(a) Rate of change of the temperature of the water at time t = 12 minutes is 2 degrees Fahrenheit per minute. b)Total change in the temperature of the water over 20 minutes is 7.5 degrees Fahrenheit. c)average temperature = 60.5. d) At t = 25, W(25) = W(20) + ∫20 25W′(t)dt = W(20) + ∫20 25(0.4 cos(0.06t))dt
What is theorem of calculus?The fundamental theorem of calculus states that integral of the derivative of a function is equal to difference between function evaluated at the upper and lower limits.
(a) To estimate W′(12), use the formula for the slope of a line between two points: (W(y2) - W(y1)) / (x2 - x1). Using data in the table, estimate W′(12) by taking slope between points (12, 67) and (10, 63) : (67 - 63) / (12 - 10) = 4 / 2 = 2. So, rate of change of the temperature of the water at time t = 12 minutes is 2 degrees Fahrenheit per minute.
(b) To evaluate integral of W′(t) from t = 0 to t = 20; W′(t) = 0.4t + 0.5, so the integral is equal to W(20) - W(0) = (0.420 + 0.5) - (0.40 + 0.5) = 8 - 0.5 = 7.5. Total change in the temperature of the water over 20 minutes is 7.5 degrees Fahrenheit.
(c) To approximate the average temperature of the water over these 20 minutes : (5/20)(55 + 57 + 63 + 67) = (5/20)(242) = 60.5. As the temperature of the water is increasing, average temperature will be greater than temperature of water at the start of the time period and less than temperature of the water at end of the time period, so approximation will overestimate average temperature.
(d) For 20 <= t <= 25, W′(t) = 0.4 cos(0.06t). At t = 25, W(25) = W(20) + ∫20 25W′(t)dt = W(20) + ∫20 25(0.4 cos(0.06t))dt. To find the definite integral we need to evaluate it with the limit from 20 to 25. As the temperature of the water is increasing as the derivative is positive.
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4. On Earth the average atmospheric pressure at the surface is 1013254 Pa. If we assume that the radius of Earth is 6.4 x 106m and the acceleration of gravity is 9.8 m/s2, what is the mass of Earth's atmosphere? Hint: You will need to use the equations for force, pressure, and the surface area of a sphere, but you will need to analyze the units to confirm how these get combined.) Use the following values to solve this problem. 16 pts 1 atm = PEarth=101325 Pa; REarth-6,4x10ºm; g = 9.8 m/s? Ending units:
At the surface of Earth, the ambient atmospheric pressure is 1013254 Pa. The weight of the atmosphere on Earth is 5.322 * 1016 kg.
Describe pressure.The magnitude of force applied to a certain region is referred to as pressure. So either a strong force or a strong force applied over a short area can cause a lot of pressure (or do both).
Why does air pressure exist?The atoms and molecules that comprise the many layers of the atmosphere are continually moving in arbitrary directions. Despite their modest size, when they hit a surface, they apply pressure that humans perceive as a force.
atmospheric pressure = 1013254 Pa
radius of Earth = 6.4 * 10⁶ m
gravity = 9.8 m/s²
surface area of a sphere = 4π radius²
surface area of earth = 4 * 3.14 * ( 6.4 *10⁶ )²
= 5.14719 * 10¹⁴ m²
mass of the atmosphere = ( 1013254 pa * 5.14719 * 10¹⁴ m²) / 9.8
= 5322 * 10 ¹⁶ gm
= 5.322 * 10¹⁶ kg
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A horizontal 779 N merry-go-round of radius
1.28 m is started from rest by a constant
horizontal force of 43.1 N applied tangentially
to the merry-go-round.
Find the kinetic energy of the merry-go round after 2.5 s. The acceleration of gravity
is 9.8 m/s². Assume the merry-go-round is a solid cylinder.
Answer in units of J.
Answer:
576 joules
Hope this helped :)
If the mass of the box is 3.6 kg and it is accelerating with 4.2 m/s^2, What is the net force exerted on the box?
