Answer: 1100 [tex]\sqrt{2[/tex] N -m
Explanation:
As work = force × displacement
4. An ice skater is spinning on the ice at 4.00 rev/s. If the skater’s nose is 0.120 m from the axis of rotation, what is the centripetal acceleration of his nose?
Answer:
a = 3.02 m/s^2
h
Explanation:
we know that centripetal acceleration (a) is
[tex] \frac{v {}^{2} }{r} = a[/tex]
since v = rω, we can substitute it into the equation, which now gives us the centripetal acceleration in terms of angular velocity and radius (check image).
now we use the values given and find the answer
If astronomers were to find they have made a mistake and our solar system is actually 7.2 (rather than 8.2) kpc from the center of the galaxy, but the orbital velocity of the sun is still 240 km/s, what is the minimum mass of the galaxy?
Assuming a circular orbit for the Sun, we can use the equation:
v^2 = GM/r
where v is the orbital velocity of the Sun, r is the distance from the center of the galaxy, G is the gravitational constant, and M is the mass of the galaxy.
We can solve for M:
M = v^2 * r / G
Using the given values of v = 240 km/s and r = 7.2 kpc = 7.2 * 3.086e+19 m, and G = 6.6743e-11 N m^2/kg^2, we get:
M = (240000 m/s)^2 * 7.2 * 3.086e+19 m / 6.6743e-11 N m^2/kg^2
M = 1.47e+42 kg
Therefore, the minimum mass of the galaxy, if the distance of the solar system from the center is actually 7.2 kpc, is approximately 1.47 x 10^42 kg.
Q37. A major source of heat loss from a house in cold weather is through the windows. Calculate the rate of heat flow through a glass window 2.0m x 1.5m in area and 3.2mm thick, it the temperatures at the inner and outer surfaces are 15.00C and 14.0°C
The rate of heat flow through the window is approximately 84.38 W.
To calculate the rate of heat flow through a glass window
The rate of heat flow through the window can be calculated using the formula:
Q = (kA (T1 - T2))/d
Where
Q is the rate of heat flowk is the thermal conductivity of the glassA is the area of the windowT1 is the temperature at the inner surfaceT2 is the temperature at the outer surfaced is the thickness of the glassWe first need to convert the temperatures to Kelvin, since temperature differences must be in Kelvin in this formula:
T1 = 15.0°C + 273.15 = 288.15 K
T2 = 14.0°C + 273.15 = 287.15 K
The thermal conductivity of glass can vary depending on the type of glass, but a typical value is around k = 0.9 W/(m·K) for plate glass.
Substituting the given values into the formula, we get:
Q = (0.9 W/(m·K) x 2.0 m x 1.5 m x (288.15 K - 287.15 K))/0.0032 m
Simplifying this expression, we get:
Q ≈ 84.38 W
Therefore, the rate of heat flow through the window is approximately 84.38 W.
Learn more about thermal conductivity here : brainly.com/question/14919402
#SPJ1
In an electric circuit, what is one material that the connector can be made of?
Need help with this
Explanation:
See image for definitions....look at the units and fill the blanks appropriatly
I need help with this ty
Answer:
4 & 2
Explanation:
If you plug in experimental values into the formula for kinetic energy, you will see the relationship.
1.
[tex]\frac{1}{2}(2 kg)(2 m/s)^{2} = 4 kg * m^{2} /s^{2} \\\\\frac{1}{2}(8 kg)(2m/s)^{2} = 16 kg * m^{2} /s^{2}\\\\\frac{16}{4} = 4[/tex]
2.
[tex]\frac{1}{2}(6 kg)(2m/s)^{2} = 12 kg * m^{2} /s^{2} \\\\\frac{1}{2}(3 kg)(2 m/s)^{2} = 6 kg * m^{2}/s^{2}\\ \\\frac{12}{6} = 2[/tex]
a person that just start driving a car is called
Answer:
A person who drives a car for themselves, generally taking themselves back and forth to work or errands, is generally referred to as a driver.
Remember the steps that the American Heart Association recommends for saying no to cigarettes. Which one of these will you use if you are faced with peer pressure to smoke? Which one of these will you use if you are faced with peer pressure to drink or take drugs? Explain the method you will use and why you chose it.
Answer: just say no and never talk to that person again.
Explanation:
because that is what i would do to prevent drugs and/or nicotine to enter my body.
