Velocity is a physical quantity that describes the rate at which an object changes its position with respect to time. It is a vector quantity, which means that it has both a magnitude and a direction.
What is velocity?From the given information, we know that the motorboat's initial velocity is 40 ft/s and its final velocity after the motor quits is 20 ft/s. We also know that the boat experiences resistance that is proportional to its velocity. This can be modeled using the differential equation:
dv/dt = -kv
where v is the velocity of the boat and k is the constant of proportionality. To solve for k, we can use the initial and final velocities of the boat:
When t = 0, v = 40 ft/s
When t = 10 s, v = 20 ft/s
Integrating the differential equation, we get:
∫ dv/v = ∫ -k dt
ln|v| = -kt + C
where C is the constant of integration.
Applying the initial condition v(0) = 40, we get:
ln|40| = C
C = ln|40|
Substituting this value into the equation, we get:
ln|v| = -kt + ln|40|
ln|v| = ln|40| - kt
Taking the exponential of both sides, we get:
|v| = e^(ln|40| - kt)
|v| = 40e^(-kt)
Applying the final condition v(10) = 20, we get:
|20| = 40e^(-k*10)
1/2 = e^(-10k)
Taking the natural logarithm of both sides, we get:
ln(1/2) = -10k
k = -ln(1/2)/10
k ≈ 0.0693
Therefore, the constant of proportionality is k ≈ 0.0693. The velocity of the motorboat at time t is given by:
v(t) = 40e^(-0.0693t)
where v is in ft/s and t is in seconds.
To know more about velocity visit:
https://brainly.com/question/30559316
#SPJ4
now suppose you turned the dac on to charge the capacitor, then unplugged the capacitor from the dac (while the dac was still on). what happens to the voltage across the capacitor after unplugging it from the dac?
The charge will not change if the capacitor is not connected to the battery. When the plates of a capacitor are shifted further apart, the capacitance Cd1 drops.
What happens to the voltage across the capacitor?The energy stored by capacitor U(=2Cq) grows when the battery is disconnected because the charge on the capacitor stays constant.
The capacitor, which we were informed was entirely depleted, has zero voltage across it when the switch is first closed, making it appear as though there is a short circuit.
The capacitor will eventually operate as an open circuit because the voltage of the capacitor will eventually equal the voltage of the battery.
Therefore, after a capacitor is simply connected across a battery, its voltage will be the same as the battery terminal voltage when the battery is disconnected, and it will have an energy reserve equal to capacitance times voltage divided by two.
Learn more about capacitor here:
https://brainly.com/question/29100869
#SPJ4
What is symmetric about this peak?
The symmetric peak divides the lights of short wavelength and long wavelength lights, which occurs at the green light boundary.
What does a symmetric of a peak mean?
A symmetric peak refers to a peak that is roughly the same shape on both sides of the highest point. This means that the left and right sides of the peak are mirror images of each other.
Symmetric peaks are often seen in graphs or charts that represent data such as intensity versus wavelength graph as shown in the diagram.
At the the symmetric peak, the wavelength of the particle is 500 mm which corresponds to wavelength of green light.
Learn more about symmetric peak here: https://brainly.com/question/17049888
#SPJ1
assume the system is diffraction limited. approximately how many pixels are subtended by the optical point spread function?
The number of pixels subtended by the optical point spread function (PSF) depends on several factors, including the aperture size of the optical system, the wavelength of the light, and the pixel size of the imaging sensor.
What is diffraction limited?The smallest object that an optical system is capable of resolving is known as the diffraction limit, and it depends on the size of the aperture and the length of the light's wavelength. A circular pattern roughly proportionate to the aperture diameter represents the diffraction-limited PSF.
Assuming a diffraction-limited optical system with an aperture diameter of D, the diameter of the PSF can be approximated as:
d = 1.22 * λ / D
where λ is the wavelength of the light.
If we assume that the pixel size of the imaging sensor is equal to the diameter of the PSF, then the number of pixels subtended by the PSF can be approximated as:
N = (d / p)^2
where p is the pixel size.
So, for example, if we assume a visible light wavelength of 500 nm, an aperture diameter of 50 mm (which would correspond to a large camera lens), and a pixel size of 5 µm (which is typical of many digital cameras), we can calculate:
d = 1.22 * 500 nm / 50 mm = 12.2 µm
N = (12.2 µm / 5 µm)^2 = 58 pixels
In this case, the PSF would therefore be subtended by 58 pixels approximately. This is only a very rough approximation, and the precise number of pixels covered by the PSF will vary depending on a variety of elements, such as the unique characteristics of the optical system and the imaging sensor.
