The acceleration due to gravity on the unfamiliar planet is approximately 9.72 m/s^2.
Given the time period (T) and the number of cycles (n), we can calculate the number of seconds per cycle (t) as:
t = T/n.
Plugging in the values from the problem, we get:
T = 141 s / 92 cycles = 1.54 s/cycle.
The acceleration due to gravity (g) on the unfamiliar planet can then be calculated as:
g = 4π^2 (L/T^2)
g = 4π^2 (53 cm / 1.54 s^2)
g = 9.72 m/s^2
Acceleration due to gravity is the acceleration of an object in a state of free fall. It is a measure of the strength of the gravitational field of a planet and is a constant value for all objects near the surface of the planet. On Earth, the acceleration due to gravity is approximately 9.8 m/s^2, or 32.2 ft/s^2.
The acceleration due to gravity determines the rate at which an object falls towards the Earth when it is in a state of free fall. The greater the acceleration due to gravity, the faster an object falls. This is why objects fall faster on planets with a stronger gravitational field than on planets with a weaker gravitational field.
The acceleration due to gravity affects the motion of objects in many ways. For example, it determines the trajectory of projectiles, such as arrows or rockets, and affects the period of a pendulum. It also determines the weight of objects, which is the force of gravity acting on the object.
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electrical power is the rate at which electrical energy is stored. the rate at which electrical energy is being wasted. the rate at which electrical energy is used. the rate at which electrical energy is transferred. t/f
This statement is True, electrical power is the rate at which electrical energy is stored. the rate at which electrical energy is being wasted. the rate at which electrical energy is used. the rate at which electrical energy is transferred.
Electrical energy is a type of energy that is produced by the movement of charged particles, such as electrons, in a conductor. It is a form of energy that can be converted into other forms of energy, such as heat, light, and motion, by the use of electrical devices.
Electrical energy is a crucial source of energy for modern societies, and it is used to power homes, businesses, and industries. It is generated from a variety of sources, including fossil fuels, nuclear energy, hydro power, wind power, and solar energy.
Electrical energy can be stored in batteries or in other forms of energy storage systems. It can also be transmitted over long distances through power lines and transformers, making it a highly efficient and convenient source of energy.
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consider the following problem. find the distance traveled in 23 seconds by an object traveling at a constant velocity of 21 feet per second. decide whether the problem can be solved using precalculus, or whether calculus is required. if the problem can be solved using precalculus, solve it. if the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Answer:
Below
Explanation:
Precalculus, pre-algebra math can be used to solve this
21 f/ s * 23 s = 483 ft
you are told to use gauss' law to calculate the electric field at a distance r away from a charged cube of dimension a. which of the following gaussian surfaces is best suited for this purpose?a sphere of radius R+ a/2a cube of dimension R + a/2a cylinder with cross sectional radius of R + a/2 and arbitrary lengthThis field cannot be calculated using Gauss' lawNone of the above
The best suited Gaussian surface for this purpose would be a sphere of radius R + a/2. Gauss' law states that the electric flux through any closed surface is proportional to the charge enclosed within that surface.
In this case, using a sphere as the Gaussian surface will enclose the entire charged cube, making it easier to calculate the electric field. The size of the sphere (R + a/2) should be chosen such that it is large enough to encompass the charged cube, but not so large as to include any other charged objects that might affect the electric field calculation. A Gaussian surface is a hypothetical surface used in physics to calculate the electric flux through a closed surface. Gaussian surfaces are often chosen for their symmetry and simplicity, and are used in conjunction with Gauss' law to calculate the electric field at a point in space. The electric flux through the Gaussian surface is proportional to the charge enclosed within the surface, and by measuring the electric flux, the electric field at the point of interest can be calculated.
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use the impulse-momentum theorem to find how long a stone falling straight down takes to increase its speed from 4.2 m/s to 10.0 m/s .
It takes the stone 0.588 seconds to increase its speed from 4.2 m/s to 10.0 m/s.
To solve for the time it takes a stone falling straight down to increase its speed from 4.2 m/s to 10.0 m/s using the impulse-momentum theorem, we can use the equation:
Δp = mΔv
where Δp is the change in momentum,
m is the mass of the stone, and Δv is the change in velocity.
