The formula of string potential energy is equal to the product of force and distance of displacement.
Also, force is nothing but the product of spring constant and displacement.
The potential energy of the spring is calculated using the formula,
PE = 1/2* k* x²
where, k is spring constant
x is displacement
The potential energy of the spring is the potential energy stored as a result of the deformation of a particular elastic object, or a spring. It describes the work done to stretch a spring and depends on the spring constant k and the distance stretched.
The spring constant is the characteristic property of the spring. It depends upon the construction material and is measured in units of Nm⁻¹.
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using flat plate theory, a ship is 125 m long with wetted area of 3500 square meters. propellers can deliver power of 1100 kw. neglect any wave drag. what is the maximum ship speed in m/s?
With a wetted area of 3500 square metres and a length of 125 metres, a ship can travel at a maximum speed of 7.2 m/s. Power output from propellers is 1100 kilowatt. Also disregarded is wave drag.
The speed of a change in an object's location in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance. Due to its lack of magnitude and merely having a direction, speed is a scalar number. Power is the quantity of energy that is transferred or transformed in a certain length of time. The watt, which is equal to one joule per second in the International System of Units, is the unit of power. Power may also be referred to as activity in earlier writings.
R is equal to 1025*125/0.00107 power, or 0.0217 v(1025/2).
V^2*3500\sV =7.2m/s
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How much energy is stored in a spring when it is stretched 0.40 meters the spring constant is 50 nm the spring energy equation PES 1 2kx 2?
The energy stored in the spring is 4 j when it is stretched 0.40 meters; the spring constant is 50 nm.
Elastic potential energy to define is the potential energy stored in spring when it is stretched by an external force. The energy remains stored before force is removed.
The force that needed to stretch the elastic body is directly proportional to displacement, means extension. It is given as
F =kx
Wherein,
k = spring constant
x = displacement
The Elastic Potential Energy Formula of the spring stretched is given as
P.E. = 1/2 k[tex]x^{2}[/tex]
Where,
P.E = elastic potential energy and it’s expressed in Joule.
To calculate P.E. =1/2 ×0.5 ×0.4 × 0.4 j
= 4j
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approximately how long after the big bang did the era of nucleosynthesis end, marking the time when the basic chemical composition of the universe was determined?
It took 5 minutes to establish the universe's primary chemical makeup.
What does nucleosynthesis mean?Nucleosynthesis is the process by which new atomic nuclei are produced from pre-existing nuclei and nucleons (protons and neutrons). According to current beliefs, a process known as Big Bang nucleosynthesis took place a few minutes after the Big Bang to produce the first nuclei through nuclear reactions.
The significance of nucleosynthesisStar nucleosynthesis offers hints on both stellar evolution and the distribution of matter across the cosmos in space-time. Chemical abundances inside the solar system, which attest to their abundance at the time of solar system creation, provide a probe to nucleosynthesis in our galaxy.
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What is the frequency of the wave use 340 m/s as the speed of the sound wave?
The frequency of the wave is 34Hz if speed of sound wave is 340m/sec and wavelength is 10Hz.
Frequency implies the amount of cycles in a particular unit of time. The support for why the sky is blue or anything contains assortment can be actually figured out by it. Besides, it can in like manner get a handle on why the voice of specific individuals is significant while for others it isn't significant. Moreover, repeat plays a significant impact on the notes of a piano or different instruments.
This number of occasions is verifiably a key property of a wave. The waves envelop people reliably. Besides, light is an electromagnetic wave and the fan is a sound wave. A wave is certainly a vibration and conveys energy with it. By and large objective, the amount of waves passing by each second suggests the repeat of the wave. Likewise, its assessment occurs in Hertz (Hz).
We know that for sound wave, there is a formula
c=ν×λ
where c is the defined as the speed of sound wave in any medium,
v is defined as the frequency of wave
and λ is defined as the wavelength of the wave
So, we have speed(c) of sound waves=340m/sec
frequency(v)=? and wavelength(λ)=10m
=>340 = v×10
=>340/10=v
=>v=34/sec or
=>v=34Hz.
Hence, frequency of wave is 34Hz.
