You did look at solar activity on the heliophysics event registry website, and we found activity on the sun on the specified day.
What three sorts of solar occurrences are there?Any natural occurrence in the upper atmosphere of the sun is referred to as a solar phenomenon. Solar flares, prominences and filaments, and coronal mass ejections are three different categories of solar phenomena.
How can I follow the cycle of solar activity the best?The simplest way we can investigate how solar activity changes over time is to survey sunspots, which is also how we track the solar cycle. Sunspots are associated with the Sun's natural 11-year cycle, during which the planet's surface changes from calm to turbulent.
To know more about solar activity visit:-
https://brainly.com/question/3013261
#SPJ4
What is the speed of a 180 g ball if its kinetic energy is 100 J?
Answer:
Velocity, V = 33.33 m/s
Explanation:
Given the following data;
Mass = 180grams to kilograms = 180/1000 = 0.18 kg
Kinetic energy = 100J
To find the speed;
Kinetic energy can be defined as an energy possessed by an object or body due to its motion.
Mathematically, kinetic energy is given by the formula;
\( K.E = \frac{1}{2}MV^{2}\)
Where;
K.E represents kinetic energy measured in Joules.
M represents mass measured in kilograms.
V represents velocity measured in metres per seconds square.
Substituting into the equation, we have;
100 = ½*0.18*V²
Cross-multiplying, we have;
200 = 0.18*V²
V² = 200/0.18
V² = 1111.11
Taking the square root of both sides, we have;
Velocity, V = 33.33 m/s
12 A car travels in a straight line at speed v along a horizontal road. The car moves
against a resistive force F given by the equation
F = 400+kv²
where F is in newtons, v in ms-1 and k is a constant.
At speed v = 15ms-1, the resistive force F is 1100 N.
a
Calculate, for this car:
i the power necessary to maintain the speed of 15ms-¹,
ii the total resistive force at a speed of 30 ms-¹,
iii the power required to maintain the speed of 30ms-¹.
Answer:
i) Power = Force * Velocity = 1100 * 15 = 16500 W = 16.5 kW(ii) Find the value of k first: F = 400 + k(15^2) k = 28/9 F = 400 +(28/9)(30^2) = 320
Explanation:
024 (part 1 of 3) 10.0 points
A 2.0 kg block is pushed 3.0 m at a constant
velocity up a vertical wall by a constant force
applied at an angle of 29.0° with the horizon-
tal, as shown in the figure.
The acceleration of gravity is 9.81 m/s².
2 kg
3 m
29°
Drawing not to scale.
If the coefficient of kinetic friction between
the block and the wall is 0.30, find
a) the work done by the force on the block.
Answer in units of J.
The work was done by the force on the block of 2 kg with an acceleration gravity of 9.81 \(m/s^2\) and at an angle of \(29^o\) 42.83 J.
What is work done?When an object is moved over a distance by an external force, at least some of that force must be applied in the direction of the displacement. This is known as work in physics. Work may be estimated if the force acting along the path is constant by multiplying the length of the path by the component of the force acting along the path.
To express this formally, the work W is equal to the force f times the length d, or W = fd. The work is W = fd cos if the force is applied at an angle to the displacement.
Given:
The mass, m = 2 kg,
The acceleration, g = 9.81 \(m/s^2\),
θ = angle between block and surface kinetic friction = μ
Calculate the work done by the formula given below,
\(W_{fy}\) = F sinθ
\(W_{fy}\) = (\(mgsin\)θ)/ (sinθ - μ * cosθ)
Substitute the values
\(W_{fy}\) = \((2*9.81 sin29^{o} )/sin29^o - 0.30cos29^o\)
\(W_{fy}\) = 42.83 J
Therefore, the work done by the force on the block of 2 kg with an acceleration gravity of 9.81 \(m/s^2\), and at an angle of \(29^o\) is 42.83 J.
To know more about Work done:
https://brainly.com/question/13662169
#SPJ1
Draw a diagram to represent conical pendulum in a non inertial frame of reference and state the equation of centrifugal force on the Bob
As the pendulum moves around the circle, the centripetal acceleration remains constant in magnitude but changes in direction. This is because the tangential velocity of the bob changes direction as it moves around the circle, but its speed remains constant.