The initial velocity of the stone is 4.2 m/s and the final velocity is 10.0 m/s, so the change in velocity is:
Δv = 10.0 m/s - 4.2 m/s = 5.8 m/s
Since the stone is only under the influence of gravity, we can assume that the net force acting on the stone is equal to its weight (mg), and therefore the change in momentum is:
Δp = mΔv
= m(10.0 m/s - 4.2 m/s)
= m * 5.8 m/s
We can use the above equation to find the time it takes for the velocity to change by solving for t:
t = Δp/F = Δp/(mg) = Δv/g
where t is the time, F is the net force (mg), and g is the acceleration due to gravity (9.8 m/s^2).
Substituting the values:
t = Δv/g = 5.8 m/s / 9.8 m/s^2 = 0.588 s
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you throw a rubber duck straight into the air and let it fall back down before you catch it. describe the direction of the velocity and acceleration vectors during the motion for the rubber duck. group of answer choices velocity and acceleration vectors will point in opposite directions for the whole motion. velocity and acceleration vectors will point in the same direction for the whole motion. velocity and acceleration will point in the same direction until the rubber duck falls back towards you. then, both vectors will then point in opposite directions. acceleration is zero for the whole motion. velocity and acceleration will point in opposite directions until rubber duck falls back towards you. then, both vectors will then point in the same direction.
As the ball is going upward, it is decelerating which is negative acceleration. The first option is the right answer.
What is Acceleration ?Acceleration can be defined as the velocity change per time taken. It is a vector quantity.
Given that a rubber duck is thrown straight into the air and allowed it to fall back down before catching it.
To describe the direction of the velocity and acceleration vectors during the motion for the rubber duck, the followings must be noted.
As the ball is going up, the velocity direction is opposite to the direction of acceleration because the ball will be decelerating. That is, velocity will be positive while acceleration will be negative. The reverse is the case when the ball is coming downward. That is, velocity will be negative while acceleration will be positive.
Therefore, velocity and acceleration vectors will point in opposite directions for the whole motion.
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A storm system moves 5000km due east, then shifts course at 40 degrees north of east for 1500km. Calculate the storm’s resultant displacement
A ball of mass m is thrown straight upward from ground level at speed vo. At the same instant, at a distance D above the ground, an- other ball of mass m is thrown straight down- ward toward the first ball, also at speed vo. Assume that gravity acts vertically downward on each mass m with a magnitude mg. Do te How far above the ground do the balls col- lide (in terms of only D, vo, and g)? Each ball has a diameter much smaller than the distance D 1. 2 (1부) g D 4. D 14 2 2 (222
As a result, the balls meet precisely at the height of the first ball's maximum height, given by h=(vo² / 2g)*0.5.
What is distance?The quantity or size of displacement between two places is defined as distance. It is important to note that the distance between two points is not the same as the distance traveled between them. The total length of the path traveled between two points is referred to as the distance traveled. Distance is the length of an object's route, whereas displacement is merely the distance between where the thing began and where it finished up. The complete length of an object's real route is referred to as distance. The displacement of an item between two places is the straight line (shortest) distance between those points, directed from one position to the other.
Here,
Let t be the time taken for the first ball to reach its maximum height, and let t' be the time taken for the second ball to reach the same height.
The first ball reaches its maximum height in t = vo / g, and the height of the second ball after t' seconds is given by,
h = D - (vo * t')² / 2g.
Setting t = t' and solving for t, we find that
t = (2D / g)*0.5.
The height of the first ball after t seconds is
h = vo * t - 0.5g * t²
= (vo² / 2g)*0.5 * (2D)*0.5 - 0.5g * (2D / g)
= (vo² / 2g - gD)*0.5.
The balls collide when h = 0, so
0 = (vo² / 2g - gD)*0.5.
Squaring both sides, we find
0 = vo² / 2g - gD.
Solving for D, we find
D = vo² / 2g * 2 = vo² / g.
So the balls collide exactly at the height of the first ball's maximum height, which is given by h = (vo² / 2g)*0.5.
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The speakers are now allowed to have different phase constants. They are adjusted so that you hear interference maxima when the adjustable speaker is at x = 0.6 m and again when it is at x = 1.05 m. What is the difference in the phase constant between the two speakers in rad?
Because of the distance between the and the in part A, the wavelength would be 0.6 m, thus my frequency would be 343 m/s / 0.6 m = 571.67 Hz (correct).
