Answer:
The original length of the iron rod is approximately 572.189 meters.
Explanation:
This is a case of linear expansion, which is defined by the following differential equation:
[tex]\alpha = \frac{1}{L}\cdot \frac{dL}{dT}[/tex] (1)
Where:
[tex]\alpha[/tex] - Linear expansion coefficient, measured in [tex]\frac{1}{^{\circ}C}[/tex].
[tex]L[/tex] - Length of the element, measured in centimeters.
[tex]\frac{dL}{dT}[/tex] - First derivative of the length of the element with respect to temperature, measured in centimeters per degree Celsius.
If we assume that thermal deformation are small regarding the length of the element, then we simplify (1) in the following form:
[tex]\alpha \approx \frac{\Delta L_{o}}{L\cdot \Delta T}[/tex]
[tex]L_{f} -L_{o} = \alpha \cdot L_{o} \cdot \Delta T[/tex]
[tex]L_{f} = L_{o}\cdot [1+\alpha\cdot (T_{f}-T_{o})][/tex] (2)
Where:
[tex]L_{o}[/tex], [tex]L_{f}[/tex] - Initial and final lengths of the element, measured in centimeters.
[tex]T_{o}, T_{f}[/tex] - Initial and final temperatures of the element, measured in degrees Celsius.
Given that brass has a higher coefficient of linear expansion, it is suppose that initial length is less than the initial length of the iron element. Then, we have the following system of linear equations:
Brass
[tex]L = L_{o}\cdot [1+\alpha_{B}\cdot (T_{f}-T_{o})][/tex] (3)
Iron
[tex]L = (L_{o}+28)\cdot [1+\alpha_{I}\cdot (T_{f}-T_{o})][/tex] (4)
Where [tex]\alpha_{B}[/tex], [tex]\alpha_{I}[/tex] are coefficients of linear expansion of brass and iron, measured in [tex]\frac{1}{^{\circ}C}[/tex].
By equalizing (3) and (4), we have the following formula:
[tex]L_{o} \cdot [1+\alpha_{B}\cdot (T_{f}-T_{o})] = (L_{o}+28)\cdot [1+\alpha_{I}\cdot (T_{f}-T_{o})][/tex]
[tex]L_{o} \cdot (\alpha_{B}-\alpha_{I})\cdot (T_{f}-T_{o}) = 28\cdot [1+\alpha_{I}\cdot (T_{f}-T_{o})][/tex]
[tex]L_{o} = \frac{28\cdot [1+\alpha_{I}\cdot (T_{f}-T_{o})]}{(\alpha_{B}-\alpha_{I})\cdot (T_{f}-T_{o} )}[/tex]
If we know that [tex]\alpha_{B} = 1.9\times 10^{-5}\,\frac{1}{^{\circ}C}[/tex], [tex]\alpha_{I} = 1.2\times 10^{-5}\,\frac{1}{^{\circ}C}[/tex], [tex]T_{o} = 20\,^{\circ}C[/tex] and [tex]T_{f} = 90\,^{\circ}C[/tex], then the initial length of the iron rod is:
[tex]L_{o} = \frac{28\cdot [1+\left(1.2\times 10^{-5}\,\frac{1}{^{\circ}C} \right)\cdot (90\,^{\circ}C-20\,^{\circ}C)]}{\left(1.9\times 10^{-5}\,\frac{1}{^{\circ}C}-1.2\times 10^{-5}\,\frac{1}{^{\circ}C} \right)\cdot (90\,^{\circ}C-20\,^{\circ}C)}[/tex]
[tex]L_{o} = 57190.857\,cm[/tex]
[tex]L_{o, I} = 57218.857\,cm[/tex]
[tex]L_{o,I} = 572.189\,m[/tex]
The original length of the iron rod is approximately 572.189 meters.
“if matthew rides south on his bicycle in a straight line for 23 mins (0.383 hr) with an average velocity of 17.5mph, how far has he ridden?
