The operational amplifier circuit that will give an output that is proportional to the integral of the input voltage is the circuit with Input 1 and Output, as this is an integrator circuit.
An integrator circuit uses an operational amplifier and a feedback resistor to generate an output voltage that is proportional to the integral of the input voltage. The integral of a signal represents the area under the curve, and the feedback resistor in an integrator circuit causes the output voltage to increase or decrease in proportion to the area under the input voltage curve. Therefore, the Output of the integrator circuit will be proportional to the integral of the Input 1 voltage.
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A block of wood is kept on table top. The mass of wooden block is 5 kg and its dimensions are 40cmx20cmx10cm. 1. Calculate the area of the wooden block in cm2 and in2. 2. Calculate the volume of the wooden block in cm3 and in3. 3. Compute the density of the wooden block in g/cm3 and lb/in3. 4. Compute the pressure. 5. Compute the pressure on top surface of the wooden block. 6. Compute the pressure on the bottom surface of the wooden block. 7. Compute the force on top surface of the wooden block. 8. Compute the force on the bottom surface of the wooden block. 9. What is the difference between the force on the bottom and the force on top?
Let's calculate the values based on the given information:
The area of the wooden block can be calculated by multiplying the length and width of one of its faces:
Area = Length * Width
Area = 40 cm * 20 cm
Area = 800 cm²
To convert to square inches, we can use the conversion factor 1 inch = 2.54 cm:
Area in square inches = Area in square centimeters / (2.54 cm/inch)²
Area in square inches = 800 cm² / (2.54 cm/inch)²
Area in square inches ≈ 124.03 in²
The volume of the wooden block can be calculated by multiplying its length, width, and height:
Volume = Length * Width * Height
Volume = 40 cm * 20 cm * 10 cm
Volume = 8000 cm³
To convert to cubic inches, we can use the conversion factor 1 inch = 2.54 cm:
Volume in cubic inches = Volume in cubic centimeters / (2.54 cm/inch)³
Volume in cubic inches = 8000 cm³ / (2.54 cm/inch)³
Volume in cubic inches ≈ 488.19 in³
The density of the wooden block can be calculated by dividing its mass by its volume:
Density = Mass / Volume
Density = 5 kg / 8000 cm³
To convert to grams per cubic centimeter (g/cm³), we can use the conversion factor 1 kg = 1000 g:
Density in g/cm³ = Density in kg/cm³ * 1000 g/kg
Density in g/cm³ = (5 kg / 8000 cm³) * 1000 g/kg
Density in g/cm³ ≈ 0.625 g/cm³
To convert to pounds per cubic inch (lb/in³), we can use the conversion factor 1 kg = 2.20462 lb and 1 inch = 2.54 cm:
Density in lb/in³ = Density in kg/cm³ * (2.20462 lb/kg) / (2.54 cm/inch)³
Density in lb/in³ = (5 kg / 8000 cm³) * (2.20462 lb/kg) / (2.54 cm/inch)³
Density in lb/in³ ≈ 0.036 lb/in³
Pressure is defined as force divided by area. In this case, we need more information to calculate the pressure. If the block is subjected to a specific force, we can divide that force by the appropriate surface area to find the pressure.
The pressure on the top surface of the wooden block depends on the force applied to it. Without information about the applied force, we cannot calculate the pressure.
Similarly, the pressure on the bottom surface of the wooden block depends on the force applied to it. Without information about the applied force, we cannot calculate the pressure.
The force on the top surface of the wooden block depends on the pressure applied and the surface area. Without information about the pressure or force applied, we cannot calculate the force.
The force on the bottom surface of the wooden block depends on the pressure applied and the surface area. Without information about the pressure or force applied, we cannot calculate the force.
Without the values for forces on the top and bottom surfaces, we cannot determine the difference between them.