Derive from first principle the equation of motion of a one dimensional standing wave
The equation of motion of a one dimensional standing wave can be derived from first principles using the wave equation.
The wave equation states that the propagation speed of a wave, c, is equal to the square root of the ratio of the wave's tension (T) to its linear mass density (μ). In other words,
[tex]c = \sqrt{ \frac{T}{\mu}[/tex]
For a one dimensional standing wave, the equation of motion can be derived by taking the second derivative of the wave equation with respect to time. This is the equation of motion that results:
[tex]F = \mu (\frac{d2y}{dt2})[/tex]
where F is the total force applied to the wave, and [tex]\frac{dy}{dt}[/tex] is the wave velocity. The equation of motion can be further simplified by substituting the wave equation for c, resulting in the following equation of motion for a one dimensional standing wave:
[tex]F = (\frac{T}{\mu }) (\frac{d2y}{dt2})[/tex]
This equation of motion describes how the total force applied to a one dimensional standing wave affects the wave's velocity.
learn more about motion Refer:brainly.com/question/22810476
#SPJ1
complete question:What is the equation of motion for a one-dimensional standing wave?
QUICK ANSWER Fiber optic cables utilize internal reflection to transmit signals. TRUE OR FALSE
PLS MRK ME BRAINLIEST
Answer:
True
Explanation:
optical fibre consists of core and cladding. The signal is converted to light using transducers. The light travels across the cable undergoing multiple internal reflections. At the other end the light is converted back to Signal using transducers.
Answer: True
Explanation: Optical fiber uses the optical principle of "total internal reflection" to capture the light transmitted in an optical fiber and confine the light to the core of the fiber.
If I get this wrong im sorry
From time to time, people claim to have invented a machine that will run forever without energy input and develop more energy than it uses (perpetual motion). What is wrong with this claim?
Explanation:
It ignores some basic laws of physics:
You cannot get more work out of a machine than goes in
You cannot ignore friction
What types of atoms are radioactive?
small atoms
atoms with many electrons
atoms with unstable nuclei
atoms with unbalanced charges
Answer:
An atom with an "unstable" nucleus is likely to split into two different atoms (elements) with emission of gamma, alpha, etc. which is radioactive radiation.
At the point 0, there are 2 point sources, emitting the same constant sound power,
with intensity in inversely proportional to the square of the distance from the source. At the point A, the sound level intensity is [tex]20dB[/tex]
(a) What is the sound level intensity at A of one source?
(b) What is the number of sources that we have to add at A so that the sound level intensity at the midpoint M of OA is [tex]30dB[/tex]?
The number of sources that we have to add at A so that the sound level intensity at M is doubled is 2.
(a) Let the distance of point A from one source be x. Then the distance from the other source is (OA - x), where OA is the distance between the two sources. The sound intensity at point A due to one source is proportional to 1/x^2. So, if the sound power of one source is P, then the sound intensity at A due to one source is given by I = P/(4πx^2), where 4πx^2 is the surface area of a sphere with radius x.
The sound level intensity is defined as L = 10log(I/I0), where I0 is a reference intensity (I0 = 10^-12 W/m^2). Since there are two sources, the total sound intensity at A is twice the sound intensity due to one source, i.e., I_total = 2I = 2P/(4πx^2). Therefore, the sound level intensity at A is L = 10log(2P/(4πx^2I0)) = 10log(2P/(4πI0)) - 20log(x).
(b) Let the distance of point M from one source be y. Then the distance from the other source is (OM - y), where OM is the distance between O and M. The sound intensity at M due to one source is proportional to 1/y^2. So, if the sound power of one source is P, then the sound intensity at M due to one source is given by I = P/(4πy^2), where 4πy^2 is the surface area of a sphere with radius y.
The sound level intensity at M due to one source is L_M = 10log(I/I0) = 10log(P/(4πy^2I0)).
Since the sound intensity is inversely proportional to the square of the distance, the sound intensity at A due to one source is four times the sound intensity at M due to one source. Therefore, I_A = 4I = 4P/(4πy^2), and the sound level intensity at A due to one source is L_A = 10log(I_A/I0) = 10log(P/(πy^2I0)).