To know more about diffraction limited visit:
https://brainly.com/question/15081792
#SPJ4
(b) A dark nebula is a type of nebula that does not emit light.
A dark nebula looks dark because it blocks the light from stars that are behind it.
Suggest why dark nebulae are thought not to contain stellar nurseries.
*******
Dark nebulae are thought not to contain stellar nurseries because they are primarily composed of gas and dust, which are the building blocks of stars, but they are too cold and dense to collapse and form stars.
What is nebula?A nebula is a distinctively luminous region of the interstellar medium, which may be made up of cosmic dust, neutral, neutrally ionized, or molecular hydrogen.
Because dark nebulae are predominantly made of gas and dust, the raw materials for stars, but are too cold and dense to collapse into stars, it is believed that they do not contain stellar nurseries.
In other words, the gas and dust in a black nebula are not in an ideal environment to start the star-forming process.
The quantity of light that is accessible for star formation may be diminished by the dust particles in dark nebulae that can absorb and scatter light.
Thus, despite the fact that black nebulae may contain a lot of gas and dust, they are not suitable for the formation of new stars, and are unlikely to contain stellar nurseries.
For more details regarding nebula, visit:
https://brainly.com/question/9497068
#SPJ9
Water in a beaker gains thermal energy at a rate of 3000 W. The water is at its boiling point. The spesific latent heat of vaporisation of water is 2260 J/g. How long does it take for 250 g of the water to vaporise?
The amount of heat required to vaporize a certain amount of water is given by:
Q = ml
where Q is the amount of heat, m is the mass of water, and l is the specific latent heat of vaporization.
In this case, the heat energy supplied to the water is:
Q = Pt
where P is the power supplied and t is the time taken.
Since the water is at its boiling point, its temperature remains constant while it is vaporizing. Therefore, the energy supplied to the water is solely used for vaporization.
Equating the two expressions for Q, we have:
Pt = ml
Solving for t, we get:
t = ml / P
where m = 250 g and l = 2260 J/g.
Substituting the values, we get:
t = (250 g) x (2260 J/g) / (3000 W) = 0.1883 hours
Converting to minutes, we have:
t = 0.1883 hours x (60 minutes/hour) = 11.3 minutes (approx.)
Therefore, it will take approximately 11.3 minutes for 250 g of water to vaporize.
a 41.0-kg child swings in a swing supported by two chains, each 2.90 m long. the tension in each chain at the lowest point is 352 n. (a) find the child's speed at the lowest point. m/s (b) find the force exerted by the seat on the child at the lowest point. (ignore the mass of the seat.)
The force exerted by the seat on the child at the lowest point is approximately 242 N.
(a) To find the child's speed at the lowest point, we can use conservation of energy. Assuming that the swing is released from rest at the highest point, we have:
Initial potential energy = mgh
Final kinetic energy = (1/2)mv^2
v is the speed of the child at the lowest point.
Since the height of the swing at the highest point is equal to the length of the chains, h = 2.9 m. We can solve for v by equating the two expressions for energy:
mgh = (1/2)mv^2
Solving for v, we get:
v = sqrt(2gh)
v = sqrt(2 × 9.81 m/s^2 × 2.9 m) ≈ 6.26 m/s
Therefore, the child's speed at the lowest point is approximately 6.26 m/s.
(b) At the lowest point, the child is moving in a circular path with a centripetal acceleration given by:
a = v^2/r
And,
T = mg + ma
Solving for a, we get:
a = (T - mg)/m
Substituting the given values, we get:
a = (352 N - 41.0 kg × 9.81 m/s^2)/(41.0 kg) ≈ 3.70 m/s^2
Substituting this value into the expression for centripetal acceleration, we get:
a = v^2/r
(3.70 m/s^2) = (6.26 m/s)^2/r
Solving for r, we get:
r = (6.26 m/s)^2/3.70 m/s^2 ≈ 10.6 m
Using Newton's second law, the force exerted by the seat is given by:
F = ma = m(v^2/r) = (41.0 kg)(6.26 m/s)^2/10.6 m ≈ 242 N
Read more about Laws of Motions:
https://brainly.com/question/16814844
#SPJ4
Due to a jaw injury, a patient must wear a strap that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?
The strap's tension needs to be changed to 4.11 N in order to deliver the required upward force, since there are no other forces acting in the upward direction.
To generate the required upward force, the tension on the strap must be adjusted, which equals T.
