1. In finding analytic solution of forced d.e's the IC's must always be evaluated after the expressions for the transient and steady state have been combined. (True)
2. The frequency at which at which sinusoidal forcing function causes the steady-state amplitude oscillations of a mass-spring-damper system to be maximum is the natural frequency. (False)
ABOUT SINUSOIDALSine waves or sinusoidal are mathematical functions which are in the form of smooth, repetitive oscillations. This function often appears in the sciences mathematics, physics, signal processing, and electrical engineering, and various other fields.
Sine waves are very important in physics because they retain their shape when added to another sine wave of the same frequency even though the phase is different. This wave is the only periodic function that has this property. This property makes these waves an important part of Fourier Analysis.
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finding expression in time An archer fires an arrow straight up into the air with a speed Vo = 14 m/s. Neglect air resistance. Write an expression for the time the arrow is in the air until it returns to launch height in terms of known quantities.
The time the arrow is in the air until it returns to launch height is given by the expression: t = sqrt(2h/g),
where h is the height of the launch point, and g is the acceleration due to gravity (9.8 m/s^2).
The time it takes for an object to reach the highest point in its trajectory, then return to its starting point, can be found using the following equation:
T = 2 * sqrt(h / g)
Where T is the time in seconds, h is the height the object reaches, and g is the acceleration due to gravity, which is 9.8 m/s^2 on Earth. The height reached by the object is given by the initial vertical velocity, Vo, multiplied by the time elapsed:
h = Vo * t - 0.5 * g * t^2
Where t is the time elapsed. We can use this equation to solve for t and substitute that value into our original equation for T to find the total time the arrow is in the air.
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A 4kg ball moving 8m/s to the right collides with a 2kg ball at rest. After the
collision, the 4kg ball moves with a new velocity of 4.8m/s to the right. Assuming
that the collision is elastic, how fast is the 2kg ball moving?
We can see that the new velocity of the 2 Kg ball is 6.4 m/s.
What is the momentum?Momentum is a measure of an object's motion. It is defined as the product of an object's mass and velocity. In physics, momentum is a vector quantity, meaning it has both magnitude and direction.
The law of conservation of momentum states that in an isolated system, the total momentum of the system remains constant if no external forces are acting upon it.
Given that we know that;
Momentum before collision = Momentum after collision
(4 * 8) + (2 * 0) = (4 * 4.8) + (2 * v)
Let v be the new velocity
32 = 19.2 + 2v
v = 32 - 19.2/2
v = 6.4 m/s
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the force shown on a force time diagram acts on a 3.7 kg object. find the impulse of the force
The impulse on the mass is equal to the area under the force -time graph. The area under the plot in the graph is 6 N.s thus the impulse is 6 Ns.
What is impulse ?Impulse of a moving object is its change in momentum. It is equal to the product of force and time. The force- time plot of a moving object can be used to determine the impulse.
From the given force- time graph, the area under the curve is :
area = area of the two triangles + area of the rectangle.
area of the triangle = 1/2 (2 N × 2s )= 2N s
area of the rectangle = 2 N × 1s = 2N s.
The second triangle have the area equal to the first one that is 2 N s.
then the total area of the curve = 2 Ns × 3 = 6 Ns.
Therefore, the impulse on the mass is 6 Ns.
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The spectrum of a continuous cool source located behind a hot cloud of gas will show group of answer choices O emission lines O absorption lines O emission and absorption lines O no spectral lines
The spectrum of a continuous cool source located behind a hot cloud of gas will show a combination of emission lines and absorption lines.
The emission lines will be from the continuous cool source, while the absorption lines will be from the hot cloud of gas. Absorption lines are dark lines in the spectrum caused by the hot gas absorbing light from the cool source. Emission lines are bright lines in the spectrum caused by the hot gas emitting light.
Emission lines are bright lines in the spectrum caused by the hot gas emitting light. They are produced when electrons in an atom or molecule make a transition from a higher energy state to a lower energy state, releasing energy as a photon of light that has a specific wavelength.
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A 5 N force is applied to a 3 kg ball to change its velocity from 9 m/s to 3 m/s. What is the change in momentum of the ball
The ball will experience an impulse of "18 kg.m/s."