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(Complete question) is:
What is the frequency of the wave use 340 m/s as the speed of the sound wave and frequency of the wave is 10Hz?
The angular momentum of the propellers of a small airplane points directly forward from the plane.
a. True
b. False
The statement "The angular momentum of the propellers of a small airplane point directly forward from the plane" is false.
Angular momentum is a measure of an object's rotational motion and is defined as the product of the object's moment of inertia and its angular velocity. In the case of an airplane, the propellers spin about an axis that is perpendicular to the plane's direction of motion, so the angular momentum of the propellers points in the direction of this axis.
This direction is not necessarily directly forward from the plane and can vary depending on the orientation of the propellers and the plane's motion. Therefore, it is not true that the angular momentum of the propellers of a small airplane points directly forward from the plane.
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the absolute temperature of a sample of monatomic ideal gas is doubled at constant volume. what effect, if any, does this have on the pressure and density of the sample of gas?
The pressure doubles and the density of sample of gas remains the same when the absolute temperature of a sample of monatomic ideal gas is doubled at constant volume.
The effect of doubling the absolute temperature of a sample of a monoatomic ideal gas is that, the pressure doubles and density of the sample of gas remains the same.
According to ideal gas equation; PV = nRT; Where P is pressure and V is the Volume, n is the number of moles, R is the ideal gas constant and T is the absolute temperature.
Therefore, when the temperature of the mono atomic ideal gas is doubled, the pressure of the gas will also doubles.
However, in a closed chamber mass of the ideal gas is invariant, since density depends only on the mass and volume therefore the density of the ideal is gas will remain the same.
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A cyclist peddles from 5ft/s to 12ft/s over the distance of 50 ft. how long did the acceleration take?
A cyclist peddles from 5ft/s to 12ft/s over the distance of 50 ft. The acceleration will take place for 1.19ft/s^2. It can be calculated by the formula v^2-u^2 = 2as.
v^2-u^2 = 2as
a=v^2-u^2/2s =144-25/2(50)
a=119/100 =1.19ft/s^2
What is acceleration?
The rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. The rate at which velocity changes is called acceleration.
What three forms of acceleration are there?
The three main types of accelerated motions are uniform acceleration, non-uniform acceleration, and average acceleration.
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A cyclist peddles from 5ft/s to 12ft/s over the distance of 50 ft. The acceleration will take place for 1.19ft/s^2. It can be calculated by the formula v^2-u^2 = 2as.
v^2-u^2 = 2as
a=v^2-u^2/2s =144-25/2(50)
a=119/100 =1.19ft/s^2
What is acceleration?The rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. The rate at which velocity changes is called acceleration.
What three forms of acceleration are there?The three main types of accelerated motions are uniform acceleration, non-uniform acceleration, and average acceleration.
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A 8.0-m long wire with a mass of 10 g is under tension. a transverse wave for which the frequency is 570 hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. the maximum transverse acceleration of a point on a wire is closest to?
The maximum transverse acceleration of a point on a wire is closest to 47,410 m/s²
The general wave function is:
y = A cos (ωt + Ф)
Where:
A = Amplitude
ω = angular frequency = 2πf
Ф = phase angle
The transverse acceleration is the second derivative of the above function:
a = d²y/dt²
= - ω²A cos (ωt + Ф)
Hence, the maximum transverse acceleration is:
a_max = ω²A
= (2πf)²A
= 4π²f²A = 4 x 3.14² x 570² x 3.7 mm/s²
= 47,410 m/s²
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a car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 50 ft/s2. what is the distance (in ft) traveled before the car comes to a stop? (round your answer to one decimal place.) incorrect: your answer is incorrect. ft
It is assumed that,
Initial speed of the vehicle: u = 50 mph = 73.34 ft/s
Finally, it stops, or v = 0 (car deceleration, a = - 44 ft/s2).
The distance traveled before the car comes to a stop must be determined. Allow the distance to be s. The third law of motion can be used to compute it as:
v² - u² = 2as
s = v² - u²/ 2a
s = 0 - ( 73.34 ft / s )² ÷ 2 - {-44} ft/ s²
s = 61.13 ft
Therefore, the car travels 61.13 feet before coming to a stop. As a result, this is the necessary solution.
