Starting from rest, a disk rotates with constant angular acceleration. If it takes 10 revolutions to reach an angular velocity, then how many additional revolutions are required to reach an angular velocity 2w?
Answers
The additional number of revolutions required to reach an angular velocity of 2ω is 2√10 times the initial number of revolutions.
To solve this problem, let's use the kinematic equation for rotational motion:
ω^2 = ω_0^2 + 2αθ
Where:
ω = Final angular velocity
ω_0 = Initial angular velocity (zero in this case, as the disk starts from rest)
α = Angular acceleration
θ = Angle of rotation (in radians)
Let's denote the number of revolutions as n.
Given that it takes 10 revolutions to reach the angular velocity ω, we can convert the number of revolutions to radians by multiplying by 2π:
θ = 10 × 2π
Substituting these values into the kinematic equation:
ω^2 = 0 + 2α(10 × 2π)
ω^2 = 40απ
Now, we want to find the number of additional revolutions, denoted as m, required to reach an angular velocity of 2ω. We can write this as:
2ω = m × 2π
Squaring both sides of the equation:
(2ω)^2 = (m × 2π)^2
4ω^2 = 4m^2π^2
ω^2 = m^2π^2
Since we already know that ω^2 = 40απ from the first equation, we can equate the two equations:
40απ = m^2π^2
Simplifying:
40α = m^2π
Now, we need to find the ratio of the additional revolutions m to the initial revolutions n:
m/n = √(40α/α)
m/n = √40
m/n = 2√10
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Related Questions
A car was moving 110. km/hour.
b) If it stopped in 35. s, what was its average acceleration (m/ s^2) as it slowed down?
Answers
Answer:
Yes.
Explanation:
What is the efficiency of a light bulb if it produces 30j of light energy, with an input of 120j of electrical energy?
Answers
The efficiency of this light bulb is 25% .
How do you calculate the efficiency of a light bulb?Utilizing the following formula, efficiency may be represented as a ratio: output input. The total quantity of beneficial work accomplished, excluding waste and spoilage, is known as output or work output. Efficiency may also be expressed as a percentage by dividing the ratio by 100.To represent the result as a percentage, divide the output by the input and then multiply by 100. Although both work and energy are measured in terms of the Joule, the calculator above has a space for a different unit. Make sure the energy and labour units are equivalent.Efficiency is essentially a measurement of the amount of labour or energy that may be saved throughout a process. In other words, it's similar to comparing the energy intake and output in any particular system.Given data :
output = 30j
Input = 120j
Efficiency = output / input x 100
= 30 / 120 x 100
= 25%
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2 What can you Infer about this source of electricity?
A It is a source of alternating current
B It Is a source of direct current
С It is a source of static electricity
D It is a source of electromagnetic radiatlon
Answers
Answer:i think it's d
Explanation:
how much does it cost to heat a 1200 sq ft house with natural gas
Answers
To heat a 1200 sq ft house with natural gas, we spend a total of $14.40 per day.
How much it costs to heat a 1200 sq ft house with natural gas relies on a number of things, such as where the house is, how well it heats, and how much natural gas costs in that area.
Sources. says that the cost per square foot for natural gas with 40 BTU is $0.00049836 per square foot per hour. If our house is 1200 square feet, we multiply this cost by 1200 and get $0.60 per hour to heat it. That means that to heat a 1200 sq ft house with natural gas, we spend a total of $14.40 per day.
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A planetesimal about to collide with a protoplanet has kinetic energy. during the collision, this energy is converted to
Answers
During the collision of a planetesimal with a protoplanet, the kinetic energy of the planetesimal can be converted into different forms of energy.
Some of the energy may be converted into thermal energy due to the friction caused by the collision, resulting in an increase in temperature of the colliding bodies.
Additionally, some of the kinetic energy may be converted into potential energy, as the colliding bodies may move away from each other due to the collision.
The potential energy can later be converted back into kinetic energy if the bodies start moving towards each other again.
Finally, some of the energy can be radiated away as electromagnetic radiation, such as light or heat, depending on the specifics of the collision.
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A cannonball is launched horizontally from the top of a 166 m
cliff with an original speed of 35.9 m/s.