How to find the calculation?As a vector, momentum points in the same direction as velocity (v). Since mass is a scalar, when velocity is in a direction that is opposed to the direction of motion, momentum will also be in that same direction.
Likewise, when velocity is in a direction that is positive, momentum will be in that same positive direction. The momentum unit in the SI is kg/m/s.
The answer to the query is
Force, F = 5 N
Mass, m = 3 kg Speed,
v1 is 9 m/s, while v2 is 3 m/s.
The fact is,
→ I = Δp
or,
→ I = mv² - mv 1
By changing the variables provided, we obtain
→ = 3 (3) - 3 (9)
→ = 9 - 27
→ = "18 kg.m/s.(Shows the reverse direction)
Therefore, the aforementioned strategy is appropriate.
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use the climber's tea problem to calculate the mass of butane (in g) needed to fuel the stove to heat the water for tea.
the mass of butane (in g)needed to fuel the stove to heat the water for tea. is 1.32g
Butane is a colorless gas with a little aroma of petroleum. It might smell so it can be transported. It is transported under its vapor pressure as a liquefied gas. Ingestion of the liquid can result in frostbite. It is quickly set ablaze. Its fumes weigh more than the air. Any leak could be a liquid or a vapor one. The canisters may violently burst and shoot into the air when exposed to fire or extreme heat for an extended period of time. It is employed in the manufacture of various compounds as well as as a fuel and an aerosol propellant.
The thermochemical equation for the combustion of butane is:
[tex]2C_4H_10(g) \:+13O_2\rightarrow8CO_2(g)\:+10H_2O(l)[/tex]
[tex]\delta H=[/tex]-5748 KJ [tex](mol)^-1[/tex]
So far, calculated the heat released by water as follows:
[tex]Q = m\times c\times \Delta v[/tex]= 0.724g x 4.18 x 43.2
Q = 130.7 (kJ)/(mol)
it can be seen that burning 1 mole of butane releases 5748 kJ of energy
( ΔH<0)
[tex]nbutane=\frac{130.9 kJ}{5748 kJ} =0.023 mol[/tex]
[tex]m_(butane)=0.023 mol \times 58.12 g (mol)^-1=1.32 g[/tex]
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A longitudinal wave moves energy that is to the direction of the wave’s movement.
A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. Since air molecules (the particles of the medium) are moving in a direction that is parallel toto the direction that the wave moves, the sound wave is referred to as a longitudinal wave.
The result of such longitudinal vibrations is a creation of compressions and rarefactions within the air.
A wave is a disturbance that propagates energy and momentum from one place to another without the transport of matter.
Based on direction of motion of particles there are two types of waves
1. Transverse waves
2. Longitudinal waves
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A longitudinal wave in which particles of the medium move in a direction of wave's movement. Explain
An amateur astronomer observes an asteroid that has an orbit with a semi-major axis of 6.3 AU. How long in Earth years will it take for the asteroid to orbit the Sun?
It will take approximately 11.86 Earth years for the asteroid to orbit the Sun.
What is amateur astronomer?Amateur astronomy is a fascinating hobby and can be an introduction to several practical and useful technologies.
The time it takes for the asteroid to orbit the Sun can be calculated using Kepler's Third Law: T^2 = 4 * π^2 * a^3 / G * M_Sun.
Where T is the orbital period in years, a is the semi-major axis in AU, G is the gravitational constant, and M_Sun is the mass of the Sun.
Plugging in values:
T^2 = 4 * π^2 * 6.3^3 / G * M_Sun
T = sqrt(4 * π^2 * 6.3^3 / G * M_Sun)
T ≈ 11.86 Earth years
Therefore, it will take approximately 11.86 Earth years for the asteroid to orbit the Sun.
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Three horizontal ropes pull on a large engine block, producing the vector forces A, B and
C as shown below. Find the magnitude and direction of a fourth force on the engine that
will make the vector sum of the forces equal zero.
Use the method of components to calculate the magnitude and represent the direction
in degrees from the positive x or from the negative x axis. Marks will be taken off if
you use other methods.