R² = T² + T² - 2T² Cosθ
where;
The resulting force, R, is
5² = 2T² - 2T² cos (75), where is the angle of inclination of the tension
25 = 1.482T²
T² = 25/1.482
T² = 16.87
T = √16.87
T = 4.11 N
In order to deliver the required upward force, the strap's tension must be set to 4.11 N.
This is due to Newton's third law, which states that for every action, there is an equal and opposite reaction. In this case, the force that the strap exerts on the chin (the action) must be equal and opposite to the force that the chin exerts on the strap (the reaction).
Therefore, to provide the necessary upward force of 5.00 N, the tension in the strap must be 4.11 N.
Learn more about tension here :
brainly.com/question/28536601
#SPJ4
A wave with a frequency of 3kHz was found to
oscillate 440 times.
Over what time period was it measured?
Give your answer to 2 decimal places.
The time interval is 0.15 s
What is the frequency of oscillation?The frequency of oscillation refers to the number of cycles of a periodic waveform that occur per unit of time, usually measured in hertz (Hz), which represents cycles per second.
Based on the information that can get in the question that has been put before us here and now;
Note that;
Frequency = Number of oscillations/Time
3 * 10^3 = 440/time
Time = 440/3 * 10^3
Time = 0.15 s
Thus we can see from the calculation that the time that is taken is 0.15 s
Learn more about frequency:https://brainly.com/question/5102661
#SPJ1
. When a grating with 300 lines per mm is illuminated normally with a parallel beam of monochromatic light a second order principle maximum is observed at 18.9degrees
to the straight through direction.
Find the wavelength of the light.
According to the problem the wavelength of the light is 5.67 μm.
What is wavelength?Wavelength is the distance between one point on a wave and the next corresponding point of the same phase on the wave. It is usually measured in meters (m) or nanometers (nm). Wavelength is closely related to frequency, as the frequency of a wave is equal to the speed of the wave divided by the wavelength. Wavelengths are used to measure various forms of electromagnetic radiation, such as visible light, radio waves, and x-rays. The wavelength of a wave determines its color, as visible light is made up of a spectrum of different wavelengths.
The angle of diffraction of a given wavelength of light through a grating is given by the equation: θ = (m*λ)/d
where θ is the angle of diffraction, m is the order of diffraction, λ is the wavelength of the light and d is the line spacing of the grating.
In this case, m = 2 (second order principle maximum), d = 300 lines/mm and θ = 18.9 degrees.
Solving for λ gives us: λ = (d*θ)/m
Substituting in the values gives us: λ = (300*18.9)/2 = 5670 nm = 5.67 μm
To learn more about wavelength
https://brainly.com/question/10728818
#SPJ1
Bone has a Young’s modulus of about
1.8 × 1010 Pa . Under compression, it can
withstand a stress of about 1.52 × 108 Pa before breaking.
Assume that a femur (thigh bone) is 0.55 m
long, and calculate the amount of compression
this bone can withstand before breaking.
Answer in units of mm.
Bone has a Young’s modulus of about 1.8 × 10¹⁰ Pa .Before breaking, the femur can withstand a compression of 5.5 mm.
How can the femur's compression be calculated?To determine how much compression the femur can withstand before breaking, we can use the stress formula.
The stress is the force exerted per unit area (1.52 10⁸ Pa); the applied force is the area, which represents the femur's cross-sectional area. Since we already know the stress and the area
The following formula can be used to determine the femur's cross-sectional area: Force = Stress * Area
A = π × r²
where:
A is the cross-sectional area
r is the radius of the femur
The radius of the femur can be calculated by dividing the diameter by 2:
r = d / 2
d is the diameter of the femur
We can find the force:
Force = 1.52 × 10⁸ Pa × π × (d / 2)²
Deformation = Stress × Length / Young's Modulus
Length is the length of the femur (0.55 m)
Young's Modulus is the modulus of elasticity of the material (1.8 × 1010 Pa)
Deformation = 1.52 × 10⁸ Pa × 0.55 m / (1.8 × 10¹⁰ Pa)
Deformation = 0.0055 m = 5.5 mm
Learn more about compression:
brainly.com/question/7602497
#SPJ1
capacitors in combination: three capacitors of equal capacitance are arranged as shown in the figure, with a voltage source across the combination. if the voltage drop across c1 is 10.0 v, what is the voltage drop across c3?
The voltage drop across C1 is 10.0 V while C3 experiences a 3.33 V voltage drop in capacitors.