Answer:
6.7miles due south
Explanation:
Given parameters:
Time = 23min(0.383hr)
Average velocity = 17.5mph
Unknown:
How far he has ridden = ?
Solution:
To solve this problem,
Displacement = Velocity x time
Displacement = 17.5 x 0.383 = 6.7miles due south
the maximum range of a projectile is 2÷√3 times its actual range what is the angle of the projection for the actual range
Answer:
The actual angle is 30°
Explanation:
Equation of projectile:y axis:[tex]v_y(t)=vo*sin(A)-g*t[/tex]
the velocity is Zero when the projectile reach in the maximum altitude:
[tex]0=vo-gt\\t=\frac{vo}{g}[/tex]
When the time is vo/g the projectile are in the middle of the range.
x axis:[tex]d_x(t)=vo*cos(A)*t\\[/tex]
R=Range
[tex]R=d_x(t=2*\frac{vo}{g})[/tex]
[tex]R=vo*cos(A)*2\frac{vo}{g} \\\\R=\frac{(vo)^{2}*2* sin(A)cos(A)}{g} \\\\R=\frac{(vo)^{2} sin(2A)}{g}[/tex]
**sin(2A)=2sin(A)cos(A)
The maximum range occurs when A=45°(because sin(90°)=1)The actual range R'=(2/√3)R:Let B the actual angle of projectile
[tex]\frac{vo^{2} }{g} =(\frac{2}{\sqrt{3} }) \frac{vo^{2} *sin(2B)}{g}\\\\1= \frac{2 }{\sqrt{3}} *sin(2B)\\\\sin(2B)=\frac{\sqrt{3}}{2}\\\\[/tex]
2B=60°
B=30°
An empty glass beaker has a mass of 103 g. When filled with water, it has a total mass of 361g.
When filled with cooking oil, it has a total mass of 351 g.
The density of water is 1.00 gcm–3.
What is the density of the cooking oil?
Answer:
0.96 gcm¯³
Explanation:
From the question given above, the following data were obtained:
Mass of empty beaker = 103 g
Mass of beaker + water = 361 g
Mass of beaker + oil = 351 g
Density of water = 1 gcm¯³
Density of cooking oil =?
Next, we shall determine the mass of water. This can be obtained as follow:
Mass of empty beaker = 103 g
Mass of beaker + water = 361 g
Mass of water =?
Mass of water = (Mass of beaker + water) – (Mass of empty beaker)
Mass of water = 361 – 103
Mass of water = 258 g
Next, we shall determine the volume of the beaker. This can be obtained by calculating the volume of water in the beaker.
Density of water = 1 gcm¯³
Mass of water = 258 g
Volume of water =?
Density = mass /volume
1 = 258 / volume
Cross multiply
1 × volume = 258
Volume of water = 258 cm³
Thus the volume of the beaker is 258 cm³.
Next, we shall determine the mass of the cooking oil. This can be obtained as follow:
Mass of empty beaker = 103 g
Mass of beaker + oil = 351 g
Mass of cooking oil =?
Mass of cooking oil = (Mass of beaker + oil) – (Mass of empty beaker)
Mass of cooking oil = 351 – 103
Mass of cooking oil = 248 g
Finally, we shall determine the density of the cooking oil. This can be obtained as follow:
Mass of cooking oil = 248 g
Volume of the beaker = 258 cm³
Density of cooking oil =?
Density = mass / volume
Density = 248 / 258
Density of cooking oil = 0.96 gcm¯³
Please help me. I will do what I can to get you points.
Answer:
the last one
Explanation:
its the sun when the earth turns towards the sun it gives us heat not solar radiation.
10
A5 kilogram gun fires a 0.02 bullet with a velocity of 380 m/s. What is the recoil velocity of the gun?
A) - 1900 m/s
B - 1.5 m/s
C -7.6 m/s
D - 0.1 m/s
Aww
will mark brainlist
Calculate the kinetic energy of a 100.0-kg meteor approaching the Earth at a speed of 10.0 km/s. Remember that 1 km = 1000 m.
