chapter 5 - problem 30. a negative charge is placed at the center of a ring of uniform positive charge. what is the motion (if any) of the charge? what if the charge were placed at a point on the axis of the ring other than the center?

Answers

Answer 1

Answer:

There is no motion of the charge except along the axis of the ring.

(All charges on the ring are equivalent, with no net force perpendicular to the axis of the ring)

The electric potential of the axis of the ring decreases as the charge is moved away from the center of the ring,

The force on the negative charge will always be directed towards the center of the ring. (It would take work to move the charge "away" from the ring)


Related Questions

to what minimum temperature should food that is cooked cold and reheated for hot holding be reheated

Answers

The minimal temperatures for cooking, cooling, and reheating food are 75 °C for cooking, 8 °C for cooling, and 165 °F for heating.

As soon as feasible, food should be refrigerated to prevent the growth of micro organisms. This should ideally cool to less than 8 degrees Celsius in 90 minutes. There are various techniques for quickly cooling food.

If at all feasible, cook food until it reaches 75 °C or higher within. The bulk of food-taining bacteria are eliminated at this stage of heat. Use a thermometer to monitor the internal temperatures of the food components as they cook. Cook mince, sausages, entire birds, and meat fillings all the way through.

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what is the speed of a point on the earth's surface located at 2/3 of the length of the arc between the equator and the pole, measured from equator? (hint: what is the radius of the circle in which the point moves?)

Answers

232.5 m/s is the speed of the earth's surface where 2/3 of the length of the arc between the poles and the equator.

Latitude is the angle between a place on the earth's surface and the planet's centre. It identifies a point's north-south location on the surface of the Earth. Latitude is an angle that can be either north or south of 0° at the equator and 90° at the poles.

The radius of the earth's surface is 6.37 X [tex]10^6[/tex] metres,

and its angular displacement from the pole is 90 degrees,

According to the information provided above.

So the 2/3 is 60 degrees.

Since v = [tex]\omega[/tex]r,

where r is the radius of the earths surface

[tex]\omega[/tex] is the angular displacement

r = 6.37x[tex]10^6[/tex] x cos(60)

r = 3.185x[tex]10^6[/tex]m,

v = 7.3x[tex]10^{-5}[/tex] x 3.185x[tex]10^6[/tex]

v =232.5 m/s

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How would the the gravitational forces between forces between a lunar lander and the moon compare to the gravitational forces between the rocket lander assembly and the earth when the rocket is sitting on the launchpad?

Answers

All physical things with mass are attracted by the gravitational force, which can be thought of as an attractive force. It is by far the weakest known natural force.

What is Gravitational Force?

Objects with mass are drawn toward one another by gravity, also known as the gravitational force. Gravitational pull from Earth is a topic that we frequently consider. Your body is held firmly in place by this force. However, every mass-bearing item pulls everything else with mass toward it through gravity.

It is possible to think of the gravitational force as an attracting force that pulls all mass-containing physical objects together. It is the known natural force with the lowest strength.

The force of attraction between any two bodies is directly inversely correlated to the square of the distance between them and is directly inversely correlated to the product of their masses, according to Newton's universal law of gravitation.

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In a pitch situation, your vehicle weight moves to either the left or right of the vehicle. TRUE FALSE Submit answer

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The given statement "in a pitch situation, a vehicle's weight moves to either the right or left of the vehicle" is false because, in a yaw situation, a vehicle weight moves to either the right or left around the center of gravity.

The Society of Automotive Engineers (SAE) describes Vehicle Dynamics as the relationship between the forces exerted on a vehicle and the resulting motion. Three important motions of a vehicle are pitch, yaw, and roll.

Pitch is indicated as the rotation of a vehicle about the transverse axis. Yaw is referred to as the rotation of a vehicle about the vertical axis.Roll is defined as the rotation of a vehicle about the longitudinal axis.

Thus, when a vehicle's weight moves either to right or left of the vehicle, it indicates a yaw situation.

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if the generators that the dam employs are 90 % efficient, what is the maximum possible electric power output?

Answers

The maximum possible electric power output is 1339 MW. The result is obtained by multiplying the efficiency by the power input.

What is efficiency?

Efficiency of an engine can be expressed as

η = P output/ P input

P is the power. Power is the amount of energy per unit of time.

