The weight of the person in the first case is 25759.44 N while in the second it is 790.86 N.
What is weight?Weight is the product of mass and acceleration due to gravity. We have to find the acceleration due to gravity in both cases.
g = GM/r^2
g1 = 6.67 × 10^−11 m3 kg−1 s−2 * 5.98×10^24 kg/(1120 * 10^3 m)^2
g1 = 3.99 * 10^14/1.25 * 10^12
g1 = 319.2 m/s^2
g2 = 6.67 × 10^−11 m3 kg−1 s−2 * 5.98×10^24 kg/( 6370 * 10^3 m)^2
g2 = 3.99 * 10^14/4.06 * 10^13
g2 = 9.8 m/s^2
The weight of the person in the first case is; 80.7 kg * 319.2 m/s^2
= 25759.44 N
The weight of the person in the second case is; 80.7 kg * 9.8 m/s^2
= 790.86 N
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Hello!
I have an equation where I can't really find To (Initial temperature). The equation is from the formula Newton's law of cooling. To is the initial temperature of the object and ln is the natural log. The -0.00124 is the constant k multiplied by the time.
I just need to find the initial temp.
Answer:
[tex]T_0=80695.17162...[/tex]
Explanation:
Given equation:
[tex]\ln \left(\dfrac{T_0-100}{T_0}\right)=-0.00124[/tex]
To solve the given equation:
[tex]\textsf{Apply log rules}: \quad e^{\ln (x)}=x[/tex]
[tex]\implies \dfrac{T_0-100}{T_0}=e^{-0.00124}[/tex]
Multiply both sides by T₀:
[tex]\implies T_0-100=T_0e^{-0.00124}[/tex]
Add 100 to both sides:
[tex]\implies T_0=T_0e^{-0.00124}+100[/tex]
Subtract [tex]T_0e^{-0.00124}[/tex] from both sides:
[tex]\implies T_0-T_0e^{-0.00124}=100[/tex]
Factor out the common term T₀:
[tex]\implies T_0(1-e^{-0.00124})=100[/tex]
Divide both sides by [tex](1-e^{-0.00124})[/tex]
[tex]\implies T_0=\dfrac{100}{1-e^{-0.00124}}[/tex]
Carry out the calculation:
[tex]\implies T_0=\dfrac{100}{1-0.99876...}[/tex]
[tex]\implies T_0=\dfrac{100}{0.001239231...}[/tex]
[tex]\implies T_0=80695.17162...[/tex]
Why was the APA not implemented early on for research on humans and these ethics of research in place?
APA not implemented early on for research on humans and these ethics of research in place because there was no stable and widely accepted system of research.
What is APA?
This is referred to a writing style used by American Psychological Association in reasearches etc.
There was no stable method of writing which was the reason why it wasn't used early for researches.
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A ball slows down as it rolls up a hill. What is the value of the change in its kinetic energy, ΔEk?
Positive
Zero
Negative
For a ball that slows down as it rolls up a hill the value of the change in its kinetic energy, ΔEk is: Negative
Meaning of Kinetic energyKinetic energy can be defined as the ability assumed by an object in motion.
Kinetic energy is also said to be a form of mechanical energy that is possessed by an object to be in motion.
Normally kinetic energy is believed to be positive by when it begins to slow down a negative effect is experienced
In conclusion, For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive
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A step-up transformer has a primary coil with 100 loops and a secondary coil with 1,500 loops. If the primary coil is supplied with a household current of 120 V and 15 A, (a) what voltage is produced in the secondary circuit? (b) What current flows in the secondary circuit?
(a) The voltage that is produced in the secondary circuit is 1,800 V.
(b) The current that flows in the secondary circuit is 1 A.
