a) The speed of waves on the rope is 1.50 m/s.
b) The length of the rope is 0.050 m or 50 cm.
c) The expression for the standing wave on the rope is: y(x, t) = A sin(kx) sin(ωt)
d) The amplitude is 0.0125 m and the maximum transverse velocity is 0.75π m/s for a point in the middle of the heavy rope when oscillating at its fundamental frequency.
a) To find the speed of waves on the rope, we can use the formula v = fλ, where v is the speed of the wave, f is the frequency, and λ is the wavelength.
In this case, the frequency is given as 30.0 Hz, and we need to find the wavelength.
Since the rope has three antinodes, the wavelength will be twice the distance between two adjacent antinodes.
Let's denote the distance between two adjacent antinodes as d.
Since the rope has three antinodes, the total length of the rope between the first and third antinode is 2d.
The length of this portion of the rope is also equal to half a wavelength (λ/2).
Therefore, we have:
2d = λ/2
Simplifying, we find:
d = λ/4
Next, we can calculate the wavelength using the displacement of the antinode.
The maximum displacement is given as 2.5 cm, which is equivalent to 0.025 m.
Since the displacement corresponds to half a wavelength, we have:
λ/2 = 0.025 m
Solving for λ, we find:
λ = 0.050 m
Now we can substitute the values of f and λ into the equation v = fλ to find the speed of waves on the rope:
v = (30.0 Hz)(0.050 m) = 1.50 m/s
Therefore, the speed of waves on the rope is 1.50 m/s.
b) The length of the rope can be calculated by multiplying the wavelength by the number of antinodes (n), excluding the fixed end.
In this case, we have three antinodes (n = 3).
Since the rope between the first and third antinode corresponds to half a wavelength, we can use the formula:
Length = (n - 1)(λ/2) = 2(0.050 m)/2 = 0.050 m
Therefore, the length of the rope is 0.050 m or 50 cm.
c) The expression for the standing wave on the rope can be written as:
y(x, t) = A sin(kx) sin(ωt)
where A is the amplitude, k is the wave number, x is the position along the rope, t is the time, and ω is the angular frequency.
In a standing wave, the displacement varies sinusoidally with position but does not propagate in space.
d) When the rope is oscillating at its fundamental frequency, with a maximum displacement at the antinode of 2.5 cm, the amplitude (A) is equal to half the maximum displacement, which is 1.25 cm or 0.0125 m.
The maximum transverse velocity (v_max) of a point in the middle of the heavy rope can be calculated using the formula v_max = Aω, where ω is the angular frequency.
For the fundamental frequency, ω = 2πf. Substituting the given frequency of 30.0 Hz, we have:
ω = 2π(30.0 Hz) = 60π rad/s
Therefore, the amplitude is 0.0125 m and the maximum transverse velocity is:
v_max = (0.0125 m)(60π rad/s) = 0.75π m/s
So, the amplitude is 0.0125 m and the maximum transverse velocity is 0.75π m/s for a point in the middle of the heavy rope when oscillating at its fundamental frequency.
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A child is riding in a wagon. What reference frame might have been used if an observer said the child was not moving.
Answer:
the wagon should be used as frame of reference if an observer said the child was not moving.
Explanation:
The state of motion of a body depends upon the frame of reference. It is the set of co-ordinates according to which the motion is analyzed. If a child is riding in a wagon, then he will be considered in motion to a person standing outside the wagon. Hence, if we take a frame of reference outside the wagon then the child must be in motion with respect to the observer. On the other hand if the observer is inside the wagon, then the child must be in rest with respect to the observer. Hence, if we take the wagon to be the frame of reference, then the child will be at rest with respect to the observer.
Therefore, the wagon should be used as frame of reference if an observer said the child was not moving.
Why is the perfect mechine is not possible in the real life?