The centripetal acceleration experienced by the bob of the conical pendulum is given by the formula \(a = v^2/r\),
Since the pendulum is rotating with a constant angular velocity, the tangential velocity is also constant, given by:
v = 2πr/T,
where T is the period of one revolution. The period is 60/20 = 3 seconds since the pendulum makes 20 revolutions per minute.
Thus, v = 2π*2/3 = 4.19 m/s.
Therefore, the centripetal acceleration is \(a = 4.19^2/2 = 8.77 m/s^2.\)
To know more about centripetal acceleration, here
brainly.com/question/14465119
#SPJ1
--The complete Question is, A conical pendulum is set up in a non-inertial frame of reference that is rotating with a constant angular velocity. The length of the string is 2 meters, and the mass of the bob at the end of the string is 0.5 kg. The pendulum makes 20 revolutions per minute. What is the centripetal acceleration experienced by the bob, and how does this acceleration change as the pendulum moves around the circle?--
A wheel is rotating about an axis that is in the z
-direction. The angular velocity ωz
is -6. 00 rad/s
at t
= 0, increases linearly with time, and is +4. 00 rad/s
at t
= 6. 00 s. We have taken counterclockwise rotation to be positive
The formula for angular velocity as a function of time when it rises linearly can be used to address this issue:
ωz(t) = ωz,0 + αz t
If t is time, z,0 is the angular acceleration at rest, and z is the starting angular velocity.
Applying the information provided, we have:
ωz,0 = -6.00 rad/s (initial angular velocity)
z (6.0 s) = +4.0 rad/s (final angular velocity)
t = 6.00 s (time elapsed) (time elapsed)
The angular acceleration z is what we're looking for.
Using the formula's supplied values as substitutes, we obtain:
-6.00 rad/s + z = +4.00 rad/s (6.00 s)
When we simplify and find z, we obtain:
Z = (5.00 rad/s - 6.0 rad/s)
/6.00 s = 1.67 rad/s^2
As a result, the wheel's angular acceleration is 1.67 rad/s2.
learn more about angular velocity here:
https://brainly.com/question/29557272
#SPJ4
How much work is done in moving a \( 25.0 \mathrm{~kg} \) book to a shelf \( 1.50 \mathrm{~m} \) high? What is the potential energy of the book as a result?
the work done to raise a 25kg book to a 1.5 m shelf is 367.5J and the potential energy of the book will be 367.5
Work done by a force is equal to the scalar product of the force applied and displacement. If d displacement happens on applying a force F, then work done, W by the force is
W = F. d
given:
mass, m = 25 kg
height, d = 1.50 m
work has to be done against the weight of the book, F = mg
work done W = F. d
W = mgd
W = (25) ×(9.8)×(1.50)
W = 367.5 J
This work is stored as the potential energy of the book.
Therefore, the work done to raise a 25kg book to a 1.5 m shelf is 367.5J and the potential energy of the book will be 367.5J
To know more about work, click here:
https://brainly.com/question/18094932
#SPJ4
After an unfortunate accident occurred at a local warehouse, you were contracted to determine the cause. A jib crane collapsed and injured a worker. The horizontal steel beam had a mass of 85. 10 kg per meter of length, and the tension in the cable was =12040 N. The crane was rated for a maximum load of 500 kg. If =5. 000 m, =0. 450 m, =2. 000 m, and ℎ=2. 250 m, what was the magnitude of L (the load on the crane) before the collapse? The acceleration due to gravity is =9. 810 m/s2
The magnitude of the load on the crane before the collapse was 7871.48 N, which is well below the maximum load rating of 500 kg.To determine the load on the crane, we need to use the principles of static equilibrium.