Voltage in the secondary coilNp/Ns = Vp/Vs
where;
Np is number of turns in primary coilNs is number of turns in secondary coilVp is voltage in primary coilVs is voltage in secondary coil100/1500 = 120/Vs
Vs = (120 x 1500)/100
Vs = 1,800 V
Current in the secondary coilIs/Ip = Vp/Vs
where;
Is is secondary currentIp is primary currentIs = (IpVp)/Vs
Is = (15 x 120)/1800
Is = 1 A
Thus, the voltage that is produced in the secondary circuit is 1,800 V.
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Pls help !!
What must be the same for two resistors that are connected in parallel?
OA. The resistance of each
OB. The voltage drop across each
OC. The power used by each
OD. The current in each
Answer
its c
Explanation:
When resistors are connected in parallel combination the voltage drop across each resistor is same. However , the total current gets branched into different amount .
Question :
— What must be the same for two resistors that are connected in parallel ?
AnswEr :
When the two resistors are connected in parallel therefore , the Voltage drop across each resistors will be same .Option B seems to be correct answer .
Using appropriate technology, you determine that Earth's magnetic field at your location has a magnitude of 5.88 10-5 T and is directed north at an angle of 56° below the horizontal. You charge a metallic projectile and fire it north with a speed of 663 m/s and at an angle of 14° above the horizontal. Determine the sign (+ or −) and charge of the projectile, if the magnetic force on the projectile is 3.22 10-10 N, directed due west.
C
The sign (+ or −) and charge of the projectile, if the magnetic force on the projectile is 3.22 10-10 N, directed due west is mathematically given as
q=+1.11524613*10^{−4}C
What is the sign (+ or −) and charge?Generally, the equation for Force is mathematically given as
[tex]F=Bqvsin\theta[/tex]
Therefore
[tex]3.22 10^{-10}= 5.88 10^{-5 } *633*sin 56*q\\\\q=\frac{3.22 10^{-10}}{5.88 10^{-5 } *633*sin 56}[/tex]
q=+1.11524613*10^{−4}C
In conclusion, the sign (+ or −) and charge
q=+1.11524613*10^{−4}C
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PLEASEEE HELP HELP PLEASE
A 0.450 kg baseball comes off a bat and goes straight up. At a height of 10.0 m, the baseball has a speed of 24.5m/s. Determine its mechanical energy at this height. Show your work
What is the baseball's mechanical energy when it is at a height of 9.0m? Explain your answer.
The mechanical energy of the baseball when it is at a height of 9.0m is 39.7 N.
What is the mechanical energy of the baseball bat?The mechanical energy of the bat is in the form of potential energy.
Potential energy = mass * acceleration due to gravity * heightAt a height of 9.0m, the potential energy of the ball = 0.45 * 9.81 *
Potential energy = 39.7 N
In conclusion, the mechanical energy of the baseball bat is the potential energy at that height.
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. An airplane is cruising at altitude 10km. The pressure outside the craft is 0.287 atm; within the passenger compartment, the pressure is 1.00 atm and the temperature is 20 degree C. A small leak occurs in one of the window seals in the passenger compartment. Model the air as an ideal fluid to estimate the speed of the air stream flowing through the leak
The model of the Air as in ideal fluid estimating the speed of air stream flowing through he leak is given as; V = 347m/s. See the calculation below.
What is a model?A model is a mathematical equation that is used to represent a real life problem.
What is the model for the problem above?
P₁ + (1/2) pv₁² + pgh₁ = p₂ + (1/2) pv₂² + pgh₂
Hence,
1 + 0 + 0 = 0.287 + (1/2) (1.2) v²
Therefore,
V = 347m/s
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A vector of magnitube 5 units is inclined at an angle 37° to the x-axis and another vector of magnitube 10 units is inclined at 53° to the x-axis. What is the magnitude of the sumbof the vector components ( i ) along the x-axis ( ii ) along the y-axis? ( sin 37° = cos 53° = 0.6 / sin 53 = cos 37° = 0.8 )
Answer:
See below
Explanation:
x axis components
5 cos 37 + 10 cos 53 = 5(.8) + 10(.6) = 1.0 units x-axis
y axis components
5 sin 37 + 10 sin 53 = 5(.6) + 10 (.8) = 1.1 units y- axis
The correct answer for the magnitude of the sum of vector is (i) along x-axis is [tex](\sqrt{10})^2[/tex] and (ii) along y-axis is [tex](\sqrt{11})^2[/tex] .
