Answer:
Urea is a compound of nitrogen that is the chief solid substance dissolved in the urine of a mammal and is formed by the breaking down of protein.
(Hope this helps! Btw, I answered first. Brainliest please! :D)
places where computers is used
Answer:
Banks and financial.
Business.
Communication.
Defense and military.
Education.
Internet.
Medical.
Transportation.
etc..
Answer:
Super markets
Hospitals
Industries
Explanation:
In supermarket's computers helps them manage and organise data .
A standing wave experiment is performed to determine the speed of waves in a rope. The standing wave pattern shown below is established in the rope. The rope makes exactly 90 complete vibrational cycles in one minute. The speed of the waves is ____ m/s.
Answer:
The speed of the waves is __6__ m/s.
Explanation:
Given
Total number of vibrations = 90
Total time taken for 90 vibrations = 60 seconds
Frequency of the wave = 90/60 = 1.5 Hz
The length of the rope as shown in the attached figure is 6 meters
The wavelength = 6/1.5 = 4.0 meters.
As we know
v=f*w
v = velocity
f = frequency
w = wavelength
Substituting the given values we get -
speed = 6.0 m/s
The speed of the waves obtained is 6 m/s
Data obtained from the question Number of complete cycles = 90Time = 1 min = 60 sLength of rope = 6 mVelocity (v) =? How to determine the frequency Number of complete cycles (n) = 90Time (t) = 1 min = 60 sFrequency (f) =?f = n/t
f = 90 / 60
f = 1.5 Hz
How to determine the velocity
Frequency (f) = 1.5 HzLength of rope (L) = 6 mWavelength (λ) = 2L / 3 = (2×6)/3 = 4mVelocity (v) =?v = λf
v = 4 × 1.5
v = 6 m/s
Complete question
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HELP PLZ 50 POINTS SPACE QUESTION
Explain how tilt results in varying sun angles that affect temperature
During the winter, the Northern Hemisphere tilted away from the sun, receiving solar radiation at more of an angle. This results in colder temperatures and more extreme temperature changes.
Find the current passing through each of the 3 resistors connected parallel to each other as shown in the figure (i1, i2, I3). Show your actions clearly.
Answer:
I1 = ε/R1
I2 = ε/R2
I3 = ε/R3
Explanation:
From the image, we see that the resistors are connected in parallel. This means that the voltage passing through them is the same.
Now, formula for current is; I = V/R
In this case, V which is voltage is denoted by ε.
Thus;
I1 = ε/R1
I2 = ε/R2
I3 = ε/R3
Consider the following situation, in which a compass is influenced by not only the force of Earth's magnetic field, but also an additional applied force.
1. Which of the following is true of the angle of deflection of the compass relative to FEarth if FEarth > FApplied?
a. The angle of deflection will be exactly 45°
b. The angle of deflection will be greater than 90°
c. The angle of deflection will be less than 45°
d. The angle of deflection will be exactly 0°
e. The angle of deflection will be greater than 45° but less than 90°
2. Which of the following is true of the angle of deflection of the compass relative to FEarth if FEarth < FApplied?
a. The angle of deflection will be exactly 45°
b. The angle of deflection will be greater than 90°
c. The angle of deflection will be less than 45°
d. The angle of deflection will be exactly 0°
e. The angle of deflection will be greater than 45° but less than 90°
Answer:
1) The angle of deflection will be less than 45° ( C )
2) The angle of deflection will be greater than 45° but less than 90° ( E )
Explanation:
1) Assuming that the force applied has a direction which is perpendicular to the Earth's magnetic field
∴ Fearth > Fapplied hence the angle of deflection will be < 45°
2) when the Fearth < Fapplied
the angle of deflection will be : > 45° but < 90°
An Olympic skier moving at 20.0 m/s down a 30.0o slope encounters a region of wet snow, of
coefficient of friction μk = 0.740. How far down the slope does she go before stopping?