Answer:
Because the mechanical advantage of the machine is affected by friction and weight but velocity ratio is not. So, mechanical advantage is less than velocity rate. Thus, the machine's efficiency is less than 100% and can't be a perfect machine
a brick is moving at a speed of 3 m/s and a pebble is moving at a speed of 5 m/s. if both objects have the same kinetic energy, what is the ratio of the brick's mass to the pebble's mass?
By the help of Kinetic energy ,the ratio of the brick's mass to the pebble's mass is \(\frac{9}{25}M = m\)
A moving item or particle might have power of a certain sort called kinetic energy. An object gains kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. Kinetic energy is a characteristic of motion that depends on the mass and speed of an object or particle. Motion includes all combinations of vibration, axis rotation, translation, and movement (along a path from one location to another).
M should represent the brick mass.
Let m represent the pebble's mass.
.\(\frac{1}{2} M(v)^2\) =KE
\(\frac{1}{2} M(3)^2\)=KE
\(\frac{1}{2} m(5)^2\)= KE
\(\frac{1}{2} M(3)^2= \frac{1}{2} m(5)^2\)
9M = 25m
\(\frac{9}{25}M = m\)
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Which one is best for health? A) Boiled Seeds B) roasted seeds c) wet swollen seeds d)Sprouted seeds
Answer:
d.) "Sprouted seeds"Explanation:
Sprouted seeds - are the best for health.
I hope it helps! Please mark my answer answer as bräinliest (if my answer is correct). Thank You!
HELP PLEASE!!!
Gravity helps us watch television, talk on the phone, and use the Intemet.
Explain whether this statement is true or false.
Support your answer with evidence from the text.
Answer:
Technically yes, it does help those objects not to float away, but that is false. gravity is not the factor that lets us watch tv, talk on the phone etc.
Gravity helps us watch television, talk on the phone, and use the Internet. This is true statement.
What is the process of satellite orbiting?The goal of satellites is to achieve balance. They rotate around the globe quickly enough to avoid being entirely drawn down into the planet's center of gravity, yet slowly enough to avoid drifting out into space.
When a satellite is travelling at the right speed, the earth's gravitational attraction is just strong enough to keep it in place. A satellite must move quicker to maintain orbit the nearer it is to the earth's surface. Additionally, satellites' orbits are circular or elliptical due to the continual pull of the curved surface of the planet.
Therefore, gravity plays a crucial role in our daily lives, whether it's keeping us anchored to the planet's surface or keeping the satellites we use to communicate and learn more about our environment in orbit.
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which object is completely opaque?
a:wooden spoon
b: drinking glass
c: wax paper
d:window
Answer:
a
Explanation:
light can not pass through it completely
The distance from Earth to the Moon is 2.389 x 10^5 mi. Convert this distance to standard form.
Answer:
convert it into distance form
Explanation:
a traveler first drives 21.0 km east, then 28.8 km southeast, and finally 10 km south. what is the magnitude
The magnitude of the traveler's displacement is approximately 39.5 km.
To find the magnitude of the traveler's displacement, we can combine the individual displacements in a vector sum.
The first leg of the journey is a displacement of 21.0 km east. We can represent this as a vector in the positive x-direction: (21.0 km, 0 km).
The second leg of the journey is a displacement of 28.8 km southeast. We can break down this displacement into its x and y components. The southeast direction is a combination of east and south. The angle between the southeast direction and the positive x-axis is 45 degrees. Using trigonometry, we can find the x and y components:
x-component = 28.8 km * cos(45°) = 20.4 km
y-component = 28.8 km * sin(45°) = 20.4 km
So, the second displacement can be represented as a vector: (20.4 km, -20.4 km).
The third and final leg of the journey is a displacement of 10 km south. We can represent this as a vector in the negative y-direction: (0 km, -10 km).
To find the total displacement, we add the individual displacements:
(21.0 km, 0 km) + (20.4 km, -20.4 km) + (0 km, -10 km) = (41.4 km, -30.4 km)
The magnitude of the displacement is given by the Pythagorean theorem:
Magnitude = √((41.4 km)² + (-30.4 km)²) ≈ 39.5 km
Therefore, the magnitude of the traveler's displacement is approximately 39.5 km.
