''In general, the normal force is not equal to the weight." Give an example where the two forces are equal in magnitude and at least two examples where they are not.

Answers

Answer 1

A normal force is a force applied perpendicular to a surface on an object in contact with it. The weight is the gravitational force imposed on an object, and it is equal to the mass multiplied by the acceleration due to gravity.

When an object is put on a scale at rest on a level surface, the normal force equals the weight. In this instance, the normal force acting upwards from the scale on the object is equal to the weight acting downwards.

Here are two instances of normal forces that are not equal to weight:

When a person stands on an inclined plane or ramp, the normal force applied by the plane is less than the person's weight, because some of the weight is resolved parallel to the plane, causing the person to slide down if enough friction exists.

The normal force exerted by the air or other medium on a person in free fall is zero, while their weight due to gravity stays constant.

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Related Questions

Which two statements are true for reversible reactions that reach dynamic
equilibrium?
I A. The products of the forward and backward reactions remain
constant at equilibrium.
B. The products of the forward reaction form more quickly than its
reactants.
C. The rate of the forward reaction is greater than the rate of the
backward reaction.
- D. The rate of the forward reaction is equal to the rate of the
backward reaction at equilibrium.

Answers

Answer:

Explanation:

In a reversible reaction which has reached dynamic equilibrium , rate of forward reaction is equal to rate of backward reaction .

Following is a reversible chemical reaction .

A + B = C + D

Rate of forward reaction = k₁ x [ A ] x [ B ]

Rate of backward reaction = k₂ x [ C ]  x [ D ]

k₁ x [ A ] x [ B ] =  k₂ x [ C ]  x [ D ]

[ A ] x [ B ] = k₂ / k₁  [ C ]  x [ D ]

[ A ] x [ B ] = k   [ C ]  x [ D ]

The products of the forward and backward reactions remain

constant at equilibrium.

Hence option A and D are correct statement .

24- What happens to a given mass of water as it is cooled from 4°C to zero?
(a) expands
(b) contracts
(c) vaporizes
(d) Neither expands, contracts, nor vaporizes.

Answers

Explanation:

A-It starts to expand. Hence ice and water of same weight has different volumes

Expansion happens to a given mass of water as it is cooled from 4°C to zero. Option A is correct.

What is temperature?

Temperature directs to the hotness or coldness of a body. In straightforward terms,

it is the method of finding the kinetic energy of particles within an entity. Faster the motion of particles more the temperature.

Water loses density when it is cooled from 4°C to 0°C. It turns out that the temperature at which liquid water has the most significant density is 4 degrees Celsius.

It will increase in size when heated or cooled. Since most liquids shrink when they are chilled, it is rare for water to expand when cooled to lower temperatures.

As a mass of water is cooled from 4°C to zero, expansion occurs.

Hence, option A is correct.

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In hiking, what fitness component is required of you

Answers

It’s strength, endurance and flexibility. Hope this helps

what causes chest pain is it by eating peppery food? ​

Answers

Answer:

Yes that is almost always the problem!

Explanation:

Answer:

the answer is Acid reflux hope this helped!

On the water surface, there are two sources of oscillating waves of the same phase located at A and B, emitting two coherent waves of wavelength λ. Let Δ be the line perpendicular to AB at B. On Δ there are 16 interference maxima, the distance between the two closest and farthest interference maxima is 2.71 cm and 229.55 cm, respectively. . Which of the following is the length of line segment AB closest to?

Answers

Two or greater sources are said to be coherent if they emit waves that have the identical wavelength (or frequency) and amplitude and which maintain a steady phase difference.

Do two coherent sources have equal wavelength?

If two sources have the identical wavelength, frequency, and segment difference, they are said to be coherent. Therefore, we can conclude that coherent sources have the identical wavelength.

Two microwave coherent factor sources emitting waves of wavelenths λare positioned at 5λdistance apart. The interference is being observed on a flat non-reflecting surface alongside a line passing through on sources ,in a course perpendicular to the line joining the two sources

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Question 4
3 pts
I am approaching a traffic light at a speed of 135 km/h when I suddenly notice that
the light is red. I slam on my brakes and come to a stop in 4.29 seconds. What is the
acceleration of the car as I screech to a complete stop? (Note that an object that slows down
simply has a negative acceleration.)
& show work please I want to also understand

Answers

Answer:

The deceleration of the car is \(\approx -0.065m/s^{2}\)

Explanation:

to solve this, we will have to apply the knowledge that will be got from the equations of motion.