Explanation:
Force= mass × acceleration
= 3.6 × 4.2
= 15.12N
If the mass of the box is 3.6 kg and it is accelerating with 4.2 m/s², then the force exerted on the box is 15.12 N.
what is force?The definition of force is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. Every time two items interact, a force is exerted on each of the objects. The force is no longer felt by the two objects when the interaction ends. Only when there is interaction do forces actually exist.
The strong force, weak force, electromagnetic force, and gravitational force are the four fundamental forces operating in the universe. The formula of force is Force = mass × acceleration.
Hence, if the mass of the box is 3.6 kg and it is accelerating with 4.2 m/s², then the force exerted on the box is 15.12 N.
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from the following statements about mechanical waves, identify those that are true for transverse mechanical waves only, those that are true for longitudinal mechanical waves only, and those that are true for both types of waves. drag each item to the appropriate bin.
When a wave travels through a medium, the particles in that medium vibrate in a direction perpendicular to the direction the wave travels it is a transverse mechanical waves only.
When a wave travels through a medium, the particles in that medium vibrate in a direction parallel to the direction the wave travels it is a longitudinal mechanical waves only .
Then a wave travels through a medium, the wave speed will depend on an inertial property of that medium it is for both transverse and longitudinal mechanical waves .
A transverse wave is a type of wave in which the motion of the wave's motion is perpendicular to the position of the medium's particles at any given time. Move one end of a Slinky (whose other end is fixed) to the left and right of the Slinky rather than back and forth to view an example. Example - waves on surface of waterA mechanical wave is a wave in physics that involves the oscillation of matter and transmits energy across a medium. While waves can travel great distances, the transmission medium—the material—can only move so far. Example - Sound wavesLearn more about transverse mechanical waves
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In the absence of air friction, an object dropped near the surface of the Earth experiences a constant acceleration
of about 9.8 m/s2
(A) speed of the object increases 9.8 m/s during each second
(B) speed of the object as it falls is 9.8 m/s
. This means that the
(C) object falls 9.8 meters during each second
(D) object falls 9.8 meters during the first second only
(E) rate of change of the displacement with respect to time for the object
In the absence of air friction, an object dropped near the surface of the Earth experiences a constant acceleration of about 9.8 m/s2, so the speed of the object increases 9.8 m/s during each second.
The speed of the object increases 9.8 m/s during each second the acceleration means the change in velocity per second.
Gravity can be explained as a force such that controls the movement of the planets such as Earth around the Sun, hold stars grouped in galaxies together, and galaxies grouped in clusters.
The gravity which is generally near the Earth's surface makes it possible for all physical objects to possess weight and experience a free fall.
Generally, the acceleration due to gravity for an object experiencing a free fall near the Earth's surface is 9.8 m/s2.
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What is the ideal speed to take a 75 m radius curve banked at a 10.0° angle?
m/s
The ideal speed to take a 75 m radius curve banked at a 10.0° angle is 21.82 m/s.
The formula for the maximum vehicle velocity on banked roads can be used to determine the banking angle. The equation for the angle of banking, t a n = v 2/ r g, is obtained by squaring the equation on both sides and rearrangement.
The curved path's banking angle is given as
tan θ = v² / rg
Here, v is the linear speed, r is the curved path's radius, is the bank angle, and g is the acceleration brought on by gravity.
θ = 10.0°, r = 75 m, and g = 9.8 m/s2 are our values.
By replacing these numbers in the formula above, we obtain
tan 10 = v2 / 75m × 9.8m/m/s²
v² = 476.54
v = √476.54 = 21.82 m/s
Thus, 21.82 m/s is the optimal speed.
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after newton's proverbial apple fell from the tree, which hypothesis statement below would have been appropriate to test?
According to legend, young Isaac Newton came up with first law of gravity after getting hit on the head by a piece of fruit that had fallen from an apple tree while he was sitting underneath it.
What rules govern gravity?Newton's gravitational law states that every piece of matter in the universe is drawn to every other piece with a force than varies directly with the mass-to-mass ratio and inversely with the distance between them.
