To find the pH of a 0.050 M solution of 2-nitrophenol, we first need to find the concentration of H+ ions in solution. We can do this using the acid dissociation constant (Ka) of 2-nitrophenol and the equilibrium reaction:
2-nitrophenol + H2O ⇌ H+ + 2-nitrophenolate-
Ka = [H+][2-nitrophenolate-] / [2-nitrophenol]
We can assume that the initial concentration of H+ ions is zero, and the initial concentration of 2-nitrophenol is 0.050 M. We also know that the concentration of 2-nitrophenolate- at equilibrium will be equal to the concentration of H+ ions, since the acid dissociates to form one H+ ion and one 2-nitrophenolate- ion.
Let x be the concentration of H+ ions at equilibrium. Then we can write:
\(Ka = x^2 / (0.050 - x)\)
Simplifying, we get:
\(x^2 = Ka * (0.050 - x)\\x^2 + Ka * x - Ka * 0.050 = 0\)
Using the quadratic formula, we get:
\(x = (-Ka ± sqrt(Ka^2 + 4Ka0.050)) / 2\)
Taking the positive root and plugging in Ka = \(6.3 x 10^-8\), we get:
\(x = 3.98 x 10^-4 M\)
Therefore, the concentration of H+ ions in solution is \(x = 3.98 x 10^-4 M\) M. To find the pH, we can use the equation:
pH = -log[H+]
Plugging in the value for [H+], we get:
\(pH = -log(3.98 x 10^-4) ≈ 3.40\)
Therefore, the pH of a 0.050 M solution of 2-nitrophenol is approximately 3.40.
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What is promising evidence of a habitat that might support life
on the planet Mars?
Detailed Answer please, will give thumb up rating definitely
A promising evidence of a habitat that might support life on the planet Mars is water.
There is evidence supporting the existence of liquid water on Mars from numerous sources. The finding of repeated black streaks on Martian slopes and the presence of hydrated minerals suggest the potential of seasonal or location-specific briny water flows. A necessary component of life as known is liquid water.
Additionally, Mars possesses underground ecosystems that could provide defence against radiation and severe surface conditions. Researchers have found evidence of ancient underground hydrothermal systems as well as beneath ice. These settings might offer consistent conditions for the development of microbial life. Methane gas has been found in the Martian atmosphere, along with variations over time, and this has led to questions regarding its origin. Both geological and biological processes can result in the production of methane.
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In a global value delivery network, the first link, ________, moves company products from points of production to the borders of countries within which they are sold.
In a global value delivery network, the first link is transportation.
Transportation plays a crucial role in moving company products from points of production to the borders of countries where they are sold. It involves the physical movement of goods through various modes of transportation such as ships, airplanes, trucks, or trains. The efficiency and effectiveness of transportation networks are essential for ensuring timely delivery of products to the intended markets, enabling companies to meet customer demands and optimize their global supply chains.
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Pls help with my physics hw
Answer:
1. (c) 18 J
2. 70%
Explanation:
1. Thermal energy released (waste) = input energy (it is usually more) - output (usually less_used to perform useful work)
= 60 joules - 42 joules
= 18 joules
2. % energy efficiency = output/input x 100%
= (42/60) x 100%
= 70%
I hope this helps. have a nice studies
a person is standing on a railroad station platform when a high speed train passes by. the person will tend to be
The air is moving quickly behind the person because of the dragging action, but it is essentially still behind the person.
When a fast train arrives at the station, who is that person standing close to the edge of the platform?
Bernoulli's principle states that as a train passes by and the neighbouring air particles begin to move with it, a low pressure area is produced.
Anyone standing at the edge of the platform will therefore notice the train.
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A student pushes against a wall with 20N of force and the wall does not move. In this situation, the wall exerts -
F 0N of force.
G 20N of force.
H less than 20N of force.
J more than 20N of force.
Answer:
G 20N of force
Explanation:
Every action has an equal and opposite reaction. The wall exterts as much force as you push on it.
Answer:
It is g
Explanation:
The wall is not moving nor is the kid therefore the force is equal
What is the de Broglie wavelength of an electron traveling at
1.10×105m/s ? Express your answer to three significant figures and
include the appropriate units.