Σ Φ
= 0
Fand = P
P
sin a b
Cosa
B (80.0 N)
30.0°
X
30.0°
53.0⁰
(40.0 N)
A (100.0 N)
·x
The magnitude and direction of a fourth force on the engine that will make the vector sum of the forces equal zero is 193.1 N with direction is 57.7° counter-clockwise from the positive x axis.
What is magnitude?The magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind.
We find the x and y components of each force:
A = 100 N, θ = 53.0° => Ax = 100 N * cos (53.0°) = 70.7 N; Ay = 100 N * sin (53.0°) = 50.0 N
B = 40.0 N, θ = 30.0° => Bx = 40.0 N * cos (30.0°) = 34.0 N; By = 40.0 N * sin (30.0°) = 20.0 N
C = 80.0 N, θ = 30.0° => Cx = 80.0 N * cos (30.0°) = 68.0 N; Cy = 80.0 N * sin (30.0°) = 40.0 N
We will find the total x and y components:
Net x = Ax + Bx + Cx = 70.7 N + 34.0 N + 68.0 N = 172.7 N
Net y = Ay + By + Cy = 50.0 N + 20.0 N + 40.0 N = 110.0 N
Finally, let's find the magnitude and direction of the fourth force, P:
P = sqrt (Net x^2 + Net y^2) = sqrt (172.7 N^2 + 110.0 N^2) = 193.1 N
θ = tan^-1 (Net y / Net x) = tan^-1 (110.0 N / 172.7 N) = 57.7°
In conclusion, if the angle is negative, the direction is clockwise from the negative x axis. In this example, the angle is positive, so the direction is 57.7° counter-clockwise from the positive x axis.
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Think of four deformation or fracture failures that have actually occurred, either from your personal experience or from items that you have read about in newspapers, magazines, or books. Classify each according to a category in Fig. 1.1, and briefly explain the reason for your classification. Case 1; Case 2; Case 3; Case 4;
Deformation or fracture failures refer to the inability of a material to withstand applied stress and maintain its original shape or structure, leading to permanent deformation or complete breakage of the material.
Four Examples of Deformation/Fracture Failures:Case 1: The collapse of the I-35W Bridge in Minneapolis, Minnesota, in 2007—this falls under the category of brittle fracture as the bridge experienced a sudden and catastrophic failure without significant deformation beforehand. The cause of the failure was found to be due to design and construction errors that led to corrosion and fatigue in the steel components.
Case 2: The failure of the Deepwater Horizon oil rig in the Gulf of Mexico in 2010—this falls under the category of ductile fracture as the failure occurred due to the slow accumulation of damage from exposure to harsh conditions and corrosion. The investigation into the disaster found that the well casing had failed due to a combination of factors, including poor design, weak manufacturing, and a lack of proper maintenance.
Case 3: The failure of the Fu.kus.hima Daiichi nuclear power plant in Japan in 2011—this falls under the category of brittle fracture as the failure was due to a massive earthquake that caused the plant to lose power and the cooling systems to fail, leading to a catastrophic release of radioactive materials.
Case 4: The collapse of the Silver Bridge in Point Pleasant, West Virginia, in 1967. This falls under the category of fatigue fracture as the failure was caused by repeated load cycles over time that caused stress cracking in the eye bar components of the bridge.
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Find the dimensions [V] of volume. Express your answer as powers of length ( l), mass ( m), and time ( t).
Find the dimensions [v] of speed.
Express your answer as powers of length ( l), mass ( m), and time ( t).
Volume is calculated as Length times Width times Height. Volume Dimensional Formula: [M0 L3 T0] M3 is the SI unit of volume.
What does physics mean when it refers to volume?L3 dimension Volume has dimension L3, or length cubed, and is the product of three lengths. Speed has the L/T or LT-1 dimension of length over time. Dimension M/L3, also known as mass over length cubed, or ML-3, describes the volumetric mass density.
What are the three dimensions of volume?Volume is a three-dimensional quantity that accounts for a figure's total length, width, and height.
Is the volume formula Lxwxh?that the dimensions of a rectangular prism are length, width, and height!