Determine the horizontal displacement (in m) of the cannonball.
Answers
The horizontal displacement of the cannonball is 65.75 meter.
What is speed?Speed is characterized as the rate at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.
original speed: u= 35.9 m/s.
acceleration due to gravity: g = 9.8 m/s².
Initial height of the cannonball = 166 m.
Hence, the horizontal displacement of the cannonball = u²/2g
= 35.9²/(2×9.8) meter
= 65.75 meter.
so, the displacement of the cannonball is 65.75 meter.
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A 2.90-kg block is released from rest and allowed to slide down a frictionless surface and into a spring. The far end of the spring is attached to a wall, as shown. The initial height of the block is 0.500 m above the lowest part of the slide and the spring constant is 443 N/m. A. What is the maximum compression of the spring?B. The spring sends the block back to the left. How high does the block rise?
Answers
Part (a)
The potential energy of the block due to its height can be given as,
\(U=\text{mgh}\)The potential energy due to presence of spring can be expressed as,
\(U=\frac{1}{2}kx^2\)Equating both the values,
\(\begin{gathered} \text{mgh}=\frac{1}{2}kx^2 \\ x^2=\frac{2mgh}{k} \\ x=\sqrt[]{\frac{2mgh}{k}} \end{gathered}\)Substitute the known values,
\(\begin{gathered} x=\sqrt[]{\frac{2(2.90kg)(9.8m/s^2)(0.500\text{ m)}}{(443\text{ N/m)}}(\frac{1\text{ N}}{1kgm/s^2})} \\ \approx0.253\text{ m} \end{gathered}\)Thus, the maximum compression of the spring is 0.253 m.
Part (b)
Since the slide is frictionless, therefore no energy loss happened during the sliding of block. Therefore, the block will rise up to the same initial height which is 0.500 m.
Read solar basics and use the information to answer the question. what factors affect the amount of solar energy that reaches the earth’s surface?
Answers
Explanation: The amount of solar energy available varies by location on earth, the time of the day at that location, the season and weather conditions. Rain, fog, and clouds will lower the amount of solar power available to gather and there are fewer hours of sun available in different seasons (winter for North America). To gather solar power, you also need a large area. This can be lessened by conditions such as snow, so that even on a sunny day, covered panels will collect less energy.
Answer:
.
Explanation:
The quantity of solar energy accessible varies by location on the planet, time of day, season, and weather conditions. Rain, fog, and clouds reduce the quantity of solar power available for collection, and various seasons have less hours of sunlight accessible (winter for North America). A big region is also required to collect solar electricity. Conditions such as snow can reduce this, such that even on a sunny day, covered panels will absorb less energy.
An object that is launched from the top of the tower is dense enough that air resistance can be ignored. The object's initial velocity has components (vx = 30 m/s, vy = 20 m/s). What are the components of the object's velocity 3 seconds after launch?
Answers
Answer:
The components of the object's velocity 3 seconds after launch are
\(v_x = 30\) m/s and \(v_y=-9.43\) m/s.
Explanation:
The given components of initial velocity are
\(v_x= 30\) m/s,
\(v_y= 20\) m/s.
Assuming the y-axis is along the direction of gravitational force, so, the velocity along the x-axis will remain unchanged.
So, the x-componebt of the velocity after 3 seconds, \(v_x = 30\) m/s.
Using the equation of motion along the y-direction, the final velocity, v, of a mass after time, t, having initial velocity, u is
v=u+at
In this case, \(u=y_y= 20 m/s, a=-9.81 m/s^2\) ( as upward direction is taken as positive)
So, at time, t=3s, the final velocity in y-direction is
\(v= 20+(-9.81)\times 3\)
\(\Rightarrow v=20-29.43\)
\(\Rightarrow v= -9.43 m/s\)
So, the y-component of the final velocity is 9.43 m/s in the downward direction.
Hence, the components of the object's velocity 3 seconds after launch are
\(v_x = 30 m/s\) and \(v_y=-9.43 m/s\).
The final vertical velocity of the object after 3 seconds is 49.4 m/s.
The final horizontal velocity of the object is 30 m/s.