What is the formula for deceleration?Deceleration is the opposite of acceleration. The deceleration will be computed by dividing the final velocity minus the initial velocity, by the amount of time is taken for this drop in velocity.
How do you find the stopping distance if the deceleration is constant?If the deceleration is constant, we know that stopping distance is equal to the area under the v − t graph or D s = 1 2 × v × t s, where ts is the stopping time. So D s = 1 2 × 13.4[m / s] × t s[s] = 0.030 m.
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a car has tires of radius 25 centimeters. as the car is accelerating from rest, the tires make 3 full revolutions and the car moves forwards by 3.5 meters. did the tires skid?
Answer:
No the car did not skid
Explanation:
What is kinetic friction?
Kinetic friction is all about trying to stop one surface from skidding against another surface. When you have two things such as the wheel and the ground sliding against each other, this is kinetic friction.
Given:
The distance cover by the car is 3.5 m
radius ,r = 0.25m
Hence ,
The disctance the car will cover :
s = revolution x 2πr
s = 3 x 2*(3.14)*0.25
s = 4.71 m
Thus the car should cover 4.71 m but it only completes 3.5m as per given scenario.
Hence , the car will not skid.
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Police investigators, examining the scene of an accident involving two cars, measure 64-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.70.Estimate the initial speed of that car assuming a level road.
The initial speed of that car assuming a level road is 29.63 m/s.
What is the acceleration of the cars?
The acceleration of the cars is calculated by applying Newton's second law of motion as shown below.
F = μmg
ma = μmg
a = μg
where;
m is the mass of the carsa is the acceleration of the carsg is acceleration due to gravityμ is the coefficient of kinetic frictionThe acceleration of the cars is calculated as follows;
a = 0.7 x 9.8 m/s²
a = 6.86 m/s²
The initial speed of the car is calculated by applying the following kinematic equation as shown below.
v² = u² - 2as
where;
v is the final velocity of the caru is the initial velocity of the cars is the length of the skida is the acceleration of the carthe final velocity of the car when it stops = 0
0 = u² - 2as
u² = 2as
u = √ (2as)
u = √ (2 x 6.86 x 64)
u = 29.63 m/s
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For what slit-width-to-wavelength ratio does the first minimum of a single-slit diffraction pattern appear at 30 degrees?
The slit width to wavelength ratio due to which the first minimum of single slit diffraction pattern appears = 1 : 0.5
According to the question, we know that we have to calculate the ratio of slit width to wavelength,
Given, A single-slit diffraction
The angle at which the diffraction pattern is occurring = 30°
Order of diffraction given = 1 ( minimum )
We could calculate the path diffraction using the formula,
d sinθ = nλ ( minimum )
d sin 30 = 1 x λ
d / λ = 1 / sin 30
d / λ = 1 / 0.5
d : λ = 1 : 0.5
Therefore, the slit width to wavelength ratio due to which the first minimum of single slit diffraction pattern appears = 1 : 0.5
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All of the following are types of perceptual constancies except __________ constancy. A. Direction b. Size c. Shape d. Color please select the best answer from the choices provided a b c d.
The hallmark of perceptual processes is the ability to determine that the direction of an object—even one that is not of a perceptual species—is the proper response. (Select A).
How should I define direction?Direction can refer to a thing's course, the route one must follow to get there in particular, the direction something is beginning to take shape, or the direction you are facing. Going straight instead than left is an example of direction.
Why do we value direction?One is given instructions when they are given what to do and in what order. You are provided a set of instructions for many of your homework tasks and assessments. Understanding the motivation behind the instructions is crucial.
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If the average kinetic energy of the molecules in an ideal gas initially at 20 degrees Celsius doubles, what is the final temperature of the gas?
The final temperature of the gas will be 40 degrees Celsius.
The average kinetic energy of gas particles is proportional to the absolute temperature of the gas, and all gases at the same temperature have the same average kinetic energy.
The temperature of a substance is directly related to its kinetic energy. Kinetic energy is the energy that a substance has because its molecules are in motion, so when a substance absorbs heat, the molecules move faster and the kinetic energy of the substance increases.