The crane is in equilibrium when the sum of the forces acting on it is zero and the sum of the torques is also zero.The forces acting on the crane are tension in the cable and the weight of the horizontal beam. the torque is due to the weight of the horizontal beam.First, calculate the weight of the horizontal beam:
W = mgL = 85.105.0009.810 = 4168.52 N, where m is the mass per meter of length, g is the acceleration due to gravity, and L is the length of the beam.Now calculating the torque due to the weight of the beam :
τ = W*(h/2) = 4168.52*(2.250/2) = 4686.03 Nm, where h is the height of the horizontal beam. since the crane is equilibrium, the tension in the cable must balance the weight of the beam which is T = W. now substituting the values we get :
=>12040 N = 4168.52 N + L=> 12040 N - 4168.52 N = 7871.48 N
To know more about torque refer to the link brainly.com/question/29024338
#SPJ4
If a current of 23A flows through a circuit and the battery produces a potential difference of 9V, calculate the resistance.
The resistance of the battery if a current of 23A flows through a circuit and the battery produces a potential difference of 9V is 0.39 ohms.
How to calculate resistance?Resistance is the force that tends to oppose motion. It is measured in ohms. The resistance of a battery can be calculated using the following formula;
V = IR
Where;
V = voltage (volts)R = resistanceI = currentAccording to this question, a current of 23A flows through a circuit and the battery produces a potential difference of 9V. The resistance can be calculated as follows:
R = V/I
R = 9/23
R = 0.39ohms
Therefore, 0.39ohms is the resistance of the battery.
Learn more about resistance at: https://brainly.com/question/13638869
#SPJ1
someone help pleaseeee
When a sound wave causes an object to vibrate at its natural frequency, it is
a. reflecting
b. refracting
c. resonating
d. diffracting
Answer:
C. resonating
an object being forced to vibrate at its natural frequency creates resonance
99. The centripetal acceleration of a ball of mass m moving at constant speed v in a horizontal circular path of radius r is
(1) zero
(2) constant in direction, but changing in
magnitude
(3) constant in magnitude, but changing in
direction
(4) changing in both magnitude and direction
The centripetal acceleration of a ball of mass m moving at constant speed v in a horizontal circular path of radius r is constant in direction, but changing in magnitude.
What is magnitude ?A mathematical object's magnitude or size is a characteristic that indicates whether it is bigger or smaller than other objects of the same kind. Formally speaking, the size of an object is the visible outcome of an ordering—of the class of objects to which it belongs.
A magnitude is a measurement of a quantity's size. For instance, an earthquake's Richter scale magnitude, which reflects the size of the earthquake and typically ranges from 1 to 10, is measured. A magnitude 8 earthquake is far more problematic than a magnitude 3 earthquake.
Thus, option 2 is correct.
To learn more about magnitude, follow the link;
https://brainly.com/question/1313542
#SPJ2
Although damages caused by a hurricane depend on several factors, the most significant factor is ________________________.
Although damages caused by a hurricane depend on several factors, the most significant factor is the intensity of the storm.
The intensity of a hurricane is typically measured by the Saffir-Simpson Hurricane Wind Scale, which categorizes storms on a scale from 1 to 5 based on their sustained wind speeds. The higher the intensity, the greater the potential for destruction, as stronger winds can cause more significant structural damages to buildings, infrastructure, and vegetation. Additionally, high-intensity hurricanes can generate storm surges, which are massive waves that can inundate coastal areas, causing flooding and eroding shorelines. Aside from intensity, other factors contributing to hurricane damages include the size of the storm, the speed at which it is moving, and the angle of approach to the coastline. The size of the storm determines the area that will be affected, with larger storms causing more widespread damages. The speed of the storm's movement can influence the duration of its impact on a region, with slower-moving storms potentially causing more prolonged and severe damages. The angle of approach can also affect the severity of storm surges, as well as the distribution of wind and rain damages.
In summary, while hurricane damages are influenced by several factors, the most significant factor is the intensity of the storm, which determines the severity of the damages that can be inflicted on affected regions.
Learn more about coastal areas
https://brainly.com/question/14105067
#SPJ11
Please Help! A 200 g toy car is sliding along a frictionless track. At the top of a hill with a 0.50 m radius of curvature, the car experiences a normal force of 0.80 N. If it then descends 2.0 m to the end of the race track, what speed does it cross the finish line at?
The speed with which the car crosses the finish line is 6.26 m/s.
Speed of the ball after crossing the finish line
Apply the principle of conservation of energy and determine the speed of the ball.
