The time interval during which the speed of the wheel is increasing is 4 s.
What is angular acceleration?Angular acceleration is the term used to describe the temporal pace at which angular velocity varies. Radians per square second is used as the measurement unit.
At time t = 0, the angular velocity is ω₁ = - 6.00 rad/s.
At time t = 10.0 s, the angular velocity is ω₂ = +4.00 rad/s.
Angular acceleration of the wheel can be written as= change in angular velocity /time interval
= ( 4.00 - (-6.00))/10 rad/s²
= 1.0 rad/s²
Hence, angular velocity becomes zero at time = ( 0 - ( -6))/1.0 s = 6 s.
So, during t = 0 to t = 6s, the clockwise angular velocity of the wheel decreases from 6.00 rad/s to 0.00 rad/s and during t = 6s to t = 10s , the counterclockwise angular velocity of the wheel increases from 0.00 rad/s to +4.00 rad/s.
Hence, the time interval during which the speed of the wheel is increasing is = 10 s - 6 s = 4 s.
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What type of mirror can produce both
converging and diverging rays?
Answer:
A convex mirror is a diverging mirror (f is negative) and forms only one type of image. It is a case 3 image—one that is upright and smaller than the object, just as for diverging lenses.
Explanation:
hope this helps have a good night :)
Concave mirror can produce both converging and diverging rays.
What is concave mirror?A hollow spherical can be made into a mirror by cutting it into pieces, painting the exterior surface, and using the interior surface as the reflecting surface. Concave mirrors are this kind of mirror.
When object is placed inside focal length, convex mirror diverges the light beams and produces virtual image.
When object is placed outside focal length, convex mirror converges the light beams and produces real and diminish image.
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What are possible formulas for impulse? Check all that apply.
Answer:
J = FΔt
J = mΔv
J = Δp
Explanation:
The Impulse Formula:Δp = Change in momentumF = Applied forceΔt = Elapsed timeThe principle of cross-cutting relationships states that certain features, such as faults, are than the rock layers they cut through. These features are breaks in Earth’s surface where rock has moved sideways, upward, or downward. formations are made of molten rock that has cooled. Those on Earth’s surface are called . Those beneath Earth’s surface are called .
In an RC parallel circuit, Et = 480 V, R = 50ko, and XC = 47 ko. What is the reactive power?
Correct question is;
In an RC parallel circuit, Et = 480 V, R = 50kΩ, and XC = 47 kΩ. What is the reactive power?
Answer:
P_r = 4.9 VARs
Explanation:
We are given;
Total voltage: Et = 480 V
Resistance; R = 50kΩ = 50000 Ω
Capacitive reactance; XC = 47 kΩ = 47000 Ω
Formula for current across the capacitor is;
Et = I_c • XC
I_c = Et/XC
l_c = 480/47000
I_c = 0.01021 A
Formula for reactive power is;
P_r = (I_c)² × XC
P_r = 0.01021² × 47000
P_r = 4.9 VARs
re testing a new amusement park roller coaster with an empty car with a mass of 100 kg. One part of the track is a vertical loop with a radius of 12.0 m. At the bottom of the loop (point A) the car has a speed of 25.0 m/s and at the top of the loop (point B) it has speed of 8.00 m/s . You may want to review (Pages 203 - 212) . For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of A vertical circle with friction. Part A As the car rolls from point A to point B, how much work is done by friction?
Answer:
-4530 J
Explanation:
Given that
Mass of the car, m = 100 kg
Speed of the car at point A, v1 = 25 m/s
Speed at point B, v2 = 8 m/s
Radius of the track, r = 12 m and with respect to the origin of the center of the track, we say that y1 = -12 at point A and y2 = 12 at point B
We also know that
W(total) = W(grav) + W(other) = K₂ - K₁
Work done by the gravitational force, W(grav) = -U(grav) = mgy1 - mgy2
Kinetic Energy, K = ½mv²
Adding all together, we have
½mv₁² + mgy1 + W(other) = ½mv₂² + mgy2
½ * 100 * 25² + 100 * 9.8 * -12 + W = ½ * 100 * 8² + 100 * 9.8 * 12
50 * 625 + 980 * -12 + W = 50 * 64 + 980 * 12
31250 - 11760 + W = 3200 + 11760
19490 + W = 14960
W = 14960 - 19490
W = -4530 J
A 3.0 x 10^3 kg truck travels through a curve with a radius of 150 m at 113 km/hr. If the curve is flat, what is the coefficient of friction required to keep the vehicle from skidding off the road? In a real-world situation, would the truck remain on the road?
