Answer: 7071.067 Joules
Explanation:
The Work [tex]W[/tex] done by a Force [tex]F[/tex] refers to the release of potential energy from a body that is moved by the application of that force to overcome a resistance along a path [tex]d[/tex].
It should be noted that it is a scalar, and its unit in the International System of Units is the Joule (like energy). Therefore, 1 Joule is the work done by a force of 1 Newton when moving an object, in the direction of the force, along 1 meter:
[tex]1J=(1N)(1m)=Nm[/tex]
Now, when the applied force is constant and the direction of the force and the direction of the movement are parallel, the equation to calculate it is:
[tex]W=(F)(d)[/tex] (1)
When they are not parallel, both directions form an angle, let's call it [tex]\alpha[/tex]. In that case the expression to calculate the Work is:
[tex]W=Fdcos{\alpha}[/tex] (2)
In this case the force and the distance in the path form an angle [tex]\alpha=45\°[/tex], so we will use the second equation, where [tex]F=400N[/tex] and [tex]d=25 m[/tex]:
[tex]W=(400 N)(25 m) cos(45\°)[/tex] (3)
Then:
[tex]W=7071.067 Nm=7071.067 J[/tex]
The work done by the sailor to pull the boat 25 meters with a force of 400 newtons at a 45-degree angle to the dock is approximately 7,071 Joules.
The amount of work done by the sailor on the boat can be calculated by using the formula for work done by a force at an angle, which is W = F imes d imes ext{cos}( heta). In this case, the force (F) is 400 newtons, the distance (d) is 25 meters, and the angle ( heta) is 45 degrees.
First, we calculate the cosine of the angle, which in this case is ext{cos}(45^{ ext{o}}) = rac{ ext{ extsqrt{2}}}{2}.
Then, we multiply the force, distance, and cosine of the angle: W = 400 N imes 25 m imes rac{ ext{ extsqrt{2}}}{2}.
Therefore, the work done by the sailor is 400 imes 25 imes rac{ ext{ extsqrt{2}}}{2}, which equals 7,071 Joules approximately.
calculate the weight of a 65 kg person on earth
Answer:
143.325 pounds (rounded to 8 digits, but you can round it to a lower amount of digits if you need to!)
Explanation:
So 1 kg = 2.205 lbs, so 65 kg = 2.205lbs * 65kg, which is equal to approximately 143.325 lbs.
( 1kg = 2.205lbs; 65 kg = ? lbs)
The atmosphere is held together by
A. the greenhouse effect
B. solar radiation
C. ozone
D. gravity
Answer:
D. gravity
Explanation:
Gravity keeps the atmosphere from escaping into space.
An exposure is made at 200 cm SID and has an intensity of 5 milliroentgens (mR), and a second exposure is made is at 100 cm SID. Calculate the intensity of the x-ray beam of the second exposure.
The intensity of X-ray beam of second exposure made at 100 cm SID is 20 mR.
Solution:
By using inverse square law formula, intensity of X-Ray beam made at different distances can be found.
[tex]\frac{I_{1}}{I_{2}}=\left(\frac{D_{2}}{D_{1}}\right)^{2}[/tex]
Where [tex]I_1[/tex] is the intensity of first exposure of X-ray-beam.
[tex]I_2[/tex] is the intensity of second exposure of X-ray beam.
[tex]D_1[/tex] is the distance at which first exposure is made.
[tex]D_2[/tex] is the distance at which second exposure is made.
[tex]\begin{array}{l}{\frac{I_{1}}{I_{2}}=\left(\frac{100}{200}\right)^{2}} \\\\ {\frac{5}{I_{2}}=\frac{1}{4}} \\\\ \bold{{I_{2}=20\ \mathrm{mR}}\end{array}}[/tex]
Options: Amplitude, crest, trough, wavelength
Jack applies a force of 30 and move 90 kg box. What is the acceleration of the box?
Explanation:
Given , F = 30N and mass m = 90kg
°•° F = ma
=> a = F/m
=> a = 30/90
=> a = 1/3m/s^2
Final answer:
To find the acceleration of a 90 kg box with a force of 30 N applied, use Newton's second law of motion. The acceleration is calculated as 0.333 m/s².
Explanation:
To calculate the acceleration of a 90 kg box when a force of 30 N is applied, we can use Newton's second law of motion, which is F = ma, where F is the force applied, m is the mass of the object, and a is the acceleration of the object. Rearranging the equation for acceleration gives us a = F / m.