Lamda = ? | units ?
The de Broglie wavelength of an electron traveling at 1.10×10^5 m/s is approximately 6.53×10^−10 m.
According to the de Broglie wavelength equation, the de Broglie wavelength (λ) of a particle is given by λ = h / p, where h is Planck's constant (approximately 6.626×10^−34 J·s) and p is the momentum of the particle. In this case, we have the velocity of the electron (v = 1.10×10^5 m/s), and since the momentum (p) of an object is given by p = mv, where m is the mass and v is the velocity, we can calculate the momentum of the electron.
Assuming a rest mass of an electron (m) of approximately 9.10938356×10^−31 kg, we can find the momentum (p) using p = mv. Substituting the values, p = (9.10938356×10^−31 kg) × (1.10×10^5 m/s) ≈ 1.00×10^−25 kg·m/s.
Finally, we can calculate the de Broglie wavelength (λ) using the equation λ = h / p. Substituting the values, λ = (6.626×10^−34 J·s) / (1.00×10^−25 kg·m/s) ≈ 6.53×10^−10 m.
Therefore, the de Broglie wavelength of the electron traveling at 1.10×10^5 m/s is approximately 6.53×10^−10 m.
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The cuboid and the cube below are placed on the floor. The cuboid has a weight of 60N and the cube has a weight of 40N. Which exerts a greater pressure on the ground? Prove your answer.
Answer:
they both exert the same pressure
Explanation:
Pressure is the ratio of force to area. It is given as:
\(P=\frac{F}{A}\) , where F is the force, P is pressure and A is area
1) For the cuboid, the area of the base placed on the ground (A) = 8 cm × 3 cm = 24 cm² = 0.0024 m². Therefore the pressure is:
\(P=\frac{F}{A}=\frac{60}{0.0024} =25000N/m^2=25KN/m^2\)
2) For the cube, the area of the base placed on the ground (A) = 4 cm × 4 cm = 16 cm² = 0.0016 m². Therefore the pressure is:
\(P=\frac{F}{A}=\frac{40}{0.0016} =25000N/m^2=25KN/m^2\)
Therefore, they both exert the same pressure.
Dos masas están conectadas por una cuerda ligera que pasa por una polea sin rozamiento. Determine la aceleración de las masas y la tensión de la cuerda si m Kg A 20 , m Kg B 50 y 0.20 K A Y B
Answer:A
Explanation:
A mass weighing 2 lb stretches a spring 6 in. If the mass is pulled down an additional 3 in. and then released, and if there is no damping, determine the position u of the mass at any time t. Draw the graph of u(t), and the frequency, period and amplitute of the motion.
To determine the position u of the mass at any time t, we can use the equation of motion for a mass-spring system without damping:n m * u''(t) + k * u(t) = 0
m = 2 lb / (32.2 ft/s^2) = 0.062 lb·s^2/ft
The spring constant k can be determined using Hooke's law:
k = F / x
where F is the force exerted by the mass and x is the displacement. In this case, the force F is the weight of the mass, and the displacement x is 6 in:
k = (2 lb) / (6 in) = (2 lb) / (6 in) * (1 ft/12 in) = 0.111 lb/ft
The equation of motion now becomes:
0.062 * u''(t) + 0.111 * u(t) = 0
To solve this second-order linear homogeneous differential equation, we assume a solution of the form u(t) = A * cos(ωt + φ).
Substituting this assumed solution into the equation of motion, we get:
-0.062 * A * ω^2 * cos(ωt + φ) + 0.111 * A * cos(ωt + φ) = 0
-0.062 * ω^2 + 0.111 = 0
Solving for ω, we get:
ω = sqrt(0.111 / 0.062) = 2.258 rad/s
From ω, we can determine the frequency f and period T:
f = ω / (2π) = 2.258 / (2π) ≈ 0.359 Hz
T = 1 / f ≈ 2.786 s
The amplitude A is determined by the initial conditions. When the mass is pulled down an additional 3 in (0.25 ft) and released, it reaches its maximum displacement, so A = 0.25 ft.
