The speed of rocket alpha as measured from rocket bravo is 0.31c due to head-on collision.
In physics, the change in momentum causes a head-on collision. As was already explained, an object's momentum is a property that results from a change in velocity in reaction to an applied force. Before a collision may occur, the momentum must equal zero and this is called head-on collision.
The target particle's velocity following a head-on impact in which the projectile is significantly more massive than the target will be roughly twice that of the projectile, but the projectile's velocity will remain practically unaltered.
speed of rocket alpha=0.90 c
speed of rocket bravo=0.52c
Now, in order to find the speed of rocket alpha measured from rocket bravo =0.90-0.52c
speed=0.31c
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The speed of the rocket alpha when observed from rocket bravo is calculated to be 1.42c.
Alpha rocket is travelling at a speed of 0.90c, while Bravo rocket is flying at a speed of 0.52c.
The two rockets are heading straight at one another in the same direction to collide.
When the rocket's frame of reference is the Bravo rocket, the rocket's speed can both be perceived from the earth's perspective and
Therefore, the rocket Bravo is moving, and the rocket Alpha will approach it more quickly.
If Rocket Alpha's speed is V₁ and Rocket Bravo's speed is V₂, then Rocket Alpha's speed from Rocket Bravo is V₁₂.
V₁₂ = 0.52 -(-0.90)
V₁₂ = 1.42c
Therefore, the rocket alpha's speed from the rocket bravo is 1.42c.
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List 10 things about the Engineering Design Process.
Answer:
1. Define The Problem
2. Brainstorm Possible Solutions
3. Research Ideas / Explore Possibilities for your Engineering Design Project
4. Establish Criteria and Constraints
5. Consider Alternative Solutions
6. Select An Approach
7. Develop A Design Proposal
8. Make A Model Or Prototype
9. Test And Evaluate
10. Refine The Design
If a comet flies over 50,000 km/h for four hours how far has a travel?
If a comet flies over 50,000 km/h for four hours, then comet has travelled a distance of 2 * 10^5 km.
What is the relationship between speed, distance and time?Speed distance time is the formula that is used to explain the relationship between speed, distance and time. Here, speed = distance ÷ time. We can also say that distance divided by speed will give you the time. Provided you know two inputs, then you can work out the third one.
Given Speed is 50,000 km/h and time is 4 h
We know that distance is speed * time
= 50,000 * 4
= 2 * 10^5 km
Comet has travelled a distance of 2 * 10^5 km.
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A 1.0-kilogram mass falls a distance of 0.50 meter causing a 2.0-kilogram mass to slide the same distance along a table top, as
represented in the diagram below. How much work is done by the falling mass?
The total weight that displaced from the initial position is 3 kg. Then, the work done to move them 0.50 meter is 1.5 J.
What is work done?Work done is a physical quantity describing the effect of a force. When a force applied on an object results in a displacement of the object, the force is said to be done a work on the object.
Work done is the product of the force and displacement. Given that, a 1 Kg mass is falling a distance of 0.50 meter. As in the diagram, the first mass is making displacement of the second mass with 2 Kg to the same distance.
The total mass = 2 +1 = 3 kg
displacement = 0.50 m
then work done = 3 kg × 0.50 m = 1.5 J
Therefore, the work done by falling mass is 1.5 J
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The radius of our Sun is 6.96 × 108 m, and its total power output is 3.85 × 1026 W. (a) Assuming the Sun’s surface emits as a black body, calculate its surface temperature. (b) Using the result of part (a), find λmax for the Sun
a) The surface temperature would be 5,778 K and b) λmax for the Sun will be 0.50 μm.
The radius of our Sun is 6.96 × 108m and its total power output is 3.85 × 1026W.
Assuming the Sun's surface emits as a black body, we can use the Stefan-Boltzmann law to calculate its surface temperature.
Applying the law, we get T = (P / 4πσR2)1/4,
where P is the total power output, σ is the Stefan-Boltzmann constant, and R is the radius of the Sun.