In this case, F = 30 N and m = 90 kg. Plugging these values into the equation yields a = 30 N / 90 kg = 0.333 m/s². Therefore, the acceleration of the box is 0.333 meters per second squared (0.333 m/s²).
How is energy transformed from one form to another?
how long does it usually take a hypothesis to become a theory
Answer:
If enough evidence accumulates to support a hypothesis, it moves to the next step (known as a theory) in the scientific method and becomes accepted as a valid explanation of a phenomenon.
Answer:
Hypothesis is usually referred as an assumption or an observation made without much proof to support the statement. Hence scientists and experimental physicists uses hypothesis and perform experiments and observations to support the theory.
The hypothesis will get transformed into a theory only when there is enough evidence to support the cause and the science behind the set of events. It is dependent upon a number of scientific tests an hence it is not possible to define a time period. It may varies from years to forever (or never).
Why is it very important that only one variable be changed in a n experiment
Answer:
There should be only one manipulated variable within a scientific experiment so that the experimenter can be certain it is this variable which causes a pattern in the resultant data, if any exists at all. ... A variable within a scientific experiment is something that is changed
Explanation:
Answer:
There should be only one manipulated variable within a scientific experiment so that the experimenter can be certain it is this variable which causes a pattern in the resultant data, if any exists at all. ... A variable within a scientific experiment is something that is changed (i.e. it varies).yes here is correct
Since lower case m stands for both the prefix.milli and for unit for length meter, how do we tell which one is meant when they are used?
A: a prefix is never used alone. So a lone m (lower case) would refer to a unit, the meter (the SI metric unit of length.)
B: the prefix Comes before the unit, so mm (both lower case) would stand for millimeter.
C: the prefix comes before the unit, so mg (both lower case) would stand for milligram.
D: all of the other 3 answer choices.
Answer:
D: all of the other 3 answer choices
Explanation:
Milli- is a prefix, so a lowercase m in front of any other letter means milli-. For example, mm = millimeter and mg = milligram.
An m by itself means meters.
Answer:
D: all of the other 3 answer choices.
Explanation:
A: a prefix is never used alone. So a lone m (lower case) would refer to a unit, the meter (the SI metric unit of length.)
Above statement is true because here we can see that when prefix is placed before any SI unit then only we use it let say if we use only unit "m" then it is clearly assumed to be meter
B: the prefix Comes before the unit, so mm (both lower case) would stand for millimeter.
TRUE
Since prefix is always used before SI unit then we have to use the prefix like it is shown here for length. when we give unit as "mm" then it will show millimeter.
C: the prefix comes before the unit, so mg (both lower case) would stand for milligram.
TRUE
Since prefix is always used before SI unit then we have to use the prefix like it is shown here for mass. when we give unit as "mg" then it will show milligram.
. From the top of a building 85.0 meters tall a ball is dropped. At the same time another ball is thrown upward from the ground with a speed of 46.0 m/s. a. How long after the balls are released will they hit? b. How high above the ground will these two balls hit?
Answer:
a) Both balls are affected by gravity in the same way. The time both balls hit each other is equal to the time the ball thrown up reaches the top of the roof, if there was no gravity. (both balls would be at the same location)
y = v*t = 85m = 46m/s * t
t = 1.85s
Check:
The equation for position is given by:
y(t) = -0.5gt² + v₀t + x₀
The position of the ball on the roof top at time t = 1.85s:
y₁(t) = -4.9t² + 85.0 = 68.3m
The position of the ball thrown up at time t = 1.85s:
y₂(t) = -4.9t² + 46 * 1.85 = 68.3m
b) the two balls hit each other at a hight of 68.3m
The ball dropped from the building hits the ground after approximately 4.16 seconds. The ball thrown upward from the ground hits the ground after approximately 9.39 seconds. Both balls hit at the ground level.
Explanation:This question involves the concepts of motion in Physics. We'll use the formulas for kinematic motion to find out when and where the two balls hit. First, let's consider the ball that's dropped.
The ball drops with an initial speed of 0 m/s as the ball is released from rest and it will cover a distance of 85.0 meters under the acceleration due to gravity. We use the second equation of motion: s = ut + 0.5gt^2. Here, s is the displacement (85 meters), u is the initial speed (0 m/s), g is the acceleration due to gravity (9.8 m/s^2), and t is the time we wish to determine. Plugging the known values, we find t = sqrt(2s/g) which gives us t ≈ 4.16 seconds.