Your question is incomplete, but most probably your full question was

When the Glen Canyon hydroelectric power plant in Arizona is running at capacity, 690 m³ of water flows through the dam each second. The water is released 220 m below the top of the reservoir. If the generators that the dam employs are 90% efficient, what is the maximum possible electric power output?

We  have

Water flow rate, Q = V/t = 690 m³/sHeight, h = 220 mEfficiency, η = 90%

Find the maximum possible power output!

The density of water is ρ = 1,000 kg/m³ and the acceleration due to gravity is 9.8 m/s².

We calculate the power of the generator (P input).

P = Energy/time

P = mgh/t

P = ρgh × V/t

P = 1000 (9.8) (220) × 690

P = 1488 × 10⁶ Watt

P = 1488 × MW

The power output depends on the efficiency of the engine.

P output = η × P input

P output = 90% × 1488 MW

P output = 0.9 × 1488 MW

P output = 1339 Mega Watt

Hence, the generator will have the maximum possible power output of 1339 MW.

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a rock is thrown downward from the top of a 37.6-m-tall tower with an initial speed of 11 m/s. assuming negligible air resistance, what is the speed of the rock just before hitting the ground?

Answers

−29.27m/s is the speed of the rock just before hitting the ground when a rock is thrown downward from the top of a 37.6-m-tall tower with an initial speed of 11 m/s. assuming negligible air resistance.

What do you mean by initial speed?

When gravity first exerts force on an object, its initial velocity describes how quickly the object moves. The final velocity, on the other hand, is a vector number which gauges a moving body's speed and direction after it has reached its maximum acceleration.

To find: the speed of the rock just before hitting the ground

v f2 =v i2 +2aΔy, with v i =−11m/s and Δy=−37.6m

vf2​ =v i2+2aΔy

v2=(−11m/s) 2+2(−9.80m/s 2)(−37.6m)

v=−29.27m/s

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if an event were to take place on the sun, how long would it take for the light it generates to reach us?

Answers

If an event were to take place on the sun, it would take 8 minutes for the light it generates to reach us.

What do you mean by astronomical unit ?

The precise distance between Earth and the Sun fluctuates depending on where the planet is in its elliptical orbit. Around 150 million kilometres separate the Earth and the Sun on average (the mean distance) (93 million miles).

One astronomical unit is another name for the average separation between the Earth and the Sun (or AU). This distance is calculated to be 149, 597, 870.7 kilometres (92,955,887.6 miles).

Around the first week of July is when the Earth's apogee, or closest point to the Sun, occurs. It is roughly 152 million kilometres away (94.4 million miles).

The first week of January marks perihelion, the point in time when the Earth is closest to the Sun. It is roughly 147 million kilometres away (91.3 million miles).

Therefore, If an event were to take place on the sun, it would take 8 minutes for the light it generates to reach us.

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a 40 kg boy on a sheet of ice is initially at rest and is holding a 5 kg jug of water. He then throws the jug of water forward. If the jug has a final velocity of 3.0 m/s what is the final velocity of the boy

Answers

Answer:

mass of boy (M)=40kg

mass of jug(m)=5kg

both are at rest so (u)=0

v of jug=3m/s

v of boy=?

Now,

using PCLM

Mu+mu=Mv+mv

0=5*3+40v

v=-15/40 m/s

Why is velocity of a ball zero at the highest point?

Answers

Velocity of a ball is zero at the highest point due to the ball is momentarily at rest and is not in motion in any x-y-z direction.

This occurs because the motion of the ball is affected by the force of gravity, which acts to pull the ball downward. As the ball is thrown or launched upward, it initially has a velocity in the upward direction. However, as it rises, the force of gravity begins to slow the ball down and eventually brings it to a stop at the highest point of its trajectory. At this point, the force of gravity is acting downward on the ball with the same magnitude as the initial upward velocity, and thus they cancel each other out, resulting in a net velocity of zero. After the highest point, the ball starts to fall and the velocity becomes negative, it starts to gain velocity as it falls.

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what changes must a gas undergo to become a liquid?

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The conversion of gas into liquid happens due to condensation.

Condensation is the process through which the physical state of matter changes from the gaseous phase into the liquid phase. For example, condensation occurs when water vapour (gaseous form) in the air changes into liquid water when it comes in contact with a cooler surface. When the water in the air comes in contact with a cold surface, it condenses to form water droplets. The opposite of condensation is evaporation reaction.When temperature is increased and pressure is decreased, the gaseous state is converted into liquid state on this impact. This also can be reversed by decreasing the temperature and increasing the pressure.

