Answer: 0.497 J
Explanation:
Spring energy
Spring energy is stored in a compressible or stretchable object like a spring or rubber band.
The work done on a spring in changing its original length is converted to its elastic potential energy or spring energy.
Given -
The spring constant is k = 20N/m,
The initial stretch is x1 = 0.16m,
The additional stretch is x2 = 0.063m,
W = 0.5k (x1 + x2)^2 - 0.5k x1^2
W = 0.5 (20 N/m) (0.16m + 0.063m)^2
W = 0.497 J
A 117-lb student races up stairs with a vertical height of 5.7 m in 5.5 s to get to a class on the second floor. How much power in watts does the student expend in doing work against gravity?
Work = (117 lbs) * (1 kg / 2.2046 lbs) * (9.81 m/s^2) * (5.7 m) = 296.8 J where 1 lb = 0.4536 kg. The time it takes for the student to climb the stairs he takes 5.5 seconds, so:
Power = work done / time taken = 296.8 J / 5.5 seconds ≈ 54 W So the power consumed by the student climbing the stairs is about 54 watts.
What is Acceleration?
Acceleration, the rate of change of velocity over time for both velocity and direction. A point or object moving in a straight line accelerates as it accelerates or decelerates. Circumferential motion is accelerated because it always changes direction even at constant velocity.
What is example acceleration?
If an object accelerates and moves in a positive direction, you have positive acceleration. The car accelerating in the first example is an example of positive acceleration. The car is moving forward and accelerating in the positive direction, so the acceleration is in the same direction as the car is moving.
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explain the similarities and differences between the observations that supported the geocentric models of the solar system and the phenomena described in the table.
Answer:
The geocentric model says that the earth is at the center of the cosmos or universe, and the planets, the sun and the moon, and the stars circles around it. The early heliocentric models consider the sun as the center, and the planets revolve around the sun.
An Atwood machine is constructed using two
wheels (with the masses concentrated at the
rims). The left wheel has a mass of 2 kg and
radius 23.1 cm. The right wheel has a mass of
2.1 kg and radius 30.77 cm. The hanging mass
on the left is 2 kg and on the right 1.69 kg.
Answer:ruedas (con las masas concentradas en las llantas). La rueda izquierda tiene una masa de 2 kg y un radio de 23,1 cm. La rueda derecha tiene una masa de 2,1 kg y un radio de 30,77 cm. La masa colgante de la izquierda es de 2 kg y la de la derecha de 1,69 kg.
Explanation:
What is the integral of the function x^4 in the interval from c to d?
The limit integral of function x⁴ from c to d is [ d⁵-c⁵]/5.
What is integration?In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data.
Integration is the action of locating integrals. . In addition to differentiation, integration is a fundamental, crucial calculus operation that helps to solve issues with the area of an arbitrary form.
The limit integral of function x⁴ from c to d is:
[tex]\int\limits^c_d {x^4} \, dx[/tex]
[tex]= [\frac{x^5}{5} ]_{x=c}^{x=d}[/tex]
= [ d⁵-c⁵]/5
Hence, the limit integral of function x⁴ from c to d is [ d⁵-c⁵]/5.
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What are centripetal acceleration and centripetal force?derive their equations.
The acceleration in uniform circular motion is centripetal acceleration. a c =v 2 /r or a c =rω 2 where v is linear velocity, ⍵ is angular velocity, and r is radius of curvature. Then centripetal force formula of linear velocity is given by: F c =m v 2 /r.
▾ Part A
Calculate the quantity of heat absorbed by 50 g of water that warms from 30°C to 90°C.
Express your answer in calories.
* Q = ___ cal
The quantity of heat absorbed by 50 g of water that warms from 30°C to 90°C is 12552J.
How to calculate heat energy?The amount of heat absorbed or released by a substance can be calculated by using the following formula;
Q = mc∆T
Where;
Q = quantity of heat absorbed or released (J)m = massc = specific heat capacity∆T = change in temperatureAccording to this question, 50g of water warms from 30°C to 90°C. The quantity of heat absorbed is as follows:
Q = 50 × 4.184 × {90°C - 30°C}
Q = 209.2 × 60
Q = 12552J
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A volume of gas starts at a pressure of 10 atmospheres (atm) and a temperature of 27°C. If the temperature is increased by 75°C and the volume of the gas remains constant, what is the new pressure?
Answer:
the new pressure is 11.64 atmospheres.