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the variation of pressure with density in a thick gas layer is given by P=CP^n, where C and n are constants. noting that the pressure change across a differential fluid layer of thickness dz in the vertical z-direction is given as dp , obtain a relation for pressure as a function of elevation z. take the pressure and density at z. Take the pressure and density at z=0 to be P0 and p0 respectively.
The relation for pressure as a function of elevation z can be obtained by integrating the given equation: P=CP^n.
The hydrostatic equationdp = (nC/p^(n-1))dz
P(z) = P0 + (nC/p0^(n-1)) z
We can rewrite this equation as dP/P^n=C*dz.Integrating this equation with respect to z, we obtain P=P0*(1+C*z)^(1/n), where P0 and p0 are the pressure and density at z=0, respectively.This relation is called the hydrostatic equation. The hydrostatic equation describes the variation of pressure with elevation by considering the pressure change across a differential fluid layer of thickness dz in the vertical z-direction.Thus, it links the pressure at any point to the pressure at the base of the fluid layer, which is given by P0.Furthermore, the equation takes into account the variation of pressure with density, which is given by P=CP^n.The relation for pressure as a function of elevation z is given as:P(z) = P0 * (p0/P0)^(z/M)where M = (1/n) * (C/g)^(1/n-1) and g is the gravitational acceleration.This relation is called the barometric formula. It states that the pressure of a gas layer decreases exponentially as the elevation increases, with a rate of decrease determined by the constants C and n. This relation is useful for calculating the pressure at different elevations in a gas layer, such as in the atmosphere.To learn more about the hydrostatic equation refer to:
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a cat slides down a rubber rod and falls from the rod into a metal pail a resting on a non-conducting shelf with two other metal pails, b and c, which are in contact, but neither is in contact with a. the shelf breaks when the cat lands in a, transferring charge to a, and all pails fall separated to the non-conducting floor. the cat then runs away.
In this scenario, the cat sliding down the rubber rod and falling into metal pail "a" caused the transfer of charge to pail "a". This transfer of charge caused pail "a" to become charged and the metal pails "b" and "c" that were in contact with it, were also charged by induction.
When the shelf broke, the metal pails fell separated to the non-conducting floor, resulting in the charge being separated and no longer being able to move from one metal pail to another.
After the cat ran away, the charged metal pails likely remained charged, as there was no conductor available for the charge to flow through and neutralize.
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PLEAS HELPPP ITS FOR A FORENSIC SCIENCE CLASS
USE COMPLETE SENTENCES PLEAS
The picture is the crime scene that you will use for the questions there are 1-9 questions and you have to draw out the picture in a peace of paper and DRAW the lines of convergence and area of convergence for question 2 you will also for question 2 For question 2 Do it in order for the question where the person got shot put it by which death is quicker
Directions: In this exam you will be asked to analyze a crime scene and describe what the blood spatter can tell us.
USE COMPLETE SENTENCES AND PROPER SPELLINGS. (You have autocorrect, please use it) blood
The scene:
You enter the scene and find 2 bodies. One has been shot in the head. The other has been shot in the chest and has blood coming from their mouth and nose.
Questions
1) Which man was shot in the head, and which was shot in the chest. Use evidence from the scene to back up your claim. (1pt)
2) Find the area of convergence for both gunshot sites. (2pts)
3) How would you find the angle that the blood impacted the ground? (1pt)
4) How would you explain the bright red smaller spatter? (1pt)
5) How would you explain the small circular drops in-between position 2 and man #2? What does this tell us? (1pt)
6) Why are there large pools of blood below both men’s bodies? (1pt)
7) How do you explain the 1 large droplet going in the opposite direction of the other 4 large droplets in position 2? (1pt)
8) What are the smaller secondary droplets around primary droplets called? (1pt)
9) Who shot first? (1pt)
1) The man who was shot in the head was shot at a closer range than the man who was shot in the chest, as evidenced by the large pool of blood around his body. The man shot in the chest was shot at a slightly further range, as evidenced by the smaller pools of blood around him.
2) The area of convergence for both gunshot sites can be found by drawing a line from the center of each pool of blood and extending it into the room. The point where the two lines meet is the area of convergence.
3) The angle that the blood impacted the ground can be determined by measuring the angle between the direction of the droplets and the ground.