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assume your eyes receive a signal consisting of blue light, 470 nm. the energy of the signal is 2.50 1014 j. how many photons reach your eyes?

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The number of photons that reach the eye from the signal of wavelength 470 nm is 59.1 x 10³¹

The wavelength of the light = 470 nm

The total energy of the signal = 2.50 x 10¹⁴ J

The photons that reach the eye can be found using the formula

          E = hc /λ

where E is the energy of one photon

           h is the Planck's constant

           c is the speed of light

           λ is the wavelength of light

Let us substitute the known values in the above equation,we get

      [tex]\displaystyle E = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{470 \times 10^{-9}}[/tex]

       

           = 0.0423 x 10⁻¹⁷

Thus, the number of photons can be found

            n = Total energy / energy of one proton

               = 2.50 x 10¹⁴ / 0.0423 x 10⁻¹⁷

              = 59.1 x 10³¹

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Sodium ions are used by your body every time you move a muscle. The difference between the na+ ions and atomic na is that.

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The sodium atom has an extra electron. If you compare the charges, it is clear that ionic sodium has one fewer electrons than atomic sodium because it has one more positive charge.

How do Na+ ions and atomic Na differ from one another?

They have different chemical properties because of variations in the number of electrons. Although the sodium atom and sodium ion have the same number of protons, the sodium atom is poisonous while the sodium ion is not poisonous, and the sodium ion is positively charged while the sodium atom is neutral.

Because we have a Na ion, the ratio of electrons to protons is not equal. Due to the presence of a cation, there are one more protons overall. Ten electrons make up the total. There are 10 electrons and 11 protons as a result.

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Assume both atlantis and zanadu produce helmets and baseballs. Using equal amounts of resources, atlantis can produce 100 helmets or 200 baseballs, whereas zanadu can produce 100 helmets or 400 baseballs.

Answers

Atlantis's opportunity cost of producing one baseball = 100 / 200 = 0.5 helmets and Zanadu opportunity cost of producing one baseball = 100 / 400 = 0.25 helmets .So , Zanadu has a comparative and absolute advantage in the production of baseballs .

The opportunity cost is the sum of the money that could be spent in other ways and the time spent studying. There is an opportunity cost connected with not growing wheat or using the resources in another way when a farmer decides to do so (land and farm equipment).

The rewards that are forgone while choosing one course of action over another are referred to as opportunity costs in economics. In essence, it is the value of the untaken path.

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The correct question is :

Assume both Atlantis and Zanadu produce helmets and baseballs. Using equal amounts of resources, atlantis can produce 100 helmets or 200 baseballs, whereas Zanadu can produce 100 helmets or 400 baseballs. Which country has an absolute advantage in the production of baseballs?

When heat flows into an object, its thermal energy increases, and so does its temperature.
What does the amount of temperature increase depend on?

Answers

An object's thermal energy and temperature rise as a result of heat flow into the thing. Three factors determine the amount of temperature increase: 1) The amount of heat added, 2) the object's size, and 3) the substance used to create the object.

What happens when thermal energy increases?

The average kinetic energy of an object's particles rises as its temperature rises. The thermal energy of the object grows as the average kinetic energy of its constituent particles rises. Therefore, when an object's temperature rises, so does its thermal energy.

Thermal energy is added to a substance during heating. As a result, its temperature increases and its particle motion accelerates. When a substance cools, thermal energy is lost, which slows down the movement of its particles and lowers the substance's temperature.

When heat enters an object, both its temperature and thermal energy rise. There are three factors that affect how much the temperature rises: The amount of heat added, the object's size, and the material it is made of are the first three variables.

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guys pls help
Question 7 (Multiple Choice Worth 2 points)
(01.01 MC)
Researchers conduct an experiment and obtain different results from the original investigation. They publish their findings as a new discovery. Which statement best describes how the researchers can make their findings more reliable?
O Scientific knowledge cannot change, so nothing will make it more reliable.
O Complete more trials and have other scientists repeat the experiment.
O Pay other researchers to show the same evidence.
O Write another article persuading why they are correct.

Answers

A study's outcome is the results of the study.All potential outcomes make up the sample space of an experiment.