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Density differences in different materials are able to change the _____________ of a wave.
Amplitude
Crest
Speed
Trough
Answer:
speed
Explanation:
question on picture ,pls help
Answer:
a. to find the volume of a shape using V=I Xw X h. Pull out your LEGO bricks and begin with a 1 by 1.
b.Direct measurement is measurement done by bringing the target into contact with the measurement system to read the length, height, or other aspect directly. Although direct measurement allows measurement results to be known as they are, errors may occur depending on the skill of the person doing the measurement.
c.1. Switch off the fan in the lab so that wind will not affect the result. 2. Ensure that the ruler has stopped moving before taking length measurement.
who was the chairman of drafting committe
Solve the rational equation:
5x/x+2 = 3x/x+1
Answer:
x = 1/2
Explanation:
5x/x + 2 = 3x/x + 1
do cross multiplication
(x + 2) * 3x = (x + 1) * 5x
3x^2 + 6x = 5x^2 + 5x
6x - 5x = 5x^2 - 3x^2
x = 2x^2
x/x^2 = 2
1/x = 2
1 = 2x
1/2 = x
need help asappppppp
Visible light, x-rays, and radio waves are forms of electromagnetic waves that can travel through vacuum and mater.
entropy is the amount of heat a system releases. true or false?
Answer:
The answer to this is FALSE.
mass of 1 kg is attached to a spring whose constant is 5 N/m. Initially, the mass is released 1 m below the equilibrium position with a downward velocity of 7 m/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 16 cos 2t + 4 sin 2t.
The equation of motion is given by:
x = e^(-t) [C1 cos 2t + C2 sin 2t] - 4/21 cos 2t + 8/21 sin 2t.
Mass, m = 1 kg
Spring constant, k = 5 N/m
Initial displacement, x = -1 m
Velocity, v = -7 m/s
The damping force is numerically equal to 2 times the instantaneous velocity.
So, damping coefficient, b = 2 m/s
For the given system, the equation of motion can be written as:
m d²x/dt² + b dx/dt + kx = f(t)
where,
m is the mass
b is the damping coefficient
k is the spring constant
f(t) is the external force
On substituting the given values in the equation of motion, we get:
1 d²x/dt² + 2 dx/dt + 5x = 16 cos 2t + 4 sin 2t ........ (i)
Let us assume a particular solution of the form:
x = Acos 2t + Bsin 2t
On substituting this in equation (i), we get:
-4A sin 2t + 4B cos 2t + 4A cos 2t + 4B sin 2t + 2(-2A sin 2t + 2B cos 2t) + 5(A cos 2t + B sin 2t) = 16 cos 2t + 4 sin 2t
Grouping the coefficients of cos 2t and sin 2t terms, we get:
-4A + 2B + 5A = 4..................(1)
4B - 2A + 5B = 0..................(2)
Solving the above two equations, we get:
A = -4/21B = 8/21
So, the particular solution is given by:
x = -4/21 cos 2t + 8/21 sin 2t
The general solution is given by the sum of the complementary function and the particular solution.
The complementary function can be obtained by solving the characteristic equation.
The characteristic equation is given by:
1 m² + 2 m + 5 = 0
On solving the above quadratic equation, we get:
m = -1 ± 2i
Therefore, the complementary function is given by:
x = e^(-t) [C1 cos 2t + C2 sin 2t]
where C1 and C2 are constants.
Substituting the values of A and B in the particular solution, we get:
x = -4/21 cos 2t + 8/21 sin 2t
The general solution is given by:
x = e^(-t) [C1 cos 2t + C2 sin 2t] - 4/21 cos 2t + 8/21 sin 2t
Hence, the equation of motion is given by:
x = e^(-t) [C1 cos 2t + C2 sin 2t] - 4/21 cos 2t + 8/21 sin 2t.