Given:
Vector A magnitude: 5 units,
angle of inclination with x-axis = 37°.
Vector B magnitude: 10 units.
angle of inclination with x-axis = 53°.
Sum of vectors along x-axis:
AB = [tex]\sqrt{5cos37^o +10cos53^o }[/tex]
= [tex]\sqrt{(5*(0.8))^2+(10*(0.6))^2}[/tex]
[tex]= (\sqrt{10})^2[/tex]
Along y-axis:
AB =[tex]\sqrt{5sin37^o +10cos53^o }[/tex]
[tex]\sqrt{5(0.6) +10(0.8) }\\\\= (\sqrt{11})^2[/tex]
Magnitude along x-axis and along y-axis is [tex]10[/tex] and [tex]11[/tex] respectively.
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After washing lettuce, you can dry the water from it using a salad spinner. You put the lettuce in the bowl, and then crank the handle, spinning and drying the lettuce.
From the frame of reference of the lettuce in the spinning strainer, what causes the water on the lettuce to come off the lettuce and go to the walls of the bowl?
The centripetal force
The force of gravity
Newton's first law of motion
The centrifugal force
Centripetal force causes the water on the lettuce to come off the lettuce and go to the walls of the bowl.
What is centripetal force?Centripetal force is the force that is necessary to keep an object moving in a curved path and that is directed inward toward the center of rotation. This force can move the body in the circular direction.
So we can conclude that Centripetal force causes the water on the lettuce to come off the lettuce and go to the walls of the bowl.
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The force that causes the water on the lettuce to come off the lettuce and go to the walls of the bowl is the centrifugal force.
What is the centrifugal force?The centrifugal force is the force that force that tends to throw an object out of the circular path. It is the opposite of the centripetal force which tends to keep the object in the circular path.
Hence. the force that causes the water on the lettuce to come off the lettuce and go to the walls of the bowl is the centrifugal force.
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A sphere of radius r has surface area
A = 4r2and volume V = (4/3r^3) The radius of sphere 2 is triple the radius of sphere 1.
(a)
What is the ratio of the areas, A2/A1?
(b)
What is the ratio of the volumes, V2/V1?
Answer:
A2/A1 = 9
V2/V1 = 27
Explanation:
Area of Sphere 1; A1 = 4πr²
Volume of Sphere 1; V1 = (4/3)πr³
Area of Sphere 2; A2 = 4π(3r)² = 9*4πr²
Volume of Sphere 2; V2 = (4/3)π(3r)³ = 27*(4/3)πr³
Thus;
A2/A1 = 9*4πr²/4πr² = 9
V2/V1 = [27*(4/3)πr³]/[(4/3)πr³] = 27
A motor hoists a mass m = 60 kg crate at a constant velocity to a height of h = 5 m in 2 s. If the indicated power of the motor is 3.2 kW, determine the motor's efficiency.
anyone solve this for mw urgently please.
Decrease.
What is the weight on the equator than at the Poles?Yes, You weigh less on the equator than at the North or South Pole, but the difference is small.
Note that your body itself does not change.
Rather it is the force of gravity and other forces that change as you approach the poles. These forces change right back when you return to your original latitude.
In short, a trip to the equator is not a viable long-term weight-loss program.
Your weight is the combination of all the large-scale, long-term forces on your body. While the earth's gravity is by far the strongest large-scale force, it is not the only one.
We experience as "something pulling you down" is actually the total of all the forces and not just gravity.
The four dominant large-scale, long-term forces are:
The earth's gravity
The sun's gravity
The moon's gravity
The earth's centrifugal force
Hence, the weight of a body at the equator will be less than at the Poles.