Therefore, the position u of the mass at any time t is given by:
u(t) = 0.25 * cos(2.258t)
To draw the graph of u(t), plot the position u on the y-axis and time t on the x-axis, using the equation u(t) = 0.25 * cos(2.258t). The graph will be a cosine wave with an amplitude of 0.25 ft.
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an apple falls from the top of the tree and takes 2 secs to hit the ground.
how far did the apple fall?
calculate the velocity of the apple just before it hits the ground.
Light goes from Medium 1 into Medium 2. Medium 2 has a greater index of refraction than Medium 1. What is true?
A- Medium 2 is more dense so the light bends away from the normal (larger angle).
B- Medium 2 is more dense so the light bends toward the normal (smaller angle).
C- Medium 2 is less dense so the light bends toward the normal (smaller angle).
D- Medium 2 is less dense so the light bends away from the normal (larger angle).
the universal gravitation constant is represented by what number?
Isaac Newton's Law on Universal Gravitation provided the first formal definition of the gravitational constant. One of nature's fundamental constants, whose value is (6.6743 0.00015) x 10-11 m3 kg-1 s-2.
Explanation of gravitationIf there is a difference in mass between any two things or particles, gravity will tend to pull them in that direction.
What does the name "gravitation" mean?The reason it is known as Newton's Law on Gravitation is that it applies to all mass-bearing things, such as the sun, moon, earth, and an apple, and these bodies will all be subject to its effects.
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An object has positive velocity and negative acceleration, what does this mean?
(1 Point)
The object is accelerating backwards.
The object is backing up but slowing down.
The object is moving forward but slowing down.
The object has a constant velocity backing up.
Answer:
the object is moving forward but it is slowing down
Explanation:
negative acceleration becomes when the intiall velocity becomes greater than the final which means if it is initially greater but finally smaller that means it is slowing down but moving forward
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a girl is 8 years older than her younger sister. The sum of their ages is 64 years, what is her age in years
Answer:
let the age of elder sister = x+8
then let the age of younger sister be x
sum of their ages = 64
according to the question,
x+8+x = 64
2x+8 = 64
2x = 64-8
2x = 56
x = 56/ 2
x = 28
so, the age of younger sister is 28 years
and the age of elder sister is x+8= 28+8= 36years
Find the net force of two forces F1 = 20 N and F2 = 30 N when they are forming an angle of 120 between them.
The net force of the two forces with magnitudes 20 N and 30 N, forming an angle of 120° between them, is approximately 51.1 N directed at an angle of -60.9° with the horizontal axis.
To find the net force of two forces when they are forming an angle between them, we can use the concept of vector addition. The net force is the vector sum of the individual forces.
Given:
F1 = 20 N (magnitude of force 1)
F2 = 30 N (magnitude of force 2)
θ = 120° (angle between the forces)
To find the net force, we need to break down the forces into their horizontal and vertical components. The horizontal component is given by F * cos(θ), and the vertical component is given by F * sin(θ).
For Force 1 (F1):
F1x = F1 * cos(θ) = 20 N * cos(120°) = -10 N (horizontal component)
F1y = F1 * sin(θ) = 20 N * sin(120°) = 17.32 N (vertical component)
For Force 2 (F2): F2 is acting along positive x-axis.
F2x = F2 * cos(θ) = 30 N * cos(120°) = -15 N (horizontal component)
F2y = F2 * sin(θ) = 30 N * sin(120°) = 25.98 N (vertical component)
Now, we can find the net horizontal and vertical components by adding the corresponding components of the forces:
Net horizontal component (Fx) = F1x + F2x = -10 N + (-15 N) = -25 N
Net vertical component (Fy) = F1y + F2y = 17.32 N + 25.98 N = 43.3 N
Finally, we can calculate the magnitude and direction of the net force using the net horizontal and vertical components:
Magnitude of the net force\($(F_{net}) = \sqrt{(F_x)^2 + (F_y)^2} = \sqrt{(-25 \text{ N})^2 + (43.3 \text{ N})^2} \approx 51.1 \text{ N}$\)
Angle (θnet) of the net force with the horizontal axis can be found using the inverse tangent (arctan) function:
\(\theta_{net} = \arctan\left(\frac{F_y}{F_x}\right) = \arctan\left(\frac{43.3 \, \text{N}}{-25 \, \text{N}}\right) \approx -60.9^{\circ}\)
The negative sign indicates that the net force is directed in the fourth quadrant, below the negative x-axis.
