The near point of the machinist with the eyeglasses is 7 cm. This is because the power of the eyeglasses is +4.25 diopters. The near point is inversely related to the power of the lenses.
What is the power ?The power is the capacity or ability to do something or act in a particular way. It can refer to physical strength, mental strength, the ability to influence people or events, or the capacity to achieve goals. Power can also refer to knowledge, control or authority over something or someone. It can be used to accomplish great things and to gain advantage over others, but it can also be abused or misused. It is important to use power responsibly and ethically, as it has the potential to cause great harm.
Therefore, when the power of the lenses increases, the near point decreases. Therefore, the near point of the machinist with the +4.25-diopter eyeglasses would be 7 cm.
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Explain why adding globes in parallel makes no difference to their brightness? What did you notice about the current?
(immediate response please)
Adding globes in parallel makes no difference to their brightness because all the bulbs glowed with the same brightness indicating that the current flowing through the bulbs had the same value.
The current in each light bulb was the same.
What is electric current?An electric current is a flow of electrons as a result of a potential difference between two points in conductor.
Electrons are negatively-charged particles that are one of the fundamental particles of an atom. The flow of electrons through a conductor is able to do work.
Two or more globes in a simple parallel circuit do not experience any drop in the voltage, thus allowing the maximum flow of electric current. Also, connecting devices in a parallel circuit ensures that if one of the component lops is disconnected, the flow of current through the other loops remains intact.
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Thomas the Train chugs along at 2 m/s. Thomas needs to go faster so more coal is shoveled into his engine and he accelerates for 10 seconds until he is going 4.33 m/s. What is Thomas' acceleration?
The acceleration of Thomas is 0.233 m/s^2.
Acceleration is the rate of change of velocity. Thomas the Train chugs along at a velocity of 2 m/s.
Thomas needs to go faster so more coal is shoveled into his engine and he accelerates for 10 seconds until he is going 4.33 m/s.
We are to find the acceleration of Thomas.
The formula for acceleration is given as :
acceleration = (final velocity - initial velocity) / time
In the given problem, the initial velocity of Thomas, u = 2 m/s.
The final velocity of Thomas, v = 4.33 m/s The time for which Thomas accelerates, t = 10 s.
Therefore, the acceleration of Thomas will be given as:
a = (v - u) / ta = (4.33 - 2) / 10s => 2.33 / 10s => 0.233 m/s^2
Thus, the acceleration of Thomas is 0.233 m/s^2.
To summarize, the acceleration of Thomas is 0.233 m/s^2.
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In the early years of the 20th century, a leading model of the structure of the atom was that of the English physicist J. J. Thomson (the discoverer of the electron). In Thomson's model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge −e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R.
A) Is equilibrium position of the electron at the center of the nucleus?
B)
In Thomson's model, it was assumed that the positive material provided little or no resistance to the motion of the electron. If the electron is displaced from equilibrium by a distance r less than R, find the net force on the electron.
Express your answer in terms of the variables r⃗ , R, e, and constants π and ϵ0.
C) Calculate the frequency of oscillation.
Express your answer in terms of the variables m, R, e, and constants π and ϵ0.
The equilibrium position of the electron at the center of the nucleus is R = 3.16 x10⁻¹⁰m.
Thomson discovered the electron and proposed a structural model of the atom. His research also led to the invention of the mass spectrometer. Thomson announced that he discovered that atoms are made up of smaller components.
Calculation:-
K = 2.304 × 20^-²⁸ / 3
f = 1/2π√k/m
4.63 × 10¹⁴ = 1/2× 3.141 √2.304 × 20^-²⁸ / R³ (9.1 × 10-31)
R = 3.16 x10⁻¹⁰m.
This discovery revolutionized the way scientists think about atoms and had a major impact on the field of physics. Thompson called them corpuscles but what he found are now commonly known as electrons. The plum pudding model is defined by an electron surrounded by a volume of positive charge like a negatively charged plum embedded in a positively charged pudding.
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If the x-component of vector A in the figure below is 3cm and the y component of A is 4cm, then what is the vector quantity of A?