What is the capacitor combination formula?This is seen below. The total capacitance of a number of capacitors connected in this fashion can be calculated by adding the individual capacitances using the method described below: C1 + C2 + C3, etc. = CTotal. An illustration would be to calculate the total capacitance of these three parallel capacitors.
The voltage drop across each capacitor is 10.0 V / 3 = 3.33 V if the voltage drop across C1 is 10.0 V.
Given that C3 is one of the series-connected capacitors, the voltage drop across C3 would also be 3.33 V.
Consequently, if C1 experiences a 10.0 V voltage drop, the 3.33 V is the voltage drop across C3.
To know more about capacitors visit:-
https://brainly.com/question/17176550
#SPJ1
From the materials in the parenthesis,Identify the best one to use for each given purpose.Then explain the reason for your choice write your explanation on the lines.
Snowy winter day((dark colored jacket,light colored jacket)).
Reason:
____________________________________________________________________________________________________________________________________
For a snowy winter day, it is best to wear dark colored jacket because, it helps to absorb heat and make us warm in the cold condition.
What is black body radiation ?A black colored body absorbs all colors but reflect no color. Hence, energy it absorbs will be emitted as heat. This is called black body radiation. The white light will absorbs all lights and reflects all light. Thus no energy is emitted as heat.
In the summer season, it is better to wear light colored dresses and uses white painted umbrellas because, they does not make us warmer and trap the heat from the surroundings.
But, in winter seasons, we need some warmth and it is better to use dark colored or black jackets to warm up ourselves. Therefore, option 1 is suit for a winter season.
Find more on heat radiation:
https://brainly.com/question/30363692
#SPJ1
how does the average speed of air molecules relate to the air temperature? a.high temperatures correspond to slower average molecule speeds b.high temperatures correspond to faster average molecule speeds c.average molecule speeds do not depend on temperature
The correct answer is option b) high temperatures correspond to faster average molecule speeds.
What are average molecule speeds?The term "average molecule speed" describes the typical speed of a gas's molecules. The root-mean-square (rms) velocity formula can be used to determine the average speed of all the molecules in a gas. Individual molecules in a gas move at different speeds as a result of collisions with other molecules.
[tex]\sqrt{3kT/m} = v[/tex]
Where T is the gas's temperature in kelvins, v is the gas molecules' average speed, k is the Boltzmann constant, and m is the mass of a single gas molecule.
The relationship between the gas's molecular mass, pressure, and temperature govern the average molecule speed. The Maxwell-Boltzmann distribution states that as the gas's temperature rises, so does its average molecular speed. Similar to this, while temperature and pressure are constant, gases with lower molecular masses move molecules more quickly on average than gases with greater molecular masses.
To know more about average molecule speeds, visit:
brainly.com/question/3052539
#SPJ4
a nasa orbiter recently captured craters and formations on mars that resembled the face of which animal?
Hundreds of millions of kilometres away, the Mars Reconnaissance Orbiter camera photographed a unique formation that, to the delight of scientists and space observers, appeared to be shaped like a bear's face.
On Mars, what face was discovered?The Viking 1 lander captured it on July 20, 1976, shortly after it landed on the planet. This new image from the Mars Reconnaissance Orbiter's HiRISE camera purports to show the face of a bear forming on the Martian surface.
What was discovered by the Mars Orbiter when it examined the Martian Face?The intriguing geological formation was photographed in December by the High Resolution Imaging Experiment (HiRISE) instrument on board the Mars Reconnaissance Orbiter.
To know more about Orbiter visit:-
https://brainly.com/question/19516096
#SPJ1
A 65kg bicyclist (including the bicycle), initially at rest, pedals to the right, generating 200N of force for 6s. During this time, they experience 40N drag. Neglect any
additional friction impeding their motion. Their net force on the bicycle is
A. 240 N
B. 160 N
C. 305 N
hazel and emilie fly from atlanta to san diego. the flight from atlanta to san diego is against the wind and takes 4 hr. the return flight with the wind takes 3.5 hr. if the wind speed is 40 mph, find the speed of the plain in still air
The speed of the plane in still air is 600 mph. the flight from Atlanta to san diego is against the wind and takes 4 hr. the return flight with the wind takes 3.5 hr.
What is the rate of a moving object?Speed is calculated by dividing the distance traveled by the distance's travel time. The equation can be used to determine speed: Speed is defined as the product of distance divided by time, and the unit of speed is the product of distance divided by time.
What does physics mean by speed?Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path. In other words, velocity is a vector, whereas speed is a scalar value.