Answer:
from what i could figure out. A 6600 pound truck traveling at 113 km/ hr will need to have 58.4070965 psi. on each wheel. if going going on a curve that have an incline of atleast 2.℅ , which is close to the average curvature of a road. But at that speed and flat angle of the road. and distance . Once the truck is in itsvturn the truck will loose 1/4 of the tires psi, adding the weight , ofvtge truck and the ineshia of the tryck as it leans to one side . The truck will not be able to with stand the force on its tires and slide to the side and roll the tryck as it slide off the road dropping atleast 1-2 inch drop off the pavement.
What is the economic term for the act of sacrificing one good or service to purchase or produce another?
Answer:
Trade-off. sacrificing one good or service to purchase or produce another.What are the things being compared in the following argument?
"The United Nations failed to intervene in Bosnia to prevent massive human rights violations and ethnic cleansing. It also failed to act to stop the murders of close to a million innocent people in Rwanda. THe UN will not intervene to stop any widespread slaughter of innocents in Nigeria."
a.
Ethnic cleansing in Nigeria and Bosnia
b.
The slaughter of innocents by the UN
c.
situations in which the United Nations might intervene
d.
Human rights violations in Rwanda and Bosnia
Answer:
C
Explanation:
The thing that is being compared in the given argument is Ethnic cleansing in Bosnia. The correct option is A.
What is Ethnic cleansing?Ethnic cleansing is the systematic removal of ethnic, racial, and religious groups from a given area with the goal of ethnically homogenizing the region.
In this group of resettled Bosnian refugees, ethnic cleansing has resulted in high rates of PTSD and depression, as well as other forms of psychological morbidity.
The long-term consequences of ethnic cleansing as a form of mass psychological trauma have yet to be studied.
Political elites seek to gain and/or consolidate political power by capitalizing on nationalism and the desire to create the domestic "other" in order to foster solidarity among the dominant nationality.
The topic under discussion in this argument is ethnic cleansing in Bosnia.
Thus, the correct option is A.
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4. What is the mass of the block
of iron illustrated below?
Ty in advance
What happens when a population exceeds its carrying capacity?
Answer:
If a population exceeds carrying capacity, the ecosystem may become unsuitable for the species to survive. If the population exceeds the carrying capacity for a long period of time, resources may be completely depleted.
A sled plus passenger with total mass m = 53.1 kg is pulled a distance d = 25.3 m across a horizontal, snow-packed surface for which the coefficient of kinetic friction with the sled is μk = 0.155. The pulling force is constant and makes an angle of φ = 28.3 degrees above horizontal. The sled moves at constant velocity.
Required:
a. Write an expression for the work done by the pulling force in terms of m, g (acceleration due to gravity), φ, μk, and d.
b. What is the work done by the pulling force, in joules?
c. Write an expression for the work done on the sled by friction in terms of m, g (acceleration due to gravity), φ, μk, and d.
d. What is the work done on the sled by friction, in joules?
Answer:
Explanation:
Force of friction
F = μ mg
μ is coefficient of friction , m is mass and g is acceleration due to gravity .