Question 9 options:
25 cm - 37 degrees
7 cm - 37 degrees
7 cm - 53 degrees
5 cm - 53 degrees
Answer:
5 cm - 53 degrees
Explanation:
\( \sqrt{ {4}^{2} + {3}^{2} } = 5cm\)
\( \tan ^{ - 1} (4 \div 3) \) = 53°
A radio antenna radiates 3.47 W of power at 185 Hz.
How many photons per second are emit-
ted by the antenna? Planck's constant is
6.63 x 10-34 J·s.
Answer:
"\(2.829\times 10^{31} \ photon/s\)" is the appropriate solution.
Explanation:
The given values are:
Power,
P = 3.47 W
Frequency,
f = 185 Hz
Planck's constant,
h = 6.63 x 10⁻³⁴ J.s
As we know,
⇒ \(n=\frac{P}{E}\)
Or,
⇒ \(n=\frac{P}{hf}\)
On substituting the given values, we get
⇒ \(=\frac{3.47}{6.63\times 10^{-34}\times 185}\)
⇒ \(=\frac{3.47}{1.22655\times 10^{-31}}\)
⇒ \(=2.829\times 10^{31} \ photon/s\)
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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Two identical tiny spheres carrying the same charge are 1.0m apart center to center in vacuum and experience an electrical repulsion of 1N. What is their charge?
The charge of the spheres can be determined using Coulomb's law of electrostatic forces. Here, the separation is 1 m and the electric force between them is 1 N. Then their charge is 1.05 × 10⁻⁵ C.
What is Coulomb's law ?Coulomb's law states the relation between the charges of two charged particles and the distance between them to the force of attraction or repulsion between them as written below:
F = k q1 q2 / r²
where q1 and q2 be the charges and r is the distance.
k = 9 × 10⁹ N m²/C²
Given r = 1m
F = 1 N
here q1 = q2 = q.
then 1 N = 9 × 10⁹ N m²/C² q²/1 m²
q² = 1.11 × 10⁻¹⁰ C²
then q = 1.05 × 10⁻⁵ C.
Therefore, the charge of the tow tiny spheres is 1.05 × 10⁻⁵ C.
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Asexual reproduction provides an advantage to organisms under which of the following conditions?
There is a decrease (less) in resources available in the habitat that the organism needs to survive.
The organisms are widely dispersed in the habitat and rarely encounter each other.
A new species is introduced into the habitat that directly competes with the organism for food.
Answer:
The organisms are widely dispersed in the habitat and rarely encounter each other...
Explanation:
As asexual reproduction needs only 1 parent.. they can do it on their own.. without encountering their mates
Select the correct answer.
The motion of a car on a position-time graph is represented with a horizontal line. What does this indicate about the car's motion?
A. It's not moving.
B.It's moving at a constant speed.
C.It's moving at a constant velocity
D.It's speeding up.
Answer:
It isn't moving
Explanation:
2. Identify the types of relationship for each of these expressions (linear, inverse, parabolic):
Between Kinetic energy and speed
Between potential energy and mass
between pressure and volume
between pressure and temperature
between displacement and velocity
Between Kinetic energy and speed: The relationship is quadratic or parabolic. According to the kinetic energy formula, KE = 1/2 mv^2, the kinetic energy is proportional to the square of the speed.
Between potential energy and mass: The relationship is linear. The potential energy is directly proportional to the mass. In simple cases, the potential energy is given by PE = mgh, where mass (m) and height (h) are directly proportional.
Between pressure and volume: The relationship is inverse. According to Boyle's law, the pressure and volume of a gas are inversely proportional when temperature is constant. Mathematically, P1V1 = P2V2.
Between pressure and temperature: The relationship is linear. According to Charles's law, the pressure and temperature of a gas are directly proportional when volume is constant. Mathematically, P1/T1 = P2/T2.
Between displacement and velocity: The relationship is linear. Velocity is the rate of change of displacement with respect to time, so the two are directly proportional.