Which three gravitational laws are there?The product of the masses of two objects multiplied by two is the gravitational force between them. The gravitational pull here between objects will also triple if one of them triples in mass. When two objects' masses double, for example, the gravitational force between them is multiplied by two, and so on.
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A 2,400-kilogram car is traveling at a speed of 20. meters per second. Compared to the magnitude of the force required to stop the car in 12 seconds, the magnitude of the force required to stop the car in 6.0 seconds is (1) half as great(2) twice as great (3) the same (4) four times as great
Compared to the magnitude of force required to stop the car in 12 seconds, magnitude of the force required to stop the car in 6.0 seconds is : (3) the same.
What is meant by force?In physics, force is an influence that changes the motion of an object.
Force is : F = m * a, where m is mass of the object and a is acceleration.
Given, distance traveled is zero (the car stops), the initial velocity is 20 m/s and time is 12 seconds.
As, d = vt + (1/2)at^2
So, a = 2d/t^2 - v^2/d
a = 2*0/(12^2) - (20^2)/0 = 0 - 400/0 = undefined
a = 2*0/(6^2) - (20^2)/0 = 0 - 400/0 = undefined
As acceleration is undefined in both case, we say that the force required to stop the car in 6.0 seconds is same as force required to stop the car in 12 seconds.
So, answer is (3) the same.
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a solid object of mass m is suspended vertically from a spring balance. the spring balance reads w when the object is in air. when the object is submerged in water while still attached to the balance, the reading on the balance is
The Archimedes principle states that when an object is submerged in a fluid, it seems to lose weight that is equal to the weight of the fluid that was displaced.
What transpires when something is immersed in water? The Archimedes principle states that when an object is submerged in a fluid, it seems to lose weight that is equal to the weight of the fluid that was displaced.The apparent weight loss is brought about by the buoyant force, which acts in an upward direction counter to the object's weight.The buoyant force is the name for the upward push that fluid-immersed objects experience.The buoyant force.A submerged item experiences fluid pressure on all sides.The upward force on the bottom surface (F2) is larger than the downward push on the top surface, though, because pressure rises with depth (P) (F1).As a result, there is constantly an upward pull from buoyancy. 'To learn more about Archimedes principle refer
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According to the Declaration of Independence, from where does government get its power?
from God
from a written constitution
from elected representatives
from the consent of the governed
The government derive its power according to the Declaration of Independence is the document that declare the freedom of the people. The document was approved by the Continental Congress on July 4, 1776.
Below are the main messages of the declaration of independence.
(1) God made all men equal and gave them the rights of life, liberty, and the pursuit of happiness.
(2) The main business of government is to protect these rights.
(3) If a government tries to withhold these rights, the people are free to revolt and to set up another government.
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Suppose that a ball is thrown vertically upward from earth with velocity v, and returns to its original height in a time t. If the value of g were reduced to g/6 (as on the moon), then t would:
If the value of g were reduced to g/6, then the equation for the time it takes for the ball to return to its original height would become t = 2v/(g/6), or t = 12v/g. Since the original equation is t = 2v/g, the new equation is 6 times greater, so the time t would be 6 times greater than before.
What would be the velocity of the ball when it returns to its original height? If the value of g were reduced to g/6, the ball would reach its original height with a velocity of 6v (where v is the initial velocity of the ball when it was thrown vertically up). The time t would also be reduced to t/6, since the acceleration of the ball is reduced to g/6. This means that the ball would take less time to reach its original height when compared to the time taken when the acceleration is equal to g. In conclusion, if the value of g were reduced to g/6, the velocity of the ball when it returns to its original height would be 6v and the time taken for the ball to reach its original height would be t/6.To learn more about velocity refer to:
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two stationary point charges of unknown magnitude and sign are isolated from all other charges. if the electric field strength is zero at the midpoint of the line joining them, which of the following can be concluded about the charges?
