A fish under water appears to be at a different depth than it actually is due to the refraction of light as it passes through the water.
When light travels through a medium with a different index of refraction, such as air to water, it bends, or refracts. This causes objects to appear displaced, or closer or farther away than they actually are. Because water has a higher refractive index than air, light bends more when it enters the water, causing objects, like fish, to appear closer to the surface than they actually are.
The result is that the fish will appear to be deeper in the water than it actually is.
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Why does temperature have no effect on mass?
The amount of matter present is simply referred to as mass. As a result, temperature change has no direct effect on mass since the amount of matter present remains constant regardless of temperature. The mass of a material in a given volume is defined as its density.
Temperature is a physical measure that quantifies our feelings of hotness and coolness. A thermometer is used to measure temperature.
Thermometers are calibrated in a variety of temperature scales that have traditionally been defined by various reference points and thermometric substances.
The most prevalent scales are the Celsius scale (previously known as centigrade), the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being used mostly for scientific reasons. The kelvin is one of the International System of Units' seven basic units (SI).
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Two particles P and Q are initially at rest 1.64 m apart, P has a mass of 1.43 kg and Q a mass of 4.29 kg. P and Q attract each other with a constant force of 1.79 x 10-2 N. No external forces act on the system. (a) Describe the motion of the center of mass. (b) At what distance from P’s original position do the particles collide?
(a)The center of mass of the system has no acceleration, and remains at the same position as it was earlier.
(b)The particle P, collide at a distance 1.23m from P's original position.
What is acceleration?Vector quantities include accelerations. The direction of the net force imposed on an object determines its acceleration in relation to that force.Acceleration in a body is the result of imbalanced forces.The three main categories of accelerated motions are uniform, non-uniform, and average acceleration. When an item moves in a straight path with an increase in speed occurring at regular intervals of time, this motion is referred to as having uniform acceleration.Any modification of motion's speed or direction is referred to as acceleration. When anything is speeding up, slowing down, or not traveling straight ahead, it is said to be accelerating.To learn more about acceleration refer to:
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Order the electromagnetic waves from lowest frequency (1) to highest (4). gamma: infrared: x-ray: visible light:
Gamma: 4
Infrared: 1
X-Ray: 3
Visible Light: 2
Infrared has the longest wavelength between the four options, meaning that it has the lowest frequency. Since the longer the frequency, the lower the frequency. While the shorter the wavelength, the higher the frequency.
The portions of the electromagnetic spectrum are called from greatest to lowest energy: gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, and radio waves. Microwaves (such as those used in microwave ovens) are a subset of the electromagnetic spectrum's radio wave segment.
Next would be visible light since it has the second longest wavelength out of the given options. Then it would be X-Ray. And finally Gamma since it has the shortest wavelength.
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a log with a mass of 14 kg is suspended by two ropes, one at either end. What is the tension force in each rope
According to the given statement The tension force in each rope is T = 14g/2Sin N, according to the information provided.
What is tension force ?Tension is the force that is transmitted through a cable, rope, or wires when it is stretched by loads exerted from opposing sides. The bodies are put through an identical degree of strain at each end of the wire by the tension force, which is exerted all along entire of the wire's length.
Let the tension in each rope be T₁ & T₂
Also, T₁ = T₂ = T
T₁ Sinθ + T₂ Sinθ = mg
2T Sinθ = mg
2T Sinθ = 14g
T = 14g/2Sinθ
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A wheel rotates at 2 rad/s. What is its period and frequency?
(1) The frequency of the oscillation is 0.32 Hz.
(2) The period of the oscillation is 3.13 seconds.
What is the period of the wheel's oscillation?
The period of the wheel's oscillation is the time taken for the wheel to make one complete oscillation.
The period of an oscillatory motion is the reciprocal of the frequency of the oscillation.
The frequency of the oscillation is the number of cycles completed by the oscillatory object in a given second.
The frequency of the wheel undergoing oscillatory motion is calculated by using the following formula.
f = ω / 2π
where;
ω is the angular speed of the wheelf is the frequencyf = ( 2 rad/s ) / 2π
f = 0.32 Hz
The period of the oscillation is calculated as follows;
T = 1 / f
T = 1 / 0.32 s
T = 3.13 seconds
Thus, the period of oscillation and frequency of the oscillation are inversely proportional.