4) The bright red smaller spatter is caused by the presence of high velocity blood droplets, which are propelled at a high velocity when the bullet impacts the body.
5) The small circular drops in-between position 2 and man #2 are likely caused by a back spatter, which is a phenomenon where blood is propelled in the opposite direction of the force that caused it. This could mean that the man in position 2 was shot first.
6) There are large pools of blood below both men’s bodies because they were both shot at a close range, which caused a large amount of blood to be expelled from their bodies.
7) The large droplet going in the opposite direction of the other 4 large droplets in position 2 is likely caused by a back spatter, which is a phenomenon where blood is propelled in the opposite direction of the force that caused it. This could mean that the man in position 2 was shot first.
8) The smaller secondary droplets around primary droplets are called satellite droplets.
9) It is not possible to tell who shot first based on the evidence provided.
An astronaut who weights 700 N on the surface of the earth lifts off from planet Zuton in a space ship. The free-fall acceleration on Zuton is 3 m/s². At the moment of lift off the space ship experiences an acceleration of 5 m/s². The acceleration of gravity is 10 m/s². What is the magnitude of the force that the space ship exerts on the astronaut?
Answer:
Explanation:
The magnitude of the force that the space ship exerts on the astronaut is 1300 N.
This can be calculated by using the formula: force = mass x acceleration.
The astronaut's mass is 700 N / 10 m/s² = 70 kg
The acceleration of the ship is 5 m/s².
So the force on the astronaut is 70 kg x 5 m/s² = 350 N.
Additionally, the astronaut also experiences the force of gravity on Zuton, which is 700 N - (70 kg x 3 m/s²) = 630 N.
So the total force on the astronaut is 630 N + 350 N = 980 N.
1. What were enron failure issue ? What were corporate Governance isues in Enron.
The Enron scandal drew attention to accounting and corporate fraud as its shareholders lost $74 billion in the four years leading up to its bankruptcy, and its employees lost billions in pension benefits.
What were Enron failure issue ?Enron's Board of Directors failed to fulfil its fiduciary duties towards the corporation's shareholders. Secondly, the top executives of Enron were greedy and acted in their own self-interest.
Enron's downfall was attributed to its reckless use of derivatives and special purpose entities. By hedging its risks with special purpose entities which it owned, Enron retained the risks associated with the transactions. This arrangement had Enron implementing hedges with itself.
Enron raised fundamental issues about corporate fraud, accounting transparency, and investor protection.
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the latitude (l) and the average temperatures in february (t) in degrees celsius ( ) of 10 world cities were measured. the calculated least squares linear regression model for this data was: a. the slope is -0.713 which interprets [ select ] . b. the relationship between latitude (l) and the average temperatures (t) of these 10 world cities is [ select ] . this means [ select ] . c. if in fact the average temperature (t) for these 10 world cities is 10 degrees celsius ( ) for a latitude of 40, the residual is [ select ] which means we have [ select ] .
According to the statement, on latitude (l) and mean temperatures in February, the least squares linear regression model calculated for these data was:
a. the slope is -0.713 which interprets that for every increase in one degree of latitude, the average temperature decreases by 0.713 degrees. b. the relationship between latitude (l) and the average temperatures (t) of these 10 world cities is negative. This means that as latitude increases, average temperature decreases. c. If in fact the average temperature (t) for these 10 world cities is 10 degrees celsius ( ) for a latitude of 40, the residual is -3.713 which means we have an error of 3.713 degrees.Learn more about temperatures:
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A physicist at a fireworks display times the lag between seeing an explosion and hearing its sound, and finds it to be 0.600 s. (Enter your answers to at least four decimal places. Use the following relationship between Kelvin and Celsius: T(K) = T(°C) + 273.15.) (a) How far away (in m) is the explosion if air temperature is 15.0°C and if you neglect the time taken for light to reach the physicist? ___m (b) Calculate the distance to the explosion (in m) taking the speed of light into account. Note that this distance is negligibly greater. ___m
The distance to the explosion (in m) taking the speed of light into account is 203.5 meters. and the distance to the explosion (in m) taking the speed of light into account is 203.4 meters.
Given data
Times lag between seeing an explosion and hearing its sound = 0.60 s.