There are several equations of motion, and depending on the parameters given in the problem, we can choose the perfect equation that can best be used to solve the problem.

In this case, since we are given the velocity and time, and we are solving for the acceleration, we will use this formula

\(v = u +at\)

where v= final velocity = 0

u = initial velocity = 135Km/h \(\approx 0.278 m/s\)

t= time = 4.29 seconds.

\(a = \frac{v - u}{t}\)

\(a =\frac{0-0.278}{4.29} \approx 0.065m/s^{2}\)

Hence, the deceleration of the car is \(\approx -0.065m/s^{2}\)

1) How much work is done when a force of 50N
pulls a wagon 20 meters?

Answers

Answer:

100J

Explanation:

50N*20m=100J

N*m=J(joule)

A sample of helium behaves as an ideal gas as it is heated at constant pressure from 283 K to 358 K. If 70 J of work is done by the gas dur- ing this process, what is the mass of the he- lium sample? The universal gas constant is 8.31451 J/mol · K. Answer in units of g.

Answers

The mass of the helium sample is approximately 0.187 g.

To solve this problem, we can use following formula:

w = nR(T2 - T1)

We can rearrange this formula to solve for n:

n = w / (R * (T2 - T1))

To find the mass of the helium sample, we can use following formula:

m = n * M

where m is the mass of the sample, n is  number of moles of gas, and M is the molar mass of helium.

Substituting the given values into the first equation, we get:

70 J = n * 8.31451 J/mol*K * (358 K - 283 K)

Simplifying this equation, we get:

n = 0.0467 mol

Substituting this value into the second equation, we get:

m = 0.0467 mol * 4 g/mol = 0.187 g

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Since illness can be caused by bacteria that live in water, pollution in water can lead to serious illness. true or false

Answers

Answer:

true, there are certain forms of bacteria in water that can cause permanent brain damage (although its rare) so further contamination of water can lead to higher chances of contracting serious illnesses caused by such bacteria.

What is the mass of a block of lead that is 30cm by 80cm by 60cm?

Answers

Calculating the mass of the block requires a bit of work. The formula for the volume of a rectangular solid is V = l*w*h, where V is the volume, l is the length, w is the width, and h is the height. Using the dimensions given, we can calculate the volume of the block as 30*80*60 = 144000 cubic centimeters.

The density of lead is approximately 11.34 grams per cubic centimeter. To calculate the mass of the block, we can use the formula m = V*d, where m is the mass, V is the volume, and d is the density. Plugging in the values we get m = 144000*11.34 = 1,634,400 grams or approximately 1.63 metric tons.

So, the mass of the block of lead is approximately 1.63 metric tons.

4) The diagram shown alongside is a parachutist who release the parachute bag before reaching the ground. When the parachute bags opens, the drag force increases enabling him to land safely. What does this show and how does it affect drag force?​

Answers

The diagram shows the concept of using a parachute to decrease the velocity of a falling object and thereby decreasing the impact when it lands on the ground.

The opening of the parachute increases the drag force acting on the object.

What is a parachute?

A parachute is described as a device used to slow the motion of an object through an atmosphere by creating drag or, in a ram-air parachute, aerodynamic lift.

The drag force is proportional to the velocity of the object and the cross-sectional area of the object.

So if the parachute is released, it increases the cross-sectional area of the object, which leads to  an increase in the drag force acting on the object.

This increase in drag force, in turn, reduces the velocity of the object and helps the person land safely.

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Need help with these two problems PLEASE

Need help with these two problems PLEASE

Answers

Answer:

a b

Explanation:

faf ggrgb  gbrsdfvbbbbbrgefdvfbdgnfhm,ilytukrjyethsfbnghhmj,io;yiltkurjyethwrgfsv

1 )5kg box
2)vertical =50n+ 50n=100n
horizontal =40n+40n=80n

help me please!!!!!!!!!!!!!!!!​

help me please!!!!!!!!!!!!!!!!

Answers

Answer: B have a good day :)

10. Refraction occurs...
A. only with light waves
B. at any, unpredictable time
C. when a wave changes speed
D. only at a wave front
E. All of the above

Answers

The answer is C! Good luck!

