The instantaneous velocity of the ball is 18ft/s.
What is velocity?
The pace at which an object's position changes as perceived from a particular point of view and as measured by a particular unit of time (for example, 60 km/h northbound) is defined as its velocity. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that deals with the motion of bodies.
In order to be defined, the physical vector quantity known as velocity needs to have both a magnitude and a direction. Speed is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI. Speed is the scalar absolute value (magnitude) of velocity (metric system).
Calculations:
at t=1s, the height is y=50(1)-16(12)=34ft.
at t=1.1s, the height is y=50(1.1)-16(1.12)=35.64ft
Between these two heights, the change in time is 0.1s. The change in height is 35.64ft-34ft=1.64ft.
Therefore [tex]V_{avg}=\frac{del y}{del t} = \frac{1.64ft}{0.1s} =16.4ft/s[/tex]
at t=1.01s, the height is y=50(1.01)-16(1.012)=34.1784ft
between t=1.01s and t=1s the change in time is 0.01s and the change in height is 0.1784ft.[tex]V_{avg}=\frac{0.1784ft}{0.01s} =17.84ft/s[/tex]
at t=1.001, the height is y=50(1.001)-16(1.0012)=34.017984ft
between t=1s and t=1.001s, the change in time is 0.001s and the change in height is 0.017984ft
[tex]V_{avg} =\frac{0.017984ft}{0.001s}=17.984ft/s[/tex]
It appears that as the time interval approaches 0, the average velocity approaches 18ft/s. Therefore it is safe to assume the instantaneous velocity at t=1s is 18ft/s.
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22. сс Peter exerts a horizontal force of 500 N on a box of mass 2.0 kg which also experiences a friction force of 200 N. If it takes 4.0 s to move the box 3.0 m, what is the efficiency in moving the box? Efficiency 2 Energy coming in energy going X 100 %. (c) ABUD 29% 40% 60% 71% FH301/P1/19 ont.
The efficiency of moving the box is 60%.
Given in the question
Force exerted by peter = 500 N
Force due to friction on box = 200 N
Distance Traveled by box = 3 meters
Now work done by the force is given by
Work Done = (Magnitude of Force) × (Distance traveled)
Let us find work done by each force,
Work done by peter
Work Done = (Magnitude of Force) × (Distance traveled)
Put in the value, we get
Work Done =500 × 3
Work Done by peter = 1500 J
Similarly, Work done by friction
Work Done = (Magnitude of Force) × (Distance traveled)
Put in the value, we get
Work Done =200 × 3
Work Done by Friction = 600 J
As we know the work done by friction force is always negative,
Work Done by Friction = -600 J
So, net Work done = Work Done by peter + Work Done by Friction
net Work done = 1500 - 600
Net Work done = 900 J
Now Efficiency = (Net work done/work done by peter) × 100
Put in the values, we get
Efficiency = (900/1500) × 100
Efficiency = (3/5) × 100
Efficiency = 300/5
Efficiency = 60 %
So, the efficiency of moving the box is 60%.
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A proton having an initial velvocity of 20.0i Mm/s enters a uniform magnetic field of magnitude 0.300 T with a direction perpendicular to the proton's velocity. It leaves the field-filled region with velocity -20.0j Mm/s. Determine(c) the distance the proton traveled in the field.
The distance the proton traveled in the field is 2.09m.
What is a proton?A stable subatomic particle known as a proton with the symbols p, H+, or 1H+ and an elementary electric charge of +1e. It has a mass that is somewhat lower than that of a neutron, and because of the proton to electron mass ratio, it has an 1836-fold greater mass than an electron. The term "nucleons" refers to protons and neutrons, both of which have masses of roughly one atomic mass unit (particles present in atomic nuclei).
In the nucleus of every atom, there are one or more protons. They offer the central force of electrostatic attraction that holds the atomic electrons together.
Explanation:
Now as the initial and final velocity makes 180degree angle, So, the proton must have travelled only half a revolution. So, the distance ,d will be :
d=2πr/2=πR
d=2.09m
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what is the total capacitance of a certain circuit containing three capacitors with capacitances of .25 microfarad, .03 microfarad, and .12 microfarad, respectively? (note: c(t)
The total capacitance of the capacitor circuit is 40 μF.
