Approximately 235 oscillations will have been completed when the amplitude of the oscillator decreases to 30% of its initial value.
To solve this problem, let's first understand the concept. The amplitude of an oscillator in simple harmonic motion decreases over time when air is admitted due to damping. We'll use the concept of exponential decay to model the decrease in amplitude.
The formula for exponential decay is:
[tex]\[ A(t) = A_0 \times e^{-\frac{t}{\tau}} \][/tex]
Where:
- A(t) is the amplitude at time t.
- [tex]\( A_0 \)[/tex] is the initial amplitude.
- [tex]\( \tau \)[/tex] is the time constant, which depends on the damping coefficient.
- e is the base of the natural logarithm.
Given that the amplitude decreases to 60% of its initial value in 50 seconds, we can use this information to find the time constant [tex]\( \tau \).[/tex]
[tex]\[ 0.6A_0 = A_0 \times e^{-\frac{50}{\tau}} \][/tex]
Solving for [tex]\( \tau \):[/tex]
[tex]\[ e^{-\frac{50}{\tau}} = 0.6 \][/tex]
[tex]\[ -\frac{50}{\tau} = \ln(0.6) \][/tex]
[tex]\[ \tau = -\frac{50}{\ln(0.6)} \][/tex]
Now, we can use the value of [tex]\( \tau \)[/tex] to find the time it takes for the amplitude to decrease to 30% of its initial value.
[tex]\[ 0.3A_0 = A_0 \times e^{-\frac{t}{\tau}} \][/tex]
Solving for t:
[tex]\[ e^{-\frac{t}{\tau}} = 0.3 \][/tex]
[tex]\[ -\frac{t}{\tau} = \ln(0.3) \][/tex]
[tex]\[ t = -\tau \times \ln(0.3) \][/tex]
Now, we need to find the number of oscillations completed during this time. We know that the frequency of oscillation is 2.0 Hz, which means the oscillator completes 2 oscillations every second.
Number of oscillations = frequency × time
Number of oscillations = 2.0 × t
Let's compute these values.
First, let's calculate the value of [tex]\( \tau \):[/tex]
[tex]\[ \tau = -\frac{50}{\ln(0.6)} \][/tex]
[tex]\[ \tau \approx -\frac{50}{-0.5108} \][/tex]
[tex]\[ \tau \approx 97.85 \, \text{s} \][/tex]
Now, let's find the time it takes for the amplitude to decrease to 30% of its initial value:
[tex]\[ t = -\tau \times \ln(0.3) \][/tex]
[tex]\[ t \approx -97.85 \times \ln(0.3) \][/tex]
[tex]\[ t \approx 97.85 \times 1.2039 \][/tex]
[tex]\[ t \approx 117.65 \, \text{s} \][/tex]
Now, let's find the number of oscillations completed during this time:
Number of oscillations [tex]= 2.0 \times t[/tex]
Number of oscillations [tex]\approx 2.0 \times 117.65[/tex]
Number of oscillations [tex]\approx 235.3[/tex]
Since the number of oscillations must be a whole number, we can assume it to be 235 oscillations.
Therefore, when the amplitude is 30% of its initial value, approximately 235 oscillations will have been completed.
Electromagnetic radiation with a wavelength of 445 nm appears as blue light to the human eye. the energy of one photon of this light is ________ j.
The energy of one photon of light with a wavelength of 445 nm can be calculated using Planck's equation, E = hv. This requires converting the wavelength to frequency using c = wavelength times frequency, and then substituting the frequency back into Planck's equation. The energy of one photon of 445 nm blue light is approximately 4.47 x 10^-19 Joules.
Explanation:To determine the energy of one photon of light with a wavelength of 445 nm (visible light electromagnetic radiation), we can use Planck's equation, which states E = hv (energy equals Planck's constant times frequency). However, we must first convert wavelength to frequency via the speed of light equation (c = wavelength times frequency). After getting the frequency, we can substitute it back into the Planck's equation.
By doing these calculations, we find:
First, we convert the wavelength from nm to m: 445 nm = 445 x 10^-9 m.Next, we determine the frequency (v) using c = wavelength(v). Since c = 3.00 x 10^8 m/s:Therefore, one photon of 445 nm blue light has an energy approximately equal to 4.47 x 10^-19 Joules.