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What are the similarities and differences between static stretching and ballistic stretching?
Explanation:
This intense stretching method uses bouncing movements to push your body beyond its normal range of motion. Whereas static stretches are performed slowly and gradually, the ballistic method stretches muscles much farther and faster. You can do many of the same stretches as ballistic or static stretches.
How much force is needed to accelerate a 63 kg skier at 6 m/s2?
Answer:
378 N
Explanation:
F = ma = (63 kg)(6 m/s²) = 378 N
A skier weighing 63 kg needs 189N of force to accelerate at 6 m/s. The magnitude of the force required to accelerate the sled is 91 newtons.
What is the necessary force to accelerate?An object's acceleration is equal to the net force acting on it divided by its mass, or a = F m, according to Newton's second law of motion. When the object's mass and the net force it is subjected to are known, this acceleration equation can be used to determine its acceleration.
By the second law of Newton, F = ma Add the following numbers:
F=189N F=63kg(2ms 2)
Which two formulas are used to determine acceleration?Formula for acceleration: there are three equations for acceleration:
a = (v_f - v_i) / t;a equals 2 / t2 (d - v_i t)a = F / m ;To learn more about Newton's second law here:
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in order to catch a ball, a baseball player moves his or her hand backward in the direction of the balls motion. doing this reduces the force of impact on the players hand principally because....
a.) the time of impact is decreased
b.) the time of impact is increased
c.)the velocity of the hand is reduced
d.) the momentum of impact is reduced
e.) none of the above
The right response is B: To catch a ball, a baseball player moves his or her hand backward in the direction of the ball's motion because the time of impact is increased.
By doing this, the force of impact on the player's hand is mostly reduced. The force needed to stop the ball will decrease as the amount of time it takes to reach zero motion increases. Consider a ball approaching you with 100 units of momentum. To stop the ball, a 100-unit impulse would be necessary. No matter how the impulse is generated, there must be 100 units of it. A force is an effect that can alter an object's motion in physics.
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A man is pushing a baby stroller. Compared to the magnitude of the force exerted on the stroller by the man, the magnitude of the force exerted on the man by the stroller is A larger. B zero. C smaller, but greater than zero. D the same
A man is pushing a baby stroller. Compared to the magnitude of the force exerted on the stroller by the man, the magnitude of the force exerted on the man by the stroller is the same.
From Newton's third law of motion, the force exerted on the stroller by the man is same as the force exerted on the man by the stroller but is in the opposite direction.
Thus, the magnitude of the force exerted on the stroller by the man and the magnitude of the force exerted on the man by the stroller is same but in opposite direction.
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You have seen how large Jupiter would be if the Sun were a 1 meter sphere. Using the same scale, how large would the other planets be
After seeing how big Jupiter is if the Sun were just a sphere measuring one meter in diameter. If somehow the solar is 1,391,000,000 meters diameter, so its diameter, if it had been a sphere, would be 7.2 × 10⁻¹⁰.
Describe planet.Celestial bodies that fit the following descriptions are considered planets: It has cleansed the space around and within its orbit because (a) it is orbiting the Sun; (b) it possesses sufficient mass for its soul to outweigh rigid body forces; and (c) it has orbited the Sun.
How far is it?An object's distance is equal to its overall directionless velocity. Depending of where it started or concluded, distance is really the amount of territory that an object has covered.
Mercury: 0.0035 meters
Venus: 0.0087 meters
Earth: 0.0092 meters
Mars: 0.0049 meters
Jupiter: 0.1028 meters
Saturn: 0.086 meters
Uranus: 0.0367 meters
Neptune: 0.0356 meters
Therefore, you have seen how large Jupiter would be if the Sun were a 1 meter sphere, the other planets distance are described above .
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After seeing how big Jupiter is if the Sun were just a sphere measuring one meter in diameter. If somehow the solar is 1,391,000,000 meters diameter, so its diameter, if it had been a sphere, would be 7.2 × 10⁻¹⁰.
Describe planet:Planets are celestial bodies that match the following criteria: Because it is circling the Sun, has enough mass for it's own soul to override rigid body forces, and has orbited the Sun, it has cleaned the space in and around its orbit.
How far is it?The distance between two objects is equal to their combined directionless velocity. Distance is basically the amount of ground that only an object has traveled, depending on where it began and ended.