We need to know about capacitor circuits to solve this problem. The capacitance will be summed up when the capacitor is combined in parallel. The total capacitance can be determined as
Ct = C1 + C2 + C3
From the question above, we know that:
C1 = 25 μF
C2 = 3 μF
C3 = 12 μF
By substituting the parameters, we can get
Ct = C1 + C2 + C3
Ct = 25 μF + 3 μF + 12 μF
Ct = 40 μF
Hence, the total capacitance of the circuit is 40 μF.
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What weight of the ore in lb would contain exactly 1lb of copper
The density of crushed iron ore is equivalent to 2 500 kg/m3, or 2.5 grams per cubic centimeter, which is the weight of the material. The density is equal to 156.07 pounds per cubic foot in either the Imperial or US customary measuring systems.
When weights are expressed in kilograms of air, the air gives buoyancy, and because a kilogram of copper has a larger volume than a kilogram of lead, it displaces more air and hence receives more support. As a result, on a scale in the air, a kilogram of lead will weigh more than a kilogram of copper. Copper has a density of 8.94 grams per cubic centimeter, or 8 940 kilograms per cubic meter, or 20°C (68°F or 293.15K), at ordinary atmospheric pressure.
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A⁵⁷ Fe Fe nucleus at rest emits a 14.0keV photon. Use conservation of energy and momentum to find the kinetic energy of the recoiling nucleus in electron volts. Use M c² = 8.60 × 10⁻⁹J for the final state of the ⁵⁷Fe nucleus.
Kinetic energy is K = 1.82 × 10⁻³ eV.
⁵⁷Fe nucleus emits 14 keV photons at rest.
We have, Mc² = 8.6 × 10⁻⁹ J in the final state of the nucleus.
Let p(nucleus) be the moment of the nucleus and p(photon) be the momentum of the photon.
Then, by conservation of momentum since the total moment is zero.
p(nucleus) = p(photon) = E(γ) / c = 140 keV / c
The energy for the recoiling nucleus is given as:
E² = p²c² + (mc²)²
Now, Mc² = 8.60 × 10⁻⁹J =5.38 × 10¹⁰ eV = 5.38 × 10⁷ keV
Therefore,
(Mc² + K²) ² = (14 keV)² + (Mc²)²
(1 + K²/Mc²)² =(14/Mc²)² +1
The term (1 + K²/Mc²)² is less than 1 therefore, (14/Mc²)² + 1 is equal to 1 by clacualtor.
Now using binomial theorem,
(1 + K²/Mc²)² = √[1 + ((14/Mc²)²] = 1 + (1/2)(14/Mc²)²
K = 1.82 × 10⁻³ eV
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inclined plane how much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200-n force at an angle of 30° from the horizontal?
The work it takes to slide a crate 20 m along a loading dock by pulling on it with a 200-n force at an angle of 30° from the horizontal is 346.4J.
What is work?
The energy that is transmitted to or from an object when a force is applied along a displacement is referred to as work in physics. In its simplest form, it is typically explained as the outcome of force and displacement. Positive work is the term for the component of a force that moves the point of application when it is applied. A force is said to do negative work if, at the point of application, one of its components points in the opposite direction of the displacement.
Calculations:
Work done= component of force along displacement x displacement
= F cosΘ x d
= 200cos 30 x2
= 346.4 J
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Using the graph provided, determine the velocity in meters per second of the object at t = 2 seconds.
+/-
The velocity in meters per second of the object at t = 2 seconds is 2.5 m/s
What is velocity?Velocity is simply defined as the rate of change of displacement with time. Mathematically, it can be expressed as:
Velocity = displacement / time
How to determine the velocity of the object at t = 2 sFrom the question given above, the following data were obtained:
Time = 2 sDisplacement = (3.33 + 6.67) / 2 = 5 mVelocity =?Velocity = displacement / time
Velocity = 5 / 2
Velocity = 2.5 m/s
Thus, the velocity is 2.5 m/s
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what is the repulsive force between two pith balls that are 11.0 cm apart and have equal charges of −36.0 nc?
The repulsive force between the two pith balls is 9.6 × 10⁻⁴ N.
A pith ball, which is a tiny pith ball suspended on a thread, may detect the presence and intensity of an electric charge in an object that is near or touching it.