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Bob is pushing a lawn mower up a hill with the mower tilting slightly to the right. suppose that we wish to use vectors to determine the total force acting on the mower. what forces should be considered?
Answer:
Applied force, weight, normal force and frictional force
Explanation:
Bob is pushing a lawn mower up a hill with the mower tilting slightly to the right. We have to write the forces acting on the mower.
The following are the forces that are acting on the mower.
1. Applied force - The force with which Bob is pushing a lawn.
2. Weight - Its weight is equal to, W = m g
3. Normal force - that balances its weight
4. Frictional force - It always opposes the motion of the mower.
Hence, this is the required solution.
The lawn mower is acted upon by four different forces.
Vector quantities are those quantities that posses both magnitude and direction. Force is a vector quantity. Hence, the resultant force acting on a lawn mover can be obtained as the resultant of the four forces that act on the mower.
The four forces that act on the lawn mower are;
Applied forceFrictional forceWeight of the mowerNormal reactionHence, the lawn mower is acted upon by four different forces.
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The distance, in feet, a moving object has traveled after t seconds is given by 2t/(4 + t). find the acceleration of the object after 5 seconds. (round your answer to three decimal places.)
Final answer:
To find the acceleration of a moving object after 5 seconds, given the distance function 2t/(4 + t), we first find the velocity by differentiating the distance function, then find the acceleration by differentiating the velocity. The acceleration after 5 seconds is approximately -0.022 m/[tex]s^2[/tex].
Explanation:
The question involves finding the acceleration of a moving object after 5 seconds, given that the distance it has traveled after t seconds is represented by the function 2t/(4 + t). To find the acceleration, we first need to determine the velocity function by differentiating the distance function with respect to t, and then find the acceleration by differentiating the velocity function with respect to t again.
The velocity v(t) is the first derivative of the distance function s(t) = 2t/(4 + t). Using the quotient rule for differentiation, v(t) = d/dt [2t/(4 + t)]. Calculating the derivative gives us v(t) = 8/(4 + t)^2.
The acceleration a(t) is the derivative of the velocity function. So, a(t) = d/dt [8/(4 + t)^2]. Differentiating this gives a(t) = -16/(4 + t)^3.
Plugging t = 5 into the acceleration function, a(5) = -16/(4 + 5)^3 = -16/729. Therefore, the acceleration of the object after 5 seconds is approximately -0.022 m/[tex]s^{2}[/tex], rounding to three decimal places.
Describe at least 2 resources (i.e. places, people, books, etc.) that can help you to maintain the life of your car.
A boy yells in a narrow valley. The sound reflects off of a boulder that is 80 m away. How long will it take to hear the echo if the speed of a sound wave is 320 m/s?
Answer:
0.50 s
Explanation:
you're welcome
A particle with charge 5 . 0- µ C is placed at the corner of a cube. (Physics Help)? A particle with charge 5.0-µC is placed at the corner of a cube. The total electric flux in N * m^2 C through all sides of the cube is: B) 7.1 x 10^4 D) 1.4 x 10^5
Gauss law states that the electric flux through any closed surface is proportional to the net electric charge inside the surface. This is expressed mathematically in the form of:
Φ = Q / εo
Where,
Φ = the electric flux = unknown (which we have to find for)
Q = the net electric charge = 5.0 µC = 5 E-6 C
εo = the permittivity of free space = a constant value = 8.85 E-12 C^2 / N m^2
Plugging in the values into the equation will result in:
Φ = 5 E-6 C / (8.85 E-12 C^2 / N m^2)
Φ = 564,971.75 Wb = 5.6 x 10^5 Wb
A measure of the total amount of matter an object contains is called
Liz rushes down onto a subway platform to find her train already departing. she stops and watches the cars go by. each car is 8.60 m long. the first moves past her in 1.80 s and the second in 1.66 s. find the constant acceleration of the train.