Now for the ball thrown upwards from the ground with an initial speed of 46.0 m/s. The ball goes upwards, then slows down, stops and starts falling down under gravity. The time when the ball hits the ground is twice the time it takes for the ball to reach the highest point. That time is given by t = u/g (since at the highest point, final velocity is 0). Thus, the total time is T = 2u/g, which gives us T ≈ 9.39 seconds.
As for where they hit, the ball dropped from the building hits the ground, and the ball thrown upwards from the ground hits the ground again after it reaches the maximum height and falls back.
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An elephant and a mouse would both have zero weight in gravity-free space. If they were moving toward you with the same speed, would they bump into you with the same effect? Explain.
The elephant and the mouse having zero weight in a gravity free space will not bump into you at the same effect.
Explanation:
When both are in a gravity free space, the weights are zero, as we know that the[tex]\text {weight of the body}=\text {mass of the body} \times \text {acceleration due to gravity}[/tex]
[tex]\text {here, the weight of elephant}=\text {mass of elephant } \times \text {zero gravti} y=zero[/tex]
[tex]\text {similarly,weight of mouse}=\text {mass of mouse } \times \text {zero gravity}=zero[/tex]
But when they will acquire the speed of same magnitude, say v, their different masses will acquire different momentum, which will make the difference in effect while bumping.
[tex]\text { momentum of elephant }=\text { mass of elephant } \times v[/tex] [tex]\text { momentum of mouse = mass of mouse } \times v[/tex]
And as we know [tex]\text { mass of elephant }>\text { mass of mouse }[/tex] Therefore, effect of impact by elephant will be more than that of mouse . An elephant breaking into you will take you back faster than a mouse in space hits you.
____ are formed where bumps from two surfaces come into contact.
the answer is Friction.
hope this heslp
Micro welds are formed where bumps from two surfaces come into contact.
Explanation:
The surface of all existing objects or elements, have some bumps and dips. Whenever the surfaces of two different bodies with bumps and dips come into contact with each other, sticking occur.
This causes the production of micro welds between the two surfaces that inhibit the smooth motion. These micro welds create a static force that opposes the smooth motion between the surfaces. This is called “friction”.
This friction force can be stopped only when it can either be dominated with the equal opposite force or inhibited with lubricating agents that reduce its effect on the surfaces of the two respective objects.
d A marathon runner runs at a average speed of 5.33 meters per second for the first
73600 seconds and then at a speed of 5.00 meters per second for the next 4200
seconds. What is the average speed of the marathon runner in meters per second?
F
5.1 m/s
G
2.6 m/s
H
0.4 m/s
J 1.06 m/s
Answer:
The average speed of the marathon runner is 5.15 meters per second
Explanation:
Lets revise the meaning of average speed
The average speed of an object is the total distance traveled by
the object divided by the time taken to cover that distance
A marathon runner runs at a average speed of 5.33 meters per second
for the first 3600 seconds
⇒ His speed = 5.33 m/s
⇒ For time = 3600 seconds
Then he runs at a speed of 5.00 meters per second for the next
4200 seconds
⇒ His speed is 5 m/s
⇒ For time 4200 seconds
Average speed = total distance ÷ total time
Lets find the total distance
Distance = speed × time
⇒ The 1st distance = 5.33 × 3600 = 19188 meters
⇒ The 2nd distance = 5 × 4200 = 21000 meters
⇒ Total distance = 19188 + 21000 = 40188 meters
Lets find the total time
⇒ Total time = 3600 + 4200 = 7800 seconds
⇒ Average speed = 40188 ÷ 7800 = 5.15 m/s
The average speed of the marathon runner is 5.15 meters per second
Compare and contrast the two main branches of physical science - please help meeeeeeeeee
Answer:
Physics
Chemistry
Explanation:
Physical science is science which studies non-living things.This covers things on earth to the universe.The main branches are physics and chemistry.The other sub-branches are Astronomy, meteorology and Geology.Physics is concerned with the basic principals of matter and energy.It covers concepts in motion, energy, force, pressure , light and many other areas we encounter in our day to day life.Chemistry is concerned with composition of matter and how it reacts.Material in chemistry is understood through observing molecules, atoms, elements and their interaction in nature including their properties.Chemistry is further divided into organic chemistry and natural chemistry sub-branches.
If two vectors are not perpendicular to each other, how should you add them?