The given parameters;
initial horizontal velocity, Vx = 30 m/sinitial vertical velocity, Vy = 20 m/stime of motion, t = 3 sThe final vertical velocity of the object after 3 seconds is calculated as follows;
\(v_f_y = v_0_y + gt\\\\v_f_y = 20 + 3(9.8)\\\\v_f_y = 49.4 \ m/s\)
The final horizontal velocity of the object is the same as the initial horizontal velocity because horizontal motion is not affected by gravity.
\(v_f_x = v_0_x = 30 \ m/s\)
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The property of matter that describes what it is made of
Answers
Answer:
Miixture
Explanation:
The answer is mixture
what does work do to energy
Answers
Answer:
Work is closely related to energy. The work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body.
Explanation:
An object has a kinetic energy of 180 J and a mass of 45 kg, how fast is the object
moving?
Your answer
Answers
An object has a kinetic energy of 180 J and a mass of 45 kg, The object is moving fast with 2.83 m/sec
What is kinetic energy?Kinetic energy is the energy of motion, which can be observed as an item, particle, or collection of particles moving. Kinetic energy is used by any moving object: a person walking, a baseball being thrown, a crumb falling off a table, and a charged particle in an electric field are all instances of kinetic energy at work.
Given that,
Kinetic energy (K.E) = 180 J
Mass (m) = 45 kg
As we know, K.E = \(\frac{1}{2}mv^{2}\)
Now we have to calculate the speed or velocity (v)
v = \(\sqrt{(2*K.E.)/m}\)
v = \(\sqrt{(2*180)/45}\)
v = 2.83 m/sec
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Water has a heat of fusion of 6.01 kJ/mol. An iceberg in the Atlantic Ocean near Newfoundland contains 1.27 x 107 mol of water. How much thermal energy does it absorb as it melts? Answer using appropriate significant digits. Please record your work in your notes for future reference.
Answers
Answer:
7.63×10⁷ kJ
Explanation:
From the question given above, the following data were obtained:
Heat of fusion (Hբ) = 6.01 kJ/mol
Number of mole of water (n) = 1.27×10⁷ moles
Heat (Q) absorbed =?
The thermal energy absorbed can be obtained as follow:
Q = n•Hբ
Q = 1.27×10⁷ × 6.01
Q = 7.63×10⁷ kJ
Thus, 7.63×10⁷ kJ of thermal energy is absorbed.
2. bacteria move back and forth using their flagella. speeds up to 50 µm/s (50 10−6 m/s) have been observed. the total distance traveled by a bacterium is large for its size, whereas its displacement is small. why? (watch this video of bacteria moving!)
Answers
Bacteria exhibit random movement with frequent changes in direction, resulting in a small net displacement despite covering a large total distance due to their flagella-driven motion.
Bacteria move back and forth using their flagella, which allows them to achieve speeds up to 50 µm/s. While the total distance traveled by a bacterium may be large compared to its size, its displacement is small. This is because bacteria exhibit random movement known as "random walk," where they change their direction frequently. As a result, their net displacement over time is relatively small compared to the total distance covered.
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Define measurement and write its importance.
Answers
Answer:
Measurement is the way humans define certain amounts of matter, and is expressed in various types of units respective to the type of matter or object being defined.
Explanation:
Measurement is extremely important because it helps one another understand how much of something is needed to accomplish something. If no method existed to define the specific amount needed, we would simply mess delicate operations up and machines, even simple recipes, would fail.
An unbalanced force of 2 newtons applied to a given mass produces an acceleration. If an unbalanced force of 1 newton is applied to the same mass, the acceleration produced will be.
Answers
If an unbalanced force of 1 newton is applied to the same mass, the acceleration produced will be twice as much.
What does acceleration mean?The rate at which velocity varies with respect to time is referred to as acceleration. Since acceleration has both a magnitude and a direction, it is a vector quantity. Additionally, it is the first derivative of velocity with respect to time or the second derivative of position with respect to time.
What exactly does force mean?If there is no opposition, it may be described as an interaction that modifies an object's motion. However, the straightforward definition of force is the push or pull that an item experiences. Force has both a magnitude and a direction since it is a vector quantity.