a.119 m
b.145 m
c.170 m
d.199 m
Answer:
Option B
Explanation:
Forces acting on the skier-
F1 [tex]= -mg sin(30)[/tex] down the slope
F2 [tex]= -mg cos(30)[/tex]
F3 = friction force [tex]= 0.74 mg cos(30)[/tex]
Net force, down the slope
[tex]= -mg sin(30)+ 0.74 mg cos(30)\\= mg(.74 cos(30)-sin(30))\\= 0.14mg\\= 1.38m[/tex]
Acceleration [tex]= F/m= 1.38[/tex] m/s2
Acceleration remains constant, initial speed is 20 m/s
Speed at time t is [tex]1.38t- 20[/tex] m/s
Distance down the slope at time t is [tex]0.69t^2- 20t[/tex]
When the skier stops, her speed is 0. Thus,
, [tex]1.38t- 20= 0\\t= 20/1.38\\= 14.5[/tex] seconds
Distance travelled in 14.5 seconds [tex]= (0.69)(14.52- 20(14.5)= -145 m[/tex](negative because it is down the slope).
Option B is correct
1. How fast is a radio wave traveling if it is 4.0 meters long and its frequency is
82 Hz?
Answer:
Speed = 328 m/s
Explanation:
Given the following data:
Wavelength = 4 m
Frequency = 82 Hz
To find the speed of the radio wave;
Speed = wavelength * frequency
Speed = 4 * 82
Speed = 328 m/s
Therefore, the radio wave is travelling at 328 meters per seconds.
Radio waves can be defined as an electromagnetic wave that has its frequency ranging from 30 GHz to 300 GHz and its wavelength between 1mm and 3000m. Therefore, radio waves are a series of repetitive valleys and peaks that are typically characterized of having the longest wavelength in the electromagnetic spectrum.
At what rate is work done if the 250 Newton object from number six is moved into a hot at 4 m in four seconds
Answer:
250w
Explanation:
W=Fd
W= 250 x 4= 1000J
P=E/t=1000/4s=250w
Rudy plans to conduct an experiment using three rosebushes of the same variety and size. His hypothesis is that the plant
receiving the most sunlight at the end of three months will show the most growth. In his plan below, he has listed how much
water, fertilizer, and sunlight each plant will receive. Why is his experiment flawed?
Answer: B) He has too many independent variables.
Explanation: Nothing in the experiment is a constant or being measured.
When U-238 transmutates into Th-234, this represents _______.
Alpha decay
Electron capture
Beta-decay
Gamma decay
Answer:
A: Alpha decay.
Explanation:
The transmutation of ²³⁸U is a nuclear reaction that yields ²³⁴Th and an alpha particle.
Now, Alpha decay is a radioactive decay whereby an atomic nucleus emits an alpha particle which then changes into an atom with a mass number that is decreased by four and atomic number decreased by 2.
In this case, mass number is reduced from 238 to 234. Thus, it's an alpha decay.
After graduation, you face a choice. You can work for a multinational consulting firm and earn a starting salary (including benefits) of $40,000, or you can start your own consulting firm using $5,000 of your own savings. If you keep your money in a savings account, you can earn an interest rate of 7 percent. You choose to start your own consulting firm. At the end of the first year, you add up all of your expenses and revenues. Your expenses include $14,000 for rent, $1,000 for office supplies, $24,000 for labor, and $4,500 for telephone expenses. After operating your consulting firm for a year, your total revenues are $88,000.
Required:
What are your total explicit cost and total implicit costs?
Answer:
Explanation:
Money is used to cover the explicit cost. They're what we're used to seeing, and they're easy to identify. There are several classifications for explicit costs; we can distinguish between fixed and variable costs, as well as direct and indirect costs. Raw materials, manpower, indirect production costs, and so on are all factors that contribute to its expense.
The opportunity cost of using a resource is the amount of money paying for it that might have been used on something else.