Let x mph be the speed in still air. Then flight against the wind is at (x-40)mph and with the wind is (x+40)mph
3.5 (x+40) =4(x-40)
3.5x +140 = 4x - 160
3.5x - 4 x = -160 - 140
-0.5x = -300
x = 300/0.5
x = 600 mph
To know more about the speed visit;
https://brainly.com/question/13943409
#SPJ4
a wire carries a current of 60 ma. how many electrons have to pass a given point in the wire in 3.00s to produce this current?
Approximately 1.12 x 10^18 electrons would have to pass through the given point in a wire in 3.00 seconds to produce a current of 60 mA.
What are electrons?Electrons are subatomic particles that have a negative charge and are fundamental components of atoms. They are located in shells or orbitals around the atomic nucleus and play a crucial role in many physical and chemical processes.
Electrons are the carriers of electric charge in materials and are responsible for the flow of current in electrical conductors. They also play a key role in chemical bonding and reactions, as they are involved in the sharing and transfer of electrons between atoms.
Electrons are extremely small and have a mass of approximately 9.11 x 10^-31 kilograms, which is about 1/1836th the mass of a proton.
To determine the number of electrons that pass through a given point in a wire, we can use the equation:
I = Q/t
where I is the current in amperes, Q is the charge in coulombs, and t is the time in seconds.
We can rearrange this equation to solve for the charge Q:
Q = I*t
Now, use the elementary charge of an electron, which is approximately 1.602 x 10^-19 coulombs, to calculate the number of electrons that pass through the wire in 3.00 seconds:
Q = (60 mA) * (3.00 s) = 0.18 C
Number of electrons = Q / e = 0.18 C / (1.602 x 10^-19 C/e) = 1.12 x 10^18 electrons
Therefore, approximately 1.12 x 10^18 electrons would have to pass through the given point in the wire in 3.00 seconds to produce a current of 60 mA.
To know more about Electrons, visit:
https://brainly.com/question/29522188
#SPJ4
bulbs a and b in the figure are identical, and both are glowing. what happens to each bulb when the switch is closed?
When a circuit is finished and current can flow, it is said to be in a closed-circuit condition. In the closed position, the current has a clear passage.
What condition in which each bulb switch is closed?The light bulb turns on when the switch is closed because current passes through the circuit. The bulb receives its full 120 volts and the intended current flow, which allows it to operate at maximum brightness.
There is a closed (or full) circuit with the bulb when the circuit's wires are attached to the metal casing and metal tip of the lightbulb. The filament will be able to conduct electricity, which will result in the bulb lighting up.
Therefore, in this case, both bulbs receive the same amount of electricity both before and after the switch is closed. Consequently, the brightness doesn't change.
Learn more about bulb here:
https://brainly.com/question/27130252
#SPJ4
suppose you charge a parallel plate capacitor with a dielectric between the plates using a battery and then remove the battery, isolating the capacitor and leaving it charged. you then remove the dielectric from between the plates. the potential difference between the plates will
If the dielectric is then removed, the capacitance of the capacitor decreases and the electric field between the plates increases.
When a parallel plate capacitor is charged with a dielectric between the plates using a battery, the charges on the plates are distributed in a way that results in a potential difference between the plates equal to the voltage of the battery. After the battery is removed and the capacitor is isolated, the charges on the plates remain fixed and the potential difference is maintained.
If the dielectric is then removed, there increase in electric field results in an increase in potential difference between the plates, and the amount of increase depends on the dielectric constant of the material used and the original capacitance of the capacitor.
To know more about the parallel plate capacitor, here
brainly.com/question/28446409
#SPJ4
a brick is moving at a speed of 3 m/s and a pebble is moving at a speed of 5 m/s. if both objects have the same kinetic energy, what is the ratio of the brick's mass to the pebble's mass?
By the help of Kinetic energy ,the ratio of the brick's mass to the pebble's mass is [tex]\frac{9}{25}M = m[/tex]
A moving item or particle might have power of a certain sort called kinetic energy. An object gains kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. Kinetic energy is a characteristic of motion that depends on the mass and speed of an object or particle. Motion includes all combinations of vibration, axis rotation, translation, and movement (along a path from one location to another).
M should represent the brick mass.
Let m represent the pebble's mass.