Air temperature = 15.0 °C
Velocity = 331 [tex]\sqrt{1.05}[/tex] = 339.1 m/sec
What is the distance of the explosion?
We know that speed can be written as,
339.1 = Distance / 0.60
Distance = 203.5 m
Thus, the distance of the explosion is 203.5 m.
Here , speed of the sound, v = 339.1 m/sec
speed of the light, c = 3 x [tex]10^{8}[/tex] m/s
We know that the lag between seeing an explosion and hearing its sound is 0.600 s. therefore,
s = 203.4 meter
Hence, the distance to the explosion (in m) taking the speed of light into account is 203.4 meters.
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550 Hz sound is emitted from a megaphone into symmetrical tubes of one top path and one bottom path. The top and bottom paths are initially identical, but the top path can be lengthened. a. Why is the interference initially constructive? b. How far do you have to raise the top part of the tube to achieve destructive interference in m?
Initially the sound waves are in phase and they overlap to form the constructive interference pattern. The length that we have to raise the top part will be equal to the wavelength of the waves in meter.
What is interference ?A wave of greater, lower, or the same amplitude is created when two waves merge through interference by combining their displacements at all points in space and time.
The interaction of waves that are coherent or correlated with one another, either because they originate from the same source or because their frequencies are similar or almost identical, leads to both constructive and destructive interference.
All sorts of waves, including light, radio, acoustic, surface water waves, gravity waves, and matter waves, can exhibit interference effects. In constructive interference, the waves are in single phase forms a resultant wave with higher amplitude.
When waves from in phase phase meets, the resultant wave will have an amplitude less than the individual amplitudes. Here
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based on the above equation, how many moles of o2 are needed to produce 18 moles of water and 30 moles of carbon dioxide?
30 moles of oxygen are needed to produce 18 moles of water and 30 moles of carbon dioxide.
The balanced chemical equation for the reaction between water and carbon dioxide to form glucose and oxygen can be written as:
C₆H₁₂O₆ + 6O₂ -> 6CO₂ + 6H₂O
From the equation, it is clear that for every mole of glucose, 6 moles of oxygen are needed. We can use this information to determine the number of moles of oxygen required to produce 18 moles of water and 30 moles of carbon dioxide.
First, we need to find the number of moles of glucose produced, which can be calculated by dividing the number of moles of carbon dioxide produced by 6:
30 moles CO₂ / 6 = 5 moles glucose
Since 6 moles of oxygen are needed for every mole of glucose, we can now calculate the number of moles of oxygen required:
5 moles glucose x 6 moles O₂/mole glucose = 30 moles O₂
So, 30 moles of oxygen are needed to produce 18 moles of water and 30 moles of carbon dioxide.
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Determine the direction of the force on each charge. Enter your answers numerically separated by commas_ AZd 01, 02 , 03, 04 ________ counterclockwise from the +x axis
The direction of the force on a charge due to an electric field depends on the sign of the charge and the direction of the electric field. The direction of the electric field is determined by the direction of the gradient of the electric potential.
In general, the direction of the electric field can be found using Coulomb's law, which states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The direction of the force is given by the direction of the vector connecting the two charges.
Given the information provided in the prompt, it is not possible to determine the direction of the force on each charge without additional information. Please provide more details.
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all access doors to interior transmitting stations for radio equipment shall be provided with ? , which disconnect all voltages above 350 volts when the door is opened.
Equipment for radio and television – Article 810. For five different system kinds, Article 800 lists general requirements.
Which chapter 8 section details the specifications for radio and television gear? Six articles, including those on radio and television equipment [810], network-powered broadband [830], and premises-powered broadband [840], are included in Chapter 8 of the National Electrical Code (NEC) that deal with communications systems.For five different system kinds, Article 800 lists general requirements.There must be a minimum voltage rating of 300 volts for communication wires and cables.A coaxial cable's individual conductors' insulation, excluding the outside conductor, must be rated for a minimum of 300 volts.If communication cables are not marked with a tag for future use or terminated at both ends with a connector or other device, they will be regarded as abandoned.To learn more about television equipment refer
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. explain why the smell of smoke when you are sitting at a campfire does not trigger alarm, but the smell of smoke in your residence hall does.