Alternative benefit options or money that we miss earning by doing such business acts are referred to as opportunity costs.
When a corporation foregoes an alternative action but does not make a bill, it incurs implicit costs. These are a company's hidden costs:
1. The use of the firm's own funds (money or assets).
2. The owner's capital, savings, and financial services are used.
From the given information:
The total explicit cost = Rent + office supplies + office staff + telephone expense
=$( 14000 + 1000 + 24000 + 4500)
= $43500
The total implicit cost = forgone salary + forgone interest
= $40000 + 7% of $5000
= $40000 + 350
=$40350
9
A canoe with a mass of 120 kg is floating downriver at a speed of 2.5 m/s. What is the canoe's kinetic eergy?
Answer:
K.E. = ½ × mv²
= ½ × 120 × (2.5)²
= 60 × 6.25
= 375 J
An object is placed in front of a thin converging lens of focal length 12 cm. The image of the object is upright and 2.5 times as tall as the actual object. What is the distance of the object to the lens?
7.2 cm
6.0 cm
4.2 cm
15 cm
The distance of the object to the lens will be a) 7.2 cm
What is focal length?The distance between the convex lens or a concave mirror and the focal point of a lens or mirror is called the focal length. It is the point where parallel rays of light meet or converge.
magnification (m) = h(image )/ h(object ) = image distance / object distance
given
h(image ) = 2.5 * h(object)
m = 2.5 * h(object) / h(object ) = 2.5
2.5 = image distance / object distance
2.5 = v / u
v = 2.5 u
using lens formula
given
focal length (f) = + 12cm
1/v - 1/u = 1/focal length
1/2.5 u - 1/u = 1/12
u = - 7.2 cm
correct option a)7.2 cm
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space question 50 points
Explain how sun angle and seasons vary as you move away from the equator.
Seasonal change in the angle of sunlight, caused by the tilt of the Earth's axis, is the basic mechanism that results both in warmth of the weather and in length of the day.
An object moves in a circle with a period of 0.025 hours. What is its frequency in Hz?
Frequency, is defined as the rate of rotation, or the number of rotations in some unit of time. Angular frequency, , is the rotation rate measured in radians. These three quantities are related by f = 1 T = ω 2 π .
what is frequency ?The frequency is the number of oscillation per unit time and it is used for defining the cyclic process like rotation, oscillation, wave etc.
The SI unit of the frequency is denoted as Hertz and the symbol λ represents it where one hertz means the wave completed one cycle in one second.
The frequency which explains the phenomenon of oscillatory and vibration like the mechanical vibration, sound signals, light, frequency waves etc. The “period” represented as the time required by the wave for one oscillation, i.e., it is inversely proportional to the frequency.
If the flashes, then the period is the time between the two flashes. And the frequency is the total number of flashes per second.
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name the three major types of clouds
Answer:
Cumulus, Stratus, and Cirrus. There are three main cloud types.
Explanation:
hopes it help^_^
A 125-g coin is placed 8.0 cm from the axis of rotation of a horizontally rotating turntable as shown. The coefficient of static friction between the coin and the turntable is μs . The turntable makes exactly 1.0 revolution per second and the coin remains in place without slipping. [a] (8 pts) Draw a free-body force diagram for the coin. [b] (10pts)What is the frictional force acting on the coin? [c] (12pts)When the rotational speed is increased to 1.2 revolutions per second, the coin starts to slip. Calculate the coefficient of static friction μs between the coin and the turntable?
Answer:
zhvshshisvdiscdoscd if vdidg
A 16 Ω resistor and a 6 Ω resistor are connected in series to an ideal 6 V battery.
Find the current in each resistor.
Answer in units of A.
b) Find the potential difference across the first
resistor.
Answer in units of V.
c) Find the potential difference across the second
resistor.