Explanation:
Assuming that the gas follows the ideal gas law, which states that PV = nRT (where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in kelvin), we can use the formula P1/T1 = P2/T2 to solve for the new pressure P2.
Converting the initial temperature of 27°C to kelvin, we get T1 = 27°C + 273.15 = 300.15 K. Increasing the temperature by 75°C gives us the new temperature T2 = 300.15 K + 75°C = 348.15 K.
Using the formula, we can solve for P2:
P1/T1 = P2/T2
10 atm/300.15 K = P2/348.15 K
Simplifying the equation, we get:
P2 = (10 atm * 348.15 K) / 300.15 K
P2 = 11.64 atm (rounded to two decimal places)
Therefore, the new pressure is 11.64 atmospheres.
You encounter a moving walkway taht is 85m long and has a speed of 1.9m/s relatice to the ground. How long will it take you to cover the 85m length of the walkway if, once you get on the walkway, you immediately turn around and start walking in the opposite direction with a speed of 1.4 m/s relative to the walkway
It will take you 24.6 sec to cover the 85m length of the walkway.
What does the word "speed" mean?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
The term "displacement" refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes.
V = 85m / 68s. = 1.25m/s Walking on ground.
t = d / V = 85m / (2.2+1.25)m/s = 24.6s.
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Two rivers have the same volume of water flow over time but fall from different heights to power hydroelectric turbines. Which river would provide the most power? Explain why you chose that answer, describing the water's kinetic energy, potential energy and the law of conservation of energy.
The higher the water fall, the more the HEP produced.
What does the height of the water fall have to do with the HEP?The height of a waterfall is directly related to the potential energy of the water and the amount of hydroelectric power (HEP) that can be generated from it. Hydroelectric power is generated by harnessing the energy of falling water to generate electricity. The height of the waterfall determines the potential energy of the water, which is then converted into kinetic energy as the water falls and drives a turbine.
The higher the waterfall, the more potential energy the water has, and the more kinetic energy it can generate as it falls. This means that a taller waterfall has the potential to generate more hydroelectric power than a shorter waterfall.
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An ideal gas is compressed at constant pressure to one-half its initial volume. If the pressure of the gas is 120 kPa, and 760 J of work is done on it, find the initial volume of the gas.
The work done on the gas can be calculated using the equation: W = -PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume. so the initial volume of gas is [tex]12.67 m^{3}[/tex]
For the given conditions, the work done is 760 J, the pressure is 120 kPa, and the change in volume is -1/2 the initial volume, so:
760 = -120 kPa * (V_initial / 2)
Expanding the right side of the equation:
760 = -60 kPa * V_initial
Dividing both sides by -60 kPa:
V_initial = [tex]760 / (-60 kPa) = 12.67 m^3[/tex]
So the initial volume of the gas is [tex]12.67 m^3.[/tex]
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A stationary mass explodes in to two parts of masses 2kg and 1kg if the smaller mass has a kinetic energy of 400J. What is the kinetic energy of the larger mass?in physics
200J is the correct answer
What is Kinetic Energy ?
Kinetic energy is the energy an object possesses due to its motion. It is a scalar quantity and is proportional to the object's mass and the square of its velocity. The equation for kinetic energy is given by:
KE = 0.5 * m * v^2
where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
Kinetic energy is a measure of an object's ability to do work, as it can be transferred to other objects through collisions or other interactions. The total energy of a system is conserved, so an increase in an object's kinetic energy corresponds to a decrease in another form of energy, such as potential energy.
K.E=400J=1/2x1xV^{2}
V=\sqrt{800}
Applying conservation of momentum
maVa+ mbVb=0 ; Va=\sqrt{200}
Therefore ; K.E of larger mass = 1/2x2x200 = 200 J
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A person jumps off a diving board 4.1 mm above the water's surface into a deep pool. The person's downward motion stops 2.3 mm below the surface of the water. Estimate the average deceleration of the person while under the water.
The average deceleration of the person while underwater can be estimated as 875 m/s².
To calculate the average deceleration, we need to find the change in velocity over the change in time. The change in velocity can be calculated as the initial velocity (which is assumed to be zero) minus the final velocity, which is the velocity just before the person stops moving downward. The change in time can be found by subtracting the starting height from the stopping height.