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A soccer ball is kicked from the top of one building with a height of H1 = 30.2 m to another building with a height of H2 = 12.0 m.
The ball is kicked with a speed of v0 = 15.10 m/s at an angle of θ = 74.1° with respect to the horizontal. The mass of a size 5 soccer ball is m = 450 g. When the ball lands on the other building, its speed is 19.89 m/s.
1. How much energy was lost to air friction? The ball is kicked without a spin.
Hi there!
Initially, we have gravitational potential energy and kinetic energy. If we set the zero-line at H2 (12.0m), then the ball at the second building only has kinetic energy.
We also know there was work done on the ball by air resistance that decreased the ball's total energy.
Let's do a summation using the equations:
[tex]KE = \frac{1}{2}mv^2 \\\\PE = mgh[/tex]
Our initial energy consists of both kinetic and potential energy (relative to the final height of the ball)
[tex]E_i = \frac{1}{2}mv_i^2 + mg(H_1 - H_2)[/tex]
Our final energy, since we set the zero-line to be at H2, is just kinetic energy.
[tex]E_f = \frac{1}{2}mv_f^2[/tex]
And:
[tex]W_A = E_i - E_f[/tex]
The work done by air resistance is equal to the difference between the initial energy and the final energy of the soccer ball.
Therefore:
[tex]W_A = \frac{1}{2}mv_i^2 + mg(H_1 - H_2) - \frac{1}{2}mv_f^2[/tex]
Solving for the work done by air resistance:
[tex]W_A = \frac{1}{2}(.450)(15.1^2)+ (.450)(9.8)(30.2 - 12) - \frac{1}{2}(.450)(19.89^2)[/tex]
[tex]W_A = \boxed{42.552 J}[/tex]
how mesuremerment of gravity using simple pendulum
Answer:
See below
Explanation:
Set up your pendulum
measure its length and time the period ( you could time 100 of them and divide the time result by 100 to get the period, T)
then use
T = 2 pi sqrt (L/g) T = period L = length g = gravity
Select the correct answer. Which segment of this graph shows a decreasing velocity? Graph representing Time in seconds on the x-axis and position in miles on the y-axis. The line starts at point A (0, 20), and passes points B (20, 20), C (40, 40), D (60, 60), E (80, 60), and F (100, 80) A. A to B B. B to C C. C to D D. D to E E. E to F
The portion that shows a decreasing velocity is D to E.
What is a position - time graph?The position time graph is used to describe the motion of a body. We know that the slope of a velocity time graph is the velocity of the graph.
If we look at the graph as shown in the image attached to the answer, we can see that the portion that shows a decreasing velocity is D to E.
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Answer:
D - E
Explanation:
hope this help
A truck is carrying a refrigerator as shown in the figure. The height of the refrigerator is 158.0 cm, the width is 60.0 cm. The center of gravity of the refrigerator is 67.0 cm above the midpoint of the base.
What is the maximum acceleration the truck can have so that the refrigerator doesn't tip over? (The static friction between the truck and the refrigerator is very large.)
The maximum acceleration the truck can have so that the refrigerator does not tip over is 4.15 m/s².
What will be the maximum acceleration of the truck to avoid tipping over?The maximum acceleration is obtained by taking clockwise moments about the tipping point of rotation.
Clockwise moment = Anticlockwise moment
Ft * 1.58 m = F * 0.67 m
where
Ft is tipping force = mass * acceleration, aF is weight = mass * acceleration due to gravity, gm * a * 1.58 = m * 9.81 * 0.67
a = 4.15 m/s²
The maximum acceleration the truck can have so that the refrigerator does not tip over is 4.15 m/s².
In conclusion, the acceleration of the truck is found by taking moments about the tipping point.
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Complete the sentence to describe how light behaves as it relates to its nature (waves or particles). light travels as and interacts with matter as .
Light behaves as it relates to its nature (waves or particles). light travels as and interacts with matter as wave particles.