What do the findings of a scientific experiment go by? A study's outcome is the results of the study.All potential outcomes make up the sample space of an experiment.So that other scientists might try to reproduce the results for future research, it is crucial for the scientist to precisely describe the experiment and how it is set up and conducted.One (or both) of the two categories of data: qualitative and quantitative—will be produced as the result of an experiment.The four main design categories with regard to user research are correlational, experimental, quasi-experimental, and single subject.These research designs progress from those with high validity and generalizability to those with less validity and generalizability.

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A child with a mass of 25 kg is riding a bike with a mass of 6.3 kg with a velocity of 6.5 m/s. What is the momentum of the bike?

A. 41 kg m/s
B. 163 kg m/s
C. 198 kg m/s
D. 203 kg m/s

Answers

The momentum of the bike is 41kgm/s (option A).

How to calculate momentum?

Momentum is the tendency of a body to maintain its inertial motion i.e. the product of its mass and velocity, or the vector sum of the products of its masses and velocities.

The momentum of an object can be calculated by multiplying the mass of the object by its velocity.

According to this question, a child with a mass of 25 kg is riding a bike with a mass of 6.3 kg with a velocity of 6.5 m/s.

Momentum of the bike = 6.3kg × 6.5m/s = 40.95kgm/s

Therefore, 41kgm/s is the momentum of the bike.

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A rock is dropped off a cliff 115 meters high. How long does it take for the rock to reach the ground?​

Answers

4.84 seconds to reach the ground

How is total magnification calculated?

Answers

Calculating total magnification involves multiplying the power of the objective and ocular lenses.

How is a microscope's magnification determined?

The microscope's magnification is relatively simple to determine. Just double the eyepiece's magnification by the objective lens's magnification. Nearly invariably, the barrel (objective) or top of a microscope's eyepieces and objectives are inscribed with the instrument's magnification (eyepiece).

In other words, the total magnification of a microscope is calculated by multiplying the objective lens's magnification by the optical lens' magnification.

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Billiard ball A, mass 0. 17 kg, is moving due east with a velocity of 4. 0 m/s. It strikes

stationary billiard ball B, which has the same mass. After the collision, ball A moves

at an angle of 30° north of east with a velocity of 3. 5 m/s. Ball B moves at an

angle of 60° south of east. What is the speed of ball B?

a

2 m/s

b

8 m/s

С

10 m/s

d

5 m/s

Answers

The system that is colliding maintains its momentum. As a result, the ball B's speed is 2m/s (option -a) when it has the same mass as the ball A.

Describe momentum.

A body's capacity to produce the greatest displacement from an applied force is known as momentum. It is the result of adding mass and speed. The two bodies' total initial momentum and total final momentum are equal in a collision.

Consequently, let u be the starting velocity and v be the ending velocity.

m₁ u₁+ m₂ u₂ = m₁ v₁ + m₁ v₂

m₁ =  0.17 kg

u₁ = 4 m/s

m₂ = 0.17 kg

u₂ = 0

Then initial momentum = 0.17 × 4 m/s + 0 = 0.68 kg m/s

v₁ = v₁ cos 30° = 3.5×√3/2

v₂ = v₂cos 60 = v/2

0.68 kg m/s = (0.17 × 3.5×√3/2 ) +  (0.17 × v₂/2)

3.5×√3/2/2 + v₂/2 = 4

3.5√3 + v₂ = 8

then v₂ = 8-3.5(1.732)

v₂ = 1.94m/s. = 2m/s

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A woman, using a manual jack to lift her car, expends 10. 0 kJ of energy in the process. If she raises her 1 500 kg car off the ground by 0. 50 m, what is her efficiency ?

Answers

The woman's manual jack has an efficiency of 7.4.

To calculate the efficiency of a system, you need to know the input energy and the output energy.

In this case, the input energy is the 10.0 KJ of energy that the woman expends using the manual jack, and the output energy is the work that she does in lifting the car off the ground.

The work that the woman does in lifting the car off the ground can be calculated using the equation: W = Fd, where

W is the work done,

F is the force applied, and

d is the distance over which the force is applied.

In this case, the force applied is the weight of the car (F = mg), and the distance is 0.50 m that the car is lifted off the ground.

Plugging these values into the equation, we find that the work done in lifting the car off the ground is:

W = (1500 kg)(9.8 m/s²)(0.50 m) = 74,000 J.

The efficiency of the system can then be calculated using the equation efficiency = (output energy) / (input energy).

Plugging in the values for the output energy (74,000 J) and the input energy (10,000 J), we find that the efficiency of the system is :

Efficiency = (74,000 J) / (10,000 J) = 7.4.