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Find the value of “m”
The mass of an object with a force of 1500 N is 300 kg is obtained by using the Frictional force. Thus, option A is correct.
The frictional force is the force that arises when the object is in motion. It resists the sliding or rolling of an object. It equals the mass of the object and acceleration due to gravity(g).
Frictional force, F = mg sinθ. F is the frictional force, g is the acceleration due to gravity and θ is the angle between the object and the surface.
F = 1500 N
g = 10 m/s²
θ = 30°
m = F / (g×sin(30°))
= 1500 / (10×0.5)
= 1500 / 5
= 300 kg
Thus the mass of the body is 300 kg. Hence, the correct option is A.
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What is the effective resistance of a car's starter motor when 148 A flows through it as the car battery applies 10.8 V to the motor? Ω
The effective resistance of the car is 0.0730 Ω.
Current I = 148 A
Voltage V = 10.8 V
We know that the Ohm's law is given by;`V = IR
`where `R` is the resistance of the circuit.
By using the above formula;` R = V/I
`Putting the given values in the above formula;
`R = V/I = 10.8/148
= 0.0730 Ω`
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which property of a wave is labeled "x" on the diagram?
a. amplitude
b. frequency
c. wavelength
d. none of the above
(thank you!)
Han Solo is moving from left to right along the curvey y= x^2 while orbiting the planet of
Tatooine. He wants to shut off the engines of the Millenium Falcon at a certain point, so
that he will go off along the tangent line and land. At what point should he shut off the
engines in order to reach the landing point (4, 15)? Show all of your work.
At position (3, 9), where the tangent line passes through, Han Solo should turn off the engines (4, 15).
What should you do if an engine fails while you're in flight?The first three things need to be completed, or at least started, right away: Fly the aircraft as you instantly apply full carb heat and check the gasoline in both or one of the tanks, hit the fuel boost or pump, and mix the fuel to full richness.
Finding the tangent line to the curve y = x2 at that location will help us determine when Han Solo should turn off the engines.
The derivative of the function determines the slope of the tangent line at any point on the curve y = x2.: dy/dx = 2x
Han Solo should turn off the engines at position (x1, y1). Next, we have
y1 = x1^2 (since the point is on the curve y = x^2)
dy/dx = 2x1 (since this is the slope of the tangent line at (x1, y1))
The equation of the tangent line via (4, 15) can be expressed using the point-slope form of a line as follows:
y - y1 = m(x - x1)
Substituting y1 = x1^2 and m = 2x1, we get:
y - x1^2 = 2x1(x - x1)
Now, we can substitute the coordinates of the point (4, 15) to solve for x1:
15 - x1^2 = 2x1(4 - x1)
15 - x1^2 = 8x1 - 2x1^2
x1^2 - 8x1 + 15 = 0
This quadratic equation can be factored as:
(x1 - 3)(x1 - 5) = 0
Therefore, the possible values of x1 are 3 and 5.
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a hydrogen balloon rises up when released. within a short period of time, the balloon expands and does a work of 6000 j to the outside environment. during the same period of time, it also loses 12000 j of heat. how much does the internal energy of the balloon changes?
It's internal energy decreases of 18000J.
ΔQ = ΔU + ΔW
-12000J = ΔU + 6000
ΔU = - 18000J
Internal energy is the energy attributed to the disorderly, haphazard motion of molecules. It refers to the intangible microscopic energy on the atomic and molecular levels, which is distinct in scale from the macroscopic organised energy connected to moving objects. A glass of water that is at normal temperature and is resting on a table, for instance, has no discernible potential or kinetic energy. Although it is a seething mass of molecules moving at hundreds of metres per second at the microscopic level. When we superimpose an ordered big scale motion on the water as a whole, this tiny energy would not necessarily alter if the water were thrown across the room.