What is light?Electromagnetic radiation that is within the region of the electromagnetic spectrum that the human eye can see is referred to as light or visible light.
The main characteristics of light include intensity, polarization, frequency or wavelength spectrum, and propagation direction. One of the fundamental constants of nature is its speed in a vacuum, which is 299 792 458 meters per second (m/s).
Light can be categorized according to two theories: the first categorizes light as particles, and the second categorizes light as waves.
The main difference between the wave and particle natures of light is that the former asserts that light can act as an electromagnetic wave while the latter asserts that light is made up of tiny particles known as photons.
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Answer: 1.waves 2.particles
Explanation: just did it!<3
An astronaut is on the moon. He drops a hammer from a height of 3.2metres and it takes 2.0 seconds to reach the lunar landscape. What is the acceleration due to gravity of the moon?
Answer:
1/6 m/s^2 ( about 1/6th gravity of Earth ( 9.81 m/s^2)
Explanation:
Displacement = yo + vo t - 1/2 a t^2
- 3.2 = 0 + 0 - 1/2 a(2.0)^2
- 3.2 = -2a
a = 3.2 / 2 = 1.6 m/s^2
An astronaut is on the moon. He drops a hammer from a height of 3.2metres and it takes 2.0 seconds to reach the lunar landscape. Then the acceleration due to gravity of the moon is 1.6 m/s².
What is gravity ?Gravity, which derives from the Latin word gravitas, which means "weight", is a basic interaction in physics that causes all objects with mass or energy to attract one another. The electromagnetic force, the weak interaction, and the strong interaction are all significantly stronger than gravity, which is by far the weakest of the four fundamental interactions. As a result, it has no appreciable impact on subatomic particle level phenomena. However, at the macroscopic level, gravity is the most important interaction between objects and governs the motion of planets, stars, galaxies, and even light.
Sublunar tides in the oceans are created by the Moon's gravity, much as gravity on Earth imparts weight to physical things (the analogous antipodal tide is generated by inertia).
according to kinematics,
S = ut + 1/2 at²
initial velocity is zero
S = 1/2 at²
putting all the values,
3.2 = 1/2a2²
6.4/4 = a
a = 1.6 m/s²
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A cube, whose mass is 0.660 kg, is attached to a spring with a force constant of 106 N/m. The cube rests upon a frictionless, horizontal surface (shown in the figure below).
The cube is pulled to the right a distance A = 0.140 m from its equilibrium position (the vertical dashed line) and held motionless. The cube is then released from rest.
(a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the cube?
________N
(b) At that very instant, what is the magnitude of the cube's acceleration (in m/s2)?
_____ m/s2
(c)
In what direction does the acceleration vector point at the instant of release?
- The direction is not defined (i.e., the acceleration is zero).
-Away from the equilibrium position (i.e., to the right in the figure).
- Toward the equilibrium position (i.e., to the left in the figure).
- You cannot tell without more information.
***Please refer to attached photo
Answer:
F = - F x force acting on cube
F = -106 N/n * .14 m = -14.8 N direction opposite to force
a = F / m = -14.8 N / .66 kg = -22.5 m/s^2 acceleration of cube
direction is towards equilibrium point (opposite F)
Elizabeth’s father is a crane operator, and she gets a chance to see him at work. He shows her a button in the crane, explaining that pushing it closes a circuit. When that happens, a car is attracted to the crane and lifted off the ground. When the button is released, the car falls back to the ground. How does the current made by the circuit produce this effect?
A: It generates force that pulls the car toward the crane lift.
B: It generates an electric field from the crane lift that affects the electricle charges in the car.
C: it generates a magnetic field that attracts the car magnetically to the crane lift
Choose ONE
The current made by the circuit produce this effect by generating a magnetic field that attracts the car magnetically to the crane lift and is denoted as option C.
What is a Crane?This is a machine which is used to lift and lower objects which are most times heavy.