As the average kinetic energy of its particles increases, the thermal energy of the object increases. Therefore, the thermal energy of an object increases as its temperature increases. Since the average Kinetic Energy has doubled, so has the absolute temperature.
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in which part of the ear does pressure need to be equalized when changing altitude or scuba diving? eustachian tube middle ear auricle ear drum
The middle ear is the part of ear that needs equalisation when changing altitude or scuba diving.
Why does the middle ear need equalisation?The water pressure you are diving through will affect the pressure in your outer ear. The Tympanic Membrane, also known as the "Eardrum," is located between the outer and middle ears. If there is an imbalance in the pressure between the two ears, the Tympanic Membrane will flex, resulting in discomfort or suffering.
The Eustachian Tubes, which are used to blow air into the middle ear, work to counteract this. Since the Eardrum is the only flexible portion of the middle ear, breathing more air into the middle ear will create pressure inside the middle ear, which will then cause the Eardrum to bend back to its original position. As a result, equalisation.
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A certain lever has a mechanical advantage of 5. 5. How heavy of a load could the lever lift with an input force of 20. 0 n?.
110 J, the lever lift with an input force of 20. 0 n is 110 J.
What do you mean when you say a "lever" has a mechanical advantage?The solution:The ratio of a lever's effort arm to its load arm determines its mechanical advantage.This is also known as the lever principle.
How are effort and load determined?The pulley's raised object is referred to as the load, and the force needed to lift it is referred to as the effort force.Inside the diagram, a pulley is used to raise a block of wood by applying a force F, also known as the effort force.The load is typically multiplied by the number on ropes to determine the effort.
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an anchor rope to anchor a ship to the pier is wrapped 2 full times around a support on the ship. a deck hand can keep the rope from slipping by applying a force of 100 n to the free end. what is the coefficient of friction between the rope and the support?
The coefficient of friction between the rope and the support is 0.34
What is the coefficient of friction?The amount of friction between two surfaces is measured by the coefficient of friction, or. A low coefficient of friction value means that less effort is needed to cause sliding than would be needed if the coefficient of friction were to be high.
We have to solve this problem by making use of the Capstan's equation
The equation is given as:
[tex]T_{load } = T_{hold} e^u^o[/tex]
u is μ , the coefficient of friction
o is Φ
the load = 7000
the hold support is 100N
Φ = 2π for a complete rotation
given that the rope is wrapped for 2 times we would have Φ = 4π
then
[tex]7000 = 100e^u^4^\pi[/tex]
take the log of both sides
u = log7000 / 100*4π
u = 0.338
Hence the coefficient of friction from what has been calculated is 0.34
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your grandfather clock's pendulum has a length of 0.9930m. if the clock loses 26 s per day, how should you adjust the length of the pendulum? .
The pendulum's length should be decreased to 0.9840 m.
Given that, clock loses 26 s per day
Length of the pendulum = 0.9930 m
In a day there are, 24* 60* 60 = 86400 sec/day
We know the formula for time period as ,
T = 2π √(l/g)
⇒ 2π* √(0.9930 / 9.8) = 2.00005277 sec
Error ratio = 26/86400 = 0.00030093 = 3.009 * 10⁻⁴
T error = 2.00005277 * 3.009 * 10⁻⁴ = 6.0181 * 10⁻⁴
T correct = T original - T error
⇒ 2.00005277 - 0.00060181 = 1.99 sec
T = 2π √(L/g), where L is the new length
Making L as subject, we have,
L = g* T²/ 4π² = 9.8* 1.99² / 4* 3.14² = 38.81/39.44 = 0.9840
Thus, to obtain the correct time, reduce the length of the pendulum to 0.9840m.
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How do you calculate the amount of energy in an elastic potential energy store?
The formula for calculating elastic potential energy stored in spring is elastic potential energy = 0.5 × spring constant ×extension square.
When an elastic body is deformed, energy stored in the body is called elastic potential energy. This energy gets stored in the object till the time it is deformed. When force is removed, this energy changes into kinetic energy.