K.E (bottom) = P.E (top)
¹/₂mv² = mgh
v² = 2gh
v = √2gh
where;
h is the height traveled by the carg is acceleration due to gravityv is the speed of the ball at bottom of the inclinev = √(2 x 9.8 x 2)
v = 6.26 m/s
Thus, the speed with which the car crosses the finish line is 6.26 m/s.
Learn more about speed of car here: https://brainly.com/question/111325
#SPJ1
what kinds of systems are most commonly described by schematics?
The systems that are most commonly described by schematics are electrical and mechanical systems. A schematic is a type of diagram that illustrates how a system works by showing the interconnections between components. It provides a visual representation of the system's architecture that is easy to read and interpret.
The schematic diagram displays the components of the system and their connections. Schematic diagrams can be used to explain complex systems in a simple way. They are particularly useful for illustrating how electrical and mechanical systems work.A mechanical schematic is a diagram that shows the mechanical components of a system, such as gears, belts, and pulleys. It provides a visual representation of how the system is designed to work, allowing engineers to identify potential problems and optimize the design. Electrical schematics, on the other hand, show the wiring and electronic components of a system. They provide a clear and concise representation of how electrical signals flow through the system, making it easy to identify potential problems and troubleshoot issues.
Schematic diagrams are used in a wide range of fields, from automotive and aerospace engineering to robotics and computer hardware design. They are an essential tool for engineers and designers who need to understand the inner workings of complex systems.
To know more about schematics visit:
https://brainly.in/question/7505980
#SPJ11
Which name is given to the force that stretches the spring with a metal that weights it down
Answer:
gravity
Explanation:
ok what i understand from your query is that a spring balance with a metal piece attached to it is weighing it down, a spring balance is measured in newtons (f=ma), the acceleration part is gravity (-9.81 m/s^2). The metal piece is attached to the string.
hope this answers your question and please take my answer with a grain of salt and refer to some webpages or videos
answer number 19 pls
Answer:
1. Net force = 90 N
2. Acceleration = 9 m/s²
Explanation:
From the question given above, the following data were obtained:
Mass (m) of bag = 10 Kg
Force applied 1 (Fₐ₁) = 45 N
Force applied 2 (Fₐ₂) = 60 N
Force of friction (Fբ) = 15 N
Net force (Fₙ) =?
Acceleration (a) =?
1. Determination of the net force acting on the bag.
We'll begin by calculating the total force applied on the bag.
Force applied 1 (Fₐ₁) = 45 N
Force applied 2 (Fₐ₂) = 60 N
Total force applied = Fₐ₁ + Fₐ₂
Total force applied = 45 + 60
Total force applied = 105 N
Finally, we shall determine the net force acting on the bag. This is illustrated below:
Total force applied = 105 N
Force of friction (Fբ) = 15 N
Net force (Fₙ) =?
Net force (Fₙ) = Total force applied – Force of friction (Fբ)
Net force (Fₙ) = 105 – 15
Net force (Fₙ) = 90 N to the right
2. Determination of the acceleration of the bag.
Mass (m) of bag = 10 Kg
Net force (Fₙ) = 90 N
Acceleration (a) =?
Force (F) = mass (m) × acceleration (a)
90 = 10 × a
Divide both side by 10
a = 90 / 10
a = 9 m/s²
Thus, the acceleration of the bag is 9 m/s² to the right.
An object that is magnetic all of the time is called a.
Answer:
Bar magnets are permanent magnets. This means that their magnetism is there all the time and cannot be turned on or off as it can with electromagnets .
Explanation:
If all the forces acting on an object are balanced then the net force acting on it is zero. True or, false?
Answer:
true
Explanation:
if all forces are equal then there would be no stronger force to give any net force so it would be zero
An airplane increases its speed at the average rate of 15 m/s². How much time does it take to increase its speed from 100 m/s to 180 m/s? A) 17 s B) 0.058 s C) 5.3 s D) 0.25 s
Answer:
C - 5.3s
Explanation:
a = v - u / t
so,
t = v - u / a
t = 180 - 100 / 15
t = 5.3s
A transformer with 1000 turns on its primary coil has an RMS potential difference across this coil of 240V. A voltmeter is connected across the secondary coil and measures 12V. How many turns are on the secondary coil?