Gold forms a solid solution with silver. Since the densities of pure gold and silver are 19.32 g/cm³ and 10.49 g/cm³, respectively, calculate the number of gold atoms per cubic centimeter for a silver-gold alloy containing 10% Au and 90% Ag by weight.

Answers

There are 3.37 × \(10^{22}\) gold atoms per cubic centimeter in the silver-gold alloy.

The density of a binary alloy can be calculated using the following equation:

ρ = w1ρ1 + w2ρ2

where,

ρ = density of the alloy

w1 and w2 = weight fractions of the two components (in this case, gold and silver)

ρ1 and ρ2 = densities of the pure components.

We are given that the alloy contains 10% gold and 90% silver by weight, so we can calculate the weight fractions as:

\(w_{Au}\) = 0.10

\(w_{Ag}\) = 0.90

We are also given the densities of pure gold and silver as:

ρ_Au = 19.32 g/\(cm^{3}\)

ρ_Ag = 10.49 g/\(cm^{3}\)

Now we can substitute these values into the density equation to find the density of the alloy:

ρ = \(w_{Au}\)ρ_Au +\(w_{Ag}\)ρ_Ag

ρ = (0.10)(19.32 g/\(cm^{3}\)) + (0.90)(10.49 g/\(cm^{3}\))

ρ = 11.08 g/\(cm^{3}\)

Next, we need to calculate the number of gold atoms per cubic centimeter in the alloy.

To do this, we can use Avogadro's number and the atomic weights of gold and silver:

\(N_A\) = 6.022 × \(10^{23}\) atoms/mol

Aum = 196.97 g/mol

Agm = 107.87 g/mol

The number of gold atoms:

\(n_{Au}\) = (\(w_{Au}\)ρ/ Aum) × \(N_{A}\)

Substituting the values, we get:

\(n_{Au}\) = (0.10 × 11.08 g/\(cm^{3}\)/ 196.97 g/mol) × 6.022 × \(10^{23}\) atoms/mol

\(n_{Au}\) ≈ 3.37 × \(10^{22}\) atoms/\(cm^{3}\)

Therefore, there are approximately 3.37 × \(10^{22}\) gold atoms per cubic centimeter in the silver-gold alloy.

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HELP ASAP WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!!
The Left and right forces acting on this cart are

A. balanced
B. super-positioned
C. unbalanced
D. counter-balanced

HELP ASAP WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!!The Left and right forces acting on this cart

Answers

Answer:

B. Super-Positioned

Explanation:

light of 650 nm wavelength illuminates two slits that are 0.21 mm apart. (figure 1) shows the intensity pattern seen on a screen behind the slits.

Answers

The distance of the screen is 107.7 meter.

What is interference of light?

When two coherent light waves from separate sources collide, the energy distribution caused by the first wave is altered by the second. The term "interference of light" refers to this alteration in the distribution of light energy brought on by the superposition of two light waves.

Given that: wavelength of light: λ = 650 nm = 650×10⁻⁷ cm.

separation between two slits: d = 0.21 mm = 0.021 cm.

According to fig. separation between two bright fringe: x = 1/3 cm

Now, from x = λD/d we get:

separation  between the screen and the slits: D = xd/λ.

= (1/3× 0.021)/ 650×10⁻⁷ m

= 107.7 meter.

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From a height of 30 meters we throw an object vertically downwards with a speed of 2 m/s. How long will it take to reach the ground and with what speed?

Answers

1. The time taken for the object to reach the ground is 2.47 s

2. The speed with which the object will reach the ground is 26.206 m/s

1. How do I determine the time taken?

We can obtain the time taken for the object to reach the ground as      follow:

Height (h) = 30 metersAcceleration due to gravity (g) = 9.8 m/s²Time taken to reach the ground (t) = ?

h = ½gt²

30 = ½ × 9.8 × t²

30 = 4.9 × t²

Divide both side by 4.905

t² = 30 / 4.9

Take the square root of both side

t = √(30 / 4.9)

t = 2.47 s

Thus, the time taken to reach the ground is 2.47 s

2. How do i determine the speed?

The speed the object will use to reach the ground can be obtained as follow:

Initial speed (u) = 2 m/sTime (t) = 2.47 sAcceleration due to gravity (g) = 9.8 m/s²Final speed (v) =?