An object that can store elastic potential energy has a high elastic limit. When an object is deformed beyond the elastic limit, it can not gain its shape after removing force.
The force that is needed to stretch the spring is directly proportional to its displacement. It is given as
F =k x
Wherein,
k = spring constant
x = displacement
The Elastic Potential Energy Formula of the spring stretched is given as
P.E. = 1/2 k
Where,
P.E = elastic potential energy and it’s expressed in Joule.
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A net force of 10. Newtons acts on an object of mass 6. 0 kilograms for 8. 0 seconds. What is the magnitude of the change in the object's momentum?.
The magnitude of the change in the object's momentum is c)80N-sec. So, option c is correct.
The momentum is defined as the consequence of a molecule's speed and its mass. Power and movement, meaning it has both greatness and the heading. As per Isaac Newton's second condition of movement, the power following up on a molecule rises to the time pace of increment of force.
We are given that the initial momentum of the system is 0.
Using the results of Newton second law of motion, we get
F = m × a
a = F/m
a = 10/6
a = 1.67 m/s²
Now, with the help of this acceleration, we can find the final velocity of the object.
So, according to first equation of motion, we get
v = u + at
v = u + (1.67)×(8)
v = 0+13.33 m
=>v=13.33 m
Now, we know momentum is given the cross product of mass and velocity.
Therefore, p = m × v
p = 6 × 13.33
or p = 80 N-s
Hence, change in object's momentum is c)80N-sec
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(Complete question) is:
A net force of 10 newtons acts on an object of mass 6.0 kilograms for 8.0 seconds. What is the magnitude of the change in the object's momentum?
a. 48 N-s
b. 60. N-s
c. 80. N-s
d. 480 N-s
if the density of gold is 19.3 x 103 kg/m3, what buoyant force (n) does a 0.60-kg gold crown experience when it is immersed in fresh water?
If placed in groundwater, a 0.60 kg gold crown would rise by a buoyant force of almost 11.58 N. You can ascertain the same using the formula provided:
Buoyant force = density of fluid x Volume of object x gravitational acceleration
= 1000 kg/m3 x 0.60 kg/m3 x 9.81 m/s2
= 11.58 N
When an item is submerged in a fluid, buoyant force, a kind of uplifting force, is applied to that item. An entity's buoyant force is proportional to the amount of both the fluid it has evacuated.
Step 1: Calculate the volume of the crown
Mass divvied up by concentration is just the formula for calculating an item's volume. The golden crown inside this instance weighs 19.3 x 103 kg/m3 in terms of density.
Volume = 0.60 kg/19.3 x 103 kg/m3
Volume = 0.0031 m3
Step 2: Determine how much water has been displaced by mass.
The crown's volume times the water is probably density gives the amount of water that is evacuated. Freshwater has a 1,000 kg/m3 density.
Mass of water moved is 0.0031 m3 times 1,000 kg/m3.Water displacement weight is equal to 3.1 kg
Step 3: Determine the buoyant force.
The buoyant force that an item experiences is proportional to the mass of the fluid which that item has displaced. The water that was removed weighs 3.1 kg in particular instance.
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the projection lens in a certain slide projector is a single thin lens. a slide 23.9 mm high is to be projected so that its image fills a screen 1.84 m high. the slide-to-screen distance is 3.05 m. (a) determine the focal length of the projection lens.
The focal length of projection lens is 0.039m.
The opposite of a concave lens is a convex lens. Contrary to concave lenses, light rays converge in convex lenses. In contrast to the concave lens, the convex lens is bigger in the middle and thinner at the edges, therefore it converges the incident rays into its central axis.
Instead of being bent inward, the convex lens' edges are curved outward. The image seems smaller and inverted when the light is extremely focused beyond the focal length of the lens.
A convex lens's opposite side's center of curvature, , creates the image of an object placed in the center of curvature, , of the lens. As seen in the given illustration, the picture that forms is inverted and the same size as the object.