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1. The area of the wooden block can be calculated using the formula for the surface area of a rectangular prism: SA = 2(lw + lh + wh), where l, w, and h are the length, width, and height of the block, respectively. Using the given dimensions, we can find the surface area in cm²:
SA = 2(40 × 20 + 40 × 10 + 20 × 10)
SA = 2(800 + 400 + 200)
SA = 2(1400)
SA = 2800 cm²
To convert cm² to in², we can use the conversion factor 1 in² = 6.45 cm². So, the area in in² is:
2800 ÷ 6.45 = 434.96 in² (rounded to two decimal places)
2. The volume of the wooden block can be calculated using the formula for the volume of a rectangular prism: V = lwh. Using the given dimensions, we can find the volume in cm³:
V = 40 × 20 × 10
V = 8000 cm³
To convert cm³ to in³, we can use the conversion factor 1 in³ = 16.39 cm³. So, the volume in in³ is:
8000 ÷ 16.39 = 487.61 in³ (rounded to two decimal places)
3. The density of the wooden block can be calculated using the formula: density = mass/volume. The mass of the block is given as 5 kg. To convert this to grams, we can use the conversion factor 1 kg = 1000 g. So, the mass in grams is:
5 kg × 1000 g/kg = 5000 g
Using the volume calculated in part 2, we can find the density in g/cm³:
density = 5000 g/8000 cm³
density = 0.625 g/cm³
To convert g/cm³ to lb/in³, we can use the conversion factor 1 g/cm³ = 0.0361 lb/in³. So, the density in lb/in³ is:
0.625 g/cm³ × 0.0361 lb/in³/g/cm³ = 0.0226 lb/in³
4. The pressure on the wooden block is given by the formula: pressure = force/area. To find the pressure, we need to know the force acting on the block. Since the block is simply resting on the tabletop, the force acting on it is due to its weight. Using the formula for weight: w = mg, where w is weight, m is mass, and g is the acceleration due to gravity (9.8 m/s²).
To find the weight in newtons (N), we can use the conversion factor 1 kg = 9.8 N. So, the weight of the block is:
5 kg × 9.8 N/kg = 49 N
Using the area of the block's base (40 cm × 20 cm = 800 cm²), we can find the pressure in N/cm²:
pressure = 49 N/800 cm²
pressure = 0.06125 N/cm²
To convert N/cm² to psi, we can use the conversion factor 1 psi = 6894.76 N/m². So, the pressure in psi is:
0.06125 N/cm² × (1 m²/10,000 cm²) × (1 psi/6894.76 N/m²) = 0.0089 psi (rounded to four decimal places)
5. The pressure on the top surface of the wooden block is the same as the pressure calculated in part 4: 0.06125 N/cm² or 0.0089 psi.
6. To find the pressure on the bottom surface of the block, we can use the formula: pressure = force/area. Since the bottom surface has the same area as the top surface, the pressure will also be the same: 0.06125 N/cm² or 0.0089 psi.
7. The force acting on the top surface of the wooden block is simply its weight, which we calculated to be 49 N in part 4.
8. The force acting on the bottom surface of the wooden block is also its weight, which we calculated to be 49 N in part 4.
9. The force on the bottom surface is equal in magnitude to the force on the top surface.
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The scatterplot shows the distance (in feet) that a person was from a motion sensor during an experiment in math class. Use the labeled points to create a linear model. About what distance in feet (y) would a person be 8 seconds after the experiment begins? 21 ft 27 ft 30 ft 57 ft.
A person would be 30 feet (y) 8 seconds (x) after the experiment begins.
The scatterplot shows a linear relationship between the distance (in feet) from the motion sensor and the time (in seconds) since the start of the experiment.
Using the two labeled points (8 seconds, 21 feet) and (15 seconds, 57 feet), we can use the line equation y = mx + b to create a linear model. The slope (m) equals (57 feet - 21 feet)/(15 seconds - 8 seconds) = 36 feet/7 seconds, and the y-intercept (b) equals 21 feet.
Using the linear model, we can estimate that a person would be 30 feet (y) 8 seconds (x) after the experiment begins.