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Record the length of the line shown in centimeters.
7.30
7.12
7.3
7.28
Please help will be marked most brainlist !!
Zooming I. On the image the red line is just short of the 3rd line past the 7 so it is not 7.3 but just a little under.
Answer: 7.28
Most meteors burn up in the
Answer:
the Mesosphere
Most meteors burn up in the mesosphere. Unlike the stratosphere, temperatures once again grow colder as you rise up through the mesosphere.
Explanation:
Have a nice day
Answer:
The Mesosphere
Explanation:
It is the coldest layer.
A simple machine where an inclined plane is wrapped in a spiral is called a centripetal ramp.
T.
True
F.
False
Answer: False
Explanation:
Two blocks with masses m1= 4.5 kg and m2= 13.33 kg on a frictionless surface collide head-on. The initial velocity of block 1 is v→1,i= 4.36 i^ms and the initial velocity of block 2 is v→2,i=-5 i^ms. After the collision, block 2 comes to rest. What is the x-component of velocity in units of ms of block 1 after the collision? Note that a positive component indicates that block 1 will be traveling in the i^ direction, and a negative component indicates that block 1 will be traveling in the −i^ direction. Please round your answer to 2 decimal places.
Since a positive component indicates that block 1 will be traveling in the i^ direction, the answer is 4.51 i^. Therefore, the required answer is 4.51. Answer: 4.51.
When two blocks with masses m1 = 4.5 kg and m2 = 13.33 kg on a frictionless surface collide head-on, block 2 comes to rest.
The initial velocity of block 1 is v→1, i = 4.36 i^ ms and the initial velocity of block 2 is v→2, i = -5 i^ ms.
We are required to find the x-component of velocity in units of ms of block 1 after the collision.
We need to find the final velocity of block 1 after the collision. We can use the law of conservation of momentum to solve this problem.
The law of conservation of momentum states that the total momentum of an isolated system of objects with no external forces acting on it is constant. The total momentum before collision is equal to the total momentum after the collision.
Using the law of conservation of momentum, we can write:
\(m1v1i +m2v2i = m1v1f + m2v2f\)
where
v1i = 4.36 m/s,
v2i = -5 m/s,m1
= 4.5 kg,m2
= 13.33 kg,
v2f = 0 m/s (because block 2 comes to rest), and we need to find v1f.
Substituting the given values, we get:
4.5 kg × 4.36 m/s + 13.33 kg × (-5 m/s)
= 4.5 kg × v1f + 0
Simplifying, we get:
20.31 kg m/s
= 4.5 kg × v1fv1f
= 20.31 kg m/s ÷ 4.5 kgv1f
= 4.51 m/s
The x-component of velocity in units of ms of block 1 after the collision is 4.51 m/s.
Since a positive component indicates that block 1 will be traveling in the i^ direction, the answer is 4.51 i^.
Therefore, the required answer is 4.51. Answer: 4.51.
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You toss a walnut at a speed of 15.0 m/s at an angle of 50.0∘ above the horizontal. The launch point is on the roof of a building that is 20.0 m above the ground.
a)How long after it is launched does the walnut reach the ground?
b)How far does the walnut travel horizontally from launch point to landing point?
c) What are the horizontal and vertical components of the walnut’s velocity just before it reaches the ground? Suppose that the +y-axis is directed upward and the +x-axis is directed horizontally from the launch point toward the landing point.
Answer:
a.3.51s
b.33.8m
c. 9.64,-22.9
Explanation:
(a) The time taken be "3.5083 sec".
(b) The distance will be "33.82 m".
(c) The horizontal and vertical components be "9.64 m/s and -22.89 m/s".