If f be the force applied to pull the sled , the horizontal component of force should be equal to frictional force
The vertical component of applied force will reduce the normal force or reaction force from the ground
Reaction force R = mg - f sin28.3
frictional force = μ R where μ is coefficient of friction
frictional force = μ x (mg - f sin28.3 )
This force should be equal to horizontal component of f
μ x (mg - f sin28.3 ) = f cos 28.3
μ x mg = f μsin28.3 + f cos 28.3
f = μ x mg / (μsin28.3 + cos 28.3 )
a )
work done by pulling force = force x displacement
f cos28.3 x d
μ x mg d cos28.3 / (μsin28.3 + cos 28.3 )
b ) Putting the given values
= .155 x 53.1 x 9.8 x 25.3 cos28.3 / ( .155 x sin28.3 + cos 28.3 )
= 1796.76 / (.073 + .88 )
= 1885.37 J
c )
Work done by frictional force
= frictional force x displacement
= - μ x (mg - f sin28.3 ) x d
= - μ x mgd + f μsin28.3 x d
= - μ x mgd + μsin28.3 x d x μ x mg / (μsin28.3 + cos 28.3 )
d )
Putting the values in the equation above
- .155 x 53.1 x 9.8 x 25.3 +
.155 x .474 x 25.3 x .155 x 53.1 x 9.8 /( .155 x .474 + .88)
= -2040.67 + 149.92 / .95347
= -2040.67 + 157.23
= -1883.44 J .
find the total electric field along the line of two of the two charges shown in figure at the point midway between them
these 14 PLEse thanks
The spaces labeled 1 through 14 in the diagram using the following terms are:
mantlelithospheric platerift valleyocean floormidocean ridgemountain rangepartially molten rock becomes new ocean floortrenchocean floorlithospheric platecontinentold ocean floor becomes partially molten rocklithospheric plate "conveyer belts"What are plate tectonics?Plate tectonics is the scientific theory that explains the large-scale motions of Earth's lithosphere (the outermost layer of the Earth) and the processes that cause these motions. The lithosphere is divided into a number of large plates that move relative to each other over the asthenosphere, the more plastic, ductile, and weaker layer below the lithosphere.
Plate tectonics explains a variety of geologic phenomena, including the formation of mountains, earthquakes, volcanoes, and the distribution of continents and oceans. According to this theory, the lithospheric plates move due to the motions of convection cells in the Earth's mantle, which is the layer below the asthenosphere.
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what is the process that creates wind.
Answer:
Winds are caused by differences in air pressure. Unequal heating of Earth’s surface creates areas of different pressure. Cooler areas have higher air pressure. Warmer areas have lower pressure. This causes air to move from high pressure to low pressure. This movement is the wind we feel.
plz mark me as brainliest.
The diagram shows a ball resting at the top of a hill. A ball is at the top of a slope at point X. The bottom of the slope is point Y. Which statement best describes the energy in this system? The potential energy in the system is greatest at X. The kinetic energy in the system is greatest at X. Total energy in the system decreases as the ball moves from X to Y.
The statement that best describes the energy in this system is: The potential energy in the system is greatest at X.
When the ball is at the top of the hill at point X, it has the greatest potential energy in the system. Potential energy is the energy an object has due to its position or configuration in a system. In this case, the ball has the potential to roll down the slope and gain kinetic energy, which is the energy of motion.
As the ball rolls down the slope from point X to point Y, it loses potential energy due to its decreasing height above the ground. However, as it gains speed and motion, it gains kinetic energy. Therefore, the statement "total energy in the system decreases as the ball moves from X to Y" is not accurate.
At the bottom of the slope at point Y, the ball has the least potential energy and the most kinetic energy. Once the ball reaches the bottom of the slope, it will have converted all of its potential energy into kinetic energy.
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Give reason why relative density of a substance remains the same in both SI and CGS unit
Answer:As relative density is the ratio of similar quantities, it has no unit.So RD remains the same in both CGS and SI unit
Explanation: i did the test
An organism is prokaryotic, unicellular, and autotrophic, and it also causes disease. Which kingdom does it belong in
pls answr
Answer:
Eubacteria Kingdom :)
Explanation:
Answer: eubacteria
Explanation:
Part C Now, grab Tracker’s protractor tool (the green angle in the video frame) and measure the angle of incidence and the angle of refraction for the frame numbers specified in the table below. Hints: To advance the video a frame at a time, use the step buttons on the right. Position the vertex of the protractor exactly at the origin of the coordinate axis. Move the arms of the protractor so that one arm is on the vertical axis (above or below, as appropriate) and the other on the light ray.