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A car traveling at 50 m/s comes to a stop in 5 seconds. What is the
acceleration of this?
Answer:
10
Explanation:
10 is the answer because you divide 50 and 5 and your answer is 10.
Hope this helps:)
Pls mark brainlist
Answer:
a = -10m/s²
Explanation:
Givens:
Vf = 0m/s
Vi = 50m/s
t = 5s
Use the following kinematic equation:
Vf = Vi+at
Rearrange
a = (Vf-Vi)/t
a = -10m/s²
How long will it take for a radioactive sample to decrease to 10% if its half-life is 22 years?
If the half-life of a radioactive sample is 22 years, it will take 73.11 years for the sample to decay to 10%.
How is half-life used to calculate radioactive decay?A fixed percentage of activity is lost during radioactive decay per unit of time. Half-life: The amount of time needed for a sample to degrade to 50% of its starting state. 1/2 = e –(λ*T1/2). constant over time and unique to each nuclide.
Do longer half-lives imply a lower radioactivity?The term (physical) half-life refers to the amount of time needed for radioactivity to decline and split in half. Half of the radioactivity will remain after a period of time equal to the half-life has passed, and a further half of the radioactivity will remain after a period of time twice as long as the half-life has passed.
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What does it mean when di is negative?
Answer:When the image distance is positive, the image is on the same side of the mirror as the object, and it is real and inverted. When the image distance is negative, the image is behind the mirror, so the image is virtual and upright.
Explanation:
Using the Left Hand Rule, if current points up and
the field is toward you, which way does the motion
point?
A. Left
B. Down
c. Up
D. Right
Using the left hand rule, if current points up and the field is toward you, the motion points up.
What is the left hand rule?The left hand rule states that if the thumb, the fore finger and the middle finger are held mutually perpendicular to each other, the thumb points in the direction motion, the middle finger points in the direction of current while the fore finger points in the direction of the magnetic field.
Thus using the left hand rule, if current points up and the field is toward you, the motion points up.
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Integrated Concepts:_______.
(a) Calculate the ratio of the highest to lowest frequencies of electromagnetic waves the eye can see, given the wavelength range of visible light is from 380 to 760 nm.
(b) Compare this with the ratio of highest (20,000 Hz) to lowest (20 Hz) frequencies the ear can hear.
a). frequency = (speed) / (wavelength)
The speed of light is around 3 x 10⁸ m/s.
For 380 nm (violet light), frequency = (3 x 10⁸ m/s) / (380 x 10⁻⁹ m)
Frequency = 7.89 x 10¹⁴ Hz
For 760 nm (red light), frequency = (3 x 10⁸ m/s) / (760 x 10⁻⁹/s)
Frequency = 3.94 x 10¹⁴ Hz
The ratio is 2 .
That's 1 octave, or 0.3 of a decade.
b). The ratio of highest/lowest sounds is (20,000 Hz/20 Hz) = 1,000
That's 3 decades, or about 10 octaves.
===> Speaking logarithmically ( ! ), ears are sensitive to a range of sound frequencies that's 10 times as wide as the range of light frequencies that eyes can detect.
A Volkswagen Bug and a Volvo truck have a head-on collision. Which statement is true??
a. The greater force acts on the Volvo truck.
b. Both forces are identical.
c. The greater force acts on the Volkswagen Bug.
d. The magnitudes of both forces are the same.
Both forces have equal amplitudes. When a Volkswagen Bug and a Volvo truck collide head-on, the statement will be accurate in this instance. Due to collision.
The force's strength to effect the required change is determined by its magnitude. It acts in a specific direction and has a certain magnitude. Contact or non-contact force is both possible. Applying force in one form or another is how almost all daily tasks are completed. A force's strength is quantified by a number called its magnitude. Take a force of 10 N, for instance, in the direction of the east. The phrase "towards east" denotes a direction, and "10" represents the force's magnitude.
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What is the work input to lift a box of 810 with a 50% mechanical efficiency?