While Kepler supported the Copernican model of the universe Kepler concluded the following
A the circular orbits of the copernican model weren’t correct paths of planets were elliptical
B all other bodies in the universe move around the earth in circular paths
C all other bodies in the universe move around the moon in triangular paths
D the circular orbits of the Copernican model weren’t correct paths of planets were rectangular
Answer:
Explanation: because Keller concluded that the circular obits of the Copernican model weren't correct paths of planets were elleptical
What is the magnetic force on a 2.0-m length of (straight) wire carrying a current of 30 A in a region where a uniform magnetic field has a magnitude of 55 mT and is directed at an angle of 20° away from the wire?
To determine the magnetic force on a straight wire carrying a current in a uniform magnetic field, we can use the formula for the magnetic force:
F = I * L * B * sin(θ)
where:
F is the magnetic force,
I is the current in the wire,
L is the length of the wire,
B is the magnitude of the magnetic field, and
θ is the angle between the wire and the magnetic field.
In this case, the values are:
I = 30 A (current in the wire)
L = 2.0 m (length of the wire)
B = 55 mT = 0.055 T (magnitude of the magnetic field)
θ = 20° (angle between the wire and the magnetic field)
Substituting the values into the formula:
F = 30 A * 2.0 m * 0.055 T * sin(20°)
Calculating sin(20°):
F = 30 A * 2.0 m * 0.055 T * 0.3420
F ≈ 1.5714 N
Therefore, the magnetic force on the 2.0-meter length of wire carrying a current of 30 A in a region with a uniform magnetic field of magnitude 55 mT and at an angle of 20° away from the wire is approximately 1.5714 N.
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A long, straight, vertical wire carries a current upward. Due east of this wire, in what direction does the magnetic field point
The magnetic field of the wire will be directed towards west. Using right thumb rule one can get the direction of field lines.
Water flows at 0.850 m/s from a hot water heater, through a 450-kPa pressure regulator. The pressure in the pipe supplying an upstairs bathtub 3.70m above the heater is 414-kPa. What's the flow speed in this pipe?
Answer:
The velocity is \(v_2= 0.45 \ m/s\)
Explanation:
From the question we are told that
The initial speed of the hot water is \(v_1 = 0.85 \ m/s\)
The pressure from the heater \(P_1 = 450 \ KPa = 450 *10^{3} \ Pa\)
The height of the hot water before flowing is \(h_1 = 0 \ m\)
The height of bathtub above the heater is \(h_2 = 3.70 \ m\)
The pressure in the pipe is \(P_2 = 414 KPa = 414 *10^{3} \ Pa\)
The density of water is \(\rho = 1000 \ kg/m^3\)
Apply Bernoulli equation
\(P_1 + \rho gh_1 +\frac{1}{2} \rho v_1^2 = \rho g h_2 + \frac{1}{2}\rho v_2 ^2\)
Substituting values
\((450 *10^{3}) + (1000 * 9.8 * 0) + (0.5 * 1000 * 0.85^2) = (1000 * *9.8*3.70) + (0.5*1000*v_2^2 )\)
=> \(v_2^2 = \frac{ (450 *10^{3}) + (1000 * 9.8 *0 ) + (0.5 * 1000 * 0.85^2) -[ (1000 * *9.8*3.70) ]}{0.5*1000}\)
=> \(v_2= \sqrt{ \frac{ (450 *10^{3}) + (1000 * 9.8 * 0) + (0.5 * 1000 * 0.85^2) -[ (1000 * *9.8*3.70) ]}{0.5*1000}}\)
=> \(v_2= 0.45 \ m/s\)
calculate the electric potential energy in a capacitor that stores 9.40 x 10 to the negative 10 C of charge at 50.0 V
The electric potential energy stored in the capacitor is 4.70 x 10^-8 Joules.
The electric potential energy stored in a capacitor is given by the formula:
U = (1/2) * C * V^2
where U is the potential energy in Joules, C is the capacitance in Farads, and V is the voltage across the capacitor in Volts.
In this case, we are given that the capacitor stores 9.40 x 10^-10 C of charge at 50.0 V. However, we are not given the capacitance value. Therefore, we cannot calculate the potential energy directly using the above formula.
To find the capacitance value, we can use the formula:
C = Q / V
where Q is the charge stored in the capacitor and V is the voltage across the capacitor.