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What is its acceleration of the highest point of its point?

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When it is maximum, acceleration is zero. The rate at which velocity changes is called acceleration. Acceleration often indicates a change in speed, but not necessarily.

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. It is a vector quantity to accelerate (in that they have magnitude and direction). The direction of the net force applied on an item determines the direction of its acceleration. According to Newton's Second Law, an object's acceleration is the result of two factors working together: the object's mass, which varies depending on the materials it is made of, and the net balance of all external forces acting on it. The magnitude of an object's acceleration is inversely proportional to the object's mass.

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PHYSICS PLS HELP!

A ball is thrown horizontally from a hill 42.9 m high at a velocity of 5.85 m/s.
Find the distance between the base of the hill and the point where the ball hits
the ground?

Answers

The horizontal distance dx is determined using the formula dx = vx * t where vx = 5.85 m/s and t is the time of hill of the ball.

What is meant by hill ?

A piece of land that rises above everything around it is called a hill. It appears to be a small Earthly bump.Hills are fantastic places to gain a nice view because they are higher than anything else around them.Mountains are more difficult to climb than hills. They are not as high and less steep.A landform that rises above its surroundings is called a hill.A mountain, on the other hand, is a steep landform that is higher than 300m. Mountains are higher, while hills are lower and less steep.A mountain is a significant landform that, in a defined area, rises above the terrain below, typically in the form of a peak. A mountain often has a steeper slope than a hill.

Solving for the time of hill t of the ball

t_hill = t_fall

h = 0.5 * g * t^2

42.0 m = 0.5 * 9.8 m/s^2 * t^2

t^2 = 42.0 m / 4.9 m/s^2

t^2 = 8.571

t = 2.927 s

Solving for the horizontal distance dx

dx = vx * t

dx = 5.85 m/s * 2.927 s

dx = 17.12 m

The ball hit the ground at 17.12 m from the base of the cliff.

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Please answer this by 8:30! Thank you!!

Answers

The organism represented below is a multicellular, heterotrophic and completely aquatic organism which carries out photosynthesis and needs oxygen. Thus, the correct option is C.

What are Hydra?

Hydra belongs to the phylum Cnidaria of the Animal kingdom, it is a fresh water form. These organisms are sessile, free swimming invertebrates. Cnidarians exhibit a blind sac body plan and these are radially symmetrical. These organisms are more advanced than that of sponges in having true tissues in their body. They are, however, also acoelomate.

The organism which is shown here lives in water and is completely aquatic which means it does goes on the land for a while. It is a heterotrophic organism as it does not make its food through the help of the process known as photosynthesis.

In this case, this organism is not a plant. This organism is a multicellular organism, which feeds on the plants or other organism present in water. This organism reproduces through asexual mode of reproduction and is therefore definitely a consumer.

Therefore, the correct option is C.

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which statement best explains why a salt solution conducts electricity? responses the ions move freely in water but lose their charges. the ions move freely in water but lose their charges. the salt crystals dissolve and form bridges by which electric charges move. the salt crystals dissolve and form bridges by which electric charges move. the ions move freely in water and carry electric charges. the ions move freely in water and carry electric charges. the salt crystals remain intact and form bridges by which electric charges move.

Answers

Pure water is not so much conductive, and only a small piece of current can move during the water. When salt or sodium chloride (NaCl) is melted in it, Yet, the salt molecules divided into two pieces, a sodium ion and a chlorine ion.

The sodium ion is lost an electron, that gives it a positive charge. The chlorine ion has an more electron, giving it a negative charge.

An electric origin sending a current through water will have two terminals: one is negative that conducts electrons into the water, and another is positive one that removes them.

Opposite charges attract, so the sodium ions are engaged to the negative terminal, and the chlorine to the positive.

The ions form a bridge, the sodium ions fascinating electrons from the negative terminal, passing them to chlorine ions and then the positive terminal.

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how did the discoveriesof copernicous and ther astronomers affect the way people viewed the universe

Answers

Copernicus and other astronomers' discoveries significantly changed how people perceived the cosmos.

Describe the universe.

All things that are present, including all matter, energy, and space, are collectively referred to as the universe. It includes every type of matter and energy in the known and undiscovered physical universe, including galaxies, planets, stars, and all other kinds of matter. The Big Bang, an enormous explosion that began time and space, is thought to have been the beginning of the universe. The universe has been growing ever since and is now thought to be more than 13.8 billion years old.The Ptolemaic system, which predates Copernicus, was the widely accepted theory that the sun, other planets, and Earth all revolved around one another. In his heliocentric theory, Copernicus

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if you are standing on mars and you stepped onto a weight scale, what would it say if on earth you weighed 150 lbs?