Two pith balls are 11 cm apart from each other and both have equal charges of -36 nC.
r = 11 cm = = 11 × 10⁻² m = 0.11 m
q = q₁ = q₂ = -36 nC = -36 × 10⁻⁹ C
According to Coulomb's law, the force between two charges is given as:
F = k [ q₁ q₂ / r² ]
The constant k = 8.99 × 10⁹ N.m² / C²
Therefore,
F = (8.99 × 10⁹ ) [ (-36 × 10⁻⁹) (-36 × 10⁻⁹) / (0.11)² ]
F = (8.99 × 10⁹ ) [ 1296 × 10⁻¹⁸ / 0.0121 ]
F = (8.99 × 10⁹ ) [ 10.7 × 10⁻¹⁴ ]
F = 9.6 × 10⁻⁴ N
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Two spheres are made of the same metal and have the same radius, but one is hollow and the other is solid. The spheres are taken through the same temperature increase. Which sphere expands more?.
The ideal selection is C. The spheres will each grow evenly.
What is the coefficient of expansion?The coefficient of expansion of any material is the property of the material which defines the expansion or contraction of the material with the variation of the temperature.
The ratio of a body's length, area, or volume at a given temperature, usually 0° C, to its length, area, or volume at that temperature, respectively, while maintaining constant pressure.
Given that two spheres with the same radius and formed of the same metal are hollow and solid, respectively. The same temperature rise is applied to the spheres.
Since both bodies in this instance are formed of the same substance, their orientation has no bearing on how much it expands. Because the materials used to create both spheres were the same, we can thus conclude that they will expand equally.
Therefore, both materials will expand equally.
The complete options are given below:-
A Hollow sphere will expand more than the solid one.
B Solid sphere will expand more than the hollow one.
C Both spheres will expand equally.
D None of these
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M Two ships are moving along a line due east (Fig. P17.58). The trailing vessel has a speed relative to a landbased observation point of v₁ = 64.0km/h , and the leading ship has a speed of v₂ = 45.0 km/h relative to that point. The two ships are in a region of the ocean where the current is moving uniformly due west at v_current = 10.0km/h . The trailing ship transmits a sonar signal at a frequency of 1200.0Hz through the water. What frequency is monitored by the leading ship?
Frequency 1200 Hz is monitored by the leading ship.
Here, the leading ship serves as the observer while the trailing ship serves as the source.
Therefore, the source's velocity is v' = 64 km/h = 17.777 m/s.
Observer's speed v "= 45 km / h = 12.5 m / s
The leading ship measures frequency using the formula f'= [(v -v ') / (v - v "()] f where v = source speed = 1520 m/s
Values obtained by substitution are f' = 1502.23/1507.5*1200 = 1195.8
The study of the frequency and distribution of a disease in a defined population isThe study of illness frequency and distribution in a specific community is known as epidemiology.
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hurriquake nails help homes better withstand the damages of both earthquakes and hurricanes. the cause is largely because the larger heads they have enable them to resist 120 kilograms of uplift force. the nails dimensions are 6.4 cm x 0.3 cm. if the nail dimensions were expressed in meters, you would have to divide each number by .
If the nails dimensions were expressed in meters, we would have to divide it by 100.
In earlier times there were 3 main types of measurement systems:
1.The CGS system(centimetre, gram and second)
2.• The FPS system( foot, pound and second)
3.• The MKS system(metre, kilogram and second)
But in the present day, we use Système Internationale d’ Unites (French for International System of Units), abbreviated as SI.
The SI Unit of length is meter, but in many cases the length is given in centimeters.
So, we have to convert the value given in centimeter to meter by using the conversion factor which is,
1 meter = 100 centimeters
1 cm = 1/100 meter
Therefore, if the nails dimensions were expressed in meters, we would have to divide it by 100.
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four solid plastic cylinders all have radius 2.33 cm and length 5.82 cm. find the charge of each cylinder given the following additional information about each one.
the charge of each cylinder given the following additional information about each one is 10434.445 coulomb, 14906.35 Coulomb, 178876.2 coulomb, 223,595.25 coulomb.
Equation :To solve this question we are to use the equation 1 below :
Charge Q = uniform charge density p × Total area of the cylinder A
From the question, we are given radius, R to be 2.33 cm and length, L to be 5.82 cm.
Calculate for the total area of the cylinder, A. equation 2
Total area of the cylinder, A = area of the top surface + area of the bottom + area of the curved surface of the cylinder.
Hence, total area of the cylinder A is;
πR^2 + πR^2 + 2πRL.
Then, total area of the cylinder A is;
(L + R)2πR.
find the charge of each cylinder equation 3
For the first cylinder; we have the uniform charge density to be 35 nC/m^2.
Therefore, the combination of equation (1) and (3) gives equation 4
Charge Q= p × (L + R)2πR
Hence,
Charge Q = 35 × [(5.82 + 2.33) 2× 3.143 × 5.82]
Charge Q = 10434.445 coulomb.
For the cylinder B, we have a uniform charge density of 50 nC/m^2.
Using equation (4),
charge Q = p × (L + R)2πR
= 50 × [(5.82 + 2.33) 2× 3.143 × 5.82]
= 14906.35 Coulomb
For The cylinder C, the uniform charge density is 600, we use of equation (4);
Charge Q = 600 × 298.127
Charge Q = 178876.2 coulomb.
For cylinder D, the uniform charge density is 750 nC/m^2. use of equation (4)
Charge Q = 298.127 x 750
charge Q = 223,595.25 coulomb.
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Plane used to remove the tip of your nose
A. Transverse (top/bottom)
B. Sagittal (sides)
C. Frontal (front/back)
Plane used to remove the tip of your nose is known to be called option C. Frontal (front/back).
What is another name for the coronal plane?In regards to biology, If a person were to cut their nose off, it is one that is known to be called coronal.
The coronal plane is said to be a term that is often referred to as the frontal plane and it is seen as any vertical plane that shares the body into ventral as well as dorsal (belly and back) parts.
Therefore one can say that the coronal Plane (Frontal plane) used to remove the tip of your nose.
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In a certain experiment, a filament in an evacuated lightbulb carries a current I₁ and you measure the spectrum of light emitted by the filament, which behaves as a black body at temperature T₁ . The wavelength emitted with highest intensity (symbolized by λmax) has the value λ₁ . You then increase the potential difference across the filament by a factor of 8 , and the current increases by a factor of 2 .(i) After this change, what is the new value of the tempera-ture of the filament? (a) 16 T₁ (b) 8 T₁ (c) 4 T₁ (d) 2 T₁ (e) still T₁
Using Stefan's equation, which states that the power of the emitted radiation will be proportional to the fourth power of the absolute temperature, we treat the filament of the evacuated light bulb as a black body.
P = σ AeT⁴
Where A is the surface area of the emitter, σ is Stefan's constant, and e is the emissivity of the surface.
Now, from Stefan's Law, the radiated power is proportional to the fourth power of temperature.
P =IV
IV ∝ T⁴
Therefore,
I₁ V₁ / (I₂ V₂) = (T₁ / T₂)⁴
T₁ / T₂ = (I₁ V₁ / I₂ V₂)^{1/4}
T₂ = T₂ [ (I₁ V₁ / I₂ V₂)^{1/4} ]
Now we have,
I₂ = 2I₁ and
V₂ = 8V₁
Therefore,
T₂ = T₁ [ (2I₁ )(8V₁)/(I₁ V₁) ]^{1/4}
T₂ = T₁ (16)^{1/4}
T₂ = 2T₁
The correct option is (d).
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A ball is thrown straight up into the air with a velocity of 63. 7 m/s. What is the velocity after 3s?
The ball that is thrown straight up into the air with a velocity of 63. 7 m/s after 3s will have a velocity of: 34.3 m/s
The formula for the vertical launch upward and the procedure we will use is:
vf = v₀ - g * t
Where:
v₀ = initial velocityg = gravityt = timevf= final velocityInformation about the problem:
g = 9.8 m/s²v₀ = 63. 7 m/st = 3 svf =?Applying the final velocity formula we get:
vf = v₀ - g * t
vf = 63. 7 m/s - 9.8 m/s² * 3 s
vf = 63. 7 m/s - 29.4 m/s
vf = 34.3 m/s
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.
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What does a radio wave do to the charges in the receiving antenna to provide a signal for your car radio?
Radio waves allows the charges in the receiving antenna to respond to the electric field portion of the carrier wave.
What is a wave?This refers to a type of disturbance which transports energy from one place to another without the actual movement of the particles and of various types such as microwaves, radio waves etc.
The radio wave allows the electrons in the rod to vibrate with amplitudes which emulates those of the carrier wave and in this case, it is the antenna thereby resulting in the signals in the car radio being provided as a result of these type of interactions.
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Helllp
What is velocity at d,e,g,h and j
PLEASEEEEE HELP NO ONE EVER HELPS ME
Switch on your light source and make sure it's shining onto a wall.hold your largest cardboard square between the light source and the wall.wha do you observe?
Light source will pass through and form a shadow, when I hold the largest cardboard between the light source and the wall. Since, the cardboard is not so thick it will allow rays to pass through it.
Light rays always travel in a straight line. A shadow is formed when the light rays hit an opaque object. Sun is a natural source of light. The rays from the sun fall on objects on earth and forms shadows. Light rays do not interfere with each other if they come cross each other. Light rays travel from the direction of source to the direction of eye. They show property of reflection wherein after colliding a surface they trace their path back.
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reduction in cerebral blood flow in areas appearing as white matter hyperintensities on magnetic resonance imaging author links open overlay paneladam m.brickman
Answer: Conclusion White matter hyperintensities predict an increased risk of stroke, dementia, and death. Therefore white matter hyperintensities indicate an increased risk of cerebrovascular events when identified as part of diagnostic investigations, and support their use as an intermediate marker in a research setting
What is the difference between a testing and outcome variable??
Answer:
The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.
Explanation:
Hope this helps!
a roller coaster has 800,000 joules of kinetic energy and is moving with a speed of 40 m/s. what is the mass of the roller coaster in kg?
1000kg is the mass of the roller coaster in kg
The speed of the roller coaster is, v=20ms−1
Ek=1/2⋅1000⋅20∧2=2⋅10∧5J
In a roller coaster, how do mass and kinetic energy relate?The mass and speed of an item affect its kinetic energy, which is the energy of motion. As the coaster cars lose height, the train accelerates. As a result, their initial potential energy, which was caused by their height, is converted into kinetic energy (revealed by their high speeds).
Kinetic energy has the following formula where m is the object's mass and v is its square velocity. The kinetic energy is measured in kilograms-meters squared per second squared if the mass is measured in kilogrammes and the velocity is measured in metres per second.
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a group of students launches a model rocket in the vertical direction. based on tracking data, they determine that the altitude of the rocket was 89.6 ft at the end of the powered portion of the flight and that the rocket landed 17 s later. the descent parachute failed to deploy so that the rocket fell freely to the ground after reaching its maximum altitude. assume that g
The speed of rocket is ,V₀ = 268.42ft/sec
A projectile is an object upon which the only force is gravity.
a rocket launched in vertical direction by a group of students.
The path of projectile will be parabola.
to find the speed of the rocket is we use the equation of a projectile motion the data determined by them is
Initial height is.[tex]y_{0 } =[/tex] 89.6 ft
final height is [tex]y_{f} =[/tex] 0ft
time taken, t = 17sec
as we know , g = 32.2 ft/s²
g is acceleration due to gravity.
[tex]y_{f} - y_{o} = V_{o}t - \frac{1}{2} g t^{2}[/tex]
0 = 89.6 + 17V₀ - 16.1 × (17)²
V₀ = 268.42ft/sec
The speed of rocket is ,V₀ = 268.42ft/sec
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20. A boy runs 400 m at an average speed of 4.0 m/
s. He runs the first 200 m in 40 s. How long does he
take to run the second 200 m?
Answer:
40s to run the second 200 m
Explanation:
the average speed is 4.0 m/s
if he is moving at a constant speed he should be able to run the first and second have at the same time
An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 350 m from the crossing and its speed is 12 m/s. If the engineer’s reaction time is 0.56 s, what should be the magnitude of the minimum deceleration to avoid an accident? Answer in units of m/s^2.
The magnitude of the minimum deceleration to avoid an accident is 2,186.5 m/s².
Minimum acceleration to avoid accidentThe minimum acceleration to avoid accident is calculated as follows;
s = ut + ¹/₂at²
where;
u is the initial velocitya is the minimum accelerationt is time of motionSubstitute the given parameters and solve for the acceleration as follows;
350 = 12(0.56) + ¹/₂(0.56²)a
350 = 6.72 + 0.157a
0.157a = 350 - 6.72
0.157a = 343.28
a = 343.28/0.157
a = 2,186.5 m/s²
Thus, the magnitude of the minimum deceleration to avoid an accident is 2,186.5 m/s².
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A conducting rod is moving perpendicularly through a uniform magnetic field. Why does the motional emf drop to zero when the conductor stops moving in the field?.
The electric charge on the rod is no longer separated.
If the magnetic field is parallel to the position of the exposed surface the magnetic flux produced will be zero if the magnetic field is non-zero. If a charged particle moving parallel to the magnetic field has a velocity parallel to the magnetic field, then the force is zero In the above case the velocity is parallel to the magnetic field lines, so the magnetic force is zero.
Induced currents can be created by changing the strength of the magnetic field changing the size of the wire loop, or changing the direction of the wire loop. The main difference between magnetic flux and flux density is that magnetic flux is a scalar quantity whereas flux density is a vector quantity. Flux is the scalar product of flux density and area vector.
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a copper cable carries a current of 300 a. if the power loss is 2 w per meter, find the radius of the cable. (the resistivity of copper is 1.7x10-8 ωm.)
The radius of the copper cable, carrying 300A current with 2 W/ m power loss, is 0.0156 m or 15.6 mm.
First, let us list the given:
Current (I) = 300 APower Loss (P) = 2 W / m Resistivity (ρ) = 1.7 X 10 -8 Ω mThe formula that will be used to solve for the radius of the cable is shown below.
Power (P) = [tex]I^{2} * R[/tex] R = (ρ*L) / AA = π*[tex]radius^{2}[/tex]Wherein: R = resistance, L= length of cable, and A = cross-section area of cable.
In solving for R, the length of the cable is assumed to be 1 m since the unit of power should be in W.
(2 W / m)(1 m) = [tex](300 A)^{2}*R[/tex]
R= 2.22 x 10 -5 Ω
Solve for the cross-section area of the cable.
R = 2.22 x 10 -5 Ω = [(1.7 X 10 -8 Ω m)*(1 m)] / A
A = 7.65 x 10 -4 square meters
Solve for the radius of the cable.
A = 7.65 x 10 -4 square meters = *[tex]radius^{2}[/tex]
radius = [tex]\sqrt{\frac{7.65x10^{-4} }{pi} }[/tex] = 0.0156 m or 15.6 mm
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The micrometer 1 is often called the micron , a) how many microns make up 1.8km ? b) how many centimeters equal 1.8 ? c) how many microns are in 1.8 yd ?
By unit conversion, the converted unit is
a. 1.8 km = 1.8 x 10⁹ μm
b. 1.8 μm = 1.8 x 10¯⁴ cm
c. 1.8 yard = 1645920 μm
We need to know about unit conversion to solve this problem. The unit conversion can be used to convert a unit to another unit. It can be defined as
a = xb
where a is unit a, b is unit b and x is the constant of conversion.
From the question above, we know that
a. 1.8 km = .... μm
b. 1.8 μm = .... cm
c. 1.8 yard = .... μm
Find the microns (1 km = 10⁹ μm)
1.8 km = 1.8 x 10⁹ μm
Find the centimeter (1 cm = 10⁴ μm)
1cm = 10⁴ μm
1/10⁴ cm = 1 μm
Hence,
1.8 μm = 1.8/10⁴ cm
1.8 μm = 1.8 x 10¯⁴ cm
Find the microns (1 yd = 914400 μm)
1.8 yard = 1.8 x 914400 μm
1.8 yard = 1645920 μm
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the gauge pressure at the bottom of a cylinder of liquid is 0.40 atm . the liquid is poured into another cylinder with twice the radius of the first cylinder. part a what is the gauge pressure at the bottom of the second cylinder?
The gauge pressure at the bottom of the second cylinder is 0.10 atm.
What do you mean by gauge pressure?The pressure of a system above the atmospheric pressure is known as gauge pressure, commonly referred to as overpressure. The pressure from the weight of the atmosphere is included in gauge pressure readings because gauge pressure is zero-referenced against ambient air (or atmospheric) pressure. This indicates that gauge pressure varies in response to both weather and height above sea level. Gauge pressure measurement is adequate for the majority of industrial applications because every operation in a refinery or manufacturing facility operates at the same air pressure. Absolute pressure is a measurement of pressure that is based on a reference pressure of zero or absolutely no pressure. The only place where this happens naturally is in a perfect vacuum, which can only be found in space.
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Two long, parallel conductors, separated by 10.0cm, carry currents in the same direction. The first wire carries a current I₁ = 5.00A, and the second carries I₂ = 8.00 A. (b) What is the force per unit length exerted by I₁ on I₂ ?
The force per unit length exerted by I₁ on I₂ is [tex]8\times10^-^5 \ N/m[/tex] .
Two long parallel conductors separated by a distance 'r' having current [tex]I_1[/tex] and [tex]I_2[/tex] have force per unit length which is given by [tex]f=\frac{u_0I_1I_2}{2\pi r}[/tex] .....(1) where [tex]u_0[/tex] is permittivity of free space whose value is [tex]4\pi \times10^-^7Tm/A[/tex]
It is given that two long, parallel conductors, separated by 10.0cm having current I₁ = 5.00A and I₂ = 8.00 A.
If the current flowing through the wire are in same direction then they the wire attract each other and if the current flowing through the wire are opposite in direction then they the wire repel each other
Putting r = 10.0cm [tex]=10\times10^{-2}m[/tex] , I₁ = 5.00A and I₂ = 8.00 A in equation (1) , we get
[tex]f=\frac{4\pi \times10^-^7\times5.00\times8.00}{2\times\pi\times10.00\times10^{-2}}\\\\f=\frac{2\times40\times10^-^5}{10} \\\\f=8\times10^{-5}N/m[/tex]
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Review. For a certain type of steel, stress is always proportional to strain with Young's modulus 20 × 10¹⁰ N/m² . The steel has density 7.86× 10³kg / m³. It will fail by bending permanently if subjected to compressive stress greater than its yield strength бy = 400MPa. A .rod 80.0cm long, made
of this steel, is fired at 12.0 m/s straight at a very hard wall.(e) the stress in the rod.
[tex]4.78\times 10^8\ \mathrm{Pa}$[/tex] is the stress in the rod.
Given:
Young's modulus, Y = [tex]20 \times 10^{10}\;N/m^{2}[/tex]
Steel density, [tex]\rho = 7.86 \times 10^{3}\;kg/m^{3}[/tex]
Length of the rod, L = 80 cm = 0.800m
The speed of the wave in the rod is,
[tex]$t=\frac{L}{v} = \frac{0.800\ \mathrm{m}}{5044\ \mathrm{m/s}} = 1.58\times 10^{-4}\ \mathrm{s}$[/tex]
Hence the time taken by the wave to travel the end of the rod is,
[tex]$t=\frac{L}{v} = \frac{0.800\ \mathrm{m}}{5044\ \mathrm{m/s}} = 1.58\times 10^{-4}\ \mathrm{s}$[/tex]
The velocity of the rod is, [tex]$v_r = 12.0\ \mathrm{m/s}$[/tex]
The other end will keep moving after the front end hits the wall until the wave reaches the other end, given the period determined by the above problem.
As a result, before the wave reaches the end of the rod, it has traveled a distance of
[tex]$\Delta L = v_r t = (12.0\ \mathrm{m/s}) (1.58\times\ \mathrm{s}) = 1.90\times 10^{-3}\ \mathrm{m} = 1.90\ \mathrm{mm}$[/tex]
The strain in the rod is given by,
[tex]$\frac{\Delta L}{L} = \frac{1.90\times 10^{-3}\ \mathrm{m}}{0.800\ \mathrm{m}} = 2.37\times 10^{-3}$[/tex]
The Young's modulus is given by,
[tex]$Y = \frac{F/A}{\Delta L/L}$[/tex]
Now, we may write that the stress is given by using the equation above,
[tex]$\frac{F}{A} = Y\frac{\Delta L}{L} = \left( 20\times 10^{10}\ \mathrm{N/m^2} \right) \left ( 2.73\times 10^{-3} \right ) = 4.78\times 10^8\ \mathrm{Pa}$[/tex]
Hence, [tex]4.78\times 10^8\ \mathrm{Pa}$[/tex] is the stress in the rod.
What is Stress?Stress is a tangible property in continuum mechanics. It happens as a result of a body being subjected to tension or compression forces. Stress is defined as a force per unit area within a material that results from externally applied forces, unequal heating, or persistent deformation and that enables an accurate description and prediction of elastic, plastic, and fluid behavior in physical sciences and engineering. By dividing a force by an area, a stress is expressed.
Various forms of stress exist. Shear stress results from forces that are parallel to and reside in the plane of the material's cross-section, whereas normal stress results from forces that are perpendicular to the area.
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