.[tex]\frac{1}{2} M(v)^2[/tex] =KE
[tex]\frac{1}{2} M(3)^2[/tex]=KE
[tex]\frac{1}{2} m(5)^2[/tex]= KE
[tex]\frac{1}{2} M(3)^2= \frac{1}{2} m(5)^2[/tex]
9M = 25m
[tex]\frac{9}{25}M = m[/tex]
Learn more about Kinetic energy
brainly.com/question/26472013
#SPJ4
questionwhat is described as the collision of the molecules of a fluid inside the surface of their container?responsespressurepressurevolumevolumegravitygravitywater
Option A: pressure is described as the collision of the molecules of a fluid inside the surface of the container.
Fluids are the liquids or gases whose particles move around in random motion and constantly collide with each other. When enclosed in a container, the continuous collision impart a pressure on the walls of the container. Since the particles are moving in constant and a quick motion, they keep bouncing-off the container.
A pressurised container experiences significantly more impacts from the pressured gas inside than from the lower pressure environment outside at any given time. Collisions inside a container can also be influenced by temperature at a given instant.
To know more about pressure, refer:
https://brainly.com/question/14443314
#SPJ4
Correct question is:
What is described as the collision of the molecules of a fluid inside the surface of their container? responses:
pressure
volume
gravity
water
today the sun appears to be located in the middle of the constellation virgo. therefore, tomorrow the sun will be in the constellation today the sun appears to be located in the middle of the constellation virgo. therefore, tomorrow the sun will be in the constellation sagittarius. libra. leo. virgo.
If today the sun appears to be located in the middle of the constellation Virgo. therefore, tomorrow the sun will be in the constellation Virgo. Hence, option D is correct.
What is a constellation?An arrangement of stars is a constellation. Others have observed patterns in the stars that are used to classify the groups. A lion's form, for instance, appears to be traced by the stars of the constellation Leo.
The western zodiac consists of the 12 constellations Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces is one constellation tradition.
Thus, if today the sun appears to be located in the middle of the constellation Virgo. Then, tomorrow the sun will be in the constellation Virgo. Hence, option D is correct.
Learn more about the constellation, here:
https://brainly.com/question/13166871
#SPJ1
what is required for the maximum high tide to occur?
Every new and full moon, when the sun, moon, and earth are in alignment, spring tides occur. When lunar and solar tides align, they reinforce one another and create a larger overall tidal.
What is the condition are required for high tide to occur?The Earth's tides are significantly influenced by the elliptical orbits of the moon around the planet and the planet around the sun. The largest spring tides happen when the moon is close to perigee and the sun is close to perihelion.
Every month, at perigee, when the moon is closest to Earth, tidal-generating forces are stronger than usual, resulting in tide ranges that are higher than typical.
Therefore, When the sun, earth, and moon are at a straight angle and the moon is in its first or third quarter, neap tides happen.
Learn more about tide here:
https://brainly.com/question/29388827
#SPJ4
A force of 100 N is applied to the brake pedal, which acts on the cylinder—called the master—through a lever. A force of 500 N is exerted on the master cylinder. Pressure created in the master cylinder is transmitted to four so-called slave cylinders. The master cylinder has a diameter of 0. 55 cm, and each slave cylinder has a diameter of 2. 50 cm. How much pressure is transmitted in the hydraulic system? Express your answer in pascals and in atmospheres
The pressure transmitted in the hydraulic system is 4.20 x 10^5 Pa or 4.15 atm.
What is pascal's Law?The principle of Pascal's Law states that pressure applied to a fluid in a closed container is transmitted equally to every part of the fluid and the walls of the container.
The force applied to the master cylinder can be expressed as:
F = A * P
where
F is the force (in newtons)A is the area (in square meters)P is the pressure (in pascals)We know that the force applied to the brake pedal is 100 N, and the force exerted on the master cylinder is 500 N. Therefore, the force amplification factor is:
FA = F_slave / F_master = 500 N / 100 N = 5
We can use this factor to calculate the pressure in the system:
P_slave = P_master / FA
The area of the master cylinder can be calculated as:
A_master = pi * (d_master/2)^2 = pi * (0.55 cm / 100 cm/m)^2 = 2.38 x 10^-4 m^2
The area of each slave cylinder can be calculated as:
A_slave = pi * (d_slave/2)^2 = pi * (2.50 cm / 100 cm/m)^2 = 4.91 x 10^-3 m^2
The pressure in the master cylinder can be calculated as:
P_master = F_master / A_master = 500 N / 2.38 x 10^-4 m^2 = 2.10 x 10^6 Pa
The pressure in each slave cylinder can be calculated as:
P_slave = P_master / FA = 2.10 x 10^6 Pa / 5 = 4.20 x 10^5 Pa
Converting to atmospheres, we get:
P_slave = 4.20 x 10^5 Pa / 101325 Pa/atm = 4.15 atm
Therefore, the pressure transmitted in the hydraulic system is 4.20 x 10^5 Pa or 4.15 atm.