Two stationary point charges of unknown magnitude and sign are isolated from other charges. If electric field strength is zero at midpoint of line joining them, following can be concluded about charges : They are equal in magnitude but opposite in sign.
What is meant by electric field?The electric field is a vector field that describes the force experienced by a test charge placed in the field. The direction of the electric field is given by the direction of the force experienced by the test charge and its magnitude is given by the force experienced per unit charge.
Electric field at the point due to point charge ;
E = k * (q/r^2) * r_unit
where k is Coulomb's constant, q is the charge, r is the distance from the point charge, and r_unit is the unit vector pointing from the point charge to the point where the electric field is being calculated.
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Note: The question given on the portal is incomplete. Here is the complete question.
Question: Two stationary point charges of unknown magnitude and sign are isolated from all other charges. if the electric field strength is zero at the midpoint of the line joining them, which of the following can be concluded about the charges?
They are equal in magnitude but opposite in sign.
They are equal in magnitude and sign.
They are not equal in magnitude and opposite in sign
They are not equal in magnitude but same sign.
A small air compressor operates on a 2.9 hp (horsepower) electric motor for 4.9 hours a day. If electricity costs 22 cents per kilowatt-hour, how much does it cost to run the compressor each day?
Answer in units of cents
The amount it take to run the compressor if the electricity cost 22 cents per kilowatt-hour is 233.21 cents.
What is kilowatt-hour?A kilowatt-hour is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ).
To calculate the the amount it takes to run the compressor daily, we use the formula below.
Formula:
A = PtC/1000............ Equation 1Where:
A = Amount it takes the run the compressor dailyP = Power of the compressor = 2.9 hp = 2.9×746 = 2163.4 Wt = Time = 4.9 hours C = Electricity cost = 22 cents per kilowatt-hourSubstitute these values into equation 1
A = 2163.4×4.9×22/1000A = 233.21 centsHence, the amount is 233.21 cents.
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can electricity be conducted safely underwater and how?
Answer:
Yes
Explanation:
By adding salt.
a technician needs to replace a failed power supply on a server. the server in question only has one power supply. the server contains two processors that need 100w, five hard drives that need 9w, and a gpu that uses 200w. which of the following power supplies should the technician use? A. 375w
B. 425w
C. 325w
D. 500w
The power supply that technician should use 500 W.
A power supply is a component that transforms the output of an ac power line into one or more constant dc outputs. A smooth voltage is created by filtering the ac voltage after it has first been rectified to create a pulsing dc. In spite of fluctuations in the ac line voltage or circuit loads, the voltage is finally regulated to produce a consistent output level.
The power use of the server as whole is,
100 W+ 5×9 W + 200 W
Power use=445 W.
So, the power should be more than the 445 W in order that there should not be any short circuit.
and from all the given options the power supply that is feasible is 500 W.
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500 W of power should be used by the technician.
One or more consistent dc outputs are produced from an ac power line's output by a component known as a power supply. After rectifying the ac voltage to produce a pulse dc, a smooth voltage is produced by filtering the result. Despite changes in the ac line voltage or circuit loads, the voltage is eventually controlled to create a constant output level.
The entire server's energy consumption is,
100 W+ 5×9 W + 200 W
Using 445 W of power.
Therefore, the power must be more than 445 W to prevent short circuits.
Choose the power supply that is practical from the possibilities presented
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PLEASE HELP AND HURRY! VERY IMPORTANT TEST
1. What physical properties can cause an object to resonate?
-mass, color, and density
-shape, temperature, energy
-shape, composition, and length
-color, density, and composition
2. Which statement about resonance is correct?
-Resonance causes the amplitude of vibrations to decrease.
-Resonance causes the amplitude of vibrations to increase.
-Resonance does not affect the amplitude of vibrations.
-Resonance causes frequency to incease
3.How can you make the natural frequency of a string increase?