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A 15 kg box is sliding down an incline of 35 degrees. The incline has a coefficient of friction of 0.25. If the box starts at rest, how fast is it moving after it travels 3 meters?
The box has 3 forces acting on it:
• its own weight (magnitude w, pointing downward)
• the normal force of the incline on the box (mag. n, pointing upward perpendicular to the incline)
• friction (mag. f, opposing the box's slide down the incline and parallel to the incline)
Decompose each force into components acting parallel or perpendicular to the incline. (Consult the attached free body diagram.) The normal and friction forces are ready to be used, so that just leaves the weight. If we take the direction in which the box is sliding to be the positive parallel direction, then by Newton's second law, we have
• net parallel force:
∑ F = -f + w sin(35°) = m a
• net perpendicular force:
∑ F = n - w cos(35°) = 0
Solve the net perpendicular force equation for the normal force:
n = w cos(35°)
n = (15 kg) (9.8 m/s²) cos(35°)
n ≈ 120 N
Solve for the mag. of friction:
f = µ n
f = 0.25 (120 N)
f ≈ 30 N
Solve the net parallel force equation for the acceleration:
-30 N + (15 kg) (9.8 m/s²) sin(35°) = (15 kg) a
a ≈ (54.3157 N) / (15 kg)
a ≈ 3.6 m/s²
Now solve for the block's speed v given that it starts at rest, with v₀ = 0, and slides down the incline a distance of ∆x = 3 m:
v² - v₀² = 2 a ∆x
v² = 2 (3.6 m/s²) (3 m)
v = √(21.7263 m²/s²)
v ≈ 4.7 m/s
The two waves shown here are the same distance from point X and are traveling toward each other.
An illustration with a crest 2.0 centimeters high traveling to the right and a second 2.0 centimeters trough traveling toward the left toward point X in the material.
What is the amplitude of the resulting wave when the two waves meet at point X?
0.0 cm
1.0 cm
2.0 cm
4.0 cm
Answer:
(C) on edge.
Explanation:
Answer:
2.0
Explanation:
trust the process.
I NEED HELP PLEASE, THANKS :) What does it mean when white light is diffracted and at a particular location the color seen is blue?
Answer:
This is because white light consists of 7 colours with different angles o deviation or retraction.
Explanation:
When a narrow beam of light is refracted by a prism the light spreads into a band of colours (called the spectrum of light )
But in this case if a blue colour is observed it is due to the angle of refraction ,for instance red is refracted the least and hence is seen
Answer:
When while light is diffracted and at a particular location blue color is seen, this means that blue color is reflected while all other colors will be absorbed. When the blue color is seen denotes the shortest wavelength being reflected and all other being absorbed at the specified location.
when nasa (national aeronautics and space administration) first tried to launch a man into orbit, there were a lot of factors that had to be considered when making the calculations (back in the day, by hand) for the launch. today, these calculations are done with computers, but still need to be entered in by the astronauts right before lift-off. some factors that need to be entered include information about weather - including temperature, wind speed, humidity and dew point. how should this information be presented to the astronaut so that they can enter it into the computers easily and correctly?
The information about weather factors such as temperature, wind speed, humidity, and dew point should be presented to the astronaut in a clear and organized format, possibly using a table or a simple list. This will ensure easy understanding and accurate entry into the computers right before lift-off, thus contributing to a successful launch for NASA (National Aeronautics and Space Administration).
To present the weather information to the astronaut in a clear and concise manner, it is important to use easy-to-read visual aids and simple language. One approach could be to display the weather information on a screen or monitor in a format that is easy to understand, such as a chart or graph. The information should be organized logically and labeled clearly so that the astronaut can quickly find the data they need. Additionally, it may be helpful to provide a brief explanation of how each piece of weather data affects the launch, so that the astronaut can understand the importance of each input. Overall, the goal should be to present the information in a way that is easy to digest and that allows the astronaut to make quick, accurate inputs into the computer system.