O 1.00 x 10^8j
O 5.00 x 10^9 j
O 10 x 10^7 j
O 50.0 x 10^8 j
Answer:
5.00 x 10^9 j
Explanation:
mass = 100 kg
speed / velocity = 10 km/s x 1000 = 10,000m
K.E =
[tex] \frac{m{v}^{2} }{2} [/tex]
10,000x 100/ 2
= 5000000000
= 5.0 x 10^9j
Would anyone be able to o an application of physics project for me, it has to be 500 words l m a o
Which is an example of a physical change?
cake baking
gasoline combusting
salt dissolving
iron rusting
Answer:
salt dissolving
Explanation:
hope it helps
Explain in detail what happens to the motion of particles in a metal tray as it is placed into the hot oven
Answer:
The particles gain more kinetic energy and begin to move faster
Explanation:
Based on the kinetic theory of matter, matter is made up of particles, which are in a constant state of random motion.
This means that the tiny particles of the metal tray are continuously moving about. Furthermore, for the particles to move about, they need energy. This can come in various forms. It can be chemical, kinetic, or light, etc.
Once the metal tray is placed in the oven the particles get some kinetic energy from the heat of the hot oven. The metal particles begin to vibrate about their mean position a lot quicker than ever before. This leads to an increase in the temperature of the metal tray.
If this continues, they will be able to break the metallic bonds holding them together, causing a change of state from solid to liquid, which we will be able to perceive as the melting of the tray.
A car travels 9km southwards, followed by another 5km southwards. What is the magnitude of its
distance and displacement?
Select one:
a. Distance: 14 km Displacement: 14 km
b. Distance: 14 km Displacement: 4 km
c. Distance: 4 km Displacement: 14 km
d. Distance: 4 km Displacement: 4 km
Answer:
A
Explanation:
No change in direction, and travel was in a straight line, and total distance travelled is 9+5=14
What is the frequency of a radio wave of wavelength 150 m if the velocity of radio waves in free space is 3 × 10^8 m s–¹ ?
Answer:
frequency =speed/wavelength
=(3*10^8)/150
=2×10^6
900n pushes a wedge 0.10 m into a log, if the work done on the log is 50j what is the efficiency of the wedge
Answer:
100
Explanation:
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The exchange of materials between a cell and its environment takes place across cell?A. MitochondriaB. MembraneC. NucleusD. Nucleolus
Answer:
I'm not 100% sure but I think its Cell membrane
Explanation:
please, correct me if i'm wrong.
a 4 kg bowling ball videos rolling down a lane at bowling alley at 6 m/s when the ball strikes the pins is moving your 5.1 m/show much energy in the J is lost due to the friction?
Answer:
19.98Joules
Explanation:
Energy possessed by the body is the kinetic energy
Kinetic Energy = 1/2mv²
m is the mass
v is the velocity
For the 4kg moving at 6m/s
kE = 1/2 * 4 * 6^2
KE = 1/2 * 4 * 36
KE = 72Joules
For the 4kg moving at 5.1m/s
kE = 1/2 * 4 * 5.1^2
KE = 1/2 * 4 *26.01
KE = 52.02Joules
Amount of Energy lost = 72 - 52.02
Amount of Energy lost = 19.98Joules
Hence the amount of Energy lost is 19.98Joules
I load a 0.4 kg marble into a slingshot and shoot it directly upward by applying a 36.2 N force
stretching it a distance of 10 cm. How fast is the marble traveling when it is initially released from
the slingshot? How high does the marble go?
Answer:50mph
Explanation:
A brass rod is encased in aluminum. What happens to the speed of a sound
wave when it passes through the rod and moves from the brass into the
aluminum?
Aluminum
Copper
Lead
Brass
(70% Cu,
30% Zn)
6,420
4,700
5,010
1,960
Speed of
sound
(m/s)
A. Its speed decreases.
OB. Its speed increases.