In order to measure the angle of incidence and the angle of refraction using Tracker's protractor tool (the green angle in the video frame), the following steps should be followed:
Step 1: Open the video in Tracker software.
Step 2: Click on the "Measure" button on the toolbar at the top of the software.
Step 3: From the dropdown menu, select "Angle".
Step 4: Click on the "protractor tool" icon (the green angle in the video frame).
Step 5: Position the vertex of the protractor exactly at the origin of the coordinate axis and move the arms of the protractor so that one arm is on the vertical axis (above or below, as appropriate) and the other on the light ray.
Step 6: Measure the angle of incidence and the angle of refraction for the frame numbers specified in the table below by using the step buttons on the right to advance the video a frame at a time.
Step 7: Record the measured angles in the table below. Note that the angle of incidence should be measured on the incident ray (the ray that is coming from the left), and the angle of refraction should be measured on the refracted ray (the ray that is coming from the right).In conclusion, by following these steps, one can measure the angle of incidence and the angle of refraction using Tracker's protractor tool.
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How does a real image differ from a virtual image?
Answers:
A real image is always upright and never inverted.
A real image is formed by extending the rays back to where they appear to come from.
A virtual image is always smaller than the object.
Light rays actually pass through a real image.
Answer:
Real images are obtained using a converging lens or a concave mirror. The size of the real image depends upon the placement of the object. A virtual image is an upright image that is achieved where the rays seem to diverge. A virtual image is produced with the help of a diverging lens or a convex mirror.
Answer:
Light rays actually pass through a real image.
Explanation:
Option C is somehow correct but the hurdle is that it's only for convex mirror
The concave mirror always produce a virtual image larger than object
So option D is correct
What does a horizonal line mean in each graph?
Answer: A straight line on the coordinate plane where all points on the line have the same y-coordinate.
Explanation: The purpule iine is the horizontal line:
Discuss the multiple ways in which intellect and aging are related
Factors such as Cognitive function, Wisdom & experience,genetics, lifestyle choices, education, etc play a role in determining how aging affects intellect.
Intellect and aging are related in multiple ways. Here are some key aspects to consider:
Cognitive Function: As individuals age, there is a general decline in cognitive function, including memory, processing speed, and problem-solving abilities. This decline can affect intellectual performance, such as reasoning and decision-making skills.
Wisdom and Experience: Despite the cognitive decline associated with aging, older adults often possess a wealth of knowledge and experience accumulated over their lifetime. This experiential wisdom can compensate for certain cognitive deficits and contribute to intellectual growth.
Lifelong Learning: Intellectual engagement and learning opportunities play a vital role in maintaining cognitive abilities as one ages. Continuing to challenge the mind through activities like reading, puzzles, learning new skills, and pursuing education can help slow down cognitive decline and promote intellectual well-being.
Expertise and Specialization: With age comes the opportunity for individuals to specialize in certain fields or develop expertise in specific areas. This specialization can lead to a deeper understanding and enhanced intellectual abilities within those particular domains.
Emotional Intelligence: Aging is often associated with increased emotional intelligence. Older adults tend to have a better understanding of their emotions and the emotions of others, which can positively impact their intellectual interactions and decision-making processes.
Neuroplasticity: Although aging is typically associated with a decline in cognitive abilities, research has shown that the brain remains capable of plasticity throughout life. This means that individuals can continue to learn, adapt, and form new neural connections, potentially offsetting some of the cognitive decline associated with aging.
Health Factors: Physical and mental health can significantly influence intellectual functioning in older adults. Chronic health conditions, such as cardiovascular disease, diabetes, or neurodegenerative disorders, can impact cognitive abilities. Conversely, maintaining good physical and mental health through regular exercise, a balanced diet, social engagement, and managing stress can support intellectual well-being.
It's important to note that the relationship between intellect and aging is complex and varies between individuals. While some may experience significant cognitive decline, others may maintain their intellectual abilities well into old age. Factors such as genetics, lifestyle choices, education, and overall cognitive reserve also play a role in determining how aging affects intellect.