It employs the use of magnetic force as it is generated when the button is switched on in this scenario.
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The atomic mass of nitrogen is 14.01, hydrogen is 1.01, sulfur is 32.07, and oxygen is 16.00. What is the molar mass of ammonium sulphate [(NH4)2SO4]?
A.
63.09 g
B.
84.17 g
C.
114.12 g
D.
118.16 g
E.
132.17 g
Reset Next
The molar mass of ammonium sulphate [(NH4)2SO4] is 132.17 g (option E). Details about molar mass can be found below.
How to calculate molar mass?The molar mass of a substance can be calculated by adding the atomic masses of the elements in the compound.
According to this question, the atomic mass of nitrogen is given as 14.01, hydrogen is 1.01, sulfur is 32.07, and oxygen is 16.00.
The molar mass of ammonium sulphate is as follows:
[(NH4)2SO4] = [14.01 + 1(4)]2 + 32.07 + 16.00(4)
= 36.02 + 32.07 + 64
= 132.09
Therefore, the molar mass of ammonium sulphate [(NH4)2SO4] is 132.17 g.
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A vector A⃗ has a magnitude of 40.0 m and points in a direction 20.0∘ below the positive x axis. A second vector, B⃗, has a magnitude of 75.0 m and points in a direction 50.0 above the positive x axis. Sketch the vectors A⃗ , B⃗ , and C⃗ =A⃗ +B⃗, and using the component method of vector addition, find the magnitude of the vector C⃗ .
The magnitude of the vector C is 96.32m
How to solve for the magnitude of vector c
Ax = AcosθA
= 40 cOS 20
= 37.59
Ay = AsinθA
-40sin20
= -13.68
Bx = B cos θ B
= 75Cos50
= 48.21
By = BsinθB
= 75sin50
= 57.45
Cx = AX + Bx
= 37.59 + 48.21
= 85.8
Cy = Ay + By
= -13.65 + 57.45
= 43.77
The magnitude is solved by
|c| = [tex]\sqrt{Cx^{2}+Cy^{2} }[/tex]
= √85.8² + 43.77²
= 96.32m
The magnitude of the vector c is 96.32m
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A javelin is thrown at 28.5 m/s from flat
ground at a 43.2° angle. How much time
is it in the air?
(Unit = s)
HELP FAST
Answer:
did you ever the answer?
Explanation:
The time for the javelin in the air will be 3.977 second
What is the period?The value of time needed to complete the upward and the downward motion is the total period. Its unit is the second and is denoted by t. T is the time at which the ball first hits the ground.
Given data;
Θ is the angle of throw = 43.2°
u is the thrown velocity = 28.5 m/s
t is the time for the javelin in the air
The time period is found as;
[tex]\rm t = \frac{2u sin \theta }{g} \\\\ t = \frac{ 2 \times 28.5 \ sin 430.2^0}{9.81 } \\\\ t = 3.977 \ sec.[/tex]
Hence the time for the javelin in the air will be 3.977 second
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Karen Horney, a prominent neo-Freudian, believed that Freud's theory Select one: A. discounted the importance of dreams. B. disputed that women never experience a phallic stage of development. C. discounted strong unconscious, aggressive desires. D. showed a masculine bias.
Karen Horney, a prominent neo-Freudian, believed that Freud's theory showed a masculine bias (Option D).
What is Freud's theory?Freud's theory, also called the psychoanalytic theory, is a model used in physiology to understand human behavior.
Freud's theory is based on the assumption that human behaviors are mainly controlled by the libido (unconscious) of people.
In conclusion, Karen Horney believed that Freud's theory showed a masculine bias (Option D).
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An ideal gas in an isentropic process has an initial pressure of 200 kPa and relative pressure is 3.482; the final pressure is now 320 kPa, find the relative pressure at this state. round to the nearest 3 decimal places
The relative pressure at this state is determined as 0.455.