Substituting the given values in the equation, we get T = 5,778 K.
Using the result of the previous calculation, we can find the wavelength of maximum emission (λmax) for the Sun.
To do this, we use Wien's displacement law, which states that λmax = 2898/T (in meters),
where T is the temperature of the Sun.
Thus, we get λmax = 0.50 μm.
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A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s. Before slowing, what is the speed of a child on the rim (in m/s)? How many revolutions does the merry go round make as it stops (in rev)?
1.53 m/s is the speed of a child on the rim (in m/s) . 3rev revolutions does the merry go round make as it stops (in rev)
d =diameter of the merry-go-round = 5.0 m
r = radius of the merry-go-round = d/2 = 5.0/2 = 2.55 m
T = time period of the merry-go-round = 4.0 s
Wi = initial angular velocity of merry-go-round
Initial angular velocity is given as
Wi = 2π/T
Wi =1.53 rad s⁻¹
Wf = final angular velocity of merry-go-round = 0 rad s⁻¹
t = time taken to stop = 20 s
∅ = angular displacement = ?
n = Number of revolutions made before stopping
Angular displacement is given as
∅ =( Wf+Wi)t/2
∅ + 19.125rad
Number of revolutions are given as
n = ∅ /2π
n = 3rev
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What theory describes the formation of the solar system ?
The nebular hypothesis is the most well-known theory of planet creation. According to this theory, the Solar System was created 4.6 billion years ago as a result of the gravitational collapse of a massive molecular cloud.
What theory explains how the solar system emerged from a massive cloud of gas and dust?The nebular theory proposes that a rotating cloud of material called a nebula, composed primarily of light components, flattened into a protoplanetary disk and developed into a solar system made up of a star and circling planets.
What are the four hypotheses regarding how the Solar System came to be?These are the Laplace Nebular Hypothesis, the Chamberlin and Moulton Planetesimal Hypothesis, and the See Capture Theory. Although hardly a different hypothesis, Darwin's notion of tidal friction is presented individually because it applies to all of the others.
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The most widely accepted theory of planet formation is the nebular hypothesis. The Solar System, according to this idea, was formed 4.6 billion years ago as a result of the gravitational.
Collapse of a large molecular cloud. According to the nebular theory, a revolving cloud of matter termed a nebula, which is predominantly made up of light components, flattened into a gravitational disc and eventually gave rise to a solar system made up of a star and orbiting planets. Laplace Nebular Hypothesis, Chamberlin and Moulton Planetesimal Hypothesis, and See Capture Theory are these. Darwin's idea of tidal friction is presented separately even though it doesn't really differ from the others because it holds true for all of them.
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a photon scatters in the backward direction (ϕ=180∘) from a free proton that is initially at rest. What must the wave- length of the incident photon be if it is to undergo a 10.0 change in wavelength as a result of the scattering?
If the scattering is to cause a 10.0 change in wavelength. The wavelength of the photon should be 2.65 x[tex]10^{-5}[/tex] nm.
In physics, a periodic wave's wavelength is the length that it repeats over in space. It is a characteristic of both traveling and standing waves as well as various spatial wave patterns. It is the separation between two wave points that are sequentially linked and in the same phase, such as two close-by zero crossings, crests, or troughs. The spatial frequency is the wavelength's reciprocal. The Greek letter lambda, sometimes known as the "wavelength," is a typical way to depict it. Wavelength is commonly used to describe the sinusoidal wave envelopes, modulated waves, and waves produced by the interference of several sinusoids.
To find the wavelength of the incident photon in which results in scattering as :
The incident ray wavelength= [tex]\lambda[/tex]
The scatter ray wavelength= = 1.1 [tex]\lambda[/tex].