Substituting the given values, we get:
C = 9.40 x 10^-10 / 50.0
= 1.88 x 10^-11 F
Now we can use the formula for electric potential energy to find the energy stored in the capacitor:
U = (1/2) * 1.88 x 10^-11 * (50.0)^2
= 4.70 x 10^-8 J
Therefore, the electric potential energy stored in the capacitor is 4.70 x 10^-8 Joules.
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If the 4th harmonic in the diagram has a wavelength = 10 m,
find the wavelengths of the other three harmonics
The wavelengths are given as
firsts harmonic = 40 m
second harmonic = 20 m
third harmonic = 13.33 m
What is wavelengthsWavelength refers to the distance between two consecutive points of a wave that are in phase, or the distance it takes for a wave to complete one full cycle. It is commonly denoted by the Greek letter lambda (λ).
Using the wavelength of the fourth harmonics as reference, we have that the full scale is 20 m
firsts harmonic = 40 m (double of the full scale)
second harmonic = 20 m (covers the full scale)
third harmonic = 20 m * 2/3 = 13.33 m (covers 2/3 of the full scale)
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For the simple harmonic oscillation where k = 19.6
N/m, A = 0.100 m, x = -(0.100 m) cos 8.08t, and v =
(0.808 m/s) sin 8.08t, determine (a) the total energy, (b)
the kinetic and potential energies as a function of time,
(c) the velocity when the mass is 0.050 m from
equilibrium, (d) the kinetic and potential energies at
half amplitude (x = A/2).
a. Total energy is 0.098 J
b. Potential and Kinetic Energies is 0.032 sin^2(8.08t) J
c. Velocity at x is -0.808 sin(8.08t) m/s
d. Potential and Kinetic Energies at x is 0.016 sin^2(8.08t) J
Step by step explanationWe can use the following formulas for the energy, velocity, and potential and kinetic energies of a simple harmonic oscillator:
Total Energy: E = 1/2 k A^2Velocity: v = -ωA sin(ωt)Potential Energy: U = 1/2 k x^2Kinetic Energy: K = 1/2 m v^2where ω = √(k/m) is the angular frequency.
Given that k = 19.6 N/m, A = 0.100 m, x = -(0.100 m) cos 8.08t, and v = (0.808 m/s) sin 8.08t, we can find the values of E, U, and K as follows:
(a) Total Energy:
E = 1/2 k A^2 = 1/2 * 19.6 * 0.1^2 = 0.098 J
(b) Potential and Kinetic Energies:
U = 1/2 k x^2 = 1/2 * 19.6 * (-0.1 cos(8.08t))^2 = 0.098 cos^2(8.08t) J
K = 1/2 m v^2 = 1/2 * (0.1) * (0.808 sin(8.08t))^2 = 0.032 sin^2(8.08t) J
(c) Velocity at x = 0.050 m:
When x = 0.050 m, cos(8.08t) = -0.5, so we have:
v = -ωA sin(ωt) = -ω(0.1) sin(8.08t) = -0.808 sin(8.08t) m/s
(d) Potential and Kinetic Energies at x = A/2:
When x = A/2 = 0.050 m, cos(8.08t) = -0.5, so we have:
U = 1/2 k x^2 = 1/2 * 19.6 * (0.050)^2 = 0.0245 J
K = 1/2 m v^2 = 1/2 * (0.1) * (0.808 sin(8.08t))^2 = 0.016 sin^2(8.08t) J
Note that the sum of potential and kinetic energies at any point in time is equal to the total energy, which is constant.
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1. A Ograph A Ograph B Ograph c Which graph represents what happens to the pressure in a tire as air is added to the tire, assuming the temperature is constant?
Answer:
Explanation:
It's graph A because the pressure in the tire is increasing as the amount of air going into it increases. B says the pressure drops exponentially as air goes in, and C says that the pressure stays the same as air goes in. Pressure in a tire increases proportionally to the amount of air in it.
What characterizes moral development in middle and late childhood? Give an Example?
Answer: what characterizes moral development in mid to late childhood is
People at this level of moral development base their decisions on what their parents and/or law enforcement says is right. Stage 3 is about social conformity. ... Stage 4 is all about law and order for all. For example, someone may think, 'If I steal, I will break the law and breaking the law is wrong.Feb 17, 2016
Explanation:
Which of the following is NOT an example of a transverse wave?