We want the total sound level intensity at M due to all sources to be L_M = L_A + 10log2, where 10log2 is the sound level intensity increase due to adding a second source. Therefore, we have:
10log(P/(4πy^2I0)) + 10log2 = 10log(P/(πy^2I0))
10log2 = 10log(4/π)
log2 = log(4/π)
2 = 4/π
π = 2
Learn more about intensity here:
https://brainly.com/question/17323212
#SPJ1
A horizontal force of 25 N is exerted on a box (mass 10 kg), as shown in the diagram. The box accelerates at 2.0 m.s-2. What is the magnitude of the frictional force acting between the box and the floor?
Answer:
the magnitude of the frictional force acting between the box and the floor is 5 N.
Explanation:
A 10,000 kg freight car is rolling along a track at 3.00m.s.Calculate the time needed for a force of 1000N for stop the car
It takes 0.3 seconds for a force of 1000 N to halt a 10,000 kg goods car moving at 3.00 m/s along a track.
Calculate the time needed for a force of 1000N for stop the carWe must first establish the car's starting kinetic energy in order to calculate the time required to stop the vehicle:
Kinetic Energy (KE) is equal to half of mass times speed, or 10,000 kg times 3.00 m/s.
KE = 45,000 J
Then, we may use the designed with the intent, which asserts that an object's change in kinetic energy equals the jobs performed by an external force: Work equals Force x Distance x Change in KE.
The gain in kinetic energy is equal to the starting kinetic energy because the car is coming to a stop: KE Change = -45,000 J
As a result, the external force's work is: Work equals force times distance, or -45,000 J.
When we solve for distance, we obtain: Work / Force = -45,000 J / 1000 N Distance
Location = -45 m
Because the force is against the direction of the car's motion, you'll see that the range is negative.
Finally, we can calculate the travel time using the kine model for uniformly accelerated motion: Distance is equal to 1/2*acceleration*time2. Time is calculated as sqrt(2 * Distance / Acceleration) as well as sqrt(2 * 45 m / (1000 N / 10,000 kg)).
time equals sqrt(0.09 s2/kg).
time = 0.3 s
To Know more about Force Visit:
brainly.com/question/1319164
#SPJ1
The following conversion equivalents are given:
1 m 100 cm 1 in = 2.54 cm 1 ft = 12 in
A bin has a volume of 1.5 m3. The volume of the bin, in ft3, is closest to:
Answer:52.972ft^3
Explanation:
It is unit conversion based and for a volume of a bin from cubic meter to cubic foot as we know 1 meter =3.281 foot.
where volume=1.5m^3
multiply 1.5*(3.281)^3 ft^3
v=52.972 ft^3
why would the acceleration not change when adding mass to an air cart?
Answer:
The acceleration of an air cart, which is an object moving on a cushion of air, would not change when adding mass to it because the force of air resistance acting on the cart is negligible compared to the force applied by the air source that propels it. Therefore, the total force acting on the cart remains almost constant, regardless of the cart's mass, and according to Newton's second law of motion, the cart's acceleration would remain the same. This assumes that the air source provides a constant force and that the added mass does not significantly affect the friction between the cart and the surface on which it is moving.
6. Construct a new physical equations having in terms of G, C and h dimensions of length where G is universal gravitational constant, c is the speed of light and I is planck's Constant.
Basic values of mass in the existing program are c1/2 G-12 h1/2 if the speed of light (c), newtonian constant (G), and Planck's parameter (h) are taken as the fundamental units.
What is the G equivalent of the principle of the universal gravitational equation?According to the Universal Gravitation Equation, G is equal to 6.673 x 10-11 N m2/kg2. Everything because of how a fruit falls from a tree to the reason the moon rotates around the earth may be explained by the Universal Gravitational Law.
What does the formula for the universal law of gravity mean?This rule states that the distance is proportional to the product of the mass of the two objects. The Universal Law of Force of gravity is summed up by the following gravitational force equation: FG = (G.m1.
To know more about speed visit :
https://brainly.com/question/28224010
#SPJ9
Cheyenne wants to show her class a model that demonstrates sound reflection. Which model best represents what happens when sound waves are reflected?
The simulation of sound waves bouncing off a flat surface is one model that most accurately depicts what happens when sound waves are reflected.
Who or what names the sound wave reflection?The term "echo" refers to a sound reflection that follows a direct sound in reaching the listener. The delay increases with the distance between the source and the listener travelled by the reflecting surface.
A sound wave belongs to what kind of wave?Longitudinal waves are those produced by sound. Compressions and rarefactions occur during the propagation of longitudinal waves through any given medium. When particles are compressed, high pressure zones are created as a result of their near proximity.