Answers

if you are standing on mars and you stepped onto a weight scale, Your weight would be 60 lbs if on earth you weighed 150 lbs because of Mars Gravity which 40% that of the earth.

What is Gravity?

The fundamental interaction which causes all objects with mass or energy to attract one another is termed as Gravity.

The moon is maintained in its orbit around Earth by gravity, as are the planets in their orbits around the sun. Ocean tides are a result of the moon's gravitational effect on the oceans. The stuff that stars and planets are comprised of is pulled together by gravity to form them.

The first to create a quantitative theory of gravity was Isaac Newton, who postulated that the force of attraction between two bodies is inversely proportional to the square of the distance between them and inversely proportional to the product of their masses.

Calculation:

The 40%of 150lbs= 40*150/100= 60lbs

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Which of the following can you do with dimensional analysis?
A. Check conversions between units using numbers only
B. Check conversions between units using units only
C. Find numeric values
D. Check conversions between units using numbers and unit​

Answers

Answer:

Explanation:

B. Check conversions between units using units only.

Which two statements are true of mechanical waves?
A. They travel by causing particles of matter to vibrate.
B. They use a medium to transfer energy.
C. They transfer energy by disturbing electric and magnetic fields.
D. They do not need a medium to transfer energy.

Answers

Two statements, that are true of mechanical waves, are:

They travel by causing particles of matter to vibrate. They use a medium to transfer energy.

What is mechanical wave?

A mechanical wave is a wave in physics that involves the oscillation of matter and transmits energy across a medium. While waves can travel great distances, the transmission medium—the material—can only move so far.

The oscillating material stays close to its initial equilibrium position as a result. Only medium with elasticity and inertia can form mechanical waves. Transverse, longitudinal, and surface waves are the three different forms of mechanical waves.

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when an object is located 36 cm to the left of a lens, the image is formed 22 cm to the right of the lens. part a what is the focal length of the lens?

Answers

The focal length of the lens when the object is at 36 cm from the lens on the left and the image is at 22cm towards the right is 13.6 cm.

In optics, the relationship between the distance of the image (v), the distance of the object (u), and the focal length (f) of the lens are given by the formula known as the Lens formula. The Lens formula is applicable for convex as well as concave lenses. These lenses have negligible thickness.

The position of the object,u= 36cm to the left of the lens.

The position of the image, v= 22 cm to the right of the lens.

According to the sign convention, if we take the direction in which the ray of light goes as the positive direction. Then u=-36cm and v=+22cm.

Now from the lens formula, 1/f=1/v-1/u, 1/f= 1/22-(-1/36), 1/f= 1/22+1/36=(36+22)/36×22 =58/792. f= 792/58 = 13.6 cm.

The focal length of the lens is 13.6cm.

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the force exerted on a particle experiencing a certain kind of force is given by f of t is equal to negative 3 times t to the 4th power plus 8 times t to the 3rd power plus 5, with f measured in newtons (n) and t measured in s. at what time is the most force exerted on the particle?

Answers

The most force is exerted on the particle when t=3/2 seconds. You can double check this by substituting t = 3/2 into the original function f(t) and see that it is indeed the maximum value of the function.

Time is scalar quantity. The international unit of time is second. To find the time at which the most force is exerted on the particle, we need to determine the maximum value of the function f(t) = [tex]-3t^4 + 8t^3 + 5.[/tex]

The first step is to find the derivative of the function f(t) with respect to t.

[tex]f'(t) = -12t^3 + 24t^2[/tex]

Now we need to find the critical points of the function by setting the derivative equal to zero and solving for t

f'(t) = 0

[tex]-12t^3 + 24t^2 =0[/tex]

[tex]t^2(2t-3)=0[/tex]

t=0, t=3/2

The next step is to check the second derivative, if the second derivative is positive then the critical point is a local minimum and if the second derivative is negative then the critical point is a local maximum.

f''(t) = [tex]-36t^2 + 48t[/tex]

f''(0) = 0 and f''(3/2) = -9, so t=0 is a local minimum and t=3/2 is a local maximum.

So the most force is exerted on the particle when t=3/2 seconds.

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