Given that the number of turns in the primary coil is
\(n_p=\text{ 1000}\)The voltage in the primary coil is
\(V_p=240\text{ V}\)The voltage in the secondary coil is
\(V_s=\text{ 12 V}\)We have to find the number of turns in the secondary coil.
Let the number of turns in the secondary coil be denoted by
\(n_s\)The formula to calculate the number of turns in the secondary coil is
\(\begin{gathered} \frac{V_p}{V_s}=\frac{n_p}{n_s} \\ n_s=\frac{V_s}{V_p}\times n_p \end{gathered}\)Substituting the values, the number of turns in the secondary coil will be
\(\begin{gathered} n_s=\frac{12}{240}\times1000 \\ =50 \end{gathered}\)Thus, the number of turns in the secondary coil is 50
Derive an expression for the speed of a particle of rest mass m in terms of its total energy E. Express your answer in terms of the variables m and E, and the speed of light c.
An expression for the speed of a particle of rest mass m in terms of its total energy E v = c√[(E²)/(m²c²) - 1].
To derive the expression for the speed of a particle with rest mass m and total energy E, we will use the energy-momentum relation from special relativity. The relation is:
E² = (mc²)² + (pc)²
where E is the total energy, m is the rest mass, c is the speed of light, and p is the momentum of the particle. The momentum can be expressed as p = mv, where v is the speed of the particle. So, the equation becomes:
E² = (mc²)² + (mvc)²
Now, we will solve for v. First, factor out the common term m²c²:
E² = m²c²(1 + v²/c²)
Next, divide both sides by m²c²:
(E²)/(m²c²) = 1 + v²/c²
Subtract 1 from both sides:
(E²)/(m²c²) - 1 = v²/c²
Finally, multiply both sides by c² and take the square root to obtain v:
v = c√[(E²)/(m²c²) - 1]
This expression gives the speed of a particle with rest mass m and total energy E in terms of the speed of light c.
To know more about energy visit:
brainly.com/question/29647468
#SPJ11
Doubling speed does what to kinetic energy?
It stays the same
The final kinetic energy is double the initial kinetic energy
The final kinetic energy is 4 times the initial kinetic energy
The final kinetic energy is half the initial kinetic energy
Answer:
Final K.E. is four times initial KE
Explanation:
K. E. = 1/2 mv ^2 now double the speed
new K.E. = 1/2 m (2v)^2
= 1/2 m 4 v^2
= 4 * 1/2 m v^2
Answer:
The final kinetic energy is 4 times the initial kinetic energy
Explanation:
Shane is riding his bike at a speed of 10m/s. He isn't watching carefully where he is going and almost hit a tree. He abruptly it's the brakes to stop in a time of 4 seconds. What is his acceleration show your work
(NO LINKS PLEASE)
Answer:
2.5m/s²
Explanation:
a = v/t
Where;
V = velocity (m/s)
a = acceleration (m/s²)
t = time (s).
According to the information provided in this question,
a = ?
v = 10m/s
t = 4
a = 10/4
a = 2.5m/s²
Select the correct words from the drop-down menus to complete the sentence.
The
v work of a machine can never exceed the
work because
some of the work.
uses
Answer:
1. C
2. B
3. B
Explanation:
Took assignment on edge
The
On average, how many stars would we have to search before we would expect to hear a signal? assume there are 500 billion stars in the galaxy.
We would have to search at least 5,000,000,000 (5 billion) stars before we would expect to hear a signal.
To find out the number of stars that we will need to search to find a signal, we need to use the following formula:
total of stars/civilizations500,000,000,000 (500 billion) stars / 100 civilization = 5,000,000,000 (5 billion)
This shows it is expected to find a civilization every 5 billion stars, and therefore it is necessary to search at least 5 billion stars before hearing a signal from any civilization.
Note: This question is incomplete; here is the complete question.
On average, how many stars would we have to search before we would expect to hear a signal? Assume there are 500 billion stars in the galaxy.
Assuming 100 civilizations existed.