Answer:
Work input = 1620
Explanation:
Given the following data;
Work output = 810
Efficiency = 50%
To find the work input;
Mathematically, efficiency is given by the formula;
\( Efficiency = \frac {Out-put \; work}{In-put \; work} * 100 \)
Substituting into the formula, we have;
\( 50 = \frac {810}{WI} * 100 \)
Cross-multiplying, we have;
\( 50I = 810 * 100 \)
\( 50I = 81000 \)
\( WI = \frac {81000}{50} \)
Work input = 1620
After a storm, a hospital may have to rely on backup generators to power some equipment. Which is the energy conversion provided by the generators?.
After a storm, a hospital may have to rely on backup generators to power some equipment.Energy conversion provided by the generators is mechanical energy to electrical energy.
ABOUT ENERGYEnergy is the ability to do work (effort). Energy is basically available in nature, everything that is available in nature and contains energy is called an energy source.
, Energy is abstract and difficult to prove but its existence can be felt. Energy cannot be created or destroyed, but can change form (conversion) from one form of energy to another. This is also known as the law of the conservation of energy. This energy needs to be converted so that it can be used according to human needs. For example, the most important source of energy on earth, the sun. Since ancient times, humans have used solar cells from the sun to produce electricity.
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PLEASE HELP 25 POINTS !!!!!!!!!!!!!!!! Add the following numbers and round your answer to the correct number of significant figures:
90.0 + 80 =
Show both the unrounded and rounded answer.
Answer:
90.0 + 80 = 170
2 signifigant figures
1.70 x 10^2
the amount of energy at the end of the system (output) is different from the starting energy (input). How does this not violate (break) the law of the conservation of energy. This question is based on solar and wind energy
Answer:
Because some of the energy escaped or was used.
Explanation:
Do you think cell division stops after a new baby is born? Why or why not?
Answer:
No.
Explanation:
The method of cell division, the transformation of the baby into an adult in itself is accomplished. Until your death, cell division continues. The formation of new white blood cells to replace the killed ones after a cut and the development of skin to replace the skin that has been cut are some examples of cell division.
The electric field from a sheet of charge is perpendicular to the sheet and has a constant magnitude of Q/(Aeo), where A is the area of the sheet and Q is the charge on the sheet. If the sheet has an area, A=32.93 cm2, and a charge of 20.93 microC, what force, in nanoNewtons, would an electron experience due to this electric field?
The exercise tells us that the electric field is given by the following equation:
\(\vec{E}=\frac{Q}{A\epsilon_0}\)And it also gives us, A and Q. Thus, our electric field inside the capacitor is:
\(E=\frac{20.93*10^{-6}}{(32.93*10^{-4})*(8.85*10^{-12})}=718181521.8\frac{V}{m}\)As we know, the electric force can be written as:
\(F=q.E\)The charge of an electron is a constant, which is q=1.6*10^(-19) C.
Finally, our force can be written as:
\(F=1.6*10^{-19}*718181521.8=1.149*10^{-19}=0.00001149microN\)Our final answer is 0.00001149 micro Newtons
What is the direct path and direction from point A to B? 1,Motion 2,Time 3,Distance 4,Displacement PLS HURRY!
The direct path and direction from point A to B is called "Displacement". (Option D).
How else can displacement be defined?Displacement is described as a change in an object's location. It is a vector quantity with a magnitude and a direction. It is depicted as an arrow pointing from the starting point to the ending point.
For instance, if an object travels from A to B, the object's location changes. Displacement is the change in the location of an item.
The mathematical expression of displacement is given as:
Δx = xf - x₀; Where
xf = Final Position
x₀ = Initial position; and
Δx = displacement.
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for the peptide with the sequence alrhen. how many positive ion peaks should appear is an esi-ms spectrum?
In an ESI-MS spectrum of the peptide ALRHEN, we would expect to observe one positive ion peak.
The charge state of the peptide ions generated during electrospray ionisation determines the number of positive ion peaks in an ESI-MS spectra for ALRHEN.