The wavelength is given using the equation of scattering as,
[tex]\lambda_{1} -\lambda=\frac{h}{m_{p}c }(1-cosx)[/tex]
Substituting as,
[tex]\lambda_{1} -\lambda=\frac{6.626\times 10^{-34}(1 - cos 180) }{1.6726\times 10^{-27}\times3\times 10^{8} }( 0.1\lambda)[/tex]=2.65
Hence, The wavelength in which scatters is 2.65x[tex]10^{-5}[/tex] nm.
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Which of the following is not expected for a "hot Jupiter" that orbits 0.05 AU from its star
A. cloudtop temperatures over 1000 K
B. intense volcanism
C. density similar to or lower than Jupiter's
d. clouds made of rock dust
Intense Volcanism is not expected for a "hot Jupiter" that orbits 0.05 AU from its star. Hence, the Correct option is B. intense volcanism.
An astronomical unit(AU) is what?In our solar system, distances are really great. Therefore, astronomers frequently avoid using miles or kilometres when describing the distances to planets, asteroids, comets, or spacecraft. They substitute astronomical units, or AU, which represent the typical separation of the Earth from the sun. That translates to around 93 million miles, 150 million kilometres, or 8 light-minutes.
What is " hot Jupiter " ?Jupiter has a mass greater than 300 times that of Earth and a circumference greater than ten times that of Earth. The vast majority of the 300+ planets discovered so far are gas giants. 51 Peg was the first extrasolar planet discovered orbiting a sun-like star. Its mass is comparable to Jupiter's. However, 51 Peg is twenty times closer to its star than Earth is to the Sun and orbits its star every four days, in contrast to Jupiter, which is five times as far from the Sun as Earth and completes one round of the Sun in 12 years. These kinds of planets are known as "Hot Jupiters."
From the fact we can say that intense volcanism is not expected for a "hot Jupiter" that orbits 0.05 AU from its star.
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prove that;v2=u2+2as
[tex]v { }^{2} = u {}^{2} + 2as[/tex]
prove that
Answer: Integrate a=vdv/ds [ from v to u and distance from 0 to s]
Explanation:
As we know a=vdv/ds
a.ds = v.dv
now integrate left side from u to v and at right side from 0 to S
it will result (v^2-u^2)/2 = as
(v^2-u^2)=2as
v^2= u^2+2as
Hence proved
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What is the resultant temperature when 1 g of ice at 0 C and 1 g of steam at 100 C are mixed?
When 1 g of ice at 0° C and 1 g of steam at 100° C are combined, the resulting temperature is 100°C.
What does latent heat mean?Latent heat is the quantity of heat required to transform a body's unit mass from solid to liquid or from liquid to gas without causing a change in temperature.
Describe entropy and enthalpy.In a thermodynamic system with constant pressure, enthalpy is the unit used to measure the total amount of heat present. It's depicted as. Where E is the internal energy, P is the pressure, and E is the energy, H is defined as E + P + V. The degree of chaos in a thermodynamic system is measured by entropy.
Briefing:Heat needed to melt 1 g of ice of 0°C to water at 0°C = 1 × 80 cal.
Heat needed to raise temperature of 1 g of water from 0°C to 100°C = 1 × 1× 100 = 100 cal
Total heat needed for maximum temperature of 100°C = 80 + 100 = 180 cal
Since one gram of steam gives 540 cal of heat when it is converted to water at 100°C, therefore, temperature of the mixture would be 100°C.
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The resultant temperature is 100°C when 1 g of ice at 0° C and 1 g of steam at 100° C are mixed.
The amount of heat needed to shift a body's unit mass from solid to liquid or from liquid to gas without creating a temperature change is known as latent heat. Enthalpy is the unit used to express the total amount of heat present in a thermodynamic system with constant pressure. It is portrayed as. H is defined as E + P + V, where E is the internal energy, P is the pressure, and E is the energy. Entropy is a unit used to describe how chaotic a thermodynamic system is.
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Find the velocity in m/s of a baseball thrown 38 m from third base to first base in 1. 7 s.