Answer:
First you have to determine the angle of the vectors. Based on this angle, you separate the horizontal and vertical components using the trigonometric functions sine and cosine. The horizontal component is solved independently from the vertical, and finally using the Pythagorean Theorem, you solve the combined answer of the vertical and horizontal components to reach your final answer.
Answer:
Resolve each vector into it's x and y components
2. An automobile with an initial velocity of 6.3 m/s to the right accelerates
uniformly at the rate of 3 m/s2 to the right. What is the final velocity of the
automobile after it travels 52 meters to the right?
Answer:
18.8 m/s
Explanation:
Given:
v₀ = 6.3 m/s
a = 3 m/s²
Δx = 52 m
Find: v
v² = v₀² + 2a(x − x₀)
v² = (6.3)² + 2(3)(52)
v² = 351.69
v ≈ 18.8
The final velocity is approximately 18.8 m/s (round as needed).
If Joey ran 60 meters in 10 seconds, then his velocity is ________ m/s.
Answer:
6 m/s
Explanation:
Martin mixed sulfur (a yellow solid) with iron filings (a black solid) in a ceramic dish called a crucible. Then he separated them using a magnet. What kind of a change is this?
A.
change in state
B.
mixing and separation
C.
replacement
D.
synthesis
Answer:
a. change in state
Explanation:
Separation of iron filings from its mixture with sulphur is an example of mixing and separation.
Answer: B. mixing and separation
Explanation:
Separation techniques exploit various physical and chemical properties of substances. When a mixture undergoes separation it may result in two or more mixtures or even pure substances. Here separation of iron filings is achieved by making use of the magnetic property of iron.
Very few substances occur in pure form in nature. In order to obtain pure substances various separation techniques have to be employed. Examples of separation techniques are chromatographic separation, centrifugation, electrophoresis etc...
According to Newton’s law of universal gravitation, which statements are true? As we move to higher altitudes, the force of gravity on us decreases. As we move to higher altitudes, the force of gravity on us increases. As we gain mass, the force of gravity on us decreases. As we gain mass, the force of gravity on us increases. As we move faster, the force of gravity on us increases.
According to Newton’s law of universal gravitation, as we move to higher altitudes, the force of gravity on us decreases and as we gain mass, the force of gravity on us increases both are the true statement.
Explanation:
Newton law of universal gravity extends gravity beyond the earth's surface. This gravity depends on the masses directly and inverse to the distance square between their centers.
[tex]F=G \frac{M \times m}{r^{2}}[/tex]
Where,
F – Force, G – gravitational constant, M and m – masses in kg, r – distance in meters.
Since force is proportional to the masses of interacting objects. If the mass of any one object increases, gravity between them also gets increased. When moving to higher altitude, force decreases as the distance is inverse proportion to gravity.
convert the following degree celsius tempture to degree fahrenheit a.40c b.30c
Answer:
a. 104°F
b. 86°F
Explanation:
To convert Celsius to Fahrenheit, use the equation:
F = 1.8C + 32
where F is the temperature in Fahrenheit and C is the temperature in Celsius.
a. F = 1.8(40) + 32
F = 104
b. F = 1.8(30) + 32
F = 86
(A) [tex]40^{\circ}C[/tex] equals [tex]104^{\circ}F[/tex]and (B)[tex]30^{\circ}C[/tex] equals [tex]86^{\circ}F[/tex].
To convert temperatures from degrees Celsius to degrees Fahrenheit, we can use the following formula:
[tex]F = \left( C \times \frac{9}{5} \right) + 32[/tex]
Let's use this equation to get the specified temperatures:
For [tex]40^{\circ}C[/tex]:[tex]F = \left( 40 \times \frac{9}{5} \right) + 32 \\\\F = 72 + 32 \\\\F = 104^\circ\text{F}[/tex]
For [tex]30^{\circ}C[/tex]:[tex]F = \left( 30 \times \frac{9}{5} \right) + 32 \\\\F = 54 + 32 \\\\F = 86^\circ\text{F}[/tex]
A family wants to determine how much of the total monthly income is going to various expenditures (food, housing, utilities, etc.). Which of the following would be most helpful in displaying this data?
circle graph
line graph
bar graph
frequency table
I NEED THIS ANWSER ASAP 98 POINTS
Answer:
circle graph
Explanation:
A circle graph it is a statistical resource that is used to represent percentages and proportions. The number of elements compared within this graph can range from two to as many as required. Thus, Using this graph you can visualize the proportion of each expense, like food and housing, with respect to the total monthly income.