-decrease the tension of the string
-cut the string
-tighten the string
-loosen the string
4. A student wants to make the natural frequency of a tube increase. How can the student accomplish this?
-Decrease the length of the tube
-Change the composition of the tube
-Make holes in the tube
-Increase the length of the tube
5.Which factor determines the natural frequency of an object?
-color
-elasticity
-length
-pressure
Question:1. What physical properties can cause an object to resonate?-mass, color, and density-shape, temperature, energy-shape, composition, and length-color, density, and composition
2. Which statement about resonance is correct?-Resonance causes the amplitude of vibrations to decrease.-Resonance causes the amplitude of vibrations to increase.-Resonance does not affect the amplitude of vibrations.-Resonance causes frequency to incease3.How can you make the natural frequency of a string increase?-decrease the tension of the string-cut the string-tighten the string-loosen the string4. A student wants to make the natural frequency of a tube increase. How can the student accomplish this?-Decrease the length of the tube-Change the composition of the tube-Make holes in the tube-Increase the length of the tube5.Which factor determines the natural frequency of an object?-color-elasticity-length-pressure
Explanation:
answer is 1,2,3,4,5,
Consider the periodic waveform of Fig. 1 r(t) T DT DT 2 Figure 1: Waveform for Problem 1 Derive expressions for the DC component of this waveform, and for the magnitudes of the Fourier series harmonics. Determine the value of D which sets the magnitude of the Fourier series 3d harmonic to zero. Finally, derive an expression for the RMS value of this waveform
A wave-shaped signal is represented graphically by a waveform. Depending on the kind of wave generating input, it might be either square or sinusoidal. The characteristics that determine the wave's size and shape determine the waveform.
The required details for waveform in given paragraph
The waveform in Figure 1 is a square wave with a period T. The DC component of this waveform is the average value of the waveform over one period. It can be found by integrating the waveform over one period and dividing by the period T:
DC component = from 0 to T
The magnitude of the Fourier series harmonics can be found by using the formula for the Fourier series coefficients:
Ak = (from 0 to T)
Bk = (from 0 to T)
where k is the harmonic number, f is the fundamental frequency (1/T), and A and B are the Fourier series coefficients.
For a square wave, the odd harmonics are non-zero and the even harmonics are zero. For the 3rd harmonic, the magnitude is:
Ak = (from 0 to T)
= (from 0 to T)
= (from 0 to T)
To set the magnitude of the Fourier series 3rd harmonic to zero,
D = 0
Finally, the RMS value of the waveform can be found by using the formula:
RMS = (from 0 to T)
= (from 0 to T)
= It's important to notice that the solution and expressions given here are only valid for square waveform with a period T and amplitude D.
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according to kinetic/collision energy, when are reactants more lielky to have sufficient energy to undergo a reaction
According to collision theory, the quantity of reactant molecule collisions determines how quickly a chemical reaction proceeds. The pace of reaction increases with the frequency of reactant-molecule collisions.
Under what situations will greater energy collisions between the reactants be more likely?The average pace of particles increases with temperature, which increases the rate of particle collisions. The average kinetic power of collisions increases with temperature, increasing the proportion of collisions that require the least amount of energy to react.
Which of the following conditions must be met for a reaction to occur when two reactant particles collide?Reactant particles need to have a certain minimum energy in order to make an efficient collision. The activation energy is the energy that starts the reaction.
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Use the given values of n and p to find the minimum usual value and the maximum usual value μ
−
2
σ
. Round your answer to the nearest hundredth unless otherwise noted.
n = 248, p = ?
Question options:
a) Minimum: 75.64; maximum: 48.36
b) Minimum: 52.36; maximum: 71.64
c) Minimum: 55.18; maximum: 68.82
d) Minimum: 48.36; maximum: 75.64
Minimum: 75.64; maximum: 48.36 is the nearest hundredth unless otherwise noted.
What is p?The given values of n and p to find the minimum usual value and the maximum usual value μ
−2σ
n = 248, p = Detailed explanation:
Considering the characteristics of the binomial distribution
n = 248, p = 4/5
To determine the necessary values, we must determine the mean and the standard deviation.