A vibration of a guitar string
B. light from a star
C. sound from a tuning fork
D. ripple on pond surface
The sound from a tuning fork is not a transverse wave but a longitudinal wave
What is a tuning fork?A tuning fork is a two-pronged steel device used by musicians, which vibrates when struck to give a note of specific pitch.However, tuning forks are used in air, meaning they generate longitudinal sound waves. Well, as Kyle said: the sound produced by a tuning fork (or any other source) is a longitudinal wave. But, the tuning fork itself does both, transversal and longitudinal.A common example of longitudinal waves is sound waves, which are pressure waves or vibrations that travel through air or other materials, like water. Tuning forks produce a single note, or a specific sound, when struck by making the arms move in and out very rapidly (hundreds or thousands of times a second).
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What is the best description of the function of stars?
Stars are the recycling centers of the universe.
Stars are the light bulbs of the universe.
Stars are the batteries of the universe.
Stars are the motors of the universe.
Answer:
Stars are the light bulbs of the universe.
Answer:
Stars are the recycling centers of the universe
Explanation:
I just did on edge C
Forces at Time 1
Forces at Time 2
The arrows represent forces. Choose all that are correct when comparing the bicyclist at Time
1 and Time 2.
A. The bicyclist is moving faster at Time 2.
B. The bicyclist is moving faster at Time 1.
C. The bicyclist is applying more force on the pedals at Time 2.
D. The bicyclist is applying more force on the pedals at Time 1.
The bicyclist is applying more force on the pedals at Time 2. Option C
What is the image?If we look at the image that have been shown, we can be able to see that the force that is acting have been shows by the arrows that have been used to label the movement of the cyclist in the image that is shown here.
We can see that the forward arrow at the time 2 is seen to be larger than the forward arrow that is shown for time 1. The implication of this is that the cyclist is cycling harder and applying more force at time 2 than at time 1.
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A still ball of mass 0.514kg is fastened to a cord 68.7cm long and is released when the cord is horizontal. At the bottom of its path, the ball strikes a 2.63kg steel block at rest on a horizontal frictionless surface. On collision, one-half the kinetic energy is converted to internal energy. Find the final speeds.
Answer:
1.21 m/s
Explanation:
From the law of conservation of energy,
U₁ + K₁ + E₁ = U₂ + K₂ + E₂
where U₁ = initial potential energy of system =initial potential energy of still ball = mgh where m = mass of still ball = 0.514 kg, g = acceleration due to gravity = 9.8 m/s² and h = height = length of cord = 68.7 cm = 0.687 m.
K₁ = initial kinetic energy of system = 0
E₁ = initial internal energy of system = unknown and
U₂ = final potential energy of system = 0
K₁ = final kinetic energy of system = final kinetic energy of ball + steel block = 1/2(m + M)v² where m = mass of still ball, M = mass of steel block = 2.63 kg and v = speed of still ball + steel block
E₁ = final internal energy of system = unknown
So,
U₁ + K₁ + E₁ = U₂ + K₂ + E₂
mgh + 0 + E₁ = 0 + 1/2(m + M)v² + E₂
mgh = 1/2(m + M)v² + (E₂ - E₁)
Given that (E₂ - E₁) = change in internal energy = ΔE = 1/2ΔK where ΔK = change in kinetic energy. So, ΔE = 1/2ΔK = 1/2(K₂ - K₁) = K₂/2 = 1/2(m + M)v²/2 = (m + M)v²/4
Thus, mgh = 1/2(m + M)v² + (E₂ - E₁)
mgh = 1/2(m + M)v² + (m + M)v²/4
mgh = 3(m + M)v²/4
So, making v subject of the formula, we have
v² = 4mgh/3(m + M)
taking square root of both sides, we have
v = √[4mgh/3(m + M)]
Substituting the values of the variables into the equation, we have
v = √[4 × 0.514 kg × 9.8 m/s² × 0.687 m/{3(0.514 kg + 2.63 kg)}]
v = √[13.8422/{3(3.144 kg)}]
v = √[13.8422 kgm/s²/{9.432 kg)}]
v = √(1.4676 m²/s²)
v = 1.21 m/s
The final speed of the given ball law of conservation of energy. The final speed of the given ball is 1.21 m/s.