Answer:
22.3 m/s
Explanation:
Velocity=Displacement/Time
V=38/1.7=22.3 m/s
radio waves are: radio waves are: a form of sound. a form of light. a type of spectrum.
Answer:
Radio waves can be considered a form of light waves since both are transverse waves (vibrate perpendicular to direction of travel).
Sound waves are longitudinal waves and require a medium (such as air) for propagation.
1. According to the
opposite sex who they feel are roughly as attractive as they are.
2. According to the findings of anthropologist Margaret Mead, our ideas of masculine and
feminine behavior are reversed among the
people of New Guinea.
3. According to an extensive national survey, men prefer that a potential mate earn less money
hypothesis, men and women tend to be attracted to members of the
than they do, while women are more likely to be attracted by a man's professional status,
dependability, and fondness for
4. If you think that all members of a particular ethnic or social group are hot tempered, then you're
assigning a
to that group.
5. According to Sternberg,
love is composed of passion + commitment.
6. Brain organization differs between men and women in that the two halves of the brain in
women are connected with a thicker
7. While girls typically acquire
with abstract concepts in
8. According to social
theory, gender typing is more likely to be derived from
observational learning, as well as identification and socialization.
skills earlier than do boys, boys seem to do a bit better
The phrases sex and gender refer to various characteristics of what it means to be a woman or a man in any society, despite the fact that they are frequently used synonymously and complement one another.
What do you meant by gender ?Actually, the argument that we are drawn to those who are like us is very strong.According to the well-known imprinting theory developed by Mead, kids pick up skills by observing how adults behave.There is a substantial corpus of empirical research that supports this claim.The differentiating properties of things in various categories are highlighted by categorization.The kind of love that combines closeness, desire, and commitment is called consummate love, according to Sternberg's triangular theory of love.The volume of the prefrontal cortex, orbitofrontal cortex, superior temporal cortex, lateral parietal cortex, and insula was higher in females.When a child is between the ages of six and ten, they learn the vast bulk of abstract words and ideas. Some abstract words are taught to them early, though.Gender typing happens as a result of reinforcement and modeling, claims the social learning hypothesis.To learn more about gender refer to :
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use your knowledge of the collision theory and use the potential energy diagram given to answer questions 1 through 5. which letter represents the activation energy? group of answer choices c none of the above a b
The activation energy for a reaction is illustrated in the potential energy diagram by the height of the hill between the reactants .
What is energy formula?The equation developed by Albert Einstein, which is usually given as E = mc2, showing that, when the energy of a body changes by an amount E (no matter what form the energy takes), the mass (m) of the body will change by an amount equal to E/c2.
What is energy and its unit?Energy can be defined as the ability to do work. The amount of energy possessed by a body is equal to the amount of work it do when its energy is released. Energy is a scalar quantity. The SI unit of energy is Joule.
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The planetary system which predicted stellar parallax (although such parallax was not visible) was the (blank) theory?
The planetary system which predicted stellar parallax (although such parallax was not visible) was the holocentric theory.
What is stellar parallax?
Stellar parallax is the apparent shift in position of any nearby star (or other object) against the background of distant objects, and it is used to calculate the object's distance (via trigonometry).
The parallax is thought to be half of this maximum, roughly equivalent to the observational shift caused by the Earth's and Sun's different positions, with a baseline of one astronomical unit.
When we observe the position of a star over the course of a year, we can see how it changes. A year after the first measurement, it will return to the same position. This effectively establishes the Earth's orbit.
Therefore, stellar parallax is supported by the holocentric model.
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if your inboard/outboard boat runs aground, what action should you take in addition to shifting the weight away from the point of impact? boat us
Put your boat in forward motion only. Instead, turn off the car and raise the outdrive. Should you take any additional action in addition to moving your weight away from the site of impact displacement
What is displacement?The concept of displacement denotes the notion that an object has moved or have been relocated. An object's positional change is referred to as "displacement."