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A 4. 0 m long steel beam with a cross-sectional area of 1. 0 x102m2 and a Young's modulus
of 2. 0 x10' N/m 2 is wedged horizontally between two vertical walls. In order to wedge the
beam, it is compressed by 0. 020 mm. If the coffecient of static friction between the beam
and the walls is 0. 70, the maximum mass (including its own) it can bear without slipping
is:
Answers
The required maximum mass that the beam can bear without slipping is 14.163 kg.
The maximum mass that a 4.0 m long steel beam with a cross-sectional area of 1.0 × 10²m² and a Young's modulus of 2.0 × 10' N/m² can bear without slipping when wedged horizontally between two vertical walls and compressed by 0.020 mm, assuming a coefficient of static friction of 0.70, is calculated as follows,
Force of friction = coefficient of static friction × normal force = Area of beam × Young's modulus × compression
Therefore, the force of friction = 0.70 × (1.0 × 10² m²) × (2.0 x10' N/m²) × 0.020 mm
Maximum mass = (force of friction) / (acceleration due to gravity)
Therefore, the maximum mass that the beam can bear without slipping is (0.70 × (1.0 × 10² m²) × (2.0 × 10' N/m²) × 0.020 mm) / (9.81 m/s²) = 14.163 kg.
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Which statements describe a situation in which work is being done? Select three options.
Answers
Answer:
here's the answers!
Explanation:
A mover carries a box up a flight of stairs.
A mover carries a box across a room.
A weightlifter lifts a barbell off the ground.
hope it helps u!
Answer:
A, D, E
Explanation:
Did it
A gyroscope slows from an initial rate of 29.6 rad/s at an angular acceleration of 0.54 rad/s2. 50% Part (a) How long does it take to come to rest in seconds? t = ?
50% Part (b) How many revolutions does it make before stopping? n= ?
Answers
The gyroscope slows from an initial rate of 29.6 rad/s at an angular acceleration of 0.54 rad/s2.
Part (a) How long does it take to come to rest in seconds? t = ?
The angular deceleration is given by the negative value of the angular acceleration; thus:
α = -0.54 rad/s2
The initial velocity is given by the value,
ω1 = 29.6 rad/s.
The final velocity, ω2 = 0 rad/s.
The formula for angular acceleration is:
ω2 = ω1 + αt,
where:
ω1 = 29.6 rad/s
ω2 = 0 rad/s
α = -0.54 rad/s
2t = ?
Substitute the values in the formula above and solve for t.
0 = 29.6 - 0.54tt = 29.6/0.54t = 54.8 seconds
Therefore, it takes 54.8 seconds to come to rest in seconds.
Part (b)The number of revolutions that the gyroscope makes before stopping is given by:
n = (ω1/2π)t,
where:
ω1 = 29.6 rad/s
t = 54.8 s
n = ?
Substitute the values in the formula above and solve for n:
n = (29.6/2π)(54.8) revolutions
n ≈ 277.4
Therefore, the number of revolutions that the gyroscope makes before stopping is approximately 277.4 revolutions.
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an apple weighs 1.02 n . when you hang it from the end of a long spring of force constant 1.50 n/m and negligible mass, it bounces up and down in shm. if you stop the bouncing and let the apple swing from side to side through a small angle, the frequency of this simple pendulum is half the bounce frequency. (because the angle is small, the back and forth swings do not cause any appreciable change in the length of the spring.)
Answers
Answer: 2.67 m
Explanation:
k = Spring constant = 1.5 N/m
g = Acceleration due to gravity = 9.81 m/s²
l = Unstretched length
Frequency of SHM motion is given by
Frequency of pendulum is given by
Given in the question
The frequency of a simple pendulum made by hanging an apple from a long spring is half the bounce frequency.
Let the mass of the apple be m = 1.02 N, and the force constant of the spring be k = 1.50 N/m. When the apple is hanging from the spring, the restoring force on the apple is given by F = -kx, where x is the displacement from the equilibrium position.
According to Hooke's law, this force is directly proportional to the displacement and acts in the opposite direction. Therefore, the apple undergoes simple harmonic motion (SHM) with a period T = 2π√(m/k).