Starting height = 4.1 mm = 4.1 × 10⁻³ m
Stopping height = 2.3 mm = 2.3 × 10⁻³ m
Change in velocity = final velocity - initial velocity
Change in velocity = 0 m/s - (-√(2gh))
Change in velocity = √(2gh)
where g is the acceleration due to gravity (9.8 m/s²) and h is the height (4.1 mm)
Change in velocity = √(2 × 9.8 × 4.1 × 10⁻³)
Change in velocity = √(79.26 × 10⁻³) = 8.9 m/s
Change in time = final time - initial time
Change in time = 0 s - (stopping height - starting height)
Change in time = (starting height - stopping height)
Change in time = 4.1 × 10⁻³ - 2.3 × 10⁻³ = 1.8 × 10⁻³ s
Change in time = 1.8 × 10⁻³ s
Average deceleration = change in velocity / change in time
Average deceleration = √(2 × 9.8 × 4.1 × 10⁻³) / (h2 - h1)
Average deceleration = 8.9 / (1.8 × 10⁻³)
Average deceleration = 875 m/s²
Therefore, the average deceleration is estimated at 875 m/s².
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while big-o notation is used to measure the worst-case complexity of our code, we may also choose to assess the best-case complexity using big-theta notation.
While big-o notation is used to measure the worst-case complexity of our code, we may also choose to assess the best-case complexity using big-theta notation. The statement is true.
Big-Theta notation is used to measure the average-case complexity of an algorithm. It provides an upper and lower bound on the growth rate of the algorithm, expressing it as the tightest asymptotic bound.
This means that the running time of an algorithm expressed in big-Theta notation lies within a constant factor of the actual running time. For example, if the running time of an algorithm is O(n²) and Θ(n²), it means that the algorithm's running time grows proportional to n², but with a constant factor that is not necessarily equal to 1.
Thus, big-Theta notation provides a more accurate representation of the algorithm's running time compared to big-O notation which only provides an upper bound.
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Your question seems incomplete, but I suppose the question was:
"While big-o notation is used to measure the worst-case complexity of our code, we may also choose to assess the best-case complexity using big-theta notation. True or false."
Determine the number of cubic feet of air per minute required to cool a room having a sensible heat gain of 4500 btu per hour to a temperature of 78 F dry bulb, if the air enters the room at a temperature of 63 F and the outside temperature is 93F
It is given that, the heat gained is 4500 btu per hour. The temperature difference here is 30 F and the specific heat of air is 0.24 btu/lb°F. Then the cubic feet of air per minute is 138.8 CFM.
What is sensible heat transfer ?The sensible heat transfer in a system can be calculated using the equation below:
q = CFM × 1.08 ×ΔT
q = CFM x 0.075 lb/ft3 x 60 min/hour x 0.24 btu/lb°F x ∆T
where, 0.24 btu/lb°F is the specific heat of the dry air.
Given that q = 4500 btu/hour.
temperature difference = 93 F - 63 F.
Then 4500 btu/hr = CFM × 1.08 × 30 F
CFM of air = 4500 btu/hr /(1.08 × 30 F ) = 138.8 CFM.
There for the number of cubic feat of air per minute is 138.8.
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A car takes off at a speed of 45 m/s. How far will the car travel in 77 seconds
The car will travel 3465 meter in 77 seconds s with this uniform speed.
What is speed?Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.
Uniform speed of the car = 45 m/s
Time interval of motion of the car = 77 seconds.
Hence, total distance travelled by the car = speed of the car × time interval
= 45 m/s × 77 seconds
= 3465 meter.
Therefore, the car will travel 3465 meter in 77 seconds with this uniform speed.
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show that the distance d between adjacent planes of index number hkl is given in terms of the cube ha by d= a/(h2 +u2+l2)1/2
To show that the adjacent planes is gin terms of the cube by d= a/(h2 +u2+l2)1/2, we have to fully analyse it. Therefore, let's go straight to the explanation.
Distance equationThe distance "d" between adjacent planes in a crystal lattice is given by the equation:
d = a / (h^2 + k^2 + l^2)^(1/2)
where "a" is the lattice parameter (length of one side of the unit cell) and (h,k,l) are the indices of the crystal plane. The indices specify the orientation of the plane in the crystal lattice and are related to the Miller indices of the plane.
The equation shows that the distance between the planes is inversely proportional to the square root of the sum of the squares of the indices.
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Analyze the word to determine its Greek prefix. Then use your understanding of the prefix meaning to choose the
correct meaning of the word.
analgesic
a medicine to increase hearing ability
a medicine to remove pain
a mixture of paint and linseed oil
The meaning of the word, " analgesic " is B. a medicine to remove pain.
What is an analgesic ?Any substance used to relieve pain is referred to as an analgesic drug, also known as an analgesic, analgaesic, pain reliever, or painkiller.