To know more about sound waves visit:-
https://brainly.com/question/29071528
#SPJ1
WHAT IS QUANTUM PHYSICS
hi!
Answer:
Quantum physics is the study of matter and energy at the most fundamental level. It aims to uncover the properties and behaviors of the very building blocks of nature.
Psi(x) = (alpha/pi) ^ (1/4) * e ^ (- (alpha * x ^ 2)/2)
Find wave function of
(Px)*2
(Pls if you know the answer writ it on the paper to be clear )
Note that the wave function of (Px)^2 is given by: (Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
What is the explanation for the above response?To find the wave function of (Px)^2, we need to use the momentum operator, which is represented by Px = -i(h/2π) d/dx.
First, let's find the wave function of Px, which is given by:
Px Psi(x) = -i(h/2π) d/dx [Psi(x)]
= -i(h/2π) [-αx Psi(x) + (α^2 x) Psi(x)]
Now, we can find the wave function of (Px)^2 by squaring the wave function of Px:
(Px)^2 Psi(x) = (-i(h/2π) d/dx) (-i(h/2π) d/dx) Psi(x)
= (h^2/4π^2) [α^2 x^2 Psi(x) - 2α x d/dx(Psi(x)) + (d^2/dx^2)(Psi(x))]
Substituting Psi(x) = (α/π)^(1/4) e^(-αx^2/2) into the above expression, we get:
(Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
Therefore, the wave function of (Px)^2 is given by:
(Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
Learn more about wave function at:
https://brainly.com/question/17484291
#SPJ1
A green ball and a blue ball have a mass of 10 kg each one. The green ball, traveling at 10 m/s, strikes the blue ball, which is at rest. Assuming that the balls slide on a frictionless surface and all collisions are head-on, find the final speed of the blue ball in each of the following situations:
a. The green ball stops moving after it strikes the blue ball
b. The green ball continues moving after the collision at 4 m/s in the same direction.
(a) The final velocity of the blue ball is 5 m/s after the collision
(b) The final velocity of the blue ball is 6 m/s after the collision.
What is the final velocity of the balls?To solve this problem, we can use the conservation of momentum and the conservation of kinetic energy. The total momentum and total kinetic energy of the system before and after the collision must be the same.
a. When the green ball stops moving after the collision, its final velocity is 0 m/s. Let's call the final velocity of the blue ball v. The conservation of momentum equation is:
m_green x v_green + m_blue x v_blue = (m_green + m_blue)v
Substituting the values, we get:
10 kg x 10 m/s + 10 kg x 0 m/s = 20 kg x v
Simplifying, we get:
v = 5 m/s
b. When the green ball continues moving after the collision at 4 m/s in the same direction, its final velocity is 4 m/s. Let's call the final velocity of the blue ball v.
The conservation of momentum equation is the same as before:
m_green x v_green + m_blue x v_blue = (m_green + m_blue)v
Substituting the values, we get:
10 kg x 10 m/s + 10 kg x 0 m/s = 10 kg x 4 m/s + 10 kg x v
Simplifying, we get:
v = 6 m/s
Learn more about linear momentum here: https://brainly.com/question/7538238
#SPJ1
A metal weigh 20N in air, 12N in water, and 14N in Kerosene. Cal the the Relative density of (a) Metal (b) kerosene
The relative density of kerosene is 0.006, or 6 kg/m³.
A metal block that weighs 60 tonnes in the air and 40 tonnes beneath water, what is its density?1 Response. Employ the Archimedes' Principle to your advantage: the buoyant force of a fluid is equal to the apparent loss of weight in water and is also equal to the weight of the displaced fluid. Weight of the displaced water equals 60 - 40 N, or the apparent loss in weight of the metal block. Water displacement mass is calculated as 20 / 9.8 = 2.04 kg.
Buoyant force = Weight of the displaced water = 20 N - 12 N = 8 N
Volume of water displaced = Buoyant force / Density of water = 8 N / 9.8 m/s² = 0.8163 kg
Density of metal = Weight of metal in air / Volume of metal = 20 N / (density of air x volume of metal)
Density of metal = 20 N / 0.8163 kg = 24.5 kg/m³
Buoyant force = Weight of the displaced kerosene = 20 N - 14 N = 6 N
Volume of kerosene displaced = Buoyant force / Density of kerosene = 6 N / 9.8 m/s² = 0.6122 kg
Density of kerosene = Mass of kerosene / Volume of kerosene displaced = 14 N / 0.6122 kg = 22.86 kg/m³
Relative density of kerosene = Density of kerosene / Density of water = 22.86 kg/m³ / 1000 kg/m³ = 0.006, or 6 kg/m³.