Mercury: 0.0035 meters
Venus: 0.0087 meters
Earth: 0.0092 meters
Mars: 0.0049 meters
Jupiter: 0.1028 meters
Saturn: 0.086 meters
Uranus: 0.0367 meters
Neptune: 0.0356 meters
Therefore, you have seen how large Jupiter would be if the Sun were a 1 meter sphere, the other planets distance are described above .
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Pls I need answer please find the attached file is scanned image in PDF format I am not sure if you have any questions or concerns please visit the plug-in settings to determine how attachments are u still ther I need/not needed
Answer:
A. 35 °C
Explanation:
You want to know which of the temperatures 5, 10, 15, or 35 °C is most favorable to mosquito breeding.
BreedingMosquitos are nonfunctional below 50 °F (10 °C), and are lethargic at 60 °F (15.6 °C). They prefer 29 °C, and their breeding falls off at higher and lower temperatures.
Of the temperature choices offered, mosquitos would breed fastest at 35 °C.
In which situation is the maximum possible work done? A. when the angle between the force and displacement is 0° B. when the angle between the force and displacement is 180° C. when the angle between the force and displacement is 45° D. when the angle between the force and displacement is 90°
As a result, the force's effort is at its greatest when there is no angle between its direction and displacement, hence option A is correct.
What is work done?According to physics, a force is an effect that has the power to change an object's motion.
A force can cause a massed item to accelerate or modify its velocity. A push or a pull is a straightforward method to explain forces. Since a force has both magnitude and direction, it is a vector quantity.
Therefore, work is therefore at its greatest when the angle between force and displacement is 0 °.
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Answer: A. when the angle between the force and displacement is 0 degrees.
Explanation:
Edmentum
Under certain circumstances, the grounded (neutral) conductors of a residential service ____ permitted to be sized smaller than the phase conductors.
Under certain circumstances, the grounded (neutral) conductors of a residential service are permitted to be sized smaller than the phase conductors.
What is conductors?
A material that easily permits the flow of electricity is referred to as an electrical conductor. Conductivity is the quality of conductors that enables them to conduct electricity.
Electric current is the name given to the movement of electrons through a conductor. Voltage is the amount of power necessary to cause that current to flow through the conductor.
What is phase ?
Phases are parts of a system that are mechanically separable from other parts of the system and are physically distinct from other parts of the system. types of substance. Solid, liquid, or gaseous phases can exist in a system. Strong atomic bonding and high viscosity, which produce a hard form in solids, are their distinguishing characteristics.
Therefore, Under certain circumstances, the grounded (neutral) conductors of a residential service are permitted to be sized smaller than the phase conductors.
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during the game, a player flies above a ring and drops a ball through from a height of 20 m. f the ball takes 7.0 seconds to fall, find the acceleration due to graviit
The acceleration due to gravity is 0.8 m/s^2.
What is an explain acceleration?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.
What is the SI unit for acceleration?In physics, acceleration is the rate at which the velocity of an object changes in relation to time. According to Newton's Second Law, the sum of all forces acting on an item results in its acceleration. Meter per second squared (m s2) is the unit of acceleration used in the SI system.
The motion of an object in free fall is a uniformly accelerated motion,
[tex]s=ut+\frac{1}{2} gt^2[/tex]
s is the vertical displacement
u is the initial velocity
t is the time of flight
g is the acceleration of gravity
For the ball dropped,
s = 20 m
t = 7.0 s
u = 0
Now, substitute values,
[tex]20=0+\frac{1}{2} g(7.0)^2[/tex]
[tex]g=\frac{2*20}{7.0^2}[/tex]
[tex]g=0.8 m/s^2[/tex]
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A 64 g plastic ball is moving to the left at 24 m/s . How much work must be done on the ball to cause it to move to the right at 24 m/s
The ball requires a total of zero work to go to the right at 24 m/s.
Take into account the ball's kinetic energy.
Vi = -24 ms-1 for the initial velocity
Final velocity: vf = +24ms⁻¹
K = 12mvf²- 12mvi² = 12m(vf² - vi²) = 12m(242 - 242) = 0,
meaning that the ball does not undergo any effort.
As an alternative, think about the effort made to stop the ball.
W1 = ½m(0 – 24²) = 0.5 × 0.06 × –576 = –17.28J
Work required to accelerate the ball from rest to +24 milliseconds per second was W2 = 12m(242 - 0) = 0.5 0.06 576 = +17.28 J.