What does a wave's phase mean?A phase in electrical signalling is a wave's location on a waveform cycle at a specific instant in time. It offers a measurement in either degrees (0-360) or radians (0-2), depending on where the wave is in its cycle. A phase is one radian, or around 57.3 degrees.
Waves can group together into what are known as wave packets, and the speed at which a wave packet moves is referred to as group velocity. Phase velocity refers to the speed at which a wave's phase moves.
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A 7.5 kg box is sitting on a scale in an elevator. Before the elevator moves, the scale reads 73.58 N. When the elevator accelerates into motion, the scale momentarily reads 76.25 N. If the magnitude of the acceleration due to gravity is 9.81 m/s2, what is the acceleration of the elevator?
Group of answer choices
0.85 m/s2
0.36 m/s2
0.27 m/s2
0.59 m/s2
The acceleration of the elevator is 0.59 m/s^2.
What is acceleration?Acceleration is the rate of change of the velocity of an object with respect to time.
The acceleration of the elevator can be found using Newton's second law of motion, which states that the net force on an object is equal to its mass times its acceleration (F = ma). In this cases, the difference between the two readings on the scale is equal to the net force acting on the box, which includes the gravitational force and the upward force due to the acceleration of the elevator.
F = ma = (76.25 N - 73.58 N) / 7.5 kg = 0.59 m/s^2
Therefore, the acceleration of the elevator is 0.59 m/s^2.
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1.How is the frequency of a wave determined?
2. What is the period of a wave?
3. How do the frequency and period of a wave relate together?
4. What do mechanical waves require in order to transfer energy?
5. What are waves called that do not require a medium through which to travel?
) through which to travel.
6. The speed of mechanical waves depend upon the (
7. How do the direction of vibration and the direction of motion of a longitudinal wave compare?
8. How do the direction of vibration and the direction of motion of a transverse wave compare?
A wave is an energetic disturbance in a medium that doesn't include any net particle motion.
What are waves?
No physical thing travels along a wave as it carries information or energy between two points in the form of signals. A time factor is added to the equation to determine a wave's frequency. All of our wireless communications are entirely dependent on waves.
1. The number of wave crests (high points) that pass the fixed point in one second, or in any other time interval, can be used to calculate the frequency of a wave.
2. The time it takes for two successive crests (one wavelength) to pass a specified point.
3. They are related inversely f= 1/t
4. mechanical waves require medium.
5. Electromagnetic waves.
6. Medium
7. Parallel
8. Perpendicular
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a spring is hung from the ceiling. when a block is attached to its end, it stretches 2.3 cm before reaching its new equilibrium length. the block is then pulled down slightly and released. for help with math skills, you may want to review: solving radical equations for general problem-solving tips and strategies for this topic, you may want to view a video tutor solution of mass on a spring.
The length of a multi-mode optical fiber required to achieve an static mode dispersion from with a particular excitation state is referred to as the equilibrium length in some cases.
Equation of state equals balance?Equilibrium is the condition in which all of the forces acting on a body are perfectly balanced and the body is immobile. An object is considered to be in an equilibrium state when all of the forces acting on it are equal and in balance. Equilibrium is the state of a thing at rest.
What 3 categories of equilibrium exist?Equilibrium comes in three flavors: neutral, unstable, and stable. Figures are used to illustrate numerous examples throughout this module. A balanced system is shown in Figure 1 as a toy doll on a man's hand, that has its gravity center exactly over the pivot and zero torque due to the total weight.
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a pair of figure skaters are performing a spin maneuver. The axis of rotation goes through the left foot of the skater on the left. What
action could increase the pair's angular velocity?
Answer:
Angular momentum
Explanation:
Angular momentum is a conserved physical quantity, similar to the way that energy is a conserved quantity
which of the following interactions is the primary influence on the interaction between hydrophobic molecules in water? group of answer choices hydrogen bonding interactions electrostatic interactions covalent interactions van der waals interactions hydrophobic effect
The primary influence on the interaction between hydrophobic molecules in water is the E: "hydrophobic effect".
The hydrophobic effect refers to the tendency of hydrophobic (water-fearing) molecules to aggregate and minimize their exposure to aqueous environments, such as water. This interaction is primarily driven by van der Waals forces, which are weak attractive forces that occur between neutral molecules.