Answer in units of V
Answer:
(a) 0.273 A
(b) 4.368 V
(c) 1.638 V
Explanation:
From the question,
(a) Applying ohm's law
V = IR'...................... Equation 1
Where V = Voltage of the battery, I = Current in each of the resistor, R' = Total resistance of the combined resistors
Since the Two resisstors are connected in series,
(i) The same current flows through both resistors
(ii) The total resistor (R') = R₁+R₂
Therefore,
V = (R₁+R₂)I
Make I the subject of the equation
I = V/(R₁+R₂)................. Equation 2
Given: V = 6 V, R₁ = 16 Ω, R₂ = 6 Ω
Substitute into equation 2
I = 6/(16+6)
I = 6/22
I = 0.273 A
(b) The potential difference across the first resisto
V₁ = IR₁...................... Equation 3
Given: I = 0.273 A, R₁ = 16 Ω
Substitute these values into equation 3
V₁ = 0.273(16)
V₁ = 4.368 V
(c) The Potential difference across the second resistor is
V₂ = IR₂.................... Equation 4
V₂ = 0.273×6
V₂ = 1.638 V
Calculate the amount, in grams, of an original 300 gram sample of potassium 40 remaining after 3.9 billion years.
a. 300
b. 150
c. 75
d. 37.5
Type the correct answer in each box. Round your answers to the nearest hundredth.
A ball with a mass of 1.5 kilograms is tied to the end of a rope. The ball is pulled to a height of 0.5 meters above the ground and released.
The ball has
joules of potential energy at position B. At position A, all of the energy changes to kinetic energy. The velocity of the ball at position A is
meters/second. Assume there’s no air resistance. Use g = 9.8 m/s2 , PE = m × g × h, and .
Hi there!
[tex]\large\boxed{PE = 7.35 J, \text{ }v \approx 3.13 m/s}[/tex]
To find the potential energy of the ball at B, we can use the equation:
PE = mgh
Plug the given gravity, mass, and height:
PE = (1.5)(0.5)(9.8) = 7.35 J
At A, all of this potential energy is changed to kinetic energy, so we can use the following equation:
v = √2KE/m
Plug in the solved for energy and mass:
v = √2(7.35)/1.5
Solve:
v ≈ 3.13 m/s
Wind power produces a lot of air pollution.
O True
O False
Answer:
Wind is a renewable energy source. Overall, using wind to produce energy has fewer effects on the environment than many other energy sources. Wind turbines do not release emissions that can pollute the air or water (with rare exceptions), and they do not require water for cooling.
Explanation:
A pendulum consists of a 2.0-kg block hanging on a 1.5-m length string. A 10-g bullet moving with a horizontal velocity of 900 m/s strikes, passes through, and emerges from the block (initially at rest) with a horizontal velocity of 300 m/s. To what maximum height above its initial position will the block swing
Answer:
The maximum height above its initial position is:
[tex]h_{max}=1.53\: m[/tex]
Explanation:
Using momentum conservation:
[tex]m_{b}v_{ib}=m_{B}v_{fB}+m_{b}v_{fb}[/tex] (1)
Where:
m(b) is the mass of the bulletm(B) is the mass of the blockv(ib) is the initial velocity of the bulletv(fb) is the final velocity of the bulletv(fB) is the final velocity of the blockLet's find v(fb) using equation (1)
[tex]m_{b}(v_{ib}-v_{fb})=m_{B}v_{fB}[/tex]
[tex]v_{fB}=\frac{m_{b}(v_{ib}-v_{fb})}{m_{B}}[/tex]
[tex]v_{fB}=\frac{0.1(900-300)}{2}[/tex]
[tex]v_{fB}=30\: m/s[/tex]
We need to find the maximum height, it means that all kinetic energy converts into gravitational potential energy.
[tex]\frac{1}{2}m_{B}v_{fB}=m_{B}gh_{max}[/tex]
[tex]h_{max}=\frac{1}{2g}v_{fB}[/tex]
[tex]h_{max}=\frac{1}{2(9.81)}30[/tex]
[tex]h_{max}=1.53\: m[/tex]
I hope it helps you!