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please help (science)
Plate Boundaries on Earth
Plate boundaries represent parts of the Earth where plates come in contact with one another. There are different ways in which these plates can move and interact. In this assignment, you will identify each type of plate movement and create an illustration to represent this.
Open the worksheet to get started. Use the criteria below to see what you should include in this assignment.
Row 1: Plate Boundary (Movement)
Write the type of plate boundary: convergent, divergent, transform.
Write the correct description for each in parentheses below the name: sliding, separating, or colliding.
Row 2: Diagram
Draw a diagram or illustration of the plate movement at the plate boundary. Include arrows to show whether the plates are colliding, separating, or dividing.
Row 3: Lithosphere (Created or Destroyed)
Identify whether the Earth's crust is created or destroyed at this type of plate boundary.
Row 4: Geologic Process
Give at least one example of the type of process or geological event that occurs on the Earth when the plates move in this manner.
Row 5: Real World Example
Give at least one example of a place on the planet where this type of plate movement is demonstrated along the plate boundary. Include both the location and name of the example.
Row 6: References
This assignment requires you to conduct formal research. When researching, make sure to use only valid and reliable resources; Wikipedia, blogs, and answer sites are not valid or reliable. References must be cited in APA format. Please provide your references in APA format in this column.
Plate Boundaries on Earth assignment involves identifying and illustrating different types of plate movements at the Earth's contact points.
Here are the steps to be followed:
Step 1: Understanding the Assignment Requirements
Read through the assignment instructions carefully to ensure a clear understanding of the tasks and expectations.
Step 2: Research
Start by conducting research on plate boundaries, their types, movements, and associated geological processes. Use reliable and valid resources such as scientific journals, textbooks, and reputable websites. Take notes on the different plate movements, their characteristics, and examples of each.
Step 3: Worksheet Setup
Create a table or chart with six rows corresponding to the six categories specified in the assignment instructions: Plate Boundary (Movement), Diagram, Lithosphere (Created or Destroyed), Geologic Process, Real World Example, and References.
Step 4: Fill in Row 1 - Plate Boundary (Movement)
In the first row, list the three types of plate boundaries: convergent, divergent, and transform. Next to each type, write the correct description in parentheses: sliding, separating, or colliding.
Step 5: Fill in Row 2 - Diagram
In the second row, draw a diagram or illustration for each type of plate movement. Use arrows to indicate the direction of movement and whether the plates are colliding, separating, or sliding past each other.
Step 6: Fill in Row 3 - Lithosphere (Created or Destroyed)
In the third row, identify whether the Earth's crust is created or destroyed at each type of plate boundary. Note the corresponding effects of plate movement on the lithosphere.
Step 7: Fill in Row 4 - Geologic Process
In the fourth row, provide at least one example of a geologic process or event that occurs as a result of plate movement at each type of boundary. This could include processes like subduction, seafloor spreading, or earthquakes.
Step 8: Fill in Row 5 - Real World Example
In the fifth row, give at least one real-world example of a location where each type of plate movement is demonstrated along a plate boundary. Include the name of the location and its corresponding plate boundary type.
Step 9: Fill in Row 6 - References
In the final row, provide the references for your research in APA format. Include the sources you used to gather information on plate boundaries, plate movements, and related geological processes.
Step 10: Review and Proofread
Review the completed assignment, ensuring that all information is accurate and properly cited. Proofread for any grammatical or spelling errors.
Note: The specific format and layout of the worksheet may vary based on your preference or instructor's instructions. Make sure to follow any specific formatting guidelines provided by your instructor.
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The fastest recorded pitch in major league baseball, thrown by Aroldis Chapman in 2010, was clocked at 169.1km/hr. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically (in meters) by the time it reached the home plate, 18.3m away?
Answer:
The ball would fall vertically for 112.45m
Explanation:
The vertical height of a horizontal throw is affected only by the speed of the throw and the acceleration due to gravity.
At this point, we may use this formula to determine the vertical height of the throw
vertical height = \(-v^2/2g\)
The initial throwing speed has to be converted to m/s to ensure uniformity during the calculations. To do this we multiply by 1000 and divide by 3600
169.1km/hr = 46.972m/s
Maximum height = \(46.972^2 /2 \times 9.81=112.45\) m
The pitch would make the ball fall vertically for 112.45m by the time it reached the home plate 18.2 m away
HELP: I’ve been stuck on this problem for a while now.