The law of conservation of energy,
U₁ + K₁ + E₁ = U₂ + K₂ + E₂
where
U₁ = initial potential energy
K₁ = initial kinetic energy
E₁ = initial internal energy
U₂ = final potential energy
K₁ = final kinetic energy
E₁ = final internal energy
So,
mgh + 0 + E₁ = 0 + 1/2(m + M)v² + E₂
mgh = 1/2(m + M)v² + (E₂ - E₁)
Given that (E₂ - E₁) = change in internal energy,
ΔE = 1/2ΔK
Where
ΔK = change in kinetic energy.
So,
ΔE = 1/2ΔK = 1/2(K₂ - K₁)
ΔE = K₂/2
ΔE = 1/2(m + M)v²/2
ΔE = (m + M)v²/4
Thus,
mgh = 1/2(m + M)v² + (E₂ - E₁)
mgh = 1/2(m + M)v² + (m + M)v²/4
mgh = 3(m + M)v²/4
v² = 4mgh/3(m + M)
Take square root of both sides,
v = √[4mgh/3(m + M)
put the values in the formula,
v = √[4 × 0.514 kg × 9.8 m/s² × 0.687 m/3(0.514 kg + 2.63 kg)
v = 1.21 m/s
Therefore, the final speed of the given ball is 1.21 m/s.
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Need help solving this problem
a) The tension in the rope is 123.9 N.
b) The moment of inertia of the wheel is 0.09 kg m².
c) The angular speed of the wheel 3.50 s after it begins rotating, starting from rest, is 58.5 rad/s.
(a) To determine the tension in the rope, we need to analyze the forces acting on the object. There are two forces: the force of gravity pulling the object down the incline and the tension force pulling the object up the incline.
The force of gravity can be broken down into two components: one parallel to the incline and one perpendicular to the incline.
The parallel component causes the object to accelerate down the incline, while the perpendicular component is balanced by the normal force of the incline.
The tension force is responsible for the object's acceleration down the incline, so we can set up the following equation:
T - mg sin(theta) = ma
where T is the tension force, m is the mass of the object, g is the acceleration due to gravity, theta is the angle of the incline, and a is the acceleration of the object down the incline.
Putting in the given values, we get:
T - (12.5 kg)(9.81 m/s²)(sin(37°)) = (12.5 kg)(2.00 m/s²)
Solving for T, we get:
T = 123.9 N
Therefore, the tension in the rope is 123.9 N.
(b) To determine the moment of inertia of the wheel, we can use the following equation:
I = (1/2)MR²
where I is the moment of inertia, M is the mass of the wheel, and R is the radius of the wheel.
Putting in the given values, we get:
I = (1/2)(12.5 kg)(0.12 m)²
= 0.09 kg m²
Therefore, the moment of inertia of the wheel is 0.09 kg m².
(c) To determine the angular speed of the wheel after 3.50 s, we can use the following equation:
ω = ω₀ + αt
where ω is the final angular speed, ω₀ is the initial angular speed (which is zero in this case), α is the angular acceleration, and t is the time.
We can find the angular acceleration using the following equation:
α = a/R
where a is the acceleration of the object down the incline (which we already know) and R is the radius of the wheel.
Putting in the given values, we get:
α = 2.00 m/s² / 0.12 m
= 16.7 rad/s²
Putting in the values for α and t, we get:
ω = 0 + (16.7 rad/s²)(3.50 s)
= 58.5 rad/s
Therefore, the angular speed of the wheel 3.50 s after it begins rotating, starting from rest, is 58.5 rad/s.
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please help thank you
Answer:
\(\theta \approx 59.036^{\circ}\), \(T_{2} \approx 23.324\,N\)
Explanation:
First we build the Free Body Diagram (please see first image for further details) associated with the mass, we notice that system consist of a three forces that form a right triangle (please see second image for further details): (i) The weight of the mass, (ii) two tensions.
The requested tension and angle can be found by the following trigonometrical and geometrical expressions:
\(\theta = \tan^{-1} \frac{W}{T_{2}}\) (1)
\(T_{1} = \sqrt{W^{2}+T_{2}^{2}}\) (2)
Where:
\(W\) - Weight of the mass, measured in newtons.