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What is the speed of a bus if it
covers 1.5km in 30 seconds?
a. 50km/Hr
b. 500m/s
c. 50m/s
d. 1500m/s
\(answer \\ = 50 \: m / s \\ solution \\ distance \: travelled\: by \: bus = 1.5 \: km \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1.5 \times 1000 \: m \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1500 \: m \\ time \: = 30 \: seconds \\ speed = \frac{distance}{time} \\ \: \: \: \: \: \: \: \: \: \: = \frac{1500m}{30s } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 50 \: m/s \\ hope \: it \: helps\)
Answer:
C. 50 m/s
Explanation:
Given:
Distance = 1.5 km = 1500 m
Time = 30 sec
Required:
Speed = ?
Formula
Speed = Distance / Time
Solution:
Putting the given in the formula
Speed = 1500/30
Speed = 50 m/s
environmental physics
ex1. Dp = Dp = 10,um 8p= 2000 kg/m² (spheres) Nin₁ = 0 Nout = 1000 $/cm³ P = 0.8 (a) what will be the Conc. after 2h if Avent = 34-¹? (6) what - if Xunt = 0.5 4²¹ ? www (C) plot the conc. time
We can see that the concentration of particles decreases exponentially with time. Therefore, the plot is an exponential decay graph.
The formula for the concentration of a spherical particle settling under gravity is given by : Ct = (3V₀/4πr₀³) exp(-4πr₀³gt/3ηV)
Where Ct is the concentration of particlesV₀ is the initial volume of suspensionr₀ is the radius of particles is the acceleration due to gravity is timeη is the viscosity of the medium is the sedimented volume of particlesPart A The given data are, Dp = 10 μmρp = 2000 kg/m³n₁ = 0 N/m³n₂ = 1000 N/m³P = 0.8
Given that, the time is 2 hours = 7200 seconds the temperature is 34°C = 307 The viscosity of air at the given temperature is η = 18.36 × 10⁻⁶ Pa.sThe acceleration due to gravity g = 9.81 m/s²The initial concentration of particles, Ct is 1. Now, the volume of a spherical particle is given by:V = 4/3 πr³Where, r = Dp/2 = 10/2 = 5 μm
Therefore, V = 4/3 × π × (5 × 10⁻⁶)³
= 5.24 × 10⁻⁹ m³ The sedimented volume of the particle is given by:
V = (n₂ - n₁) / ρp g = (1000 × 10⁻⁴) / (2000 × 9.81)
= 5.1 × 10⁻⁶ m³The value of the concentration of particle is given by:Ct = (3V₀/4πr₀³) exp(-4πr₀³gt/3ηV)
Substituting all the given values in the above equation, we get, Ct = (3×1/4π(5×10⁻⁶)³) exp(-4π(5×10⁻⁶)³×9.81×7200/3×18.36×10⁻⁶×5.1×10⁻⁶) ≈ 4.7 × 10⁻⁸
Part B The given data are:Dp = 10 μmρp = 2000 kg/m³n₁ = 0 N/m³n₂ = 1000 N/m³P = 0.8Xunt = 0.5 4²¹
The temperature is not given, hence, we assume it to be the same as Part A, i.e., 34°C = 307 K The viscosity of air at the given temperature is η = 18.36 × 10⁻⁶ Pa.sThe acceleration due to gravity g = 9.81 m/s²The initial concentration of particles, Ct is 1. At t = Xunt = 0.5 4²¹ seconds, the value of the concentration of particle is given by: Ct = (3V₀/4πr₀³) exp(-4πr₀³gt/3ηV)
Substituting all the given values in the above equation, we get, Ct = (3×1/4π(5×10⁻⁶)³) exp(-4π(5×10⁻⁶)³×9.81×0.5 4²¹/3×18.36×10⁻⁶×5.1×10⁻⁶) ≈ 4.8 × 10⁻⁸
Part C The concentration of particles with respect to time is plotted below.
We can see that the concentration of particles decreases exponentially with time. Therefore, the plot is an exponential decay graph.
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define unit aland how many types of unit are there . Name them?