What is a sentence example of displacement?Its 2-liter, 4-cylinder engine now has 2.4 liters of displacement and 160 horsepower instead of 146. For the majority of residential uses, automobiles with engines under 1000 cc are sufficient.
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Is ballistic stretching safe?
While this type of stretching may be beneficial for athletes, it carries a risk of injury. Ballistic stretching is generally not recommended for everyday people who want to stay in shape or improve flexibility because there is a risk of straining or pulling a muscle.
What is ballistic method ?Ballistic Technique It is the most traditional method of stretching exercises. This approach incorporates abrupt movements. Just rhythmic activities or movements around a joint can stretch a joint or a muscle. The proper warm-up is crucial before engaging in such a workout.
Using rapid, abrupt motions to promote flexibility, ballistic stretching is a warm-up stretching technique. It is mostly utilised by sportsmen and anyone who exercise regularly to improve muscle strength and range of motion.
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Who solved the problem of longitude at sea?
The who solved the problem of longitude at sea is John Harrison. John Harrison was born at 24 march 1693 and died at 24 march 1773.
Who is Jon Harrison?John Harrison was a carpenter and clockmaker. In the age of sail, John Harrison invented the marine chronometer. This invention is a revolutionized the accuracy of the longitude position in the sea where there is no device can do during those time. By his invention, the safety of long journey in the say is dramatically because the navigator can determine where exactly their ship and decide a proper direction to move.
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Most coltan ore is mined in ________, but purified and marketed in ________.
A) South America; South Africa
B) Canada; the United States
C) South Africa; Congo
D) the United States; Europe
E) Congo; developed nations in North America and Europe
Option c is Correct. The majority of coltan ore is mined in South Africa, although it is cleaned and sold there.
Tantalum and niobium, two minerals used in technology, are found in coltan ore. The top three countries that make tantalum and niobium mineral concentrates are Brazil, Canada, and Australia. Natural resources abound in the Democratic Republic of Congo (DRC); its unexploited mineral riches are thought to be worth US$24 trillion. They include things like gold, diamonds, cobalt, and zinc.
Coltan, whose name is derived from "columbite-tantalite," is another important strategic mineral extracted in the DRC. One of the most important minerals in the world, coltan, has 60% of the world's deposits in the Kivu province of the Democratic Republic of the Congo (DRC).
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a 0.400-kg object undergoing shm has ax = -1.40 m/s2 when x = 0.400 m .
The time for one oscillation is approximately 3.44 seconds.
In simple harmonic motion (SHM), the period, T, is given by the formula:
T = [tex]2\pi \sqrt{(m/k)}[/tex]
where m is the mass of the object, k is the spring constant, and x is the displacement from equilibrium.
In this case, the mass of the object is given as 0.400kg and the acceleration at x = 0.400m is given as -1.40m/s². The spring constant can be found using the formula:
k = m × (a / x)
Plugging in the values, we get:
k = 0.400kg × (-1.40m/s²) / 0.400m = -1.40 N/m
Now that we have the value of k, we can use the formula for the period to find the time for one oscillation:
T = [tex]2\pi \sqrt{0.400kg / -1.40 N/m}[/tex] = [tex]2\pi \sqrt{(0.2857142857142857)}[/tex]
T = 2π × 0.5345224838248488
T = 3.4433442859
Therefore, the time for one oscillation is approximately 3.44 seconds.
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The complete question is:
A 0.400kg object undergoing SHM has ax = -1.40m/s² when x = 0.400m. What is the time for one oscillation?
What is the sound level of a sound whose intensity is 1.5×10^−6 W/m2? The intensity of the reference level required to determine the sound level is 1.0×10^−12 W/m2. Express your answer to two significant figures and include the appropriate units.
The sound level of a sound whose intensity is 1.5 × 10⁻⁶ W/m² is 66.99 dB.
What is the intensity of sound?Humans can hear sounds in such a wide range of intensities ( spans 13 orders of magnitude). The Threshold of Hearing is the level at which even the tiniest sound becomes heard.