Learn more about stars in: https://brainly.com/question/2166533
vector = 6.0 m and points 30° north of east. vector = 4.0 m and points 30° west of south. the resultant vector is given by
The resultant vector has a magnitude of approximately 8.4 m and points at an angle of about 10.3° east of north.
To find the resultant vector, first resolve the given vectors into their components.
Vector 1:
- x-component: 6.0 m * cos(30°) = 5.2 m (east)
- y-component: 6.0 m * sin(30°) = 3.0 m (north)
Vector 2:
- x-component: 4.0 m * sin(30°) = 2.0 m (west)
- y-component: 4.0 m * cos(30°) = 3.5 m (south)
Now, sum the components:
- x-total: 5.2 m (east) - 2.0 m (west) = 3.2 m (east)
- y-total: 3.0 m (north) - 3.5 m (south) = 0.5 m (north)
Next, calculate the magnitude of the resultant vector: sqrt(3.2^2 + 0.5^2) ≈ 8.4 m.
Lastly, find the angle: tan^-1(0.5/3.2) ≈ 10.3° east of north.
Learn more about vector here:
https://brainly.com/question/31551501
#SPJ11
A mercury thermometer is constructed as
shown. The capillary tube has a diameter
of 0.0057 cm, and the bulb has a diameter of
0.37 cm.
Neglecting the expansion of the glass, find
the change in height of the mercury column
for a temperature change of 26 ◦C. The
volume expansion coefficient for mercury is
0.000182 (◦C)^−1
.
Answer in units of cm.
The change in height of the mercury column for a temperature change of 26 °C is 0.000175 cm.
What is mercury?Mercury is the smallest and innermost planet in the Solar System. It is about one-third the size of the Earth and has no moons. It has a very thin atmosphere consisting almost entirely of a small amount of helium and sodium. Mercury's surface is heavily cratered and is similar in appearance to Earth's Moon. It has a very large iron core that makes up most of its mass.
The change in height of the mercury column is given by the equation:
Δh = V * β * ΔT
Where V is the volume of the mercury, β is the volume expansion coefficient of mercury, and ΔT is the change in temperature.
The volume of the mercury can be calculated as follows:
V = π * r² * h
Where r is the radius of the bulb and h is the height of the mercury column.
Substituting these values into the equation, we get:
Δh = π * (0.37/2)² * 0.0057 * 0.000182 * 26
Δh = 0.000175 cm
Therefore, the change in height of the mercury column for a temperature change of 26 °C is 0.000175 cm.
To learn more about mercury
https://brainly.com/question/29321317
#SPJ1
(PLS HELP ME NOW!!!!!)
Answer:
D
Explanation:
Part A
Choose the correct SI form for kN/ms.
a. MN/s
b. mN/s
c. GN/s
d. N/s
mN/s is the correct SI form for kN/ms.
Hence, Option B is correct.
Système Internationale, or SI, is the abbreviation for our metric system of measurements. It is a system that has been universally standardized, providing a common language between countries and among the various branches of science and technology. The International System of Units (SI), also known as the French Système International d'Unités, is a weights-and-measures system used internationally that extends the metric system of units. The metric system, also known as the International System of Units (SI), is the accepted unit of measurement on a global scale. The International Treaty of the Meter was signed on May 20, 1875, in Paris by seventeen nations, including the United States, and is now recognized as World Metrology Day worldwide.
To know more about SI here
https://brainly.com/question/24119811
#SPJ4
Two identical balls are thrown from the top of a cliff, each with the same speed. One is thrown straight up, the other straight down. How do the kinetic energies and speeds of the balls compare as they strike the ground?
A) The ball that is thrown straight up will have more kinetic energy but less speed than the ball that is thrown straight down.
B) The ball that is thrown straight up will have more kinetic energy and more speed than the ball that is thrown straight down.
Both balls will have the same kinetic energy and speed.
C) The ball that is thrown straight up will have more kinetic energy but less speed than the ball that is thrown straight down.
D) The ball that is thrown straight down will have more kinetic energy and more speed than the ball that is thrown straight up.
Answer:
the answer is B.