Therefore, the sum of the work is W = W1 + W2 = -17.28 + 17.28 = 0 J.
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A 1 kilogram object is thrown horizontally and a 2 kilogram object is dropped vertically at the same instant and from the same point above the ground. If friction is neglected, at any given instant both objects will have the same
a) Total velocity
b) Momentum
c) Height
d) Kinetic energy
If friction is neglected, at any given instant both objects will have the same c) Height.
What is friction?
Friction is the resistance to motion that results from two objects rubbing against one another. Two objects rubbing against one another causes friction. Motion is opposed by friction, which works against the motion.
When an object slides over another object, friction slows it down. As a result, energy is used. However, the energy does not fade away. Kinetic energy, also referred to as moving energy, is transformed into heat energy. We rub our hands together when it's cold because of this. Rub them together, and friction and heat will result.
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Two spherical objects have masses of 8,000 kg and 5.0 kg. Their centers are separated by a distance of 1.5 m. Find the gravitational attraction between them.
The gravitational force of attraction between them is 3.56 * 10⁻⁴ N
What is Gravitational attraction?F = G*M1M2/d²,
where G = 6.67 * 10⁻¹¹ Nm²Kg⁻²,
M1 = 8000Kg and M2 = 1500 Kg,
F = 6.67 * 10⁻¹¹ * 8000 * 1500 / (1.5)² F = 3.56 * 10⁻⁴ N
The gravitational force of attraction between them is 3.56 * 10⁻⁴ N.
The universal gravitational law of Newton. According to this law, every body in the universe is attracted to every other body with a force that is inversely proportional to the square of the distance between them and proportional to the product of their masses.
Therefore, The gravitational force of attraction between them is 3.56 * 10⁻⁴ N.
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Normal
Question
Question 22
A projectile is launched into space where there is very little friction. According to Newton's law of inertia, the projectile willmost likely continue to travel in a straight line and?
The projectile will probably keep moving in a straight line and at a constant speed as long as no unbalanced forces are acting on it, according to Newton's law of inertia.
What is law of inertia?The law of inertia, also known as Newton's first law, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by a net external force. In simple words, an object will remain in the same state of motion unless acted upon by an external force. This law explains why it is difficult to start an object moving and easy to keep it moving once it is in motion. This law applies to all objects and is a fundamental principle of physics. It also helps to understand the concept of force, motion and energy in physics.To learn more about law of inertia refer:
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can u pls solve this question thank u!! i having my physics paper tomorrow!!
Answer:
13.875Ω & 5Ω
Explanation:
in the first diagram:-
R = Rs + Rp + Rs'
Rp => [tex]\frac{1}{7} + \frac{1}{1} = \frac{1+7}{7} = \frac{8}{7} \\[/tex]
Rp = [tex]\frac{7}{8}[/tex] = 0.875
4 + 0.875 + 9 = 13.875Ω
in the second diagram:-
R= Rp + Rs + Rp'
Rp => 1/6 + 1/3 = 1+2/6 = 3/6 => 2
Rp' => 1/3+1/3+1/3 = 3/3 => 1
R = 2 + 2 + 1 = 5 Ω
What is called solar energy?
Answer:
energy from the sun
Explanation:
the sun radiates energy known as solar energy.
what is the reading of the energy meter in figure 1 when an appropriate laser is used in pac to dissociate a particular chemical bond?
According to this, the laser always has higher energy than what is required to break the bond. A portion of the energy is utilized to break the bond, the rest is transformed into heat.
How is an energy meter measured?Kilowatt-hours are the unit used by your electric meter to measure power use. One kilowatt hour is equal to one thousand watt-hours. For instance, the energy usage is computed as 100 watts x 10 = 1,000 watts if a 100-watt light bulb is on for 10 hours.
How is electrical energy measured?Watts are units used to measure the power of electricity. One ampere under the pressure of one volt is equal to one watt of electrical power. The power of one watt is negligibly little.
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A standing wave is set up in a pipe with both ends open. The frequency of its first harmonic is 300 Hz. What is the length of the pipe? Take the speed of sound to be 340 m s–1. Give your answer in meters
When the frequency of a standing wave set up in a pipe (with both ends open) first harmonic is 300 Hz, the length of pipe is 0.567 metres.