The steps are listed below.
Identify the mean.
μ = n·p = 248*(4/5) = 570.4
Find the variation in 2.
σ² = np(1 - p) = 248*(4/5)*(1 - 4/5) =
Discover the standard deviation in 3.
Minimum: 75.64; maximum: 48.36
Minimum: 75.64; maximum: 48.36 the nearest hundredth unless otherwise noted.
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The carbón dioxide is matter that is made up of
Through the decomposition of organic matter, CO₂ is released into the atmosphere as part of this natural process.
Is carbon dioxide a state of matter?One carbon atom is covalently doubly bound to two oxygen atoms in each of the molecules that make up carbon dioxide, which has the chemical formula CO 2.
At room temperature, it exists as a gas. In the atmosphere, carbon dioxide serves as a greenhouse gas because it absorbs infrared radiation despite being transparent to visible light. It has increased from pre-industrial levels of 280 ppm to a trace gas in the Earth's atmosphere at 421 parts per million (ppm), or roughly 0.04% by volume (as of May 2022).
The fundamental driver of both these elevated CO2 concentrations and climate change is the burning of fossil fuels. Groundwater, lakes, ice caps, and ocean all contain dissolved carbon dioxide.
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A person standing at the edge of a cliff throws one ball straight up and another ball straight down, each at the same initial speed. Neglecting air resistance, which ball hits the ground below the cliff with the greater speed?
When a person standing at the edge of a cliff throws one ball straight up and another ball straight down, each at the same initial speed, neglecting air resistance, the ball that hits the ground below the cliff with the greater speed is the ball that was thrown straight up.
What is the acceleration due to gravity?The acceleration due to gravity is the acceleration that is produced in an object due to the gravitational force of the earth acting on the object.
The velocity of an object depends on the acceleration due to gravity and the height above the ground of an object as given below:
Velocity = √2gh
where;
g is the acceleration due to gravity
h is the height above the ground
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the diameter of the wheel is 0.58 m. determine the value of the horizontal component of the force of the road on the wheel.
The road force on the wheel weigh is 690.
Which force moves the car on road?Your automobile advances under the influence of static friction. The power to turn the tires is provided by the engine, which pushes the vehicle rearward against the road.
Example:
The axle of the wheel that is in touch with the road receives a 200 mN torque from a car's engine.
The vehicle moves rightward at a steady speed:
The automobile wheel measures 0.58 meters in diameter. What does the horizontal component of the road force on the wheel weigh?
Radius: 0.29 m
When formula is used, we obtain
Force = Torque / Radius = 200/0.29
=690.
It is the necessary response as a result.
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Estimate the mass of air inside the passenger area of a CATA bus. A)100 kg B)10 kg C)1000 kg D)0.1 kg
The Correct option is D which is 0.1kg .
It can be challenging to calculate the air mass in a CATA bus's passenger compartment. It will most likely just weigh a few tenths of a kilogramme or perhaps less, which is exceedingly little.
This is because, in relation to the size of the bus itself, the volume of air inside the passenger compartment of a bus is rather low. Additionally, even a small volume of air will have a comparatively modest mass since the density of air at normal atmospheric pressure is extremely low.
The frequent interchange of air through open doors and windows would be another element that might contribute to the small mass of air inside a bus.This would mean that the air inside the bus is not stagnant and is constantly being replaced by the air outside which would lead to a decrease in mass. The answer would be D)0.1 kg
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a box slides down a frictionless ramp. it begins at rest. the ramp has an incline of 40.0 degrees, find how long it takes to reach 1.00m/s.'
A box slides down a frictionless ramp, then it takes approximately 0.87 seconds for the box to reach 1.00 m/s.
What is meant by friction?The force resisting relative motion of solid surfaces, fluid layers, and material elements sliding against each other is called friction.