The hydrophobic effect is important in biochemistry as it plays a role in stabilizing the structures of proteins, lipids, and other biological molecules. By aggregating and reducing their exposure to water, hydrophobic molecules increase the stability of the overall structure, helping to preserve its functional integrity.
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Assume a 15 cm diameter wafer has a cost of 12, contains 84 dies, and has 0.020 defects/cm
2
.
Assume a 20 cm diameter wafer has a cost of 15, contains 100 dies, and has 0.031 defects/cm
2
.
a) Find the yield for both wafers.
As part of this problem, you will want to derive a formula for the die area (note that this will be an approximation).
Cost per die= cost per wafer / Dies per wafer X yield
dies per wafer =wafer area/ die area
yield= 1 / (1+ (defects per area X die area/2))
2
For both wafers, give your calculated value (use 3.14 for
π
) of die area (in cm
2
,
two decimal places) and the value of yield to four decimal places.
b) Find the cost per die for both wafers.
The problem does not specify the unit of cost (it is simply 12 and 15). Therefore, your answer will not have a specific unit either.
The yield to both wafer are Wafer 1: 0.959 and wafer 2 : 0.909. The cost per die for both wafers are wafer 1: 0.148 and wafer 2 : 0.165.
we need determine the yield to both wafer
yield= 1/(1+(defects per unit area*dies per unit area/2))²
Wafer 1:
Radius=Diameter/2=
Radius=15/2=7.5 cm
Total Area=πr²=π(7.5)²=176.71 cm^2
Area per dice= 176.71/84=2.1 cm²
yield 1= 1/(1+(0.020*2.1/2))²
yield 1=1/1.04244=0.959
Wafer 2:
Radius=Diameter/2=20/2=10 cm
Total Area=πr²=π(10)²=314.159 cm²
Area per die= 314.159/100=3.14 cm²
yield 2= 1/(1+(0.031x3.14/2))²
yield 2=1/1.0997=0.909
Then we can determine the cost per dies for both wafers.
Cost per die= cost per wafer/Dies per wafer*yield
Wafer 1:
Cost 1=12/84x0.959=0.148
Wafer 2:
Cost 2=15/100x0.909=0.165
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Aristotle represents what
Aristotle is a towering figure in ancient Greek philosophy, who made important contributions to logic, criticism, rhetoric, physics, biology, psychology, mathematics, metaphysics, ethics, and politics.
12.which of the following variations would increase the force experienced by the egg upon landing? select all that apply. increase the mass of the egg. decrease the mass of the egg. increase the drop height decrease the drop height. change the surface to a hard floor change the surface to a box of foam.
The following variations would increase the force experienced by the egg upon landing:
Increase the mass of the egg
Increase the drop height
Change the surface to a hard floor
And the following variations would decrease the force experienced by the egg upon landing:
Decrease the mass of the egg
Decrease the drop height
Change the surface to a box of foam.
Force experienced by an egg upon landing is determined by the formula: Force = mass x acceleration, where acceleration is due to gravity and is equal to 9.8 m/s².
Force is a physical quantity that measures the push or pull on an object. It is a vector quantity, meaning it has both magnitude and direction. Forces can cause an object to accelerate, change its shape, or alter its motion. There are several types of forces, including gravitational, electromagnetic, and strong and weak nuclear forces. The most commonly studied force is the force of gravity, which is the force that attracts two masses towards each other. Friction, air resistance, and tension are examples of contact forces, while the force exerted by a magnet is an example of a non-contact force. Newton's laws of motion describe the relationship between forces and motion, and are widely used in physics and engineering.
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Focal length of a convex lens in air is 25 cm. If it is immersed in water, then calculate the
focal length of the lens. (nw
=
4
3
, ng
=
3
2
)
Answer:the focal length of the convex lens in water is 33.33 cm.
Explanation:The formula for the change in focal length of a lens when it is immersed in a medium with a different refractive index is given by:
f' = f * (n2 / n1), where f is the focal length in air, n1 is the refractive index of air, and n2 is the refractive index of the new medium.
Given that n1 = 1 (refractive index of air) and n2 = 4/3 (refractive index of water),
f' = 25 * (4/3 / 1) = 25 * (4/3) = 33.33 cm
So, the focal length of the convex lens in water is 33.33 cm.