\(T_{1}\), \(T_{2}\) - Tensions from the mass, measured in newtons.
If we know that \(W = 20\,N\) and \(T_{2} = 12\,N\), then the requested values are, respectively:
\(\theta = \tan^{-1} \frac{20\,N}{12\,N}\)
\(\theta \approx 59.036^{\circ}\)
\(T_{2} = \sqrt{(20\,N)^{2}+(12\,N)^{2}}\)
\(T_{2} \approx 23.324\,N\)
What is the zeroth law of black hole thermodynamics?
Answer:
The horizon has constant surface gravity for a stationary black hole.
Explanation:
Answer:
all parts of the event horizon of a black hole at equilibrium have the same surface gravity g
Explanation:
Block B, which has a mass of 4t kg, is moving at a constant velocity across a flat surface. As shown in the diagram, it is being pulled forward by a force of 100 N. What is the magnitude of the force ?
Block B, which has a mass of 4t kg, is moving at a constant velocity across a flat surface, the magnitude of the force is F=100 N. This is further explained below.
What is the magnitude of the force?Generally, Force is simply defined as a function of mass and time.
In conclusion, A requirement of balance is that the left side exerts the same force as the right, therefore if 100 N is applied to the right, then 100 N must be exerted on the left.
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two point charges of 5*10^-19 C and 20*10^-19C are separated by a distance of 2m. at which point on the line joining them will have the electric field zero?
Answer:
On that line segment between the two charges, at approximately \(0.7\; \rm m\) away from the smaller charge (the one with a magnitude of \(5 \times 10^{-19}\; \rm C\),) and approximately \(1.3\; \rm m\) from the larger charge (the one with a magnitude of \(20 \times 10^{-19}\; \rm C\).)
Explanation:
Each of the two point charges generate an electric field. These two fields overlap at all points in the space around the two point charges. At each point in that region, the actual electric field will be the sum of the field vectors of these two electric fields.
Let \(k\) denote the Coulomb constant, and let \(q\) denote the size of a point charge. At a distance of \(r\) away from the charge, the electric field due to this point charge will be:
\(\displaystyle E = \frac{k\, q}{r^2}\).
At the point (or points) where the electric field is zero, the size of the net electrostatic force on any test charge should also be zero.
Consider a positive test charge placed on the line joining the two point charges in this question. Both of the two point charges here are positive. They will both repel the positive test charge regardless of the position of this test charge.
When the test charge is on the same side of both point charges, both point charges will push the test charge in the same direction. As a result, the two electric forces (due to the two point charges) will not balance each other, and the net electric force on the test charge will be non-zero.
On the other hand, when the test charge is between the two point charges, the electric forces due to the two point charges will counteract each other. This force should be zero at some point in that region.
Keep in mind that the electric field at a point is zero only if the electric force on any test charge at that position is zero. Therefore, among the three sections, the line segment between the two point charges is the only place where the electric field could be zero.
Let \(q_1 = 5\times 10^{-19}\; \rm C\) and \(q_2 = 20 \times 10^{-19}\; \rm C\). Assume that the electric field is zero at \(r\) meters to the right of the \(5\times 10^{-19}\; \rm C\) point charge. That would be \((2 - r)\) meters to the left of the \(20 \times 10^{-19}\; \rm C\) point charge. (Since this point should be between the two point charges, \(0 < r < 2\).)
The electric field due to \(q_1 = 5\times 10^{-19}\; \rm C\) would have a magnitude of:
\(\displaystyle | E_1 | = \frac{k\cdot q_1}{r^2}\).
The electric field due to \(q_2 = 20 \times 10^{-19}\; \rm C\) would have a magnitude of:
\(\displaystyle | E_2 | = \frac{k\cdot q_2}{(2 - r)^2}\).
Note that at all point in this section, the two electric fields \(E_1\) and \(E_2\) will be acting in opposite directions. At the point where the two electric fields balance each other precisely, \(| E_1 | = | E_2 |\). That's where the actual electric field is zero.