Answer:
7. They arethe meter (m), the kilogram (kg), the second (s), the kelvin (K), the ampere (A), the mole (mol), and the candela (cd)
Explanation:
7. They arethe meter (m), the kilogram (kg), the second (s), the kelvin (K), the ampere (A), the mole (mol), and the candela (cd)
36. A block and tackle pulley must lift a box with 50 N. The pulley has 5 sections. What is the Newton of force for each section? What is the IMA? 37. What is the formula for IMA?
If the pulley has 5 sections, it means that it is a block and tackle system with a mechanical advantage of 5. This means that the force required to lift the box is 1/5 of the weight of the box.
Force for each section = Force required to lift the box / Number of sections
Force for each section = 50 N / 5
Force for each section = 10 N
Therefore, the Newton of force for each section is 10 N.
The IMA (ideal mechanical advantage) of a pulley system is calculated by dividing the distance over which the effort force is applied by the distance over which the load is moved. Since the pulley system does not change the direction of the applied force, the IMA is simply equal to the number of sections in the pulley.
IMA = Number of sections
IMA = 5
The formula for IMA (ideal mechanical advantage) of a simple machine is:
IMA = Distance over which the effort force is applied / Distance over which the load is moved
In the case of a pulley system, the formula can be simplified to:
IMA = Number of sections
This is because the pulley system does not change the direction of the applied force, and each section of the pulley contributes to the mechanical advantage equally.
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2. A 50.0 kg shell was fired from a cannon at earth's surface to a
maximum height of 400. m.
a. What is the potential energy at maximum height?
b. It then fell to a height of 100. m. What was the loss of PE as
it fell?
Answer: a) 196000 Joules
b) 147000 Joules
Explanation:
a. Potential energy is the energy possessed by an object by virtue of its position.
\(P.E=m\times g\times h\)
m= mass of object = 50.0 kg
g = acceleration due to gravity = \(9.8ms^{-2} \)
h = height of an object = 400 m
Putting in the values we get:
\( P.E=50kg\times 9.8ms^{-2}\times 400m=196000kgm^2s^{-2}=196000Joules\) \((1kgm^2s^{-2}=1Joule )\)
Thus the potential energy at maximum height is 196000Joules.
b. \( P.E=50kg\times 9.8ms^{-2}\times 100m=49000kgm^2s^{-2}=49000Joules\) \((1kgm^2s^{-2}=1Joule )\)
Thus loss in P.E = (196000Joules-49000Joules) = 147000 Joules
A 3.0-kg block sits on top of a 5.0-kg block which is on a horizontal surface. The 5.0-kg block is pulled to the right with a force F as shown in the fiaurefFiaure 1). The coefficient of static friction between all surfaces is 0.58 and the kinetic coefficient is 0.36. What is the minimum value of F needed to move the two blocks? Express your answer using two significant figures. If the force is 10% greater than your answer for (a), what is the acceleration of each block? Express your answer using two significant figures.
The minimum value of F needed to move the blocks is 28.5 N. If the force is 10% greater, the acceleration of 5.0-kg block and 3.0-kg block is 0.57 m/s² and 9.5 m/s².
To calculate the minimum force F needed to move the blocks, we need to determine the maximum force of static friction acting on the blocks.
First, we calculate the maximum force of static friction between the 5.0-kg block and the horizontal surface:
f_static_max = μ_static * N = μ_static * m1 * g
= 0.58 * 5.0 kg * 9.81 m/s²
= 28.5 N
The force F must be greater than or equal to this value in order to overcome the force of static friction and move the blocks.
Therefore, the minimum value of F needed to move the two blocks is 28.5 N.
To calculate the acceleration of each block when the force is 10% greater than the minimum value
F = 1.1 * 28.5 N = 31.35 N
The net force acting on the system is
F_net = F - f_static_max
For the 5.0-kg block
F_net = ma
a = F_net / m1
= (F - f_static_max) / m1
= (31.35 N - 28.5 N) / 5.0 kg
= 0.57 m/s²
For the 3.0-kg block
F_net = ma
a = F_net / m2
= f_static_max / m2
= 28.5 N / 3.0 kg
= 9.5 m/s²
Therefore, the acceleration of the 5.0-kg block is 0.57 m/s² and the acceleration of the 3.0-kg block is 9.5 m/s².
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