Answer:
circle graph
Explanation:
did the test
Which of the following can be natural sources of water pollution? a. volcanic activity b. earthquakes c. algae blooms d. all of the above Please select the best answer from the choices provided A B C D
The natural sources of water pollution are algae blooms.
Answer: Option C
Explanation:
The natural form of water pollution is due to water erosion, the composition of minerals, leaves, human/animal droppings, etc. Algae blooms are the development of phytoplankton (a tiny floating plants in fresh and salt water).
Algae bloom also causes problems in the aquatic ecosystem. The excessive algae can block sun rays and hence affect important aquatic habitats.
This can also be seen in the fish gills and inhibit their breathing. When a significant bloom of algae dies, they can damage the available oxygen in the water and make it uninhabitable for other life forms.
Answer:
C. Algae blooms
Explanation:
Algae blooms grow largely and rapidly in fresh and marine water. It discolors the water. These can produce toxins in water and are very harmful for marine life as it blocks the sunlight from reaching the depth. Also, marine life struggles to find food and eventually leaves the area. It also badly impacts the local economy. It is the natural source of water pollution.
a ball is thrown inclined in to the air with a initial velocity of u. if it reaches the maximum height in 6 seconds , find the ratio to the distance travelled in 1 second to the 7th second... plzz help me
Answer:
11:1
Explanation:
At constant acceleration, an object's position is:
y = y₀ + v₀ t + ½ at²
Given y₀ = 0, v₀ = u, and a = -g:
y = u t − ½g t²
After 6 seconds, the ball reaches the maximum height (v = 0).
v = at + v₀
0 = (-g)(6) + u
u = 6g
Substituting:
y = 6g t − ½g t²
The displacement between t=0 and t=1 is:
Δy = [ 6g (1) − ½g (1)² ] − [ 6g (0) − ½g (0)² ]
Δy = 6g − ½g
Δy = 5½g
The displacement between t=6 and t=7 is:
Δy = [ 6g (7) − ½g (7)² ] − [ 6g (6) − ½g (6)² ]
Δy = (42g − 24½g) − (36g − 18g)
Δy = 17½g − 18g
Δy = -½g
So the ratio of the distances traveled is:
(5½g) / (½g)
11 / 1
The ratio is 11:1.
How do a neutron and a proton compare?
O A. The neutron has much less mass.
O
B. The neutron is farther from the nucleus.
O
C. They are equal in number in a neutral atom.
D. The proton has a positive charge, while the neutron has no charge.
Answer:
it would be d
Explanation:
because the neutron has a neutral charge so it has no charge at all
A neutron is electrically neutral and has a similar mass to a proton, which has a positive charge. While they both are part of the nucleus and contribute to an atom's mass, only the proton's charge affects the atom’s chemical properties. So the correct option is D.
Explanation:Comparing a neutron and a proton, option D is the correct answer: The proton has a positive charge, while the neutron has no charge. Both neutrons and protons reside in the nucleus of an atom and have approximately the same mass, which is about 1.67 × 10-24 grams, also known as one atomic mass unit (amu) or one Dalton. However, they differ significantly in terms of their electric charge. A proton has a positive charge (+1), essential in determining the atomic number and the chemical properties of an element. In contrast, a neutron is electrically neutral, carrying no charge at all, and contributes to the mass of an atom without affecting its electric charge. The number of protons and neutrons in the nucleus can vary; in a neutral atom, the number of electrons, which are negatively charged, is equal to the number of protons, balancing the net charge to zero.
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If the current through a resistor is cut in half, how does the power dissipated by the resistor change? (P=0VI=1^ 2 R= V^ 2 R )
Answer:
1/4
Explanation:
P = IV, and V = IR, so P = I²R.
If R is held constant, and I is cut in half, then power becomes:
P = (I/2)²R
P = 1/4 I²R
So the power reduces by a factor of 4.
The resistor change 1/4
P = IV, and V = IR, so P = I²R.
If R is held constant, and I is cut in half, then power becomes:
P = (I/2)²R
P = 1/4 I²R
So the power reduces by a factor of 4.
How does the resistance of the resistor exchange?The resistance of all substances modifications to their temperature modifications. If the temperature is diminished, resistance (commonly) declines. In fact, if cooled sufficiently, the material becomes a "superconductor" without huge resistance. Increasing the temperature (normally) will increase resistance.