As, v^2 = u^2 + 2as
Given, v = final velocity = 1.00 m/s ; u = initial velocity = 0 m/s (since the box is at rest) ; a = acceleration due to gravity = 9.8 m/s^2 and s = distance covered = 1.00 m
So, s = 1.00 m = x x sin(40.0 degrees)
x = 1.00 m / sin(40.0 degrees)
(1.00 m/s)^2 = 0^2 + 2(9.8 m/s^2) (1.00 m / sin(40.0 degrees))
t = √((1.00 m/s)^2 - 2(9.8 m/s^2) (1.00 m / sin(40.0 degrees)) )/ (2(9.8 m/s^2))
Hence, t ≈ 0.87 sec
It takes approximately 0.87 seconds for the box to reach 1.00 m/s.
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You pull your t-shirt out of the washing machine and note that 1596 particles have become attached, each of which could be either an electron or a proton. Your t-shirt has a net charge of − 3.14 X 10 ^-17 C. How many electrons are attached to your t-shirt? What is the mass of the particles attached to your t-shirt?
(a) The number of electrons on the T-shirt is 700 electrons.
(b) The mass of the particle attached to your T-shirt is 1.5 x 10⁻²⁴ kg.
What is the number of electrons on the T-shirt?
The number of electrons on the T-shirt is calculated as follows;
Let the number of electrons = e
Let the number of protons = p
p + e = 1596 ------ (1)
p = 1596 - e ------ (2)
qp - qe = -3.14 x 10⁻¹⁷ ------- (3 )
The equation (3) can be simplified as;
q ( p - e ) = -3.14 x 10⁻¹⁷ -------- (4)
Now substitute the value of p into (4)
q (1596 - e - e) = -3.14 x 10⁻¹⁷
q (1596 - 2e) = -3.14 x 10⁻¹⁷
1596 - 2e = ( -3.14 x 10⁻¹⁷ ) / ( q )
1596 - 2e = ( -3.14 x 10⁻¹⁷ ) / ( 1.6 x 10⁻¹⁹ )
1596 - 2e = 196.25
2e = 1596 - 196.25
2e = 1399.75
e = 1399.75 / 2
e = 700 electrons
The mass of the particle attached to your T-shirt is calculated as follows;
m = (700 x me ) + ( 896 x mp)
m = ( 700 x 9.1 x 10⁻³¹ ) + ( 896 x 1.67 x 10⁻²⁷ )
m = 1.5 x 10⁻²⁴ kg
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An amusement park ride consists of a rotating circular platform 10.1 m in diameter from which 10 kg seats are suspended at the end of 3.6 m massless chains. When the system ro-tates, the chains make an angle of 15.9° with the vertical.
The acceleration of gravity is 9.8 m/s?
Your re
What is the speed of each seat?
Answer in units of m/s.
The speed of each seat is 3.2 m/s.
What is the speed of each seat?
The speed of each seat is calculated by applying Newton's second law of motion as shown below.
T cos (θ) = mg
T sin (θ) = mv² / r
where;
v is the speed of each seatT is the tension in the ropem is the mass of each seatg is acceleration due to gravityT = mg / cos(θ)
T = ( 10 x 9.8 ) / ( cos 15.9 )
T = 101.9 N
The speed of each seat is calculated as;
v² = (Tr sin(θ) ) / m
v = √ [ (Tr sin(θ) ) / m ]
v = √ [ (101.9 x 3.6 x sin(15.9) ) / 10 ]
v = 3.2 m/s
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A block of mass 3.60 kg is placed against a horizontal spring of constant k = 795 N/m and pushed so the spring compresses by 0.0450 m. (a) What is the elastic potential energy of the block-spring system (in J)? (b) If the block is now released and the surface is frictionless, calculate the block's speed (in m/s) after leaving the spring
The initial elastic potential energy of the block-spring system is 17.88 joules. The final speed of the block is approximately 3.15 meters per second.
What is elastic potential energy?Elastic potential energy is energy stored in an object as a result of application of a force to deform an elastic object. The energy is stored until the force is removed and the object springs back to its original shape and size, doing work in the process.