Learn more about pascal's Law here : brainly.com/question/4262025
#SPJ1
A 10 kg object is hanging stationary on the end of a vertical spring which has a spring
constant of 250 N/m. What is the elongation of the spring?
To find the elongation of the spring, we can use Hooke's Law, which states that the force exerted by a spring is proportional to its elongation. The formula for Hooke's law is:
F = -kx
where F is the force, k is the spring constant, and x is the elongation.
In this case, the force is equal to the weight of the object (10 kg), which can be calculated as:
F = m * g
where m is the mass of the object (10 kg) and g is the acceleration due to gravity (9.8 m/s^2).
So, the force can be calculated as:
F = 10 kg * 9.8 m/s^2 = 98 N
Using Hooke's law, we can find the elongation of the spring:
F = -kx
98 N = -250 N/m * x
x = 98 N / 250 N/m = 0.392 m
So, the elongation of the spring is 0.392 m.
_________________________________________________________
Hey brother, no problem for the answer but could you give 5 stars and a thanks!
All love, Johnny Sins :)
6. Calculate the gravitational force on the earth due to the sun. It is this force which holds the earth in its orbit. Mass Sun = 1.99 x 10 30 kg Mass Earth = 5.98 X 10 24kg R = 1.5 x 10 11 m
Answer:
[tex]F = \boxed{3.53002 \times 10^{22} \;N}[/tex]
Explanation:
The formula used to calculate the gravitational force between two objects
[tex]F = G \dfrac{m_1m_2}{r^2}[/tex]
where
m₁ and m₂ are the masses of the two objects
G is the universal gravitational constant =6.6743 × 10⁻¹¹ m³/kg·s²
r is the average distance between the two objects
We are given
mass of earth = m₁ = 5.98 X 10²⁴ kg
mass of sun = m₂ = 1.99 x 10³⁰ kg
r = 1.5 x 10¹¹ m
Therefore
[tex]F\:=\:6.6743\:\times \:10^{-11}\times \dfrac{\left(5.98\:\times 10^{24}\times 1.99\:\times 10^{30}\right)}{\left(1.5\:\times \:10^{11}\right)^2}[/tex]
[tex]F = \boxed{3.53002 \times 10^{22} \;N}[/tex]
A 3.68 kg box is being pushed up the incline of 85.61 degrees with an acceleration of 11.63 m/s2. Chasadie is pushing the box with a force of 217.41 N. What is the friction force?
The friction force experienced by the box is approximately 77.96 N.
What is frictional force?Frictional force is a force that opposes the motion or attempted motion between two surfaces in contact. It is caused by the irregularities in the surfaces of objects that come into contact with each other, and it acts in the direction opposite to the direction of motion or attempted motion.
We can begin by drawing a diagram of the situation and labeling the forces acting on the box:
where:
Fp is the force applied by Chasadie.
Ff is the force of friction.
mg is the weight of the box (mass times gravity)
We can then use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration:
ΣF = ma
where ΣF is the sum of all the forces acting on the box.
In the vertical direction, we have:
ΣFy = N - mg = 0
where N is the normal force, which is equal and opposite to the weight of the box.
Since the incline is at an angle of 85.61 degrees, we can use trigonometry to find the components of the weight and normal force:
N = mg cos θ = (3.68 kg)(9.81 m/s²) cos (85.61°) ≈ 18.77 N
mg sin θ = (3.68 kg)(9.81 m/s²) sin (85.61°) ≈ 36.24 N
In the horizontal direction, we have:
ΣFx = Fp - Ff - mg sin θ = ma
Plugging in the given values and solving for Ff:
Ff = Fp - ma + mg sin θ
= (217.41 N) - (3.68 kg)(11.63 m/s²) + (3.68 kg)(9.81 m/s²) sin (85.61°)
≈ 77.96 N
Therefore, the friction force is approximately 77.96 N.
To know more about Newton's second law of motion, visit:
https://brainly.com/question/29775827
#SPJ1
The diagram for the solution of the question is as follows:
a building consists of two floors. the first floor is attached rigidly to the ground, and the second floor is of mass slugs and weighs 16 tons (32,000 lbs). the elastic frame of the building behaves as a spring that resists horizontal displacements of the second floor; it requires a horizontal force of 5 tons to displace the ssecoonod floor a distance of 1 ft. assume that in an earthquake the ground oscillates horizontally with amplitude and circular frequency , resulting in an external horizontal force on the second floor. (a) what is the natural frequency (in hertz) of oscillations of the second floor? (b) if the ground undergoes one oscillation every 2.25s with an amplitude of 3in, what is the amplitude of the resulting forced oscillations of the second floor? (c) what is the name of the architect who designed the building?