Therefore the answer is 0.567 m.
The speed of sound in air is approximately 340 m/s, and the wavelength of the first harmonic of a standing wave in an open pipe is twice the length of the pipe. Therefore, if the frequency of the first harmonic is 300 Hz, the wavelength can be calculated as:
wavelength = speed of sound / frequency
wavelength = (340 m/s) / (300 Hz)
The length of the pipe can be calculated as half the wavelength:
L = wavelength/2
L = (340 m/s) / (2×300 Hz)
L ≈ 0.567 m
So the length of the pipe is 0.68 m
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Two pendulums have the same dimensions (length L) and total mass 1m2. Pendulum A is a very small ball swinging at the end of a uniform massless bar. In pendulum B, half the mass is in the ball and half is in the uniform bar. Find the period of each pendulum for small oscillations. Which one takes longer for a swing
For pendulum A, the period of oscillation is T = 2π × √(L/g). For pendulum B, the period of oscillation is T = 2π × √(2L/g). As we can see from the formula, Pendulum B takes longer for a swing as its period of oscillation is longer than pendulum A due to the fact that half the mass is distributed along the uniform bar.
The period of a pendulum is given by the formula T = 2π × √(L/g) where L is the length of the pendulum and g is the acceleration due to gravity.
For pendulum A, the total mass is concentrated in the small ball at the end of the massless bar, so the period of oscillation is T = 2π × √(L/g)
For pendulum B, half the mass is in the small ball, and half is distributed along the uniform bar, so the period of oscillation will be T = 2π × √(2L/g)
In both cases, the length of the pendulum is the same, so the period of oscillation for pendulum A is shorter than the period of oscillation for pendulum B. Therefore pendulum B takes longer to swing.
It's worth noting that these calculations are based on small oscillations, when the angle of oscillation is small, as the period of a pendulum is dependent on the angle of oscillation.
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Which of the following types of microscopes reveals the surface features of small molecules? - a confocal microscope - a fluorescent microscope - a transmission electron microscope (TEM) - an atomic force microscope
The types of microscopes that reveals the surface features of small molecules is an atomic force microscope.
The Atomic Force Microscope (AFM) is useful for imaging the surface topography of living, soft materials in their natural settings. It can be used to examine the inherent elastic modulus and receptor-ligand interactions of cells and extracellular matrix, among other mechanical properties. SEM pictures can investigate surface features that are several tenths of a nanometer in size, but AFM resolution is less than 0.1 nm. As a result, AFM can discern objects on flat surfaces with molecular dimensions.
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2. Yvonne van Gennip of the Netherlands ice skated 10.0 km with an aver- age speed of 10.8 m/s. Suppose van Gennip erosses the finish line at her average speed and takes a huge bouquet of flowers handed to her by a fan. As a result, her speed drops to 10.01 m/s. If van Gennip's mass is 63.0 kg, what is the mass of the bouquet
The mass of the bouquet can be calculated using the equation m = F/a. Which is equal to 0.9kg.
Since van Gennip’s speed dropped from 10.8 m/s to 10.01 m/s after she took the bouquet, this indicates that a force was applied to her causing her to slow down.
The applied force can be determined by taking the difference between her final and initial momentum, which is p = mv.
Thus, the applied force can be calculated by F = Δp/Δt.
Plugging in the given values, the mass of the bouquet can be calculated as
m = F/a = (63.0 kg × (10.8 m/s - 10.01 m/s))/10.01 m/s² = 0.9 kg.
Therefore, the mass of the bouquet is 0.9 kg.
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Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each satellite are given below. Which satellite has the greatest speed? Mass Radius (A) ½m R (B) m ½R (C) m R (D) m
Correct option is B, satellite that has the greatest speed has Mass Radius m ½R.
Because the satellite orbits the earth, the gravitational pull of the planet on the satellite supplies the necessary centrifugal force. In a circular orbit, the gravitational force is constant, hence the satellite's velocity is also constant.
Kepler's third law informs us that
V² = GM/R
Therefore, v = (GM/R)
Where;
V is the speed
G stands for gravity constant.
Mass is M.
R is radius
Let's begin by examining the first choice, which is Option B.
Here, mass equals m and radius equals (1/2)R.