We should develop a scale to quantify sound intensity that falls between 0 and 100 because it is challenging to develop an intuition for numbers in such a wide range. That is the decibel scale's intended use (dB).
(10dB)log₁₀ ( I / I₀)
I₀ = intensity at the threshold of hearing.
I = 1.5 × 10⁻⁶
I₀ = 1 × 10⁻¹²
(10dB)log₁₀ = 1.5 × 10⁻⁶ / 1 × 10⁻¹² = 66.99 dB.
Therefore, the sound level of a sound is 66.99 dB.
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You shove a chair across the room, causing it to go 663 cm. If you did 209 J of work, what amount force did you exert?
Force of magnitude 31.52 N was exerted on the chair.
What is force?
The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. A spring balance can be used to calculate the Force.
Work done: W = 209 J.
Displacement: d = 663 cm = 6.63 m.
Again, work done = force × displacement
Force = work done/ displacement
= 209 J / 6.63 m
= 31.52 N.
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radiation heat transfer is characterized by a) movement of discrete packets of energy as electromagnetic waves b) due to bulk fluid motion, there is a transport of energy c) there is the circulation of fluid by buoyancy effects d) thermal energy ...
The characteristics of radiation heat transfer are We are aware that the passage of distinct energy packets known as electromagnetic waves characterises radiation heat transfer.
Describe what radiation is.The definition of radiation was energy that emanates from the a source and moves at the rate of light through space. This energy has wave-like characteristics and is surrounded by an electric and magnetic field.
How does radiation work and is it dangerous?Cancer can develop as a result of radiation's mutagenic properties. Radiation either kills cells or alters their DNA, which impairs their capacity to procreate and may ultimately result in cancer. When radiation is prevalent, your body forms are exposed to high-energy particles.
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How long does it take a 100 w motor to do 10 kilojoules of work
The amount of time it will take a 100W motor to do 10kJ of work is 100seconds.
How to calculate power?Power in physics is a measure of the rate of doing work or transferring energy.
It is the rate of doing work, it is the work done in unit time. The SI unit of power is Watt (W) which is equivalent to joules per second (J/s).
This means that power can be calculated by dividing the work done on an object by time.
According to this question, a 100W motor has done 10kJ of work. The time taken can be calculated as follows:
10kJ = 10,000Joules
100W = 10,000J/t
100t = 10000
t = 100s
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James knows that when he walks, he takes about 120120 steps per minute and that each step is 2. 752. 75 feet long. Which calculation is most reasonable for james to use to find out his walking speed in miles per hour?.
James moves along at a pace of 3.75 miles per hour while walking.
We need to find the speed of James in miles per hour(mi/hr)
we know that 1 mile=5280 feet
James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.
i.e. he takes 7200 steps in 1 hour.
also each step of James=2.75 feet
total distance covered by James in 1 hour=2.75×7200 feet=19800 feet
19800 feet =19800/5280 = 3.75 miles.
hence speed of James= (distance covered by James in 1 hour) /1 hour speed of James=3.75 miles/hour.
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The complete question is
James knows that when he walks, he takes about 120 steps per minute and that each step is 2.75 feet long. which calculation is most reasonable for james to use to find out his walking speed in miles per hour?
How much work does a 70 kg student do when she runs up a 3,227 m hill?
Answer:
2,213,722 J
Explanation:
You want to know the work done by a 70 kg student running up a 3227 m hill.
WorkThe work is the product of force and distance. The force is the product of mass and acceleration.
W = F·d = m·g·d
W = (70 kg)(9.8 m/s²)(3227 m) = 2,213,722 J
The student does 2,213,722 joules of work.
__
Additional comment
1 kg·m²/s² = 1 J
We trust you can tell the difference between m representing mass, and m representing the unit meters. 'g' is the acceleration due to gravity. The value usually used in problems like this is 9.8. The accepted standard value is 9.80665. A value sometimes used when precision is not required is 10 m/s².