The maximum height above its initial position is: [tex]h_{max}[/tex]=1.53m
What is simple harmonic motion?Simple harmonic motion is the periodic motion or back and forth motion of any object with respect to its equilibrium or mean position. The restoring force is always acting on the object which try to bring it to the equilibrium.
Using momentum conservation:
[tex]m_bv_{1b}=m_Bv_{fB}+m_bv_{fb}[/tex]
Where:
m(b) is the mass of the bullet
m(B) is the mass of the block
v(ib) is the initial velocity of the bullet
v(fb) is the final velocity of the bullet
v(fB) is the final velocity of the block
Now for finding the value of final velocity VfB
[tex]m_b(v_{1b}-v_{fb})=m_Bv_{fB}[/tex]
[tex]v_{fB}=\dfrac{m_b(v_{1b}-v_{fb})}{m_B}[/tex]
[tex]v_{fB}=\dfrac{0.1(900-{300})}{2}[/tex]
[tex]v_{fB}=30\ \frac{m}{s}[/tex]
We need to find the maximum height, it means that all kinetic energy converts into gravitational potential energy.
[tex]\dfrac{1}{2}m_Bv_{fB}=m_Bv_{fB}[/tex]
[tex]h_{max}=\dfrac{v_{fB}}{2g}[/tex]
[tex]h_{max}=\dfrac{30}{2\times 9.81}[/tex]
[tex]h_{max}=1.53\ m[/tex]
Thus the maximum height above its initial position is: [tex]h_{max}[/tex]=1.53m
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a student throws a coin vertically downward frok the top of a building. the coin leaves the throwers hand with a speed of 15.0m/s. what is its speed after falling freely for 2.00s?
Answer:
Final speed after 2 seconds = 34.6 m/s
Explanation:
Given:
Initial speed of coin (u) = 15 m/s
Time taken = 2 seconds
Find:
Final speed after 2 seconds
Computation:
Gravitational acceleration of earth = 9.8 m/s²
Using first equation of motion;
v = u + at
or
v = u + gt
where,
v = final velocity
u = initial velocity
g = Gravitational acceleration
t = time taken
v = 15 + 9.8(2)
v = 15 + 19.6
Final speed after 2 seconds = 34.6 m/s
Spiral fracture of bone: Spiral fracture of bone occurs due to twisting of the limb, and is a very common skiing accident. The fracture plane is helical, and is very difficult to heal. Mechanically, it occurs due to an applied torsion load on the bone. Recall that a state of pure shear occurs within the material when torsion is applied on a cylinder, and the bone can be idealized as a cylinder. Let a femur bone be subjected to a torque of T 50 N-m. Assume body weight of the person to be W- 80 Kgs, while each leg is subjected to half of that weight. Given radius of the bone r 10 mm. Compute the principal stresses and shear stresses, as well as orientation of planes on which these stresses are realized.
Answer:
principal stresses :б1 = 32.62mPa б2 = 31.38mPa
Max Shear stress : 16.31 mPa
Orientation of max principle plane = 44.43°
Orientation of minimum principal plane = 134.43°
Explanation:
Given data:
Torque = 50 N-m
weight = 80 kgs
half of weight is subjected to each leg
radius of bone = 10 mm = 0.010 m
a) Determine the principal stresses and shear stress
first calculate the max shear stress ( this will occur in the outermost element
= 16T / π*d^3 where : T = 50 , d = 0.020 m
hence max shear stress = 32 mPa
next determine compressive stress
= ( 40*g) / π/4*d^2 . where : d = 0.020 m , g = 9.81
hence compressive stress = 1.24 mPa
draw and calculate the radius of Mohr's circle
radius of Mohr's circle = 32.0060
Hence principal stresses = 32.0060 ± 0.62
б1 = 32.62mPa
б2 = 31.38mPa
attached below is the remaining part of the solution