Answer:
a.work done=force *displacement
=500N*46m
=23000 Joule
b.power=work done/time taken
=23000/25
=920 watt
c.GPE=m*g*h(m=mass,g=gravity due to acceleration,h=height)
=60kg*9.8m/s*14m
=8232 joule
Explanation:
What is the force on a 1,250 kg elevator that is in free fall at 9.8 m/s²? Ignore air
resistance, round your answer to the nearest tenth and use appropriate units.
Answer:
\(\boxed{12250N}\)
Explanation:
Assuming we disregard air resistance, the only force acting on the elevator will be its weight.
\(F \implies w=m\cdot g\)
where:
\(F=\) force
\(w=\) weight
\(m=\) mass → 1250kg
\(g=\) gravity acceleration → 9.8m/s^2
Then:
\(F= 1250kg \cdot 9.8m/s^2\\F=12250 kg\cdot m/s^2= 12250N\)
Hope it helps.
\(\text{-B$\mathfrak{randon}$VN}\)
On an aircraft carrier, a catapult provides an accelerating force on the aircraft. The catapult provides a constant force for a distance of 150 m along the deck. Calculate the resultant force on the aircraft as it accelerates. Assume that all of the kinetic energy at take-off is from the work done on the aircraft by the catapult.
To calculate the resultant force on the aircraft as it accelerates from the catapult, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Since all of the kinetic energy at take-off is from the work done on the aircraft by the catapult, we can equate the work done by the catapult to the kinetic energy of the aircraft at take-off, that is:
Work done by catapult = kinetic energy of aircraft at take-off
The work done by the catapult is given by the force provided by the catapult multiplied by the distance over which it acts, that is:
Work done by catapult = force × distance
The distance over which the force provided by the catapult acts is given as 150 m, so we have:
Work done by catapult = force × 150
The kinetic energy of the aircraft at take-off is given by:
(1/2) × mass × velocity^2
Since the aircraft is initially at rest, its initial velocity is zero, so we have:
kinetic energy of aircraft at take-off = 0.5 × mass × (final velocity)^2
Using the work-energy principle, we can equate the two expressions for work done and kinetic energy, that is:
force × 150 = 0.5 × mass × (final velocity)^2
Solving for force, we get:
force = 0.5 × mass × (final velocity)^2 / 150
Therefore, the resultant force on the aircraft as it accelerates is given by:
force = 0.5 × mass × (final velocity)^2 / 150
Note that we need to know the mass and final velocity of the aircraft in order to calculate the resultant force.
Mark weighs 375 N and is carrying a full-sized cello as he climbs the stairs to a height of 4 m. It takes him 3 seconds to do this.
How does the amount of work he does change if he were to climb the same flight of stairs again in the same amount of time, but this time without the cello?
A) It depends on the weight of the cello.
B) It remains the same.
C) It increases
D) It decreases.
Mark's work decreases when he climbs the same flight of stairs again in the same amount of time without the cello.
The correct answer is option D.
The amount of work Mark does depends on the weight of the cello, as well as the distance he climbs and the time it takes. Work is calculated using the formula :
Work = Force × Distance.
In the given scenario, Mark is carrying a full-sized cello while climbing the stairs. The weight of the cello adds to the force he exerts. So, the total force Mark exerts is the weight of the cello plus his own weight (375 N).
When Mark climbs the stairs with the cello, he is doing work against the force of gravity.
The work done is equal to the force exerted multiplied by the distance climbed (375 N + weight of cello) × 4 m.
Now, if Mark were to climb the same flight of stairs again in the same amount of time (3 seconds), but this time without the cello, the amount of work he does would decrease. This is because without the cello, the force exerted would only be Mark's weight (375 N), which is less than the total force exerted with the cello.
Therefore, mark's work decreases.
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Which of these will have the same units if acceleration is multiplied by time? Force Time velocity Pressure
Answer:
Velocity
Explanation:
Velocity equals the original velocity... Plus
the acceleration is multiplied by time.