Analgesics, commonly known as painkillers, are drugs that treat a variety of pains, such as headaches, injuries, and arthritis. Both opioid analgesics and anti-inflammatory analgesics alter how the brain interprets pain. Some analgesics, such as stronger OTC medicines, combination analgesics, and all opioids, must be purchased with a prescription.
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A man pushes a lawn mower on a level lawn with a force of 186 N. If 26% of the force is directed horizontally, how much work is done by the man in pushing the mower 6.5 m?
Answer:
Work = 1243.17 J
Explanation:
Work = Force × Distance × Cosine (Angle)
Work = 186 N x 6.5 m x Cosine (26°)
Work = 186 N x 6.5 m x 0.906
Work = 1243.17 J
At the county fair, Chris throws a 0.15kg baseball at a 2.5kg wooden milk bottle, hoping to knock it off its stand and win a prize. The ball bounces straight back at 15% of its incoming speed, knocking the bottle straight forward.
Part A
What is the bottle's speed, as a percentage of the ball's incoming speed?
6.6% is the percentage of bottle speed to ball entry velocity.
What is the simple definition of velocity?
Velocity is defined as: The rate of change of the object's position in any direction. Velocity is measured as the ratio of distance traveled and time traveled. Velocity is a scalar quantity because it has only direction and not magnitude.
What are the some examples of speed?
If you know the distance an object travels in a given time, you can find the speed of the object. For example, if a car travels 70 miles in one hour he travels 70 miles per hour (miles per hour).
Why measure speed?
Measuring movement speed can be very useful in saving time. A speedometer is used to measure speed of an car. An odometer is useful for measuring mileage.
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A hockey player hits a hockey puck sitting at rest and applies an average force of 440.0 N to the 0.15 kg
hockey puck for a time of 0.01 seconds. How fast does the puck go after the hit in m/s?
Answer:
29.333
Explanation:
This is a standard F=ma problem which then uses kinematics.
The 440 newtons is the force applied to the puck, the mass is the mass obviously. F+ma turns into A=F/m, A=440/.15 which equals 2933.333.
Vf=Vi+aT.
Vi=0, A=2933.333, T=.01
Vf = 29.333
given planet mass, radius, object mass, and height how to find gravitational force acting on the object
The gravitational force (F) acting on an object can be calculated using the formula:
What is gravitational force?
Gravitational force is the force of attraction between two masses that results from the interaction of their gravitational fields. This force is proportional to the product of their masses and inversely proportional to the square of the distance between them.
[tex]\mathbf{F = G \times (m_1 \times m_2) / r^2}[/tex]
Where:
G is the gravitational constant (approximately equal to 6.67 x 10⁻¹¹ N m² / kg²)m1 is the mass of the planetm2 is the mass of the objectr is the distance between the centre of the planet and the center of the objectTo find the gravitational force, you need to know the mass of the planet and the object, as well as the radius of the planet and the height of the object above the planet's surface. The distance between the center of the planet and the center of the object can be calculated as:
r = R + h
Where:
R is the radius of the planeth is the height of the object above the planet's surfaceSo, substituting r into the formula for the gravitational force, you get:[tex]\mathbf{F = G \times (m_1 \times m_2) / (R+h)^2}[/tex]
Now you can substitute in the values for the mass, radius, and height to find the gravitational force.
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Open the phase diagram for CO2 given in the introduction again. Use the phase diagram for CO2 in the interactive activity and determine which of the following statements are correct. CO2 is a gas under normal conditions of temperature and pressure.
All three phases of CO2 exist simultaneously at the triple point. When the pressure is 4 atm and the temperature is more than −56.7∘C, CO2 exists as a solid. When the pressure is 1 atm, there is no temperature at which the liquid phase of CO2 exists.
Movement across boundary line BO corresponds to a phase change.
CO2 forms a supercritical fluid at temperatures less than 31∘C.
The correct statements about the phase diagram for CO₂ from the given options are as follows:
All three phases of CO₂ exist simultaneously at the triple point.When the pressure is 1 atm, there is no temperature at which the liquid phase of CO₂ exists.CO₂ is a gas under normal conditions of temperature and pressure.Movement across boundary line BO corresponds to a phase change.The correct options are A, B, C, and D.
What is CO2's triple point?The parameters of temperature and pressure at which CO₂ is simultaneously present in all three physical states of matter are referred to as the triple point of CO₂.
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show that, according to the distortion-energy criterion, the yield stress in plane strain is 1.15y, where y is the uniaxial yield stress of the material.