Explanation:
The ball that is thrown straight up has more kinetic energy and more speed than the ball that is thrown straight down. Both balls have the same kinetic energy and speed.
What is the kinetic energy and potential energy?The kinetic energy of a body can be determined as the energy of a moving physical system because of its motion. Work has to be done on an object to change its kinetic energy.
The kinetic energy of the moving system can be expressed as K.E. = ½mv² where ‘m’ is mass while ‘v’ is the velocity of the object.
The potential Energy of the physical system can be described as the energy stored due to its position. The mathematical formula for the calculation of the potential energy can be expressed in the form of P.E = m×g×h where ‘g’ is the gravitational acceleration, ‘m’ is the mass and ‘h’ is the height in meters
When two identical balls are thrown from a cliff, each with the same speed. One ball is thrown straight up, and the other ball is straight down. Both balls will have the same kinetic energy as well as speed.
Learn more about kinetic energy and potential energy, here:
brainly.com/question/15764612
#SPJ2
A brass rod and an iron rod differ in length by 28cm at 20°C. What should be the original length of the iron rod for the difference in length to remain the same when both rods are heated to 90°C? Linear expansivity of brass=1.9×10^-5. Linear expansivity of iron=1.2×10^-5.
Pls show workings.
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:
\(\alpha = \frac{1}{L}\cdot \frac{dL}{dT}\) (1)
Where:
\(\alpha\) - Linear expansion coefficient, measured in \(\frac{1}{^{\circ}C}\).
\(L\) - Length of the element, measured in centimeters.
\(\frac{dL}{dT}\) - 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:
\(\alpha \approx \frac{\Delta L_{o}}{L\cdot \Delta T}\)
\(L_{f} -L_{o} = \alpha \cdot L_{o} \cdot \Delta T\)
\(L_{f} = L_{o}\cdot [1+\alpha\cdot (T_{f}-T_{o})]\) (2)
Where:
\(L_{o}\), \(L_{f}\) - Initial and final lengths of the element, measured in centimeters.
\(T_{o}, T_{f}\) - 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
\(L = L_{o}\cdot [1+\alpha_{B}\cdot (T_{f}-T_{o})]\) (3)
Iron
\(L = (L_{o}+28)\cdot [1+\alpha_{I}\cdot (T_{f}-T_{o})]\) (4)
Where \(\alpha_{B}\), \(\alpha_{I}\) are coefficients of linear expansion of brass and iron, measured in \(\frac{1}{^{\circ}C}\).
By equalizing (3) and (4), we have the following formula:
\(L_{o} \cdot [1+\alpha_{B}\cdot (T_{f}-T_{o})] = (L_{o}+28)\cdot [1+\alpha_{I}\cdot (T_{f}-T_{o})]\)
\(L_{o} \cdot (\alpha_{B}-\alpha_{I})\cdot (T_{f}-T_{o}) = 28\cdot [1+\alpha_{I}\cdot (T_{f}-T_{o})]\)
\(L_{o} = \frac{28\cdot [1+\alpha_{I}\cdot (T_{f}-T_{o})]}{(\alpha_{B}-\alpha_{I})\cdot (T_{f}-T_{o} )}\)
If we know that \(\alpha_{B} = 1.9\times 10^{-5}\,\frac{1}{^{\circ}C}\), \(\alpha_{I} = 1.2\times 10^{-5}\,\frac{1}{^{\circ}C}\), \(T_{o} = 20\,^{\circ}C\) and \(T_{f} = 90\,^{\circ}C\), then the initial length of the iron rod is:
\(L_{o} = \frac{28\cdot [1+\left(1.2\times 10^{-5}\,\frac{1}{^{\circ}C} \right)\cdot (90\,^{\circ}C-20\,^{\circ}C)]}{\left(1.9\times 10^{-5}\,\frac{1}{^{\circ}C}-1.2\times 10^{-5}\,\frac{1}{^{\circ}C} \right)\cdot (90\,^{\circ}C-20\,^{\circ}C)}\)
\(L_{o} = 57190.857\,cm\)
\(L_{o, I} = 57218.857\,cm\)
\(L_{o,I} = 572.189\,m\)
The original length of the iron rod is approximately 572.189 meters.