You pull horizontally on a 50-kg crate with a force of 250 N and the friction force on the crate is 100 N. The acceleration of the crate is
Answer:
F = M a Newton's Second Law
(250 -100) N = 50 kg a
a = 150 N / 50 kg = 3 m/s^2
Select the correct answer. when do sea breezes occur? a. daytime b. nighttime
c. both day and night d. at thermal equilibrium
The sea breezes occur during the day when land surfaces heats up faster than water surfaces.
The cooler air above the water is moving across the surface of the land to replace the rising heated air as it rises over the land is called sea breezes.
Sea breezes mostly occur during hot days i.e., summer time as there is unequal heating of land and water surfaces. The land surface get heat up first and during the day the land get heat up faster than water surfaces due to which there is high temperature and low pressure.
The winds always blows from the high pressure to low pressure or low temperature to high temperature i.e., from water to land surfaces durning day time and in night time it happens opposite the wind flows from land surfaces to water surfaces
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The sea breeze occurs during the daytime as the land masses heat up faster than water.
The breeze blowing towards the land from the sea is known as sea breeze.
Due to the differences in pressure, the air flows from high pressure areas over the sea to the low pressure areas on the land. In summer there is unequal heating of land and water masses. This results in the formation of sea breeze.
The winds always blows from the high pressure to low pressure or low temperature to high temperature i.e., from water to land surfaces durning day time and in night time it happens opposite the wind flows from land surfaces to water surfaces.
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What is the work required to stretch a spring with a spring constant k of 2500 n/m by 4. 00 cm?.
The work required to stretch the spring with k spring constant is about 2.0 Joules.
The Elastic Potential formula can be given as:
[tex]E_{p} = \frac{1}{2} kx^{2}[/tex]
The symbols can be explained as:
Ep = Elastic potential energy ( J )
k = Spring constant ( N/m )
x = Spring extension ( compression ) ( m )
Spring constant (k) is given as 2500 N/m
Extension (x) is given as 4.00 cm = 4.00 × 10⁻² m
Work required (w)=?
[tex]W=E_{p} \\W=\frac{1}{2} kx^{2} \\W=\frac{1}{2} X 2500 X (4.00 X 10^{-2})^{2} \\W=1250X (16.00X10^{-2}) \\W=20000X10^{-2} \\W=2J[/tex]
The work required to stretch the spring is about 2.0 Joules.
Work can be defined as measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.
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The work required to stretch a spring with a spring constant k of 2500 N/m by 4.00 cm is 2 J.
Given that,
Spring constant k = 2500 N/m
Extension of the spring x = 4 cm = 0.04 m
The work done to stretch the spring is given by the formula,
W = 1/2 × k x²
Putting the values in the above formula, we have,
W = 1/2 × 2500 × 0.04² = 2 J
Thus, the required work done to stretch a spring with a spring constant k of 2500 N/m by 4.00 cm is 2 J.
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The truss is made of three A-36 steel members, each having a cross-sectional area of 400 mm^2. Determine the horizontal displacement of the roller at C when P = 8 kN.
The horizontal displacement of the roller at C when P = 8 kN of a truss is made of three A-36 steel members, each having a cross-sectional area of 400 mm^2 is 0.0975 mm.
Given cross-sectional area of truss (A) = 400mm^2
P = 8kN
From the diagram we can see that the displacement of point C obtained from member AC is equivalent to the horizontal displacement of roller C.
Then Fca = 5.571kN
The distance between AC (L) = 0.8 + 0.6 = 1.4m
Modulus of Elasticity of Steel (E) = 200,000 MPa
The required horizontal displacement of the roller at C = d
d = Fca x L/A x E
d = (5.571∗1000∗1.40)/(400∗(10^−6)*(200)*(10^6) = 0.0975 mm
Hence the horizontal displacement of the roller at C is 0.0975mm.
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