The value of Ey is greater than 1, it follows that:
σ = y * √(Ey / 1) > y
According to the distortion-energy criterion, the yield stress in plane strain is greater than the uniaxial yield stress, and is typically taken as 1.15y, where y is the uniaxial yield stress of the material.
Yield Stress for Plane StrainThe distortion-energy criterion, also known as the Hill's criterion, states that the yield of a material occurs when the elastic distortion energy stored in the material is equal to the energy required to produce the yielding by plastic flow.
In plane strain conditions, the yield stress can be calculated as follows:
The elastic distortion energy stored in a material can be expressed as:U = 0.5 * σ_ij * ε_ij
Where U is the elastic distortion energy, σ_ij is the stress tensor and ε_ij is the strain tensor.
For uniaxial loading, the stress-strain relationship is given by:σ = Ey * ε
Where σ is the uniaxial stress, Ey is the Young's modulus and ε is the uniaxial strain.
Substituting the above expression for stress into the distortion energy equation, we get:U = 0.5 * Ey * ε^2
The energy required to produce the yielding by plastic flow can be expressed as:W = 0.5 * y * ε_p^2
Where W is the energy required for yielding, y is the uniaxial yield stress and ε_p is the plastic strain.
Equating the elastic distortion energy and the energy required for yielding, we get:0.5 * Ey * ε^2 = 0.5 * y * ε_p^2
Dividing both sides by 0.5 * ε^2, we get:Ey = y * ε_p^2 / ε^2
Substituting the definition of the uniaxial strain, we get:Ey = y * ε_p^2 / (ε/Ey)^2
Simplifying the above expression, we get:Ey = y * ε_p^2 * Ey^2 / ε^2
Finally, dividing both sides by Ey, we get:1 = y * ε_p^2 / ε^2
Rearranging, we get:ε^2 = y * ε_p^2 / 1
Taking the square root of both sides, we get:ε = √(y * ε_p^2 / 1)
Since ε = σ/Ey, substituting the uniaxial stress-strain relationship, we get:σ/Ey = √(y * ε_p^2 / 1)
Multiplying both sides by Ey, we get:σ = Ey * √(y * ε_p^2 / 1)
Finally, substituting the value of Ey, we get:σ = y * √(Ey / 1)
Since the value of Ey is greater than 1, it follows that:σ = y * √(Ey / 1) > y
Therefore, according to the distortion-energy criterion, the yield stress in plane strain is greater than the uniaxial yield stress, and is typically taken as 1.15y, where y is the uniaxial yield stress of the material.
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Four lightweight balls A, B, C, and D are suspended by threads. Ball A has been touched by a plastic rod that was rubbed with wool. When the balls are brought close together, without touching, the following observations are made: Balls B, C, and D are attracted to ball A. Balls B and D have no effect on each other. Ball B is attracted to ball C.
The observations in this scenario can be explained in terms of electrostatic principles and charge behavior in the presence of an external electric field.
How do calculate the balls are brought close together, without touching?This is an example of an electrostatic interaction involving charge. Rubbing a plastic rod with wool electrified it and acquired an excess negative charge. This left an excess positive charge on the wool.
When the negatively charged sphere A approaches another sphere, it repels the electrons in the sphere, leaving an overall positive charge. Therefore, balls B, C, and D are attracted to ball A. Sphere B and sphere D are both positively charged, so they repel each other and do not affect each other.
Ball B is attracted to ball C because it has the opposite charge. Ball C is attracted to ball A, but ball B is not attracted to ball A. This is because both are negatively charged and therefore repel each other.
Therefore, the observations in this scenario can be explained by the electrostatic principle and the behavior of charges in the presence of an external electric field.
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Select the correct answer from each drop-down menu. What procedure is necessary when a person does not have a heartbeat? Martin, a caregiver, finds five-year-old Jessa unconscious and not breathing, Martin performs CPR balance Jessa's body fluids start Jessa's lungs manually circulate Jessa's blood and keep oxygen flowing Reset Next to help
Answer:
need points srr
Explanation:
For a simple harmonic oscillator, which of the following pairs of vector quantities can’t both point in the same direction? (The position vector is the displacement from equilibrium.) (a) position and velocity (b) velocity and acceleration (c) position and acceleration
The restoring force and acceleration are always in the same direction for a simple harmonic oscillator.
A simple harmonic oscillator is what?
A driven or dampened oscillator is known as a simple harmonic oscillator. It typically consists of a mass "m" that is pulled in the direction of the point x = 0 by a single force "F" that solely depends on the body's position "x" and a constant "k."