Velocity and DirectionAccording to the question,
Speed, V₀x = 15 Cos (50.0°)
= 9.64 m/s
V₀y = 15 Sin (50.0°)
= 11.49 m/s
Vertical displacement = -20.0 m
(a) We know the relation between displacement, time and acceleration
→ y = vt + \(\frac{1}{2}\)at²
By substituting the values,
→ -20.0 = 11.49 t - 4.9 t²
4.9 t² - 11.49 t - 20.0 = 0
t = \(\frac{11.49 + \sqrt{132.02+392} }{9.8}\)
= \(\frac{11.49 + 22.89}{9.8}\)
= 3.5083 sec
(b) We know the formula,
Distance = Speed × Time
or,
→ X = 9.64 t
= 9.64 × 3.5083
= 33.82 m
(c) Again by using the above relation, we get
Vx = V₀x
= 9.64 m/s
Vy = V₀y - gt
By substituting the values,
= 11.49 - 9.8 × 3.5083
= 11.49 - 34.38
= -22.89 m/s
Thus the response above is correct.
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Choose the nonmetallic elements from the list. Check all that apply.
Yttrium
Oxygen
Boron
Polonium
Argon
Gallium
Carbon
Answer:
Oxygen, Argon, Carbon
edge2020
Answer:
carbon, oxygen, argon,
Explanation:
:)
WHAT IS COMPUTER ? EXPLAIN IT .
Answer: it's an electronic device
Explanation: it's where you store and process data, it acts according to the instructions given to it in a variable program.
Sorry if this wasn't the answer you were looking for.
The tape timer used in this experiment marks the paper tape with dots at fixed time intervals. How does it do that?.
The ticker tape is pulled through the timer once it's powered, which creates a dot along the length of this paper tape at fixed time intervals.
What is a ticker timer?A ticker timer can be defined as a scientific apparatus that is designed and developed to measure time in seconds. Thus, a ticker timer can be used to measure short intervals of time by making dots on a paper tape at regular (fixed) intervals.
By design, a ticker timer comprises a magnet, carbon paper disk and a ticker tape which is pulled through the timer once it's powered, so as to create a dot along the length of this paper tape at fixed time intervals.
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A 10-A current is maintained in a simple circuit with atotal resistance of 209 ohm. What net charge passes through any point in a circuit during a 1-minute interval?
Answer:
I = Q / t definition of current I
Q = i t = 10 Coul/sec * 60 sec = 600 Coul
A 10-A current is maintained in a simple circuit with a total resistance of 209 ohms, then the net charge passes through any point in a circuit during a 1-minute interval would be 6000 Coulombs.
What is an electric charge?Charged material experiences a force when it is exposed to an electromagnetic field due to the physical property of electric charge. You can have a positive or negative electric charge.
Electric current is defined as the charge per unit of time.
The mathematical relation between current and the electric charge
I =Q/T
Let us first convert the time period of minutes into seconds
1 min = 60 seconds
10 min = 10*60 seconds
=600 seconds
Q = I*t
=10*600
=6000 Amperes
Thus, the net charge that passes through any point in a circuit during a 1-minute interval would be 6000 Amperes.
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Why is the handle made of a different material than the rest of the pot?
Answer:
Hi there!
Your answer is:
The handle is made from a different material than the rest of the pot because you want to be able to safely move & touch the handle without getting burnt. The pot is made of conductors, like metal, to help it get hot quickly and cook evenly. You need to be able to touch the handle without being in danger, so the handle is made of an insulator, like wood, which doesn't get hot easily
I hope this helps!
Answer: the handle is made up of different material than the rest of the pot because the handle can conduct heat into your hand if its the same material.
For a constant applied force, how does increasing the mass of an object affect it acceleration?
particles q1=+18.1uC, q2=-11.2uC, and q3=+5.67uC are in a line. particles q1 and q2 are separated by 0.280m and particles q2 and q3 are separated 0.350m. what is the net force on particle q2?
The net electric force on particle q2 is 27.81 N.
What is the net force on the particle q2?The net force on the particle q2 is calculated by applying Coulomb's law of electrostatic force.