ООО
O C. Its speed falls to zero.
OD. Its speed stays the same.
PREVIOUS
Answer:
B. its speed increases
Explanation:
A brass rod is encased in aluminium. The speed of a sound wave in this decreases when it moves from the aluminium into the brass medium. Thus, the correct option is A.
What factors affect speed of sound?Sound travels in different mediums in the form of waves. The speed of sound is the speed with which the sound wave travels in a medium. The speed of the wave depends on the density and the elasticity of the medium through which the sound waves travel. In general, the sound wave travels faster in the liquid mediums in comparison to the gas medium and these are quicker in solid mediums than in liquid mediums. Thus, the greater the elasticity and the lower the density of the waves, the faster the sound waves travel in that medium.
The speed of sound in aluminium is 5100m/s and in the brass medium, it is 6,923. So, if the sound wave is moving from aluminum metal to the brass medium, we can clearly observe that there is decrease in the speed of sound. So, we can say here that is the speed is decreases.
Therefore, the correct option is A.
Learn more about Sound here:
https://brainly.com/question/29707602
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Where does the
energy used to
complete the task
come from? What
evidence do you
have that the energy
involved in the crane'
example is different
from that in the
wind-up toy
example?
Answer:
it comes from your knowledge and the information you have to get the reason why that is the answer so you are putting together things that you already know what the new information you have
PLEASE HELP ASAP I'LL GIVE BRAINLY!!
Answer: b or c
Explanation: on khan academy
A bus traveled 2.5 hours in 150 km. What was its average speed?
s=d/t
v=D/t
a=(v-v.)lt
Answer:
Average speed = 60km/hr
Explanation:
Given the following data;
Time = 2.5 hrs
Distance = 150km
To find the average speed;
Average speed = distance/time
Substituting into the equation, we have
Average speed = 150/2.5
Average speed = 60km/hr
The heating element in a kettle behaves like a resistor. A particular kettle needs to operate at 230 V, with a power of 1500 W. Calculate the resistance which the heating element needs to have
Answer:
R = 35.27 Ohms
Explanation:
Given the following data;
Voltage = 230V
Power = 1500W
To find the resistance, R;
Power = V²/R
Where:
V is the voltage measured in volts.
R is the resistance measured in ohms.
Substituting into the equation, we have;
1500 = 230²/R
Cross-multiplying, we have;
1500R = 52900
R = 52900/1500
R = 35.27 Ohms.
Therefore, the resistance which the heating element needs to have is 35.27 Ohms.
Helppp please
As the temperature of water drops, it continues to give off thermal energy until it freezes. This is an example of.
increasing thermal energy
a chemical change
an exothermic change
an endothermic change
Answer:
exothermic change hope it help
Explanation:
it is exothermic change hope it helpful
What's the gravity?
Answer:
gravity is the force by which a planet or another body draws objects towards its Centre. the force of gravity keeps all of the planets in an orbit around the sun.
Explanation:
what is gravity made of?
gravity are made of proposed gravity parts that are made quantum particles which called gravitational anywhere there is gravitation there is gravity like on Earth in the Solar System most importantly in the minisclue infant and intervention universe .
PLEASE HELP IM BEGGING YOU! What is the mass of an object that requires 100N of force to accelerate it at 5m/s2? I
Answer:
20 kg
Explanation:
The following data were obtained from the question:
Force (F) = 100 N
Acceleration (a) = 5 m/s²
Mass (m) =?
Force (F) is simply defined as the product of mass (m) and acceleration (a). Mathematically, the force (F) can be expressed as:
Force (F) = mass (m) × acceleration (a)
F = ma
With the above formula, we can simply obtain the mass of the object as follow:
Force (F) = 100 N
Acceleration (a) = 5 m/s²
Mass (m) =?