v = u + gt

v = 2 + (9.8 × 2.47)

v = 2 + 24.206

v = 26.206 m/s

Thus, the speed is 26.206 m/s

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Suppose in Example 7.13that the arrival process is a Poisson process and suppose that the policy employed is to dispatch the train every t time units.(a) Determine the average cost per unit time.(b) Show that the minimal average cost per unit time for such a policy is approximately c/2plus the average cost per unit time for the best policy of the type considered in that example

Answers

If the arrival process is a Poisson process, the average cost per unit time can be calculated using the following formula:

Average Cost per Unit Time = (c * t * λ) / 2

where c is the cost of dispatching the train, t is the time interval between each dispatch, and λ is the average number of arrivals per unit of time.

To find the minimal average cost per unit time for a policy of dispatching the train every t time units, we need to minimize the expression (c * t * λ) / 2. Taking the derivative with respect to t, we get

d(c * t * λ) / 2dt = c * λ

Setting this equal to 0 and solving for t, we get t = 0, which gives us the minimal average cost per unit time of c/2. Thus, the minimal average cost per unit time for a policy of dispatching the train every t time units is approximately c/2 plus the average cost per unit time for the best policy of the type considered in that example.

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Can someone find the answer and explain part b of this problem? Please provide me with the equation, too.

Can someone find the answer and explain part b of this problem? Please provide me with the equation,

Answers

a.The direction of the magnetic field at point P, located above a long straight wire carrying current, is perpendicular to the wire and depends on the direction of the current, as determined by the right-hand rule, and b.the magnitude of the magnetic field at point P is 0.01 Tesla.

A magnetic field is a physical field that is created by electric charges in motion, such as an electric current or a moving magnet. It exerts a force on other moving charges and magnetic objects and is an essential component of many modern technologies including electric motors, generators, and magnetic storage devices.

a. Using the right-hand rule for the magnetic field around a straight wire, we can determine that the direction of the magnetic field at point P is perpendicular to both the direction of the current and the vector pointing from the wire to point P. Specifically, the magnetic field points out of the plane of the paper (or screen) if the current is flowing from left to right, and into the plane of the paper (or screen) if the current is flowing from right to left.

b. We can use the formula for the magnetic field around a straight wire to calculate the magnitude of the magnetic field at point P:

B = μ₀I/(2πr)

where B is the magnetic field, μ₀ is the vacuum permeability constant (4π x 10^-7 T m/A), I is current, and r is the distance from the wire to the point of interest. In this case, I = 50 A and r = 2.5 mm = 0.0025 m. Substituting these values into the formula, we get:

B = (4π x 10^-7 T m/A)(50 A)/(2π x 0.0025 m) ≈ 0.01 T

So, the magnitude of the magnetic field at point P is approximately 0.01 Tesla.

Therefore, According to the right-hand rule, the magnetic field at point P, which is placed above a long, straight wire carrying current, is perpendicular to the wire and depends on the direction of the current. Its strength is also 0.01 Tesla.

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The first step of making the scientific method involves making ----------

Answers

Answer: Objective Observations

Explanation: The first step in the Scientific Method is to make objective observations. These observations are based on specific events that have already happened and can be verified by others as true or false

Calculate the net force on the particle q1.

Calculate the net force on the particle q1.

Answers

Answer:

-12.1

Explanation:

i’m almost sure this is it, i’m checking my old answers

if not let me know and i’ll give you some more answers

Three particles having charges of equal magnitude q are fixed at the conrners of an equilateral triangle as shown. two of the charges are negative: the other is positive. which of the following vectors best represents the direction of the resultant electric field at point p, the center of the triangle?

Answers

Vector B of the following vectors best represents the direction of the resultant electric field at point p, the center of the triangle.

What is vector?

A  quantity or phenomenon that has two independent properties i.e magnitude and direction is named as vector.

At the middle, where it is zero, one can see that the three charges each produce cancelling fields thanks to symmetry.In addition to the triangle's center, the second panel of the picture shows three additional sites in the middle of each triangle leg where E=0, however they are more challenging to calculate analytically.

Adding the electric field vectors resulting from each of the two lower point charges will yield the electric field at point P.

E = E1+ E2.

According to the bottom panel of the picture, a point charge's electric field has the formula E = kr2qr.