The force on particle q1 due to particle q2 is calculated as;
F ( 12 ) = kq₁q₂/r²
where;
q1 is the charge of particle 1q2 is the charge of particle 2r is the distance between particle 1 and 2k is Coulomb's constantF ( 12 ) = ( 9 x 10⁹ x 18 x 10⁻⁶ x 11.2 x 10⁻⁶ ) / ( 0.28² )
F ( 12 ) = 23.14 N
The force on particle q3 due to particle q2 is calculated as;
F (23) = kq₃q₂/r²
F (23) = (9 x 10⁹ x 5.67 x 10⁻⁶ x 11.2 x 10⁻⁶)/(0.35²)
F (23) = 4.67 N
The net electric force on particle q2 is calculated as follows;
F (net) = 23.14 N + 4.67 N
F (net) = 27.81 N
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How do i solve the eqaution (9/4x^2-1)-(3/2x-1)^2?
The solution to the equation (9/4x²-1) - (3/2x-1)² is x = 3/2.
To solve the equation (9/4x²-1) - (3/2x-1)², we can follow these steps:
Expand and simplify the expression within the parentheses.
(3/2x - 1)² = (3/2x - 1) * (3/2x - 1)
= (9/4x² - 3/2x - 3/2x + 1)
= (9/4x² - 6/2x + 1)
= (9/4x² - 3/x + 1)
Substitute the expanded expression back into the original equation.
(9/4x² - 1) - (9/4x² - 3/x + 1)
Simplify the expression by combining like terms.
Distribute the negative sign to every term within the second set of parentheses:
(9/4x² - 1) - 9/4x² + 3/x - 1
Combining like terms, we have:
9/4x² - 9/4x² + 3/x - 1 - 1
The x² terms cancel out, and we are left with:
3/x - 2
The equation is now simplified to 3/x - 2 = 0.
To solve for x, we can isolate the term with x by adding 2 to both sides:
3/x = 2
Then, we can cross multiply to solve for x:
3 = 2x
Finally, divide both sides by 2 to solve for x:
x = 3/2
Therefore, the solution to the equation (9/4x²-1) - (3/2x-1)² is x = 3/2.
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Co-efficient of volume expansion of
aluminium
The coefficient of volume expansion of a material is a measure of how much its volume changes with a change in temperature. For aluminium, the coefficient of volume expansion is approximately \(7.1 \times 10^{-5}\) per degree Celsius (\(K^{-1}\)).
For aluminium, the coefficient of volume expansion is approximately \(23.1 \times 10^{-6}\) per degree Celsius. This means that for every degree Celsius increase in temperature, the volume of aluminium will increase by approximately 23.1 parts per million (ppm).
This coefficient of volume expansion is an important property of aluminium, as it affects its behaviour in a variety of applications. For example, in the aerospace industry, aluminium is used extensively in the construction of aircraft because of its low weight and high strength-to-weight ratio. However, as the temperature of the aircraft changes during flight, the volume of the aluminium components will also change, potentially affecting the structural integrity of the aircraft.
Understanding the coefficient of volume expansion is therefore essential for engineers and designers working with aluminium in a variety of fields, from aerospace to construction to electronics.
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(ii) Let R be a rotation and S be a reflection of the euclidean plane E. Give a precise deion of RS, relating it to the classification of isometries of E². Be careful of special cases.
RS is a composition of rotation and reflection in the Euclidean plane E². The precise description of RS depends on the specific properties of the rotation R and reflection S.
In general, if R and S have the same axis or line of symmetry, the composition RS results in a translation. If R and S have intersecting lines of symmetry, RS yields a glide reflection. If R and S have perpendicular lines of symmetry, RS produces a rotation.
It is important to consider special cases, such as parallel lines of symmetry, coinciding axes, or perpendicular lines of reflection, as they may lead to different outcomes. The classification of isometries in E² involves understanding how rotations and reflections combine to create different transformations in the plane.
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