The average velocity can be calculated using the formula:
v = d / t
For the 1st car, the velocity is calculated as:
v1 = 8.60 m / 1.80 s = 4.78 m / s
While that of the 2nd car is:
v2 = 8.60 m / 1.66 s = 5.18 m / s
Now we can solve for the acceleration using the formula:
v2^2 = v1^2 + 2 a d
Rewriting in terms of a:
a = (v2^2 – v1^2) / 2 d
a = (5.18^2 – 4.78^2) / (2 * 8.6)
a = 0.23 m/s
Therefore the train has a constant acceleration of about 0.23 meters per second.
F a thermometer is calibrated to the nearest degree, to what part of a degree can you estimate the temperature it measures?
By dividing the temperature by two and adding 30 to the result, you can convert a temperature in Celsius to Fahrenheit. You will receive a rough temperature in Fahrenheit from this.
What is the reason Fahrenheit used instead of Celsius?For more accurate temperature measurements, use Fahrenheit. Additionally, it is preferable since people are more concerned about air temperature than water temperature.
Because of these factors, we ought to embrace Fahrenheit as a unit of temperature measurement rather than reject it in favor of its metric equivalent.
Fahrenheit and Celsius temperature scales are seen on the majority of thermometers. Read the °F figures (degrees of Fahrenheit).
Therefore, To get a more accurate approximation, multiply the temperature by 2, take out 10%, and then add 32 to the result.
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4 1/2 x -17/9. please helpp
How much work is done when a 185 g tomato is lifted 17.9 m ?
The work done when lifting a 185 g tomato by 17.9 m is approximately 32.5 joules, calculated using the weight of the tomato as the force and the distance it is lifted.
Explanation:To calculate the work done when lifting an object, we can use the formula Work (W) = Force (F) × Distance (D) × cos(θ), where θ is the angle between the force and the displacement. In the case of lifting an object vertically, the angle is 0°, so the cosine term is 1, and the equation simplifies to W = F × D. For a 185 g tomato lifted 17.9 m, we first need to convert the mass of the tomato to kilograms by dividing by 1000, which gives us 0.185 kg. The force is equal to the weight of the tomato, which is the mass (m) multiplied by the acceleration due to gravity (g = 9.8 m/s²), F = m × g. Thus, the force is F = 0.185 kg × 9.8 m/s² = 1.813 N. The work done is then W = 1.813 N × 17.9 m = 32.463 J, which we round to 32.5 J when expressing it with three significant figures.
The angular speed of the minute hand of a watch is:
The angular speed of the minute hand of a watch is calculated by dividing the total angle of rotation (2π rad) by the period of rotation (3600 s), which equals 0.1047 rad/min. This indicates the degree of the minute hand's rotation per minute. The right-hand rule also designates the angular velocity's direction.
Explanation:The angular speed of the minute hand of a watch refers to the degree of rotation of the minute hand per unit of time. In the particular case of a watch, the minute hand completes one full revolution (360° or 2π rad) in one hour (60 minutes or 3600 seconds). Therefore, the angular speed ω can be calculated as the total angle of rotation (2π rad) divided by the period of rotation, which is 3600 seconds.
Thus, the angular speed is calculated as ω = 2π rad/3600 s. By converting this to radian per minute, which is a more typical unit for a watch, we obtain that the angular speed of the minute hand of a watch is 0.1047 rad/min. This means that in each minute, the minute hand rotates 0.1047 radians.
This concept and calculation is part of what's studied in rotational motion in physics, where the right-hand rule can also be used to determine the direction of the angular velocity vector.
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PLEASE HELP NOW!! Which of the following must be the same for two isotopes of an element?
A. The number of neutrons
B. The atomic number
C. The mass
D. The charge
<<<<<<<<<< B is the answer >>>>>>>
What process is used when electrons are transferred from one object to another to produce static electricity?
Only a _______ technician may wear the ASE insignia on his or her uniform. A. full-time B. certified C. qualified D. dues-paying
Answer:
B. Certified
Explanation: I agree with the other person and i also believe it is correct
The. Is the time it takes for a wave to complete one cycle
Answer:
Time period
Explanation:
The time taken by a wave to complete one cycle is called the time period of a wave. It is denoted by T. The number of vibration per second is called the frequency of the wave.
The relation between the time period and the frequency is inverse i.e.
[tex]T=\dfrac{1}{\nu}[/tex]
If the number of vibrations increases its time period will decrease.