To know more about density visit:-
https://brainly.com/question/6329108
#SPJ9
EARTH AND SPACE SCIENCE! PLEASE HELP! Question: Tree with unknown height has a shadow that is 4200 centimeters long while a meter stick has a shadow when held vertical that 325 centimeters long. Identify below, the height of the tree in centimeters. The height of the meter stick is 100 centimeters(cm).
Potential answers:
a.) 1292 cm
b.) 1520 cm
Therefore, the answer is (a) 1292 cm is stick has a shadow when held vertical.
What causes the shadow's location to change?Additionally, since light moves in a straight path from its source to an object, the shadow of the object moves with the light source.
Let's use h centimetres to represent the tree's height. We have the following percentage in the problem:
height of tree/length of its shadow = height of meter stick/length of its shadow
or
h / 4200 = 100 / 325
We can solve this proportion for h:
h = 4200 * 100 / 325 = 1292.31 cm
Rounding to the nearest centimeter, we get:
h ≈ 1292 cm
To know more about vertical visit:-
https://brainly.com/question/11679227
#SPJ1
A geographer wants to organize data on the changing economies of two
countries. The data show that one country's economy grew rapidly over 10
years, while the other country's economy declined slightly over the same
period.
The best way for the geographer to organize these data would be a
Answer:
line graph. A line graph is the best way to show changes in data over time. The geographer can plot the economic growth of one country as a line going up over the 10 years, and the economic decline of the other country as a line going down slightly over the same period. This will allow for a clear visual comparison of the changes in the economies of the two countries over time.
Find the position of the center of mass of the system of the sun and Jupiter. (Since Jupiter is more massive than the rest of the planets combined, this is essentially the position of the center of mass of the solar system.)
it's only beyond the surface of the sun! There is a barycenter throughout our entire solar system. All of the planets in the solar system, including the sun, center of mass.
Is the Sun more massive than the solar system as a whole?The sun is significantly more massive than Earth and has a radius that is likewise much greater. The mass of the sun is more than 333,000 times more than the mass of the Earth and makes up nearly all of the solar system's mass (99.8%).
How much more does the Sun compare to Jupiter?The Sun is 1000 times more than Jupiter, the solar system's most planet , but Jupiter is still 1000 times less than it.
To know more about center of mass visit :-
https://brainly.com/question/28996108
#SPJ1
A machine has a velocity ratio of 5. ut requires a 50kg weight to overcome 20kg weight. calculate the efficiency of the machine ( take g= 10m/s^2)
Answer:
The answer is 8%
Explanation:
We know that the efficiency of the machine is given by,
E=(M.A)*100
=([tex]\frac{20}{50}[/tex])*[tex]\frac{1}{5}[/tex]*100
=8%
A student decides to devise a new temperature scale with the freezing and boiling points at 0° X and
70° X. What Celsius temperature would correspond to a temperature of 35° X?
O 50
O 35
O 90
O 70
Answer:
To convert temperature from the new scale (X) to Celsius, we simply subtract 0 from the value in X and then multiply the resulting number by a factor of 100/70. This gives us the Celsius temperature.
For 35° X, we can use the formula as follows:
C = (35 - 0) * (100/70)
C = 35 * 1.4286
C = 50°C
Therefore, the correct answer is option A, which is 50.
Cathode ray tubes (CRTs) used in old-style televisions have been replaced by modern LCD and LED screens. Part of the CRT included a set of accelerating plates separated by a distance of about 1.70 cm. If the potential difference across the plates was 24.5 kV, find the magnitude of the electric field (in V/m) in the region between the plates.
the magnitude of the electric field in the region between the plates is 1.44 × [tex]10^6[/tex]V/m.
The electric field between the plates of the CRT can be calculated using the formula:
E = V/d
where E is the electric field, V is the potential difference across the plates, and d is the distance between the plates.
Substituting the given values, we get:
E = 24.5 kV / 0.017 m
Converting kV to V and simplifying, we get:
E = 24.5 × [tex]10^3[/tex]V / 0.017 m
E = 1.44 × [tex]10^6[/tex] V/m
An electric field is a force field created by a charged object or collection of charged objects that exerts a force on other charged objects within its vicinity. The electric field is a vector quantity and is measured in units of volts per meter (V/m).
