PLS HELP ME
7. An electric current can perform work as long as there is a battery to produce current, some device to operate, and everything is connected in a complete _?_.
8. What is the formula for Ohm's Law? What units are used to express current? What units are used to express potential difference?
9. What do you know about the number of turns of wire in the secondary coil of a step-down transformer compared to the number of turns in its primary coil?
10. Coulomb's Law states that the force between two charged particles equals kq1q1/ d2. How is this relationship similar to the gravitational force between two objects, and how is it different?
11. There are some very small pieces of hair in a bottle of baby oil. Marvin rubbed a balloon on his sweater and then put the balloon near the bottle. The hairs in the bottle all lined up pointing toward the balloon. Explain what is happening.
12. Bridget tried to play with her magnet while taking a steaming hot bath, but it didn't work very well. Why?
13. Osgood connected a loop of wire to the terminals of a toy railroad transformer. At one point in the loop, the wires came very close together. When Osgood turned on the power, the wires seemed to push apart where they were closest. Explain.
14. A circuit has three lights. Jezebel removed one light from the circuit, and the other two glowed more brightly. Were the lights connected in series or parallel? Explain.
Answers
7. An electric current can perform work as long as there is a battery to produce current, some device to operate, and everything is connected in a complete path.
- An electric current can only flow when there is a closed path in which electrons can move. A complete path is required for charge to flow in a flashlight. Batteries must also be placed so that charge can flow negative to positive, passing through the bulb. This is an example of why an electric current can perform work as long as their is a complete path.
8. Formula of Ohm's law is V = IR (V = Voltage, I = Current, R = Resistance).
Amp or ampere is used for measuring current. It's the International Unit.
Potential difference is defined as the amount of work done in moving unit positive charge from one point to another.
It SI unit is volt.
Volt = Joule/Coulomb
9. A step down transformer has more turns of wire on the primary coil and less turns of wire on the secondary coil. This makes a smaller induced voltage in the secondary coil.
10. The gravity force has the same shape as Coulomb's law for electric charge forces, i.e., it is an inverse square law force that depends on the product of the two interacting sources. Coulomb's and gravitational forces are both directly proportional to the product of the body's charges and masses. Coulomb's and gravitational forces are both inversely proportional to the square of the distance between them. Both of these factors are central.
11. When two items rub together, such as your hair and the balloon, one loses part of its electrons to the other. As a result, one object is positively charged while the other is negatively charged. The opposites are then drawn to one other.
12. The heating of the steaming hot bath is actually having negative effects on the magnetism and magnetic field of the magnet. To explain further: As a result, heating a magnet breaks the domain walls, making it easier for magnetic domains that are normally aligned to spin and become misaligned. They are now less aligned and point in the opposite direction to their neighbors, resulting in a drop in magnetic field and magnetism loss.
13. When current flows, it generates a magnetic field surrounding the wire, which may be calculated using the right hand thumb rule. Magnetic fields can be represented by lines of force. These force lines are similar to rubber bands. When stretched, they try to shrink. When pressed against one other, they tend to push each other away.
14. When one bulb burns out, it creates an open circuit. Current does not flow in that branch, but it does flow in the parallel circuit's other branch. As a result, the other bulb continues to light. Also, the voltage across the other bulb remains constant, therefore the power given to it remains constant, and it continues to shine with the same brightness. What makes these lights parallel is because one light went out and the others remained bright. To give a better idea, here is a example, Assume that one lamp breaks and the other lamp continues to illuminate. Most homes have their lights wired in parallel. This means that they all receive the full voltage, and if one bulb fails, the others continue to operate. The current from the power source is larger than the current in each branch of a parallel circuit. This is the same case but with 3 lights, so therefore the light connected were parallel.
Related Questions
The drawings show the mass and weight of four objects on different planets:
(see the picture)
(a)
On which of the four planets is the object with the largest mass?
Answers
The object with the highest mass is the one on planet D. This is because mass is a measure of the amount of matter an object contains, and is not affected by gravity. Therefore, although the weight of the object on planet D is lower than that of the other planets, its mass remains the same.
Weight, on the other hand, is a measure of the gravitational force acting on an object. Therefore, the weight of an object will vary on different planets due to different gravitational forces. As shown in the drawings, the object on planet A has the greatest weight, but nevertheless the greatest mass.
In summary, the object with the greatest mass is on planet D, while the object with the greatest weight is on planet A.
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you push a shopping cart with 2 packs of water bottles. you stop the cart and add two more packs. you push the cart again. does the cart behave differently? explain using science terms.
Answers
Answer:
Yes
Explanation:
The cart will definitely behave differently because more weight is added to it.
In order to successfully push a cart, the applied force must exceed the force of the weight of the cart along with its constituents and the frictional force between the tyres and the floor.
When more weights are added (the 2 packs of water bottles), it means that more force would be needed to overcome the opposing forces to the movement of the cart in order to successfully push the cart again.
Please someone help me. I don't know how to do this and it's due tonight.
Answers
Answer:
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Two train cars with the same mass (30,000 kg) are traveling in the same direction when they collide