Using the right-hand rule, in which direction will the single wire move, and in which direction will the loop rotate?
Single Wire moves down, loop rotates left.
About single wireA single-wire system is a method of transmitting power or signals using only a single conductor. This is in contrast to the usual use of a pair of wires to provide a complete circuit, or an electrical cable containing (at least) two conductors for this purpose.
A single-wire transmission line is not the same as a single-wire earth return system. This is beyond the scope of this article. The latter system relies on reverse current flow through earth, using earth as a second conductor between earth terminal electrodes. A single-wire transmission line does not have a second conductor of any kind.
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wind energy is increasingly relied upon to help meet global energy needs. wind energy can be used to generate electricity using wind turbines. question which of the following best describes electricity generation using wind turbines?
The best describes electricity generation using wind turbines is: Wind turbines can be constructed on either vertical or horizontal axes. The correct option is B.
Axes of wind turbines can be either vertical or horizontal; there are benefits (and drawbacks) to each type. Turbines aligned on a horizontal axis are the primary type seen and are common in large-scale operations. Turbines with vertical axis blades are perpendicular to the ground and work well in more extreme conditions.
What is wind energy?Wind energy refers to the process of creating electricity using the wind, or air flows which happen naturally in the earth's atmosphere. Wind energy is produced by wind power. Modern wind turbines are used to collect kinetic energy from the wind and generate electricity.
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Although part of your question is missing, you might be referring to this full question: Wind energy is increasingly relied upon to help meet global energy needs. Wind energy can be used to generate electricity using wind turbines. Which of the following best describes electricity generation using wind turbines?
a. Newer wind turbines can generate consistent electricity even when there is no wind.
b. Wind turbines can be constructed on either vertical or horizontal axes.
c. Wind turbines are rarely used offshore because they tend to float in rough seas.
d. Wind turbines can be used by individual homeowners but have limited effectiveness when connected to the electrical grid.
Ancient astronomers knew about precession of the _, which means that as time passes, it points at a different O ecliptic, planet O north celestial pole, star O north pole, planet O celestial equator, star
Ancient astronomers knew about precession of the equinoxes, which means that as time passes, it points at a different star.
The north celestial pole currently points to within just 1° of the star Polaris. The North Pole of the Earth and the celestial equator are two other points of reference that ancient astronomers used to observe and measure the stars.
Precession of the ecliptic is a slow, continuous change in the orientation of Earth's axis of rotation, which causes the direction of the north celestial pole to slowly change over time. This phenomenon is caused by a combination of gravitational forces from the Sun, Moon, and other planets.
The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere.
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What is the gravitational force between two students if one has mass 75 kg and the other has mass 54 kg, and their centers are separated by a distance of 0.45 m?
The gravitational force between two students is 5.336*10^-8 N.
According to universal gravitational law, the force acting on two bodies is given by the formula = F = (G *m1*m2)/r^2
Here mass of one student =m1=75kg,another student m2=54kg
Distance of separation =0.45m, r =0.45/2=0.225m
Force = 6.67*10^-11 (75*54)/(0.225)^2
F=5.336*10^-8 N
The force between two students is 5.336*10^-8 N.
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25. a charged particle of mass m and charge q is travelling in a uniform magnetic field with speed v such that the magnetic force on the particle is f. the magnetic force on a particle of mass 2m, charge q and speed 2v travelling in the same direction in the magnetic field is
As a result, the magnetic force acting on the second particle is twice as powerful as the magnetic force acting on the first particle.
What is magnetic field?A magnetic field is a vector field that explains the magnetic impact on moving charges, currents, and magnetic materials. A moving charge in a magnetic field is subjected to a force that is perpendicular to both its own velocity and the magnetic field. Magnetic fields form anytime charge moves. The intensity of a magnetic field grows as more charge is moved. Magnetism and magnetic fields are manifestations of the electromagnetic force, one of nature's four basic forces.
Here,
The magnetic force on a charged particle is given by the equation:
f = qvB
where f is the magnetic force, q is the charge, v is the velocity of the particle, and B is the magnetic field strength.
For the first particle, the magnetic force is:
f = qvB
For the second particle, the magnetic force is:
f' = q(2v)B = 2qvB = 2f
As a result, the magnetic force on the second particle is twice as strong as the magnetic force on the first particle.