Now, when the apple is displaced and released from a small angle, it behaves as a simple pendulum. The period of a simple pendulum is given by T' = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity.
Since the angle is small, the length of the spring does not change significantly, so we can assume that the length of the simple pendulum is the same as the unstretched length of the spring. Therefore, T' = 2π√(l/g) ≈ 2π√(k/mg), where g = 9.81 m/s² is the acceleration due to gravity.
The frequency of the bounce motion is given by f = 1/T, and the frequency of the pendulum motion is given by f' = 1/T'. From the above equations, we get:
f' = 1/T' = 1/(2π) √(mg/k) = 1/(2π) √(1.02*9.81/1.50) Hz
f = 1/T = 1/(2π) √(k/m) = 1/(2π) √(1.50/1.02) Hz
Therefore, the frequency of the simple pendulum is half the bounce frequency, as given in the problem statement.
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Which parts differentiate ray diagrams of reflected and refracted light?.
Answers
μ1 and μ2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
The different parts that differentiate ray diagrams of reflected and refracted light include the following:
Reflected light: A ray of light incident on a reflecting surface forms an angle of incidence
(i) with the normal at the point of incidence.
A ray of light reflected from a surface forms an angle of reflection (r) with the normal to the surface at the point of incidence. Both the incident and reflected rays are in the same plane and on the same side of the normal to the surface.
Refraction: When light passes through a medium and encounters a boundary with another medium of different density, it refracts (bends). The incident ray, the normal, and the refracted ray all lie in the same plane.
The angle of incidence and the angle of refraction are related as per the Snell's law:
μ1sinθ1
= μ2sinθ2
Where μ1 and μ2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
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a propeller is modeled as five identical uniform rods extending radially from its axis. the length and mass of each rod are 0.711 m and 2.99 kg, respectively. when the propellor rotates at 569 rpm (revolutions per minute), what is its rotational kinetic energy?
Answers
The rotational kinetic energy of five identical uniform rods is 9436.21 joule.
We need to know about rotational kinetic energy to solve this problem. Rotational kinetic energy can be defined as the energy of a rotating object. The magnitude of rotational energy is
KE = 1/2 . I . ώ²
where KE is rotational kinetic energy, I is inertia and ώ is angular velocity.
From the question above, the given parameters are
L = 0.711 m
m = 2.99 kg
N = 5
ώ = 569 rpm = 59.59 rad/s
Find the total inertia of five identical rods
I = N . 1/2 . m . L²
I = 5 . 1/2 . 2.99 . 0.711
I = 5.31 kg.m²
Calculate the rotational kinetic energy
KE = 1/2 . I . ώ²
KE = 1/2 . 5.31 . 59.59²
KE = 9436.21 joule
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suppose you are standing on the center of a merry go round that is at rest. you are holding a spinning bicycle wheel above your head so that its angular velocity vector is pointing upward. the wheel is rotating counterclockwise when viewed from above. suppose you now grab the edge of the wheel with your hand, stopping it from spinning. what happens to the merry go round?
Answers
B) it starts to spin in the other direction (as observed from above). As far as we are aware, there is no external torque acting on the wheel and merry-go-round mechanism.
What factors influence torque?A rigid body's torque is determined by three factors: the force applied, the lever arm vector connecting the torque measurement point to the force application point, and the angle between the force and lever arm vectors.
What factors affect the torque a force produces on an object?When forces are applied to an object with the tendency to generate rotation, we say the force is producing a torque.
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4 In which one of the following cases will the distance covered and
the magnitude of the displacement are not the same? Justify.
(1) A passenger in a train travels from Delhi to Kolkata.
(ii) A raindrop falling in still air.
(iii) An athlete completes one lap in a race.