Similarly, for a simple pendulum the time period to complete one cycle is :
[tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
l and g are length of pendulum and acceleration due to gravity.
When you drop a sugar cube in a glass of water, at first the water doesnât taste sweet. later, it tastes very sweet.what causes the change in the waterâs taste?
If mechanical energy is conserved, then a pendulum that has a potential energy of 20 J at its highest point and 0.5 J at its lowest point has _____ as its kinetic energy at its lowest point.
20 J
0.5 J
19.5 J
20.5 J
Answer:
The third answer is correct:)
Explanation:
A car accelerates from rest at a constant rate of 2m/s2 for 5s. what is the speed of a car at the end of that time?
Moving your finger across a textured surface can produce vibrations that are interpreted as texture. these vibrations are defined as _____.
a. temporal cues
b. parietal cues
c. spatial cues
d. olfactory cues
Determine the density of a rectangular piece of concrete that measures 3.7 cm by 2.1 cm by 5.8 cm and has a mass of 43.8 grams.
The density of the concrete is approximately 0.965 g/cm³. The result does not support the statement that rebar is mostly iron.
Explanation:The density of a substance can be calculated by dividing its mass by its volume. In this case, the mass of the concrete is 43.8 grams and the volume is calculated by multiplying the length, width, and height, which is 3.7 cm x 2.1 cm x 5.8 cm = 45.4014 cm³ (rounded to the nearest 0.0001 cm³). Therefore, the density of the concrete is 43.8 g / 45.4014 cm³ ≈ 0.965 g/cm³.
(b) Since the density of the concrete in (a) is less than the density of iron (approximately 7.87 g/cm³), the result does not support the statement that rebar is mostly iron.
What is the half-reaction that occurs at the cathode during the electrolysis of molten potassium bromide?
Final answer:
During the electrolysis of molten potassium bromide, the half-reaction that occurs at the cathode is the reduction of potassium ions (K+) to form potassium metal (K).
Explanation:
The half-reaction that occurs at the cathode during the electrolysis of molten potassium bromide is the reduction of potassium ions (K+) to form potassium metal (K).
The half-reaction can be represented as:
2K+ + 2e- -> 2K
At the cathode, positive ions are reduced and gain electrons to form neutral atoms or molecules.
Which one of the following does not accurately describe the universal gravitational law? A. Gravitational force is proportional to the square of the distance between the centers of both bodies. B. The object with the smaller mass does most of the moving because the object with the larger mass has too much inertia to move any noticeable amount. C. Gravitational force is proportional to the product of the two masses. D. Every object in the universe that has mass attracts every other object in the universe that has mass.
How much work does the up escalator do on you when you ride it from the lower level to the upper level?
Describe how water molecules do not travel with the wave and the transfer of energy in water waves.
The mass of the parts is always ___ the mass of the whole when looking at nuclear masses.
Answer:
greater than
Explanation:
When looking at nuclear masses, the mass of the parts is always greater than the mass of the whole.
Example with helium:
The atomic number of helium is 2, which means that it has two protons in its nucleus. The most common isotope of helium, ^4He, has two neutrons in addition to the two protons, giving it a mass number of 4. The mass of a proton is about 1.0073 atomic mass units (amu), and the mass of a neutron is about 1.0087 amu. Therefore, the total mass of the four nucleons (two protons and two neutrons) in the ^4He nucleus is:
2 protons x 1.0073 amu/proton + 2 neutrons x 1.0087 amu/neutron = 4.0314 amu
However, the actual (whole) mass of ^4He nucleus is found to be slightly less than the sum of the parts of the masses of its constituent nucleons. This means that the mass of the parts is always greater than the mass of the whole.
A ball thrown with 50N of force accelerates at 25 m/s2. What is the mass of the ball?
the contribution of Tycho Brahe was primarily his
calculations
observation
inventions
theories
A 1.0 kg football is given an initial velocity at ground level of 20.0 m/s [37° above horizontal]. It gets blocked just after reaching a height of 3.0 m.
(a) What is the velocity of the football when it first reaches a height of 3.0 m above the level ground?
(b) What horizontal distance has the ball travelled when it first reaches a height of 3.0 m above ground?
How do scientists determine the age of the solar system?