If you boom the wide variety of lamps in a sequence circuit, there will be less modern-day. The lamps resist modern-day, so in case you placed extra lamps into the circuit, there may be more resistance. You can increase or lower the resistance in a circuit through the usage of a variable resistor.
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The relationship among force, mass, and acceleration is stated in ___
A. The law of conversation of momentum
B. Newton's first law of motion
C. Newton's second law of motion
D. Newton's third law of motion
The relationship between force, mass, and acceleration is delineated in Newton's second law of motion. This rule, summarized as F = ma, implies that force equals mass times acceleration, and it describes how an object's velocity changes when an external force is applied.
Explanation:The relationship among force, mass, and acceleration is stated in C. Newton's second law of motion. Newton's second law states that force equals mass times acceleration often expressed as F = ma. In this equation, F stands for force, m for mass, and a for acceleration. This law describes how the velocity of an object changes when it is subjected to an external force. For example, if you push a skateboard (imparting a force), it will accelerate depending on both the force of your push (how much you pushed) as well as the mass of the skateboard.
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Which state of matter has a definite volume but a variable shape?
Liquid. Liquids have a definite volume but take up the shape of whatever they are in.
Happy to help!
What does mass, volume, and temperature measure?
Answer:
The metric system measures mass in grams or kilograms, distance in meters or kilometers, and volume in liters. It measures temperature in Kelvin or Celsius degrees instead of the Fahrenheit degrees used in the imperial system.
Answer:
The mass of a body is a measure of the resistance against a change of motion state of the body itself. That's why they usually call it "inertial mass" and is somehow an exclusive property that doesn't depend on "where" the body is in the space.
The volume of a body literally the amount of three-dimensional space that the body occupies.
The temperature of a body is a measure of the kinetic energy that the body has. The more the atoms of the body are moving, the hotter the body will be. Absolute zero (i.e. 0° K) is a state where all of the atoms of a body are motionless.
With reference to the international system of units, mass is measured in kilograms, volume in cubic metres and temperature in Kelvin.
Why does a heavier object fall faster
Explanation:
In a vacuum (no air resistance), it doesn't. All falling objects, regardless of mass, accelerate at the same rate.
However, when air resistance is taken into account, heavier objects indeed fall faster than lighter objects, provided they have the same shape and size. For example, a lead ball falls faster than a styrofoam ball.
To understand why, first look at what factors affect air resistance:
D = ½ρv²CA
where ρ is air density,
v is velocity,
C is drag coefficient,
and A is cross sectional area.
As falling objects accelerate, they eventually reach a maximum velocity where air resistance equals weight. This is called terminal velocity.
D = W
½ρv²CA = mg
v = √(2mg/(ρCA))
If we increase m while holding everything else constant, v increases. So two objects with the same size and shape but different masses will have different terminal velocities, with the heavier object falling faster.
Before you ask why, you need to know whether.
On the moon, or any other airless body, all objects fall together, no matter how much each one weighs. We've known this for a good 500 years.
On Earth, if one object falls slower, it's only because the air caught it and held it back.
Two exactly similar wire of steel and copper are stretched by equal force.if the total elongation is 10cm.find how much each wire is elongated given young's modules for steel =2×10^10 N/M^2 and Young's modules for copper 2×10^10N/M^2.
Answer:
The copper wire stretches 6.25 cm and the steel wire stretches 3.75 cm.
Explanation:
Young's modulus is defined as:
E = stress / strain
E = (F / A) / (dL / L)
E = (F L) / (A dL)
Solving for dL:
dL = (F L) / (A E)
The wires have the same force, length, and cross-sectional area. So:
dL₁ + dL₂ = (FL/A) (1/E₁ + 1/E₂)
Given that dL₁ + dL₂ = 0.10 m, E₁ = 20×10¹⁰ N/m², and E₂ = 12×10¹⁰ N/m²:
0.10 = (FL/A) (1/(20×10¹⁰) + 1/(12×10¹⁰))
FL/A = 0.75×10¹⁰ N/m
Solving for dL₁ and dL₂:
dL₁ = (FL/A) / E₁
dL₁ = (0.75×10¹⁰ N/m) / (20×10¹⁰ N/m²)
dL₁ = 0.0375 m
dL₂ = (FL/A) / E₂
dL₂ = (0.75×10¹⁰ N/m) / (12×10¹⁰ N/m²)
dL₂ = 0.0625 m
The copper wire stretches 6.25 cm and the steel wire stretches 3.75 cm.