Answers
Answer:
the answer of this question is iii .
if the answer is wrong so sorry
In first one the path will have turns so the distance might not be same as displacement
In second one displacement is 0 as it is a lap which is like a circle
In third one the drop of water will use the shortest path so distance will be equal to displacement
A U-tube uniform cross-sectional area and open to the atmosphere is partially filled with Mercury. Water then is then poured into both arms. If the equilibrium configuration of the tube is as shown in the figure with h2=1.04cm determine the value of h. There's no need to consider the weight of the of the extra air on the right-hand side
Answers
Motion parallax is a cue to depth which:_________
a. depends exclusively on object motion
b. is generally less informative than stereopsis
c. assumes disparity is zero
d. is available to monocular observers
Answers
Motion parallax is a cue to depth which depends exclusively on object motion. So, the correct option is (a).
When an observer moves laterally, it causes the relative motion of objects at various distances, which gives birth to the monocular depth cue known as motion parallax. Several eye movement systems are active as the observer translates, maintaining attention on a specific object in the scene.
The term "motion parallax" describes how objects that are moving across the frame at a constant speed may appear to move more when they are closer to the observer (or camera) than when they are farther away.
Therefore, motion parallax is a cue to depth which depends exclusively on object motion. So, the correct option is (a).
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A battery of emf 5V and internal resistance 2ohm is joined to a resistor of 8ohm.Calculate the terminal potential difference.
Answers
Answer:
4V
Explanation:
First, we calculate the total resistance to the given battery cell of emf 5V. The total resistance is the sum of all the resistance in the cell i.e.
Total resistance = 2Ω + 8Ω = 10Ω
Using ohms law equation to calculate the current passing through the battery cell:
V = IR
Where; V = voltage, I = current, R = resistance
5V = I × 10Ω
I = 5/10
I = 0.5A
Terminal voltage is calculated by the us of the following equation:
V=emf−IR
Where; R is internal resistance
V = 5 - (0.5 × 2)
V = 5 - 1
V = 4V
Therefore, the potential difference across the terminals of the battery cell is 4V
The minute hand on a watch is 3. 00 cm in length. Assume the origin of the xy -plane is at the center of the clock face, the x -axis points in the same direction as the minute hand at 8:15 a. M. , and the y -axis points in the same direction as the minute hand at 8:00 a. M
Answers
To determine the position of the minute hand at 8:15 a.m., we can use the following approach:
Convert the time to radians: At 8:15 a.m., the minute hand is 75% of the way from the 8:00 a.m. mark to the 9:00 a.m. mark. Since the minute hand travels 360 degrees in 60 minutes, it travels 6 degrees per minute. Therefore, at 8:15 a.m., it has traveled 90 degrees from the 8:00 a.m. mark. This is equivalent to (90/360) x 2π radians = π/2 radians. Use trigonometry to determine the position: Since the minute hand is 3.00 cm long and pointing in the direction of the positive x-axis at 8:15 a.m., its position can be described by the coordinates (3.00 cos(π/2), 3.00 sin(π/2)) = (0, 3.00). Therefore, the minute hand is pointing straight up at 8:15 a.m. Note that the x-axis points in the same direction as the minute hand at 8:15 a.m., while the y-axis points in the same direction as the minute hand at 8:00 a.m. This means that the x-axis is perpendicular to the minute hand at 8:00 a.m., and the y-axis is perpendicular to the minute hand at 8:15 a.m.
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A water wave has a frequency 0.50 hz, an amplitude of 0.35 m and a speed of 1.34 m/s. what is the value of the wavelength if the amplitude doubles?
Answers
By applying the wave equation, the wavelength is 2.68 meters.
We need to know about wave equations to solve this problem. The displacement of the wave on the y-axis can be explained by the wave equation
y = A cos (kx - ωt)
where y is y-axis displacement, A is amplitude, k is wave number, x is x-axis displacement, ω is angular speed and t is time.
the wavenumber and angular speed of the wave equation can be determined respectively by
k = 2π / λ
ω = 2πf
where k is the wavenumber, λ is wavelength and f is frequency.
From the question above, we know that:
f = 0.5 Hz
A = 0.35 m
v = 1.34 m/s
When the amplitude is doubled, it doesn't affect the wavelength. Hence
v = λ . f
1.34 = λ . 0.5
λ = 2.68 m
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Why is it important to try to use as many renewable resources as possible?
Answers
Answer:
It is important to use renewal resources because we use so many non- renewable resources that we may lose the ability to make a lot of things like gasoline or power for our cities.