The electric field at a point in space is defined as the force per unit charge acting on a positive test charge placed at that point. The direction of the electric field is given by the direction of the force that would be experienced by a positive test charge placed at that point.
Learn more about electric field here:
https://brainly.com/question/15800304
#SPJ1
answer and solution to this question
Frequency= 30 Hz, Period= 0.0333 s, Wave Number=15.708 rad/m, Wave Function= y(x, t) = 0.05 sin(15.708x - 94.248t), Transverse displacement= -0.013 m, Time= 0.297 s.
How to calculate the frequency?(a) To find the frequency (f), we can use the equation: wave speed = frequency x wavelength. Rearranging this equation, we get:
frequency = wave speed / wavelength
Substituting the given values, we get:
frequency = 12 m/s / 0.4 m = 30 Hz
Therefore, the frequency of the wave is 30 Hz.
To find the period (T), we can use the equation:
period = 1 / frequency
Substituting the frequency value we just calculated, we get:
period = 1 / 30 Hz = 0.0333... s (rounded to four decimal places)
Therefore, the period of the wave is approximately 0.0333 s.
To find the wave number (k), we can use the equation:
wave number = 2π / wavelength
Substituting the given values, we get:
wave number = 2π / 0.4 m = 15.708 rad/m (rounded to three decimal places)
Therefore, the wave number of the wave is approximately 15.708 rad/m.
(b) The wave function for a transverse wave on a string is given by:
y(x, t) = A sin(kx - ωt + φ)
where A is the amplitude, k is the wave number, x is the position of the point on the string, t is the time, ω is the angular frequency, and φ is the phase constant.
We already know the values of A, k, and ω from the previous calculations. To find φ, we can use the given initial condition: "at t = 0 end of the string has zero displacement and is moving upward". This means that y(0,0) = 0 and ∂y/∂t(0,0) > 0. Substituting these conditions into the wave function, we get:
0 = A sin(0 + φ)
∂y/∂t = -Aω cos(0 + φ)
Since sin(0 + φ) = sin(φ) = 0 (because sin(0) = 0), we get:
φ = nπ, where n is an integer
Since cos(0 + φ) = cos(φ) = 1 (because cos(0) = 1) and ∂y/∂t(0,0) > 0, we get:
n = 0 or 2
Therefore, the possible values of φ are 0 or 2π.
Substituting the values of A, k, ω, and φ, we get:
y(x, t) = 0.05 sin(15.708x - 94.248t)
Therefore, the wave function describing the wave is:
y(x, t) = 0.05 sin(15.708x - 94.248t)
(c) To find the transverse displacement of a wave at x = 0.25 m and t = 0.15 s, we can use the wave function we just found:
y(0.25, 0.15) = 0.05 sin(15.708(0.25) - 94.248(0.15))
y(0.25, 0.15) ≈ -0.013 m (rounded to three decimal places)
Therefore, the transverse displacement of the wave at x = 0.25 m and t = 0.15 s is approximately -0.013 m.
(d) To find how much time must elapse from the instant in part (c) until the point at x = 0.25 m has zero displacement,
From part (c), we know that the transverse displacement of the wave at x = 0.25 m and t = 0.15 s is approximately -0.013 m. We need to find the time it takes for this point to return to zero displacement.
We can use the wave function we found in part (b) and set y(0.25, t) = 0:
0 = 0.05 sin(15.708(0.25) - 94.248t)
Since sin(θ) = 0 when θ = nπ (where n is an integer), we get:
15.708(0.25) - 94.248t = nπ
Solving for t, we get:
t = (15.708(0.25) - nπ) / 94.248
To find the smallest positive value of t that satisfies this equation, we need to use the smallest positive value of n that makes the right-hand side of the equation positive (because we want to find the time it takes for the point at x = 0.25 m to return to zero displacement, which happens after the point has completed a full cycle). We can see from the equation that n must be an even integer to make the right-hand side positive. The smallest even integer greater than zero is 2. Substituting n = 2, we get:
t = (15.708(0.25) - 2π) / 94.248
t ≈ 0.297 s (rounded to three decimal places)
Therefore, the time it takes for the point at x = 0.25 m to return to zero displacement is approximately 0.297 s.
Know more about displacement here:
https://brainly.com/question/30087445
#SPJ1