E =k ea2q uphill and to the right at 60, and E2 =kea2q upward and to the left at 60.

Therefore, E= E1 + E2 = kea2q[(cos60i+sin60j) + (cos60i+sin60j)] = kea2q[2(sin60j)

= 1.73kea2qj. i.e vector B

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How much ice at a temperature of -22.3 ∘C must be dropped into the water so that the final temperature of the system will be 30.0 ∘C ?How much ice at a temperature of -22.3 ∘C must be dropped into the water so that the final temperature of the system will be 30.0 ∘C ?

Answers

Answer:

111.6 g or 0.112 kg

Explanation:

specific heat of liquid water = 4190 J/kg⋅K

specific heat of ice = 2100 J/kg⋅K

heat of fusion for water = 3.34*10^5 J/kg

You didn't state the mass of the beaker, so, I will be assuming that the mass is negligible.

Assuming that the mass of ice required is m kg

Then the heat gained by the ice to attain zero degree will be

= m * 22.3 * 2100

= 46830m J

The heat gained by the ice to melt

= m * 3.34*10⁵ J

= 334000m J

The heat gained by water at zero degree to warm up to 30° =

m * 4190 * 30 = 125700m J

Total heat gained = 506530m J

Note: You didn't state the mass of the water and it's temperature, so I will be assuming that the mass of water is 0.3 kg, and it's temperature was 75° C

The heat lost by hot water to cool up to 30°

= .3 * 4190 * (75 - 30)

= 1257 * 45

= 56565 J

Using the relation, Heat lost = heat gained

506530m = 56565

m = 56565 / 506530 kg

m = 0.112 kg or 111.6 g

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Calculate forces and accelerations for a horizontal spring system. A 0.350 kg object attached to a spring of force constant 1.30 x 10 N/m is free to move on the frictionless horizontal surface. If the object is released from rest at x = 0.100 m, find the force on it and its acceleration at x = 0.100 m, x-0.0500m, x = 0. x= -0.0500m and x = -0.100 m.​

Answers

The force and acceleration alter as the object moves away from its equilibrium position.

How to calculate force and acceleration?

The force on the object at any point is given by Hooke's Law:

F = -kx

where F = force, k = force constant of the spring, and x = displacement of the object from its equilibrium position.

The acceleration of the object at any point is given by Newton's Second Law:

a = F/m

where a = acceleration, F = force, and m = mass of the object.

Using these equations, calculate the force and acceleration at each of the specified points:

At x = 0.100 m:

F = -kx = -(1.30 x 10 N/m)(0.100 m) = -0.130 N

a = F/m = (-0.130 N)/(0.350 kg) = -0.371 m/s² (the negative sign indicates that the acceleration is in the opposite direction to the displacement)

At x = 0:

F = -kx = -(1.30 x 10 N/m)(0) = 0 N (the spring is at its equilibrium position)

a = F/m = 0 N/0.350 kg = 0 m/s²

At x = -0.0500 m:

F = -kx = -(1.30 x 10 N/m)(-0.0500 m) = 0.065 N (note that the force is positive because the displacement is negative)

a = F/m = (0.065 N)/(0.350 kg) = 0.186 m/s²

At x = -0.100 m:

F = -kx = -(1.30 x 10 N/m)(-0.100 m) = 0.130 N

a = F/m = (0.130 N)/(0.350 kg) = 0.371 m/s²

So, the force and acceleration change with the displacement of the object from its equilibrium position.

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A student builds an electromagnet using a battery, an iron nail, and some insulated wire. The wire is wrapped around the nail 50 times, then connected to the
battery. What changes could the student make to increase the strength of the electromagnet?
1. wrap more wire around the nail
2. increase the voltage of the battery
3. use a switch to turn the electromagnetic on and off
4. increase the size of the nail

A. 1 and 2
B. 2 and 4
C. 1,2 and 4
D. 1,2,and 3

Answers

Answer:

a

Explanation:

its right

To increase the electromagnet's strength, the student must enlarge the nail, wrap more wire around the nail, and increase the voltage of the battery. Option c is the correct answer.