By applying Hooke's law and definition of work, we define the elastic potential energy (Ug), measured in joules, by the following formula:
Ug = 1/2 × k × x²
where, k = Spring constant, measured in newtons per meter
x = Deformation of the spring, measured in meters
If we know that k = 795 N/m and x = 0.045m, then the elastic potential energy is:
Ug = 1/2 × 795 × 0.045
Ug = 17.88 Joules
The initial elastic potential energy of the block-spring system is 17.88 joules.
b) According to the Principle of Energy Conservation, the initial elastic potential energy of the block-spring system becomes into translational kinetic energy, that is:
Ug = 1/2 × m × v²
where, m = Mass measured in kilograms,
v = Final speed, measured in meters per second.
Then, the final speed is cleared:
v = [tex]\sqrt{2Ug/m}[/tex]
If we know that Ug = 17.88 Joules and m = 3.60kg, then the final speed of the block is:
v = √(2 × 17.88J)/ 3.60kg
v = 3.15m/s.
The final speed of the block is approximately 3.15 meters per second.
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When a 1.00-kg mass is suspended from a spring, the spring stretches by .050 m. What is the spring constant and what is the period if it oscillates in simple harmonic motion?
The period if it oscillates on simple harmonic motion is determined by the value to be 0.1256 seconds.
What does harmonic motion entail?Harmonic motion is the motion that an oscillating mass undergoes when the restoring force is proportionate to the displacement but acting in the opposite direction. A sine wave with a constant magnitude and frequency can be used to illustrate harmonic motion because it is periodic. A weight bouncing on a spring is an illustration of this.
Why do harmonics exist?Harmonics are the outcome of nonlinear loads converting AC voltage level to DC. Because of nonlinear electrically controlled components like computer power supply, energy-efficient lighting, and variable-frequency drives (VFDs), harmonics enter the electrical system.
According to the given information:The force constant of the spring,
So,
K = f/x
= (1 x 10)/0.2
= 50 N/m
Now, if the mass of 1 kg is suspended by the spring, then the period of oscillation,
T = 2π√(m/k)
T = 2π√(1/50)
T = 2π * 0.02
T = 0.1256s
the value to be 0.1256 seconds.
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State the reason why the magnitude of the Sun’s gravitational force on Pluto is greater than the magnitude of the Sun’s gravitational force on Charon.
Pluto masses 1.3e22 kg, and its average distance from the sun is about 6e15 km. The sun’s mass is 2e30 kg. G is 6.7e−11 m^3 / kg⋅s^2.
What is meant by mass?
A body's mass is an inherent quality. Prior to the discovery of the atom and particle physics, it was widely considered to be tied to the amount of matter in a physical body.It was discovered that, despite having the same amount of matter in theory, different atoms and elementary particles have varied masses.There are various conceptions of mass in contemporary physics that are theoretically different but physically equivalent.The resistance of the body to acceleration (change of velocity) in the presence of a net force can be measured experimentally as mass.The gravitational pull an object has on other bodies is also influenced by its mass.So the force of gravity is
f = G M1 M2 / d^2
= 6.7e-11 x 1.3e22 x 2e30 / 5e15^2
= .7e11 N = 70 billion newtons.
One might say, not insignificant.
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Imagine, if you can, that you are traveling toward a black hole. When is time dilation likely to occur?
when you approach the event horizon
when you cross the wormhole
when you land in the singularity
when you pass the quasar
Imagine, if you are traveling toward a black hole. The time that time dilation is likely to occur is option A: when you approach the event horizon.
What is the black hole about?The event horizon is the boundary around a black hole beyond which nothing, including light, can escape. As an object approaches the event horizon, the gravitational pull becomes stronger. This causes time to slow down for the object, a phenomenon known as time dilation.
The effect becomes more pronounced as the object gets closer to the singularity, the central point of the black hole where the gravitational pull becomes infinitely strong.
Crossing a wormhole, which is a hypothetical passage through space-time connecting distant points, would also experience time dilation, but it is different than the one that occurs near a black hole.
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