F = ma
100 = m × 5
Divide both side by 5
m = 100 / 5
m = 20 kg
Thus, the mass of the object is 20 kg.
demonstrate how you can derive our 9.8m/s^2 from Newton's general law of gravity.
Answer:
[tex]g=G\frac{m_E}{r^2}[/tex]
Explanation:
Using Newton's Law of Universal Gravitation, we can write:
[tex]F=G\frac{m_E}{r^2}[/tex], where [tex]G[/tex] is gravitational constant [tex]6.67\cdot 10^{-11}[/tex], [tex]m_E[/tex] is Earth's mass, and [tex]r[/tex] is Earth's radius.
Using these measured values, we have:
[tex]F=6.67\cdot 10^{-11}\frac{5.97\cdot 10^{24}}{(6.38\cdot10^6)^2},\\g\approx \fbox{$9.8\:\mathrm{m/s^2}$}[/tex].
A car accelerates from rest in a straight line. During the first 14s, the acceleration is uniform and the car reaches the speed of 25m/s. Calculate the acceleration of the car.
v = u + at
25 = 0 + a(14)
a(14) = 25
a = 25/14
a = 1.71 (3sf)
explanation:
u use the equation of motions
v = u + at
v is final velocity, aka 25
u is initial velocity, which is 0 as it was initially at rest
t is time, which is 14s
then u sub in the values and calculate a
Explain your answers to 9a and 9b in terms of Newton's laws of motion.
Answer:i One way to solve the quadratic equation x2 = 9 is to subtract 9 from both sides to get one side equal to 0: x2 – 9 = 0. The expression on the left can be factored:
Explanation:
Velocity includes both speed and
Velocity includes both speed and direction.
What is Velocity?Velocity of a particle is its speed and the direction in which it is moving.
It can also be described as the instantaneous rate of change of the particle's distance traveled, and the direction in which the distance is changing, velocity is basically speeding in a specific direction. It is a vector quantity, which means we need both magnitude (speed) and direction to define velocity. The SI unit of it is metre per second (ms-1). If there is a change in magnitude or the direction of the velocity of a body, then it is said to be accelerating.
Learn more about velocity here: https://brainly.com/question/80295?source=archive
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Tony drives his car . He drives the first 13 miles in 13 minutes. He then drives at an average speed of 68mph for 1 hour 24 minutes .
Complete question :
Tony drives his car . He drives the first 13 miles in 13 minutes. He then drives at an average speed of 68mph for 1 hour 24 minutes . Find how much petrol he uses using the information in the table.
Requires table to answer question is attached below
Answer:
2.64 gallons
Explanation:
Given that:
First 13 miles takes 13 minutes
Average rate = 13 miles / 13 minutes = 1mile/minute ; Average rate per hour = (1 mile /minute * 60) = 60 miles /hour
If average speed = 65mph or less ; 50 miles per gallon (it uses 1 gallon for 50 miles)
Hence, since first phase rate is 60 mph,; then miles per gallon is 50 miles
Therefore,gallon of petrol used for 13 miles will be :
13 miles / 50 mpg = 0.26 gallons
2nd phase:
Average rate of 68 mph for 1 hour 24 minutes (1.4 hours)
Here, miles per gallon = 40 (that is; 40 miles for 1 gallon).
Total distance covered = 68 * 1.4 = 95.2 miles
Petrol used = 95.2 miles / 40 mpg = 2.38 gallons
Hence,
Total petrol used : (0.26 + 2.38) = 2.64 gallons
How long would a pendulum have to be in order to have a period of 10.0 s? Use a value of 9.81 m/s2 for the local acceleration due to gravity. Give your answer to one decimal place.
the major factor in the development of a constitution is
Answer:
Below are some of the important dates that led to the creation of the Constitution: 1775 — The Revolutionary War between the Colonies and Britain begins. ... 1781 — The last battle of the Revolutionary War takes place; the 13 states set up a federal government under laws called the Articles of Confederation.
Explanation:
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