Consequently, v = (Gm/(R/2)) = (2Gm/R)
After carefully examining each choice, it is evident that option B will have the highest velocity because its numerator is the largest, which will result in a higher velocity.
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Patrick and Emily are walking to the grocery store to buy some treats. They walk 3.0
km in 900.0 s. What was their average speed in m/s?
Answer:
3.33 m/s
Explanation:
(3.0 km)(1000 m/km) = 3000 m
Avg. Speed = distance/time = 3000 m/900 s = 3.33 m/s
We are warmed by condensation because water molecules in the air that strike our bodies
A. form an insulating layer on our bodies
B. gain kinetic energy as they change state
C. transfer some of their kinetic energy to us
Condensation warms us because airborne water molecules that impact our bodies give up some of their kinetic energy to us.
What is kinetic energy?
Kinetic energy is the energy of motion. It is the energy that a moving item possesses.It is typically measured in joules and is equal to the work done to accelerate the object from its rest state to its current state. Kinetic energy can be found by multiplying the mass of an object by its velocity squared, divided by two. The kinetic energy of an object increases as its velocity increases.Kinetic energy exists in both linear and rotational forms. Linear kinetic energy is the energy of an object moving in a straight line, while rotational kinetic energy is the energy an object has due to its spinning or rotating motion.
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An object with mass of 50kg moves with
velocity of 11. 2m/s and an event occur
whereby it transfers 1539 of energy to
another objects as work.
What is the new
velocity of the object after the event??
The new velocity of the object after the event is 7.99m/s.
We are given that,
Mass = m = 50kg
Initial velocity = v = 11.2m/s
Energy = E = 1539j
The kinetic energy of object can be calculated as,
K= (1/2)mv²
K = (50×125.44)/2
K = 3136J
Consequently, since both the initial kinetic energy and the total amount of energy transferred are known. The article's resulting energy is easily discernible.
Final energy = initial kinetic energy - the ending energy
Final energy = 3136-1539= 1597 joules
Therefore, using the equation for kinetic energy derivation, the speed of the object can now be determined.
K.E = 1/2MV²
1597 = 50/2V²
3194 = 50V²
V = 7.99m/s
Therefore , the new velocity of the object after the event would be 7.99m/s.
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Find the interaction energy for two point charges, q1 and q2, a distance a apart. [Hint: Put q1 at the origin and q2 on the z axis; use spherical coordinates, and do the r integral first.]
The interaction energy for two point charges, q₁ and q₂, a distance 'a' apart is q₁q₂/4πε₀a.
In physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being evaluated. The interaction energy generally depends on the relative position of the objects.
For example q₁q₂/4πε₀Δr is the electrostatic interaction energy between two objects with charges q₁ and q₂.
[tex]W_{tot}[/tex] = ε₀/2(∫E²dτ)
= ε₀/2{(∫E₁ + E₂)²dτ}
= ε₀/2(∫E₁² + E₂² + 2E₁E₂)dτ
= W₁ + W₂ + ε₀(∫E₁ × E₂)²dτ
E₁ = 1/4πε₀(q₁/r²)r
E₂ = 1/4πε₀(q₂/ᴫ²)ᴫ
[tex]W_{i}[/tex] = ε₀q₁q₂/(4πε₀)²[∫{(1/r²ᴫ²)cosβr²sinθdrdθdφ}]
Where (from the figure)
ᴫ = √(r² + a² - 2ra cosθ), cosβ = (r - a cosθ)/ᴫ
Therefore
[tex]W_{i}[/tex] = {q₁q₂/(4π)²ε₀} 2π∫{(r - acosθ)/ᴫ³} sinθ drdθ
First do the r integral first, changing variables to ᴫ:
2ᴫdᴫ = (2r - 2a cosθ)
⇒(r - a cosθ)dr = ᴫdᴫ
As r : 0→∞, ᴫ : a→∞, so
[tex]W_{i}[/tex] = {q₁q₂/8πε₀a} [tex]\int\limits^\pi _0[/tex](∫limit 0 to ∞ 1/ᴫ² dᴫ) sinθ dθ
The ᴫ integral is 1/a, so
[tex]W_{i}[/tex] = {q₁q₂/8πε₀a} [tex]\int\limits^\pi _0[/tex] sinθ dθ
[tex]W_{i}[/tex] = q₁q₂/4πε₀a
This is the exact interaction energy of two-point charges.
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