In ESI-MS, peptides absorb or lose protons to generate charged ions. pH and analyte determine charge state.
ALRHEN peptides have many ionisation sites and charge states. The amino and carboxyl termini and charged amino acids like lysine and arginine are the most typical peptide ionisation sites.
The peptide ALRHEN has an N-terminus and a C-terminus, but no charged amino acid residues. In the absence of other ionizable groups, the peptide would have a net charge of +1, equating to a single charged ion.
ESI-MS spectrum ions represent peptide charge states. The spectrum should show one positive ion peak as the peptide ALRHEN has a net charge of +1.
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An Olympic sprinter runs two laps around an 800 m circular track in 5 minutes.
What is the sprinter's displacement after she returns to her initial position?
O
O
O
0m
800 m
160 m
1,600 m
The sprinter's displacement after she returns to her initial position is 0 m.
option A is the correct answer.
What is displacement of the sprinter?
The displacement of the sprinter is the change in the position of the sprinter after the race. It is also the shorted distance between the initial position of the sprinter and the final position of the sprinter.
Mathematically, the formula for the change in the position of the sprinter is given as;
Δx = xf - xi
where;
xf is the final position of the sprinterxi is the initial position of the sprinterwhen the sprinter starts from point A of a circular track and returns to the starting point A, that is one lap. When the sprinter moves again and returns to the same starting point A, that is two laps.
From the above illustration, the final position of the sprinter is equal to the initial position of the sprinter.
Δx = xf - xi
xf = xi
Δx = 0 m
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plzs help me asap!!!!!
Directions: Write a T in the blank for True, or an F for False.
6. Newton's First Law states that every action has an equal/opposite reaction.
7. Newton's Second Law can be simplified to F=ma.
8. An object will move in the same direction as the unbalanced force acting upon it.
9. Friction always acts in the same direction as the motion of the object.
10. If there is no next force acting on an object, that means in ALL SITUATIONS that the object will not move.
Answer:
6. False 7. True 8. False (Unbalanced forces acting upon an object changes the object's motion) 9. False 10. True (I'm not 100% sure if these answers are right though.)
Answer:
I confirm that answer LOL
Explanation:
Express 48 m/s in terms of
1.km/h
2.m/min
3.km/s
4.km/minutes
48 m/s in terms of km/h is 720.8 km/h. In terms of m/min is 2880 m/min, in terms of km/s is 0.048 km/s and in terms of km/min is 2.88 km/min.
To solve this question, we need to understand some terms. The unit of velocity is measured in m/s. It can be expressed in different units of velocity.
1 km (kilometer) = 1000 meter
1 h (hour) = 3600 seconds
1 minutes = 60 seconds
To convert m/s into km/h,
48 m/s * 3600/1000 = 172.8 km/h
To convert m/s into m/min,
48 m/s * 60 = 2880 m/min
To convert m/s into km/s,
48 m/s ÷ 1000 = 0.048 km/s
To convert m/s into km/minutes,
48 m/s * 60 / 1000 = 2.88 km/min
Therefore, the 48 m/s expressed is 172.8 km/h, 2880 m/min, 0.048 km/s and 2.88 km/min.
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48 m/s is equivalent to 172.8 km/h, 2880 m/min, 0.048 km/s, and 2.88 km/minute.
To express 48 m/s in different units of velocity:
km/h (kilometers per hour):
To convert m/s to km/h, we can use the conversion factor of 3.6 since 1 m/s is equal to 3.6 km/h.
48 m/s * (3.6 km/h / 1 m/s) = 172.8 km/h
Therefore, 48 m/s is equivalent to 172.8 km/h.
m/min (meters per minute):
To convert m/s to m/min, we can use the conversion factor of 60 since there are 60 seconds in a minute.
48 m/s * (60 m/min / 1 s) = 2880 m/min
Therefore, 48 m/s is equivalent to 2880 m/min.
km/s (kilometers per second):
Since 1 kilometer is equal to 1000 meters, to convert m/s to km/s, we divide the value by 1000.