\(| E_1 | = | E_2 |\) means that \(\displaystyle \frac{k\cdot q_1}{r^2} = \frac{k\cdot q_2}{(2 - r)^2}\).
Simplify this expression and solve for \(r\):
\(\displaystyle q_1\, (2 - r)^2 - q_2 \, r^2 = 0\).
\(\displaystyle 5\times (2 - r)^2 - 20\, r^2 = 0\).
Either \(r = -2\) or \(\displaystyle r = \frac{2}{3}\approx 0.67\) will satisfy this equation. However, since this point (the point where the actual electric field is zero) should be between the two point charges, \(0 < r < 2\). Therefore, \((-2)\) isn't a valid value for \(r\) in this context.
As a result, the electric field is zero at the point approximately \(0.67\; \rm m\) away the \(5\times 10^{-19}\; \rm C\) charge, and approximately \(2 - 0.67 \approx 1.3\; \rm m\) away from the \(20 \times 10^{-19}\; \rm C\) charge.
A model rocket is fired straight up from the top of a 45-m-tall building. The rocket has only enough fuel to burn for 4.0 s. But while the rocket engine is burning fuel, it produces an upward acceleration of 55 m/s2. After the fuel supply is exhausted, the rocket is in free fall and just misses the edge of the building as it falls back to the ground. Ignoring air resistance, calculate (a) the height above the ground and the velocity of the rocket when its fuel runs out; (b) the maximum height of the rocket; (c) the time the rocket is in the air; and (d) the rocket's velocity the moment before it hits the ground.
Answer:
a)y = 485 m , v = 220 m / s , b) y = 2954.39 m , c) t_total = 51 s ,
d) v = 240.59 m / s
Explanation:
a) We can use vertical launch ratios for this exercise
the speed of the rocket the run out the fuel is
v = v₀ + a t
the rocket departs with initial velocity v₀ = 0
v = a t
v = 55 4
v = 220 m / s
the height at this point is
y = y₀ + v₀t + ½ a t²
y = y₀ + 1/2 a t²
y = 45 + ½ 55 4²
y = 485 m
b) the maximum height of the rocket is when its speed is zero
for this part we will use as the initial speed the speed at the end of the fuel (v₀´ = 220 m / s) and the height of y₀´ = 485 m
v² = v₀´² + 2 g (y-y₀´ )
0 = v₀´² + 2 g (y-y₀´ )
y = y₀´ + v₀´² / 2g
y = 485 + 220 2/2 9.8
y = 2954.39 m
c) the time that the rocket is in the air is the acceleration time t₁ = 4 s, plus the rise time (t₂) plus the time to reach the ground (t₃)
let's calculate the rise time
v = v₀´- g t
v = 0
t₂ = v₀´ / g
t₂ = 220 / 9.8
t₂ = 22.45 s
Now let's calculate the time it takes to get from this point (y₀´´ = 2954.39 m) to the floor
y = y₀´´ + v₀´´ t - ½ g t²
0 = y₀´´ - ½ g t²
t = √ (2 y₀´´ / g)
t = √ (2 2954.39 / 9.8)
t = 24.55 s
the total flight time is
t_total = t₁ + t₂ + t₃
t_total = 4 + 22.45 + 24.55
t_total = 51 s
d) the veloicda right now
v = vo + g t
v = 9.8 24.55
v = 240.59 m / s
Calculate the velocity of the man if he moves 6 m to the right and 4 m [i.e. the man ends up at 2 m to the right in the positive direction] to the left within 4.4 seconds as shown in the figure below?
The velocity of the man given the data from the question is 0.45 m/s
What is velocity?Velocity is simply defined as the rate of change of displacement with time. Mathematically, it can be expressed as:
Velocity = Change of displacement / time
Data obtained from the questionFrom the question given above, the following data were obtained:
Displacment 1 = 6 m right Displacement 2 = 4 m leftChange of displacement = 6 - 4 = 2 m rightTime = 4.4 secondsVelocity = ?How to determine the velocity of the manThe velocity of the man can be obtained as follow:
Velocity = Change of displacement / time
Velocity = 2 / 4.4
Velocity = 0.45 m/s
Thus, the velocity of the man is 0.45 m/s
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