Initial pressure of the ideal gasThe pressure of the ideal gas given rise to the relative pressure is calculated as follows;
R.P = P2/P1
P2 = P1(R.P)
P2 = 200 kPa x (3.482)
P2 = 696.4 kPa
New relative pressureR.P = (P3)/(P2)
R.P = (320)/(696.4)
R.P = 0.455
Thus, the relative pressure at this state is determined as 0.455.
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You drive 7.50 km in a straight line in a direction 10° East of North.
(a) Find the distances you would have to drive straight East and then straight North to arrive at the same point. (This is equivalent to finding the components of the displacement along the East and North directions.)
km East
km North
(b) Show that you still arrive at the same point if the East and North legs are reversed in order.
a)The distance in the east direction and distance in the north direction will be 1.302 km and 7.386 km respectively.
b)Both the routes have the same distance.
What is displacement?Displacement is defined as the shortest distance between the two points.
Distance is the horizontal length covered by the body, while displacement is the shortest distance between the two points. Displacement is a vector quantity.
Given data;
Distance,d = 7.5 km
Angle,θ=10° E of N
From the triangle ABD and ABC it is obtained that;
AC = AB sinθ
AC=7.5 sin(10°)
AC=1.302 km
CB = 7.5 cos 10°
CB = 7.386 km
AC is the distance in the east direction = 1.302 km
CB is the distance in the north direction = 7.386 km
Both the routes have the same distance. Hence you still arrive at the same point if the East and North legs are reversed in order.
Hence the distance in the east direction and distance in the north direction will be 1.302 km and 7.386 km respectively.
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The stool is 120 cm tall. How tall is it in inches? Note: there are 2.54 cm in 1 inch
Answer:
47.24 in
Explanation:
120 / 2.54 = 47.24
A treasure chest full of silver and gold coins is being lifted from a pirate ship to the shore using two ropes as shown in the figure. The mass of the treasure chest is 75.6 kg.
If the tension in rope A is 7.42x10^2 N and the tension rope B carries is 7.52x10^2 N, what is the tension in rope C?
The tension in rope C is determined as 122.23 N.
Tension in rope CThe tension in rope C is calculated as follows;
B² = A² + C²
C² = B² - A²
C² = (752²) - (742²)
C² = 14,940
C = √14,940
C = 122.23 N
Thus, the tension in rope C is determined as 122.23 N.
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The water is flowing through the horizontal constricted pipe. The pressure at one end is 4500Pa, speed is 3m/s and area of cross-section is A, Calculate the speed and pressure at another end where the area of cross-section is A/3.
The speed and pressure at another end will be 9 m/sec and -31500 pascals.
What is gauge pressure?The difference between absolute pressure and atmospheric pressure is known as gauge pressure. Relative pressure is another name for gauge pressure.
Given data in problem is;
For horizontal pipe, Z₁=Z₂
Pressure at end 1, P₁ = 4500Pa
Speed at end 1, V₁ = 3 m/sec
Speed at end 2, V₂ = ? m/sec
Area of cross-section at end 1,A₁ =A
Area of cross-section at end 1,A₂ = A/3
From the continuity equation;
A₁V₁=A₂V₂
A× 3 = (A/3)×V₂
V₂ = 9 m/sec
From Bernoulli's equation;
[tex]\rm \frac{P_1}{\rho g} + \frac{v_1^2}{2g} +Z_1 = \frac{P_2}{\rho g} + \frac{v_2^2}{2g} +Z_2 \\\\ \frac{P_1-P_2}{\rho g } = \frac{v_2^2-v_1^2}{2g} \\\\ \frac{P_1-P_2}{\rho} = \frac{v_2^2-v_1^2}{2} \\\\ \frac{4500-P_2}{1000} = \frac{9^2-3^2}{2} \\\\ 4500 -P_2 = 36000 \\\\ P_2 = - \ 31,500 \ pa[/tex]
Hence the speed and pressure at another end will be 9 m/sec and -31500 pascals.
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