The image is inverted
h/H
= -1.8/0.024
the distance from slide to screen d=p+q=76p
M =75
d=p+q=76p
p= 0.0395m
p= 39.5cm and q = 75p = 2.96
and
a)1/0.395+1/2.96=1/f
f = 0.039m
b) from above p = 39.5 mm
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Explain how Newton’s second law and third laws are used to calculate the force needed to hold a 0.003 kg sheet of paper and keep it from falling. (g = 9.8 m/s2)
The force needed to hold a 0.003 kg sheet of paper and keep it from falling is equal to 0.0294 N.
What is the third law of motion?According to Newton's 3rd law of motion, when two objects interact and exert force on each other, these forces are called action-reaction pairs. Force can be defined as a push or pull exerted resulting in its interaction with another.
From the second law of motion, the force is equal to mass time acceleration in the case of free fall gravitational acceleration.
Given the mass of the sheet paper, m = 0.003 Kg
The acceleration due to gravity, g = 9.8 m/s²
The weight of the sheet of paper can be calculated as:
W = mg
W = 0.003 ×9.8
W = 0.0294 N
Therefore, the force required to prevent the paper from keep falling will be equal to 0.0294 N.
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If the car moving with 2,000N of force and has a mass 16,000N ,how fast could it accelerate.
Answer:
On the other hand, acceleration is inversely proportional to the mass of the body being accelerated. That is, the greater the mass, the less acceleration.
Explanation:
neglecting friction, what happens to the total mechanical energy as the pendulum swings from position a to position b?
If the potential energy of pendulum increases then the kinetic energy decreases and if the kinetic energy increases then the potential energy decreases, thus conservation of energy remains constant.
what is conservation of energy?According to the work power theorem the total energy of any object will remain constant like the sum of the kinetic and the potential energy of the object will remain constant.
The potential energy of any object is due to its position with respect to the ground. If the object is at a height of H then it will have a potential energy because some energy is given to that object against the gravity to move it to the height H.
The kinetic energy is the energy due to the velocity of the object and is given as the product of half mass to the velocity square.
we will express it in the form of the formula for better understanding:
Mechanical energy = Kinetic energy + potential energy
Now in the pendulum the motion is back and forth with respect to its mean position. So the mechanical energy (total energy) in the pendulum is the sum of the kinetic energy and the potential energy.
Now if the pendulum attains the maximum displacement from its mean position then it will have maximum potential energy and zero kinetic energy at this point.
Now if the pendulum is at the mean position now it will have maximum kinetic energy and zero potential energy at this point.At this point the potential energy totally converted to the kinetic energy.
Now at the maximum displacement the kinetic energy totally converts into the potential energy of the pendulum.
Thus If the potential energy of pendulum increases then the kinetic energy decreases and if the kinetic energy increases then the potential energy decreases.
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4.)a gamma-ray photon produces an electron and a positron, each with a kinetic energy of 375 ke v. determine the energy and wavelength of the photon
a gamma-ray photon produces an electron and a positron, each with a kinetic energy of 375 keV.
wavelength of photon = 7.019 × 10⁻¹³ m
Total energy of photon = 1.77 MeV.
What is kinetic energy?An object's kinetic energy is the energy it has as a result of motion. Applying force is necessary if we wish to accelerate an item. We must put forth effort in order to apply a force. Once the job is finished, energy is transferred to the item, which then moves at a new, constant speed.
The rest mass energy for electron and positron:
E₀ = m₀c²
E₀ = (9.1 × 10⁻³¹) × (3 × 10⁸)
E₀ = 8.198 × 10⁻¹⁴ J
E₀ = 512.4 × 10³ eV or 512.4 KeV
Total energy of photon:
= [2 × (375)] + [2 × ( 512.4 )]
= 1774.8 KeV
= 1.77 MeV.
Energy = hc/λ
or, λ = (6.626 × 10⁻³⁴) × (3 × 10⁸)
or, λ = 7.019 × 10⁻¹³ m
Thus, wavelength of photon = 7.019 × 10⁻¹³ m
Total energy of photon = 1.77 MeV.
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At a frequency ω1 the reactance of a certain capacitor equals that of a certain inductor.a. If the frequency is changed to ω2= 7 ω1,b. what is the ratio of the reactance of the inductor to that of the capacitor?c. If the frequency is changed to ω3=ω1/ 7,d. what is the ratio of the reactance of the inductor to that of the capacitor?