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suppose you carry a box of mass 8m a distance of d, and another box of mass 3m a distance of 2d in the same amount of time. compare the work done and power required.
The work done and power required for mass1 is more when compared to mass2. workdone of mass1 and mass2 are 8mgd & 6mgd. Power required of mass1 and mass2 are 8mgd/t & 6mgd/t.
How is the velocity of work related?vi is the beginning speed of an item in metres per second. In accordance with the work-energy principle, a particle's change in kinetic energy is equivalent to the sum of all the loads exerted on it, or the work of the force applied F(in subscript resultant).
Mass1 = 8m; d1 => d
Mass 2 = 3m; d2=>2d
The time take for both the mass to travel is same.
Work done by mass1 = m1xgxd1
=> 8mgd
Work done by mass2 = 3mxgx2d
=> 6mgd
Power required mass1 => W/t = 8mgd/t
mass2 => W/t => 6mgd/t
What is power, exactly?In science and engineering, power is the rate during which work is completed or energy is delivered. It may be expressed as the product of the work completed (W) or the energy transferred (E) divided by the time interval (t), or W/t.
What drives the action of force x distance?Every time a force pushes something over a distance, work is done. By multiplying the force by the distance travelled in the force's direction, you may calculate the energy transferred, or work done.
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while sitting on a dock of the bay, you notice a series of waves going past. you observe that 11 waves go past you in 45 s and that the distance from one crest to the next trough is 3.0 m.
The period of the wave is 4.1s and the speed of these waves is found to be 1.44m/s.
What is the formula for the relationship between frequency and velocity?A wave's fundamental property is frequency. It is a method for determining how many waves pass through a point in a certain amount of time. The distance that a point on a wave moves determines its velocity. The relation between frequency and velocity for every wave is normally proportional.
Period = T= t/n = 45/11 = 4.1s
Frequency => f = 1/T => 1/4.1 => 0.24Hz
The distance from one crest to the next trough is mentioned as 3.0 m. Hence, The wavelength λ = 2 x 3m = 6m
Speed of the wave v = λ xf => 6x 0.24 => 1.44m/s
How many waves of water pass a particular location in a given time?Wave frequency is the quantity of waves that move past a specific place in a specified amount of time. The number of wave crests (high points) that pass the reference position in one second, or in any other time interval, can be used to calculate the frequency of a wave. The frequency of the waves rises as the number rises.
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while sitting on a dock of the bay, you notice a series of waves going past. you observe that 11 waves go past you in 45 s and that the distance from one crest to the next trough is 3.0 m.
Find the (a) period, (b) frequency, (c) wavelength, and (d) speed of these waves.
to find the distance traveled, use the formula that expresses the distance d in terms of the velocity r and time t.True or False
When using a constant velocity, the equation for length as a time function is the simplest. Therefore, D(t) = Vt Read "distance... " where D(t) is distance.
How do you calculate the distance travelled?
Just use formula that defines the distance (d) in term of the velocity (r) and time (t) to determine the distance travelled. False or True Use the formula d = str, or distance equal speed times time, to find the distance. Since both represent a certain amount of distance per unit of time, such as miles an hour or kilometres per hour, rate and velocity are comparable.
How do you calculate the distance travelled?
Use the equation that gives to determine the distance travelled in this example
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Answer:
True
Explanation:
the answer is true
A 508g mass oscillates with an amplitude of 13.0cm on a spring whose spring constant is 23.0N/m . A. Determine the period T= ....... s B. Determine the maximum speed Vmax= ...... m/s C. Determine the total energy Wtotal= ........ J
The period T = 0.933 sec ; The max speed Vmax = 0.87m/s; The total energy or work done = 0.211J.
Is time a fixed quantity in SHM?For a single particle conducting SHM, the only constant is its periodic time, or simply time period. Due of the solutions' flexibility in scaling, the period remains constant. Therefore, you can scale this motion upward or downward by any factor s and still obtain a valid motion s if you have any valid motion (t) representing the pendulum's angle as a function of time t. (t).