The natural frequency (in hertz) of oscillations of the second floor
(a) To find the natural frequency of oscillation of the second floor, we can use the formula:
ω_n = √(k/m)
where ω_n is the natural frequency, k is the spring constant, and m is the mass of the second floor.
The spring constant k can be found by using the given information that a horizontal force of 5 tons (10,000 lbs) is required to displace the second floor by 1 ft. This means that the spring constant is:
k = F/x = (10,000 lbs) / (1 ft) = 10,000 lb/ft
Converting the mass of the second floor to slugs, we get:
m = 32,000 lbs / g = 32,000 / 32.2 = 994.4 slugs
Substituting the values of k and m, we get:
ω_n = √(k/m) = √(10,000 lb/ft / 994.4 slugs) ≈ 10.05 rad/s
Converting to Hertz, we get:
f_n = ω_n / 2π ≈ 1.6 Hz
Therefore, the natural frequency of oscillation on the second floor is approximately 1.6 Hz.
(b) The amplitude of the forced oscillations of the second floor can be found using the formula:
x = (F_0 / m) / √(ω² - ω_n²)
where x is the amplitude of the forced oscillations, F_0 is the amplitude of the external force, ω is the circular frequency of the ground oscillations, and ω_n is the natural frequency of the second floor.
Substituting the given values, we get:
x = (F_0 / m) / √(ω² - ω_n²)
= (10,000 lbs / 994.4 slugs) / √((2π/2.25 s)² - (10.05 rad/s)²)
≈ 0.11 ft
Converting to inches, we get:
x ≈ 1.3 in
Therefore, the amplitude of the forced oscillations of the second floor is approximately 1.3 inches.
To Learn More About oscillations click
https://brainly.com/question/30111348
#SPJ4
two pennies lie on the surface of a turntable. as the turntable spins faster, which penny slides first?
As the turntable spins faster, the penny that is furthest from the turntable's centre will slide first.
Centripetal force increases as the turntable spins faster, exerting more force on the pennies. The centripetal force is proportional to the angular velocity squared and the angle of deflection from the turntable's centre. In other words, the penny that is farther away from the turntable's centre experiences a stronger centripetal force than the penny that is closer to it.
With the centripetal force, the frictional force between the pennies and the turntable likewise grows. Nevertheless, the coefficient of static friction—a feature of the surface where the pennies and turntable are placed—limits the frictional force. For the penny that is nearer to the turntable's centre than for the coin that is farther away, the coefficient of static friction
Learn more about frictional force here:
https://brainly.com/question/30280752
#SPJ4
you are standing on a scale in an elevator. for a brief time, the elevator descends with free-fall acceleration. what does the scale show your weight to be during that time interval?
During the brief time interval when the elevator is descending with free-fall acceleration, the scale would show your weight to be zero.
What is free-fall acceleration?Free-fall acceleration is the acceleration that an object experiences due to the force of gravity, assuming no other forces are acting on the object. In the absence of air resistance or any other resistance, all objects near the surface of the Earth, regardless of their mass or composition, will experience the same constant free-fall acceleration due to gravity, which is denoted by the symbol "g" and has a value of approximately 9.8 meters per second squared (m/s²) or 32.2 feet per second squared (ft/s²).
This means that if an object is dropped from rest near the surface of the Earth, it will fall with a constant acceleration of g, and will increase its velocity by 9.8 m/s or 32.2 ft/s every second. Similarly, if an object is thrown upwards, it will experience a deceleration of g due to gravity until it comes to rest at the highest point of its trajectory, after which it will begin to fall downwards with free-fall acceleration.
If the elevator is in free-fall acceleration, it means that the only force acting on you is the force due to gravity, and there is no normal force acting on you from the scale. In this case, according to Newton's second law of motion, your weight is equal to the force due to gravity acting on your mass.
So, during the brief time interval when the elevator is descending with free-fall acceleration, the scale would show your weight to be zero. This is because your body is in a state of weightlessness, as you and the scale are accelerating downwards at the same rate.
To know more about free-fall acceleration, visit:
https://brainly.com/question/29308592
#SPJ4