(a.) At frequency ω2, the reactance of the inductor will be 7 times the reactance of the capacitor. (b). The ratio of the reactance of the inductor to that of the capacitor is 7:1. (c.) At frequency ω3, the reactance of the inductor will be 1/7th the reactance of the capacitor. (d.) The ratio of the reactance of the inductor to that of the capacitor is 1:7.
a. When the frequency is changed to ω2 = 7ω1, the ratio of the reactance of the inductor to that of the capacitor is 1:7. This is because when the frequency increases, the reactance of the inductor increases while the reactance of the capacitor decreases.
b. The formula for calculating the ratio of the reactance of an inductor to that of a capacitor is Xl/Xc = (ω2/ω1)^2. Therefore, the ratio of the reactance of the inductor to that of the capacitor when the frequency is changed to ω2 = 7ω1 is 49:1.
c. When the frequency is changed to ω3 = ω1/7, the ratio of the reactance of the inductor to that of the capacitor is 1:49. This is because when the frequency decreases, the reactance of the inductor decreases while the reactance of the capacitor increases.
d. The formula for calculating the ratio of the reactance of an inductor to that of a capacitor is Xl/Xc = (ω3/ω1)^2. Therefore, the ratio of the reactance of the inductor to that of the capacitor when the frequency is changed to ω3 = ω1/7 is 1:49.
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Two bowling balls are rolling towards each other. The first has a mass of 5 kg and is rolling with a speed of
4 m/s to the right. The seconds has a mass of 6 kg and is rolling with a speed of 7 m/s to the left. After the
collision, the first bowling ball rolls away with a speed of 5 m/s to the left. How fast is the second ball
rolling after the collision?
a. 7.5 m/s
b. 6.2 m/s
c. 0.5 m/s
d. 0.9 m/s
Answer:
the answer is 0.5 m/s it's c
what is the best approximation for the area of this circle? use 3.14 to approximate pi.
The best approximation is 201.0 [tex]in^{2}[/tex]
we know that
The area of the circle is equal to
[tex]A= \pi r^{2}[/tex]
In this problem we have
r =8 in
[tex]\pi =3.14[/tex]
substitute
A= (3.14) ([tex]8^{2}[/tex]) =201.0 [tex]in^{2}[/tex]
What is Pi ?pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.Pi is most commonly used in certain computations regarding circles. Pi not only relates circumference and diameter. Amazingly, it also connects the diameter or radius of a circle with the area of that circle by the formula: the area is equal to pi times the radius squared. Additionally, pi shows up often unexpectedly in many mathematical situations. For example, the sum of the infinite series.To learn more about pi refer to:
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a ball is thrown upward at a velocity of 19.6 m/s. how long time does it take to come back to its original height?
Time taken by the ball to reach its original height is 4 seconds.
How is time, height and gravity related in motion?The vertical motion is a motion that occurs when we toss an object completely up. Because the initial velocity or force is only applied in the vertical axis, this motion only moves vertically; if there is any horizontal movement, the air is to blame.Because a uniformly accelerated motion typically goes in the "x" axis, the vertical motion could be viewed as a version that moves in the "y" axis. The acceleration of the vertical motion will be equal to the gravity, therefore it can be thought of as a uniformly accelerated motion.
Given that gravity is an acceleration that points downward, it will always have a negative sign. One of the key prerequisites for vertical motion is that the object's initial velocity must be greater than zero; otherwise, the object will begin to rise and slow down until its initial velocity equals zero, at which point it will begin to fall and its velocity will steadily increase in the opposite direction until it collides with the ground.
The time take by the ball to reach back to its original height will be equal to twice of time taken to reach its maximum height.
According to the kinematic equations of motoion we know that
v = u + at
Here v = final velocity, u = initial velocity , a = acceleration, t = time taken to reach maximum height
We know that;
v = 0 m/s
u = 19.6 m/s
g = -9.8 m/s^2
Thus
t = v - u/a
= 0 - 19.6/ (-9.8)
= 2s
Thus time taken by the ball to reach its original height is 2 x t = 4s.
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