How does an electromagnet work?The mechanics of an electromagnet are not overly complicated. It is accomplished by wrapping a length of conductive wire, usually copper, around a metal object.Until electricity is introduced, this appears to be nothing more than a jumbled collection of parts, similar to Frankenstein's monster. An electromagnet, on the other hand, does not require a storm to be activated. A current is introduced and flows through the wire, which can come from a battery or another source of power.As a result of the magnetic field created around the coiled wire, the metal is magnetized as if it were a permanent magnet. Electromagnets are useful because they can be activated and deactivated by closing and opening a circuit.

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What is Energy in physics?

Answers

Answer:

Energy, in physics, the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or other various forms. There are, moreover, heat and work—i.e., energy in the process of transfer from one body to another.

Explanation:

Hope this helps!

Tarik winds a small paper tube uniformly with 175 turns
of thin wire to form a solenoid. The tube's diameter is 8.05 mm
and its length is 2.37 cm
. What is the inductance, in microhenrys, of Tarik's solenoid?

Answers

The value of the inductance, in , microhenrys of Tarik's solenoid is approximately 1.6239 microhenrys.

How to solve

To calculate the inductance of a solenoid, we can use the formula:

L = (μ₀ * N² * A) / l

where L is the inductance, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), N is the number of turns, A is the cross-sectional area of the solenoid, and l is the length of the solenoid.

In this case, we have:

N = 175 turns

Diameter = 8.05 mm = 0.00805 m (converted to meters)

Radius = Diameter / 2 = 0.00805 m / 2 = 0.004025 m

Length (l) = 2.37 cm = 0.0237 m (converted to meters)

First, let's find the cross-sectional area (A) using the formula for the area of a circle:

A = π * r² = π * (0.004025 m)² ≈ 5.08398 × 10⁻⁵ m²

Now we can plug in the values into the formula for inductance:

L = (4π × 10⁻⁷ T·m/A * (175)² * 5.08398 × 10⁻⁵ m²) / 0.0237 m

L ≈ (1.2566 × 10⁻⁶ * 30625 * 5.08398 × 10⁻⁵) / 0.0237

L ≈ (38.5086 × 10⁻⁶) / 0.0237

L ≈ 1.6239 × 10⁻⁶ H

Now, let's convert the inductance from henrys to microhenrys:

L ≈ 1.6239 × 10⁻⁶ H * 10⁶ μH/H ≈ 1.6239 μH

So the inductance of Tarik's solenoid is approximately 1.6239 microhenrys.

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I NEED HELP WITH THIS QUESTION

I NEED HELP WITH THIS QUESTION

Answers

The charge R is positive and the charge L is negative hence, the correct option is option D.

The electric charges are of two types and they are positive and negative charge. There is an attractive force between the two charges. The electric field is formed around the charges and the electric field is denoted by using field lines around it.

The field lines are emerging from positive charge and end up in a negative charge. The field lines never intersect with each other. Hence, from the given, the field lines emerging from the positive charge(R) and end up in the negative charge(L).

Hence, the ideal solution is option D.

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State the hamilton's equation of
motion and derive each of them

Answers

Hamilton's equations of motion are a set of equations that describe the dynamics of a classical mechanical system in terms of a generalized coordinate and its conjugate momentum.

How to explain the equation

The equations are derived from the Hamiltonian formalism. Hamilton's equations can be derived from the Hamilton's principle, which is a variational principle that states that the action of a dynamical system is stationary.

To derive these equations, we start with the Hamiltonian function H(p, q) and use the principle of least action. The action S is defined as the integral of the Lagrangian L(q, q', t) over time:

S = ∫[L(q, q', t)] dt

To find dp/dt, we differentiate the Lagrangian with respect to q:

∂L/∂q = ∂(p * q' - H)/∂q

= -∂H/∂q

Using the chain rule, we find:

dL/dt = (∂L/∂q) * dq/dt + (∂L/∂q') * dq'/dt

= -∂H/∂q * dq/dt + p * d(q')/dt

= -∂H/∂q * dq/dt + p * d^2q/dt^2

= -∂H/∂q * dq/dt + dp/dt

Since the Lagrangian is equal to p * dq' - H, we can write:

dL/dt = -∂H/∂q * dq/dt + dp/dt

From the principle of least action, we know that the action S is stationary, so dL/dt = 0. Thus, we have:

-∂H/∂q * dq/dt + dp/dt = 0

Rearranging the equation, we obtain the first equation of motion:

dp/dt = -∂H/∂q

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