If the acceleration is multiplied by time then we get velocity as a result, therefore velocity has the same unit.
What is pressure?Pressure is measured as the amount of force applied in the one-meter of area. Pascal is used as the SI unit of it. The amount of pressure can be calculated by dividing the amount of force by the area of force applied. In relation to atmospheric pressure, the pressure is measured. Pressure does not represent any direction, so it comes under a scalar quantity. Many scientific and day-to-day life equipment use pressure principles like gauge meter thermometers in designing cars, ships, and every mechanical part.
We know that acceleration has an SI unit of m /\(s^{2}\) So if we multiply the time with an acceleration whose unit is second we will get m / s which is the unit of velocity.
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A polystyrene rod consisting of two cylindrical portions AB and BC is restrained at both ends and supports two 6-kip loads as shown. Knowing that E = 0.45 X 106 psi, determine (a) the reactions at A and C, (b) the normal stress in each portion of the rod.
The normal stress in portion AB is σ₁ = 79.48 psi and the normal stress in portion BC is σ₂ = 47.69 psi.
We can start by drawing a free body diagram of the polystyrene rod and identifying the unknown reactions at A and C:
|-------- 6 kips --------|
A C
|-----------------------|
| |
| BC |
| σ₂ |
| L₂ |
| |
|-----------------------|
| |
| AB |
| σ₁ |
| L₁ |
| |
|-------- 6 kips --------|
Where σ₁ and σ₂ are the normal stresses in portions AB and BC of the rod, respectively.
Next, we can use the equations of static equilibrium to solve for the reactions at A and C. Taking moments about point A, we have:
6 kips * L₂ + 6 kips * (L₁ + L₂) - Cz = 0
where z is the distance from A to the line of action of the force at C. Since the rod is symmetric about the midpoint of portion BC, we can take z = L₁ + L₂/2. Substituting the given values, we have:
6 kips * L₂ + 6 kips * (L₁ + L₂) - C(L₁ + L₂/2) = 0
Solving for C, we get:
C = (12 kips * L₁ + 18 kips * L₂) / (3 L₁ + 2 L₂)
Taking vertical forces, we have:
A + C - 12 kips - 6 kips - 6 kips = 0
Substituting the value of C we just obtained, we get:
A = 12 kips - C - 6 kips - 6 kips = 0.4 kips
Therefore, the reactions at A and C are A = 0.4 kips and C = 11.6 kips.
Next, we can calculate the normal stresses in each portion of the rod. Using the formula for normal stress, we have:
σ₁ = P₁ / A₁ = A₂ / A₁ * σ₂
where P₁ and A₁ are the axial load and cross-sectional area of portion AB, and A₂ is the cross-sectional area of portion BC. Since the rod is of uniform diameter and the areas of the cylindrical portions are proportional to their lengths, we have:
A₂ / A₁ = L₂ / L₁
Substituting this into the equation for σ₁, we get:
σ₁ = (L₂ / L₁) * σ₂
Substituting the given values, we have:
σ₂ = P₂ / A₂ = 6 kips / (π/4 * (0.6 in)^2) = 47.69 psi
σ₁ = (2.5 ft / 1.5 ft) * 47.69 psi = 79.48 psi
Therefore, the normal stress in portion AB is σ₁ = 79.48 psi and the normal stress in portion BC is σ₂ = 47.69 psi.
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A certain compact disc (CD) contains 783.216 megabytes of digital information. Each byte consists of exactly 8 bits. When played, a CD player reads the CD's information at a constant rate of 1.5 megabits per second. How many minutes does it take the player to read the entire CD? Express your answer using two significant figures
Answer:
69.62 minutes
Explanation:
From the information we have here,
1 byte is = 8 bits
So 1 megabyte = 8 megabits
Then
783.216 x 8 megabits = 6265.728 megabits
This player has its reading capacity at 1.5 megabits / second
So 1 minute = 60x1.5
= 90 megabits / min
Then we have the entire reading time of this CD player to be =
6265.728/90
= 69.62 minutes.
This answers the question