K= string constant = 23N/m
Amplitude a => 13 cm
Mass = 508g
T= 2π√(m/k)
=> 2π √(0.508/23) => 0.933 sec
Maximum speed => √(k/m) x a
=> √(23/0.508) x 0.13
=> 0.87m/s
The total energy of string => 1/2 k a^2
=> 1/2 x 23x 0.13^2
=> 0.211J
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the 20-kg chandelier is suspended from the wall and ceiling using rods ab and bc , which have diameters of 3 mm and 4 mm , respectively. (figure 1)
So the angle u required to have the same average normal stress in both rods is tan^(-1) (16/9).
What is stress?In physics, stress is defined as the force acting on a material's unit area. Strain is the term used to describe the effect of stress on the body. Stress can cause physical deformities. The total force exerted per unit area is defined as stress. In terms of units, stress equals pressure (Newtons per meter).
Here,
The average normal stress in both rods can be calculated using the equation for stress, σ = F/A, where F is the force and A is the cross-sectional area. The force can be calculated from the weight of the chandelier, W = m * g, where m is the mass and g is the acceleration due to gravity.
Let's call the angle between the rod AB and the vertical axis u. The forces in the two rods can then be calculated as follows:
F_AB = W * sin(u)
F_BC = W * cos(u)
Next, we need to find the cross-sectional area of each rod:
A_AB = π * (d_AB/2)^2
A_BC = π * (d_BC/2)^2
where d_AB and d_BC are the diameters of rods AB and BC, respectively. Substituting these values into the equation for stress:
σ_AB = F_AB / A_AB
σ_BC = F_BC / A_BC
For the average normal stress in both rods to be the same, we need to set σ_AB = σ_BC and solve for the angle u:
σ_AB = σ_BC
F_AB / A_AB = F_BC / A_BC
W * sin(u) / (π * (d_AB/2)^2) = W * cos(u) / (π * (d_BC/2)^2)
Solving for the angle u, we find:
tan(u) = (d_BC/2)^2 / (d_AB/2)^2 = (4/3)^2
u = tan^(-1) (16/9)
So the angle u, such that the average normal stress in both rods is the same, is equal to tan^(-1) (16/9).
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complete question:
The 20-kg chandelier is suspended from the wall and ceiling using rods AB and BC , which have diameters of 3 mm and 4 mm, respectively. Determine the angle u so that the average normal stress in both rods is the same.
Extreme-sports enthusiasts have been known to jump off the top of El Capitan, a sheer granite cliff of height 910 m in Yosemite National Park. Assume a jumper runs horizontally off the top of El Capitan with speed 4.0 m/s and enjoys a free fall until she is h = 150 m above the valley floor, at which time she opens her parachute.
So the jumper falls from the summit of El Capitan to a height of 150 m in 4.1 seconds, at which time she releases her parachute.
What is free fall?An item falling in a vacuum is subject to just one external force, gravitational force, which is quantified as the object's weight. A free falling object is one that moves only due to the effect of gravity, and its motion is defined by Newton's second law of motion. A body is considered to be in freefall when it moves only under the influence of Earth's gravity. The ball's motion will be accelerated by an external force operating on it. This free-fall acceleration is also known as gravity acceleration.
Here,
The time taken for the free fall from the top of El Capitan to a height of h = 150 m can be calculated using the kinematic equation:
h = vi * t + (1/2) * g * t^2
where h is the height, vi is the initial vertical velocity (0 m/s), g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken. Solving for t, we get:
t = sqrt(2 * h / g)
Plugging in h = 150 m and g = 9.8 m/s^2, we get:
t = sqrt(2 * 150 m / 9.8 m/s^2)
t = 4.1 s
So, it takes 4.1 seconds for the jumper to fall from the top of El Capitan to a height of 150 m, at which point she opens her parachute.
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when the following metals are heated in a flame, they give off characteristic colored light. which metal gives off light with the shortest wavelength?
What happens to the period of the Earth if the mass of the Earth is reduced to ½?
What happens to the period of the Earth if the mass of the Earth is doubled?
If the mass of the Earth is reduced to ½, time period increases √2 times.
If the mass of the Earth is doubled, time period decreases 1/√2 times.
What is time period?The Time Period is the length of time required for a single full oscillation to take place. T stands for it. Seconds are its measure.
Time period of earth's rotation is inversely proportional to the square root of mas of the Earth.
Hence,
if the mass of the Earth is reduced to ½, time period increases √2 times.
If the mass of the Earth is doubled, time period decreases 1/√2 times.
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