Our sense of smell can adapt or become habituated to familiar and continuous stimuli, like the scent of smoke at a campfire.
The different reactions to the smell of smoke in these two situations are due to context and prior associations. When sitting at a campfire, the scent of smoke is typically associated with a positive and relaxing experience, while in a residence hall, the scent of smoke is more likely to be associated with a potential fire or danger.
The brain processes these different associations and can trigger a different response, such as an alarm or heightened state of alertness in response to smoke in a residence hall.
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a 550 g squirrel with a surface area of 860 cm2 falls from a 4.8-m tree to the ground. estimate its terminal velocity. (use the drag coefficient for a horizontal skydiver. assume that the squirrel can be approximated as a rectanglar prism with cross-sectional area of width 11.1 cm and length 22.2 cm. note, the squirrel may not reach terminal velocity by the time it hits the ground. give the squirrel's terminal velocity, not it's velocity as it hits the ground.)
The terminal velocity of the squirrel is approximately 29.5 m/s.
The terminal velocity of an object can be calculated using the equation:
[tex]V_t = \sqrt{(2mg / (C_d \times A \times p))[/tex]
where V_t is the terminal velocity,
m is the mass of the object (550 g = 0.550 kg),
g is the acceleration due to gravity ([tex]9.8 m/s^2[/tex]),
[tex]C_d[/tex] is the drag coefficient for a horizontal skydiver (approximately 0.75),
A is the surface area of the object, and p is the density of air (approximately 1.225 kg/m^3 at sea level).
Since the squirrel can be approximated as a rectangular prism with a cross-sectional area of width 11.1 cm and length 22.2 cm,
We can calculate A as follows:
A = [tex]2 \times (11.1 cm) \times (22.2 cm)[/tex]
= [tex]484 cm^2[/tex]
Converting the surface area to square meters:
A = [tex]484 cm^2 \times (10^-4 m^2/cm^2)[/tex]
= [tex]0.0484 m^2[/tex]
Finally, calculate the terminal velocity:
[tex]V_t = \sqrt((2 \times 0.550 kg \times 9.8 m/s^2) / (0.75 \times 0.0484 m^2 \times 1.225 kg/m^3))[/tex]
= 29.5 m/s
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A car is travelling in a straight line and has its velocity uniformly reduced from 20 m * s ^ - 1 to 12m * s ^ - 1 in a distance of 80 m. The car the travels at the lower velocity for 1 minute, and then decelerates uniformly to rest in a further 12 sec. show the whole journey on a velocity-time graph and calculate
(i) the initial deceleration and the time taken to travel 80 m.
(ii) the final deceleration
(iii) the total displacement for the whole journey
i) The initial deceleration of the car is -1.6 m/s² and the time taken is 5 seconds
ii) The final deceleration is -1 m/s²
iii) The total dispalcement = 1016 m
What is the initial deceleration of the car?The initial deceleration of the car is given by the formula below:
v² = u² + 2as
where;
v is the initial velocityu is the final velocitya is acceleration/decelerations is the displacementSolving for a;
12² = 20² + 2 * a * 80
a = -1.6 m/s²
Time taken, t = v - u / a
t = 12 - 20 / (-1.6)
t = 5 seconds
Final deceleration:
a = v - u / t
a = 0 - 12 / 12
a = -1 m/s²
iii) Displacement at constant velocity = 12 * 1 * 60
Displacement at constant velocity = 720 m
Final displacement, s = ut + 0.5at²
s = 12 * 12 + 0.5 * 1 * 12²
s = 216 m
Total dispalcement = 80 + 720 + 216
Total dispalcement = 1016 m
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acceleration is the change in velocity over some period of time. this can be represented mathematically as blank . multiple choice question. a
Acceleration is the change in velocity over some period of time. this can be represented mathematically as, a = Δv/t (acceleration= change in velocity/time). Thus, option A is correct.
What is Acceleration?In mechanics, acceleration refers to the rate at which an object's veolcity with respect to time changes. The vector quantity of accelerations (in that they have magnitude and direction). The acceleration of an object is determined by the direction of the net force acting on it. Newton's Second Law states that two factors working in concert determine how much an object accelerates:
According to the materials used to make the object, the mass of the object is either directly proportional to the mass or inversely proportional to the magnitude of the net balance of all external forces acting on that object.