48 m/s / 1000 = 0.048 km/s
Therefore, 48 m/s is equivalent to 0.048 km/s.
km/minute (kilometers per minute):
To convert m/s to km/minute, we first need to convert m/s to km/s (as calculated in the previous step) and then multiply by 60 to convert seconds to minutes.
0.048 km/s * 60 = 2.88 km/minute
So, 48 m/s is equivalent to 2.88 km/minute.
Hence, 48 m/s is equivalent to approximately 172.8 km/h, 2880 m/min, 0.048 km/s, and 2.88 km/minute.
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A rock is thrown straight upward with an initial velocity of 20 m/s where the downward acceleration due to gravity is -10 m/s^2. How long is the ball in the air before it returns to the thrower's hand?
Answer:
4 seconds
Explanation:
Given:
Δy = 0 m
v₀ = 20 m/s
a = -10 m/s²
Find: t
Δy = v₀ t + ½ at²
0 m = (20 m/s) t + ½ (-10 m/s²) t²
0 = 20t − 5t²
0 = 5t (4 − t)
t = 4
How much the aproximate number of atoms in bacteria.assume that average mass of an atom in bacteria is ten times the mass of hydrogen atom
Ice cubes float in a glass of iced tea. why would cooling be less if the cubes were instead on the bottom of teh drink?
Ice cubes float in a glass of iced tea because due to a lack of convection, ice cubes will cool more slowly if they are on the bottom. Ice is denser than water at 4° C.
Heat is transferred through convection, which is the large-scale movement of molecules inside gases and liquids. Conduction is used to move heat from the object to the fluid initially, but the fluid motion is responsible for the bulk of the heat transfer.
Natural convection is caused by the fact that most fluids have a tendency to expand when heated, which causes them to become less dense and rise due to the increased buoyancy. Heat is transferred between two bodies by currents of moving gas or fluid, which is known as convection. In free convection, air or water rises and is replaced by a cooler parcel of air or water as it moves away from the hot body.
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A car travels from rest (0) to 60 m/s in 5 seconds. What is its acceleration?
Answer:
12 meters per seconds......
Explanation:
60/5=12
A car travels from rest to 60 m/s in 5 seconds, so its acceleration is 12 m/\({s}^2\) (60-0/5), and the acceleration is calculated by subtracting the final from the initial and by diving with the time.
What is the significance of the acceleration?Acceleration is the unit that describes the change in velocity, such as the quickness or slowness of the car, and when the acceleration is very high, there is a high chance of colliding and an accident occurring, but this is important for vehicles such as sports cars and racing cars. While low acceleration is used in magnetic resonance imaging in the medical field, it is also used in the industrial sector for robotics, etc.
Hence, a car travels from rest to 60 m/s in 5 seconds, so its acceleration is 12 m/\({s}^2\) (60-0/5), and the acceleration is calculated by subtracting the final from the initial and by diving with the time.
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a boat ended up with a velocity of 30.m/s [N30.E] after it experienced an acceleration of 3.0m/s^2 [S] for a period of 4.0s what displacement did the boat cover
Answer:
96 m
Explanation:
The average velocity over those 4 seconds is the velocity after 2 seconds:
30 m/s -(2 s)(3.0 m/s^2) = 24 m/s
The displacement is the product of this average velocity and the duration of the acceleration:
d = (24 m/s)(4 s) = 96 m
The boat covered 96 m while being accelerated.
A hockey player skates across a rink of length 75m in 8.9 seconds. What is the average speed of the hockey player? The hockey player is moving at a speed of 9.5 m/s. If it takes him 2 seconds to come to a stop under constant acceleration, how far does he travel while stopping?
The average velocity is given by
\(v=\frac{d}{t}\)Where d is the distance covered and t is the time taken.
For the given case, we have
d = 75 m
t = 8.9 s
\(v=\frac{d}{t}=\frac{75}{8.9}=8.43\; \frac{m}{s}\)Therefore, the average speed of the hockey player is 8.43 m/s
The hockey player is moving at a speed of 9.5 m/s.