Consider a straightforward pendulum that displays SHM at low displacements. The location vector points upward while the acceleration and velocity vectors point downward during the downswing. The acceleration vector points downward while the location and velocity vectors point upward during an upswing. Therefore, unless they are both 0 at equilibrium, the acceleration always points in the opposite direction to the position vector. The acceleration and force of restoration are always in same direction .
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or this assignment, you submit answers by question parts. The number of submissions remaining for each
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Compute the density in g/cm³ of a piece of metal that has a mass of 0.470 kg and a volume of 77 cm³.
X g/cm³
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The density of the metal is determined as 6.1 g / cm³.
What is the density of the metal?
The density of the metal is defined as the ratio of the mass per unit volume of the metal.
Mathematically, the formula for density is given as;
ρ = m / V
where;
m is the mass of the metalV is the volume of the metalThe density of the metal is calculated as follows;
ρ = ( 0.47 kg x 1000 g/kg ) / ( 77 cm³ )
ρ = 6.1 g / cm³
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using the bohr model, determine the energy, in joules, necessary to ionize a ground-state hydrogen atom.
The energy necessary to ionize a ground-state hydrogen atom using the Bohr model is approximately 2.18 x 10⁻¹⁸ J.
What is energy?
Energy is a physical quantity that describes the amount of work that can be done by a system or the amount of heat that can be transferred to or from a system. It is a scalar quantity and has units of joules (J) in the SI system of units. Energy can take many forms, including kinetic energy, potential energy, thermal energy, and electromagnetic energy.
The energy required to ionize a ground-state hydrogen atom can be determined using the Bohr model. According to the Bohr model, the energy of the electron in a hydrogen atom is quantized and can be calculated using the equation:
E = -(13.6 eV) / n²
where n is the principle quantum number. For the ground state (n = 1), the energy is -13.6 eV. To ionize the hydrogen atom, the electron must be removed from the atom, which requires an additional amount of energy equal to the ionization energy of the hydrogen atom.
The conversion factor from electron volts to joules is 1 eV = 1.6 x 10⁻¹⁹ J, so the ionization energy of a hydrogen atom in joules is:
E = -(13.6 eV) * (1.6 x 10⁻¹⁹ J/eV) = -2.18 x 10⁻¹⁸ J.
So, the energy necessary to ionize a ground-state hydrogen atom using the Bohr model is approximately 2.18 x 10⁻¹⁸ J.
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A sinusoidal wave of frequency 710 Hz has a speed of 360 m/s. (a) How far apart are two points that differ in phase by π/2 rad? (b) What is the phase difference between two displacements at a certain point at times 4.00 ms apart?
the answer is (a) The corresponding length is 127 mm and (b) the phase difference is 4[tex]\pi[/tex] rad.
Using v = fλ,
we find the length of one cycle of the wave is
λ = 360 / 710
= 0.508 m
λ = 508 mm.
From f = 1 / T,
we find the time for one cycle of oscillation is
T = 1 / 710 = 0.002 × [tex]10^{-3}[/tex] s
T = 2.00 ms.
(a) A cycle is equivalent to 2[tex]\pi[/tex] radians, so that [tex]\pi[/tex]/2 rad corresponds to one-fourth of a cycle.
The corresponding length, therefore, is [tex]\pi[/tex]/4 = 508 / 4 = 127 mm.
(b) The interval 4.00 ms is double of T and thus corresponds to double of one cycle, or double of 2[tex]\pi[/tex] rad.
Thus, the phase difference is 2 × 2[tex]\pi[/tex]= 4[tex]\pi[/tex] rad.
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(c) An experiment was carried out in the laboratory to obtain the acceleration due to gravity 'g' as Shown in Fig. 1. The observations recorded were entered in the Table 1 as shown below. Table 1 S/N 1 2 3 4 5 L (cm) 100.00 90.00 70.00 50.00 40.00
No of Oscillation. 50 50 50 50 50
Mean time (s) 102.00 85.50 64.50
T (s) 1.92 1.47 T'(s)
The acceleration due to gravity can be obtained from the experiment.
How do you obtain the acceleration due to gravity experimentally?We know that when we talk about the acceleration due to gravity what we mean is that we want to know the magnitude of the gravitational pull in a given area and this can be known when we look at the data that we have from the oscillation experiment.
As such gravity is the force that causes the oscillation of the material to stop and such the magnitude can be determined from the experiment.
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