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Complete question:
Acceleration is the change in velocity over some period of time. This can be represented mathematically as ______.
a. a = Δv/t
b. [tex]a_{n}=a_{1}+(n-1)d[/tex]
c. [tex]ax^2+bx+c=0[/tex]
vector A is added to vector B, which has a magnitude of 5.0, the vector representing their sum is perpendicular to A and has a magnitude that is twice that of A. What is the magnitude of A?
Answer:
Below
Explanation:
5 will be the hypotenuse of a right triangle with A and 2A as legs
pythagorean theorem
5^2 = A^2 + (2A)^2
25 = 5A^2
A^2 = 5
A = sqrt 5
Metamorphism occurs when a rock ________.
a. experiences conditions that include high pressures
b. experiences conditions that include high temperatures
c. experiences conditions that are similar to those that formed the rock
d. experiences conditions that are significantly different from those that formed the rock
Metamorphism occurs when rocks experience conditions significantly different from those under which they were formed.
Metamorphism is the process by which existing rocks are transformed into new forms by temperature, pressure, and chemically active fluids. There are three types of metamorphism: contact metamorphism, regional metamorphism, and dynamic metamorphism. Contact metamorphism occurs when magma comes into contact with existing rock masses. When this happens, the temperature of the existing rock increases and liquids from the magma seeps in. The word metamorphosis is of Greek origin and means "change of shape". Metamorphic rocks are derived from igneous or sedimentary rocks that have changed shape (recrystallized) due to changes in the physical environment.
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A person stands on a scale in a elevator at rest. The scale reads 900N. 1) what is the persons mass 2) the elevator accelerates up at 2.5m/s^2. What does the scale read now ? 3)The elevator then continues to move upwards with a steady speed of 4m/s for 5 seconds. What does the scale read during this period 4)the elevator now decelerates at 1.8m/s^2 until it reaches zero velocity. What does the scale read during this period[/B]
1. Mass of the person is 91.84 kg
2. The scale reads 917.4 N
3. The scale reads 917.4 N
4. The scale reads 905 N
Since the gravity acceleration (g) is not stated, assume it is 9.8 m/s^2
1. To calculate their mass, the formula m = F/g (where m is mass, F is weight (or force), and g is the acceleration due to gravity) would need to be used with the known weight and acceleration due to gravity (9.8 m/s^2). So, m = 900 N / 9.8 m/s^2 = 91.84 kg.
2. When the elevator accelerates upward at 2.5 m/s^2, the scale reading will increase. This is because the apparent weight of the person will be greater than their actual weight due to the upward acceleration of the elevator. The formula for apparent weight is Fapparent = m * g + ma (where m is mass, g is the acceleration due to gravity, and a is the acceleration of the elevator). So, Fapparent = 91.84 kg * 9.8 m/s^2 + 91.84 kg * 2.5 m/s^2 = 917.42 N.
3. During the steady speed of 4m/s, the scale will still read 917.42 N because the apparent weight does not change with constant velocity.
4. When the elevator decelerates at 1.8 m/s^2, the scale reading will decrease. The apparent weight will be less than the person's actual weight due to the downward acceleration of the elevator. The formula for apparent weight will be the same as in step 2, using the negative value of the deceleration of the elevator. So, Fapparent = 91.84 kg * 9.8 m/s^2 - 91.84 kg * 1.8 m/s^2 = 905.00 N.
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A ball is thrown upwards. Its acceleration is: A. upward during both ascent and descent B. upward during ascent and downward during descent C. downward during both ascent and descent D. downward during ascent and upward during descent E. downward at all times except at the very top, when it is zero
A ball is thrown upwards. Its acceleration is: C. downward during both ascent and descent
What is vertical launch upwards?In physics vertical launch upwards is the motion described by an object that has been launched vertically upwards in which the height and the effect of the earth's gravitational force on the launched object are taken into account.
In the vertical launch upwards movements, the acceleration due to the gravity is always acting downward, this is because of attraction that the earth exerts on all bodies pulling them toward its center
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