3. A class took a field trip to a music studio. The students watched through thick glass as the musicians played
music inside the studio. The students could only hear the music when the studio door was open. The less
separating the musicians from the students is made with two layers of thick glass. The space between the glass
Layers has had all the air removed, creating a vacuum.
Which statement best explains why the students were able to see the musicians even while they were unable to
hear them?
Answer:
Sound can't travel in a vaccum.
Explanation:
Sound waves need a medium in order to travel (e.g. air, water, glass)
Since there was a vaccum between the glass the sound couldn't travel since vaccum's contain a very small amount of atoms.
A circuit diagram with a power source labeled 12 V is connected to 3 resistors in series. The resistors are labeled 1.0 Ohms, 2.0 Ohms, and 3 Ohms. Calculate the equivalent resistance in the circuit shown.
0.55 Ω
1.8 Ω
2.0 Ω
Its A "0.55" I guessed and got it right
Answer:
there it is fella u were right with ur answer
From his observations of the phases of venus, galileo concluded that the ptolemaic model of planetary motion was wrong because it predicted.
Galileo’s telescopic discoveries of the moons of Jupiter are often mentioned. But they did not amount to proof that the Ptolemaic system was incorrect.
It's hard to tell you how big a shakeup this caused in astronomy at the time. Thanks to Galileo, we now knew that planets weren't perfect, ethereal lights in the sky. That things could orbit them, same as (most astronomers thought) things did around Earth, making Earth less special, and providing evidence that maybe that heliocentric theory wasn't that out there.
Basically, before Galileo, astronomers were looking at an unchanging, heavenly firmament, separate from Earth by its very heavenly nature.
After, they were studying planets - actual worlds like ours - and moons and the physical (as opposed to heavenly) reality of their place in the universe.
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Smaller the surface area greater the gravitational force and vice–versa yes or no? justify the statement.
Answer:
It is true that Smaller the surface area greater the gravitational force and vice versa
Explanation:
The gravitational force depends on the distance between the two objects
F=GMm/r2
where G = gravitational constant
M = mass of one object
m = mass of second object
r is the distance between the two objects
Gravitational force is inversely proportional to the square of the distance between two objects. Hence, it can be said the Gravitational force is inversely proportional to the area and hence as the area increases gravitational force will decrease or vice versa
When kayla stands on her trampoline, it sags by 0. 23 m. Now she starts bouncing. How much time elapses between the instant when she first lands on the trampoline's surface and when she passes the same point on the way up?
Kayla stands on her trampoline, it sags by 0.23 m. Now she starts bouncing, it takes approximately 1.89 seconds for Kayla to pass the same point on the trampoline's surface after bouncing up from it.
Let's assume that Kayla's motion can be modeled by simple harmonic motion. In this case, the time elapsed between successive passages through the same point is given by
T = 2π√(m/k)
Where m is the mass of the object and k is the spring constant of the trampoline.
Assuming Kayla has a mass of 50 kg, we can estimate the spring constant of the trampoline using Hooke's Law
F = -kx
Where F is the force applied by the trampoline, x is the displacement from equilibrium, and k is the spring constant. Since the trampoline sags by 0.23 m when Kayla stands on it, the force applied by the trampoline can be estimated as
F = mg + kx = (50 kg)(9.81 m/\(s^{2}\)) + k(0.23 m)
Where g is the acceleration due to gravity. Solving for k, we get
k = (mg + F)/x = [(50 kg)(9.81 m/\(s^{2}\)) + (50 N)]/0.23 m ≈ 2.61 × \(10^{3}\) N/m
Substituting this value into the equation for the period of simple harmonic motion, we get
T = 2π√(m/k) = 2π√(50 kg)/(2.61 × \(10^{3}\) N/m) ≈ 1.89 s
Therefore, it takes approximately 1.89 seconds for Kayla to pass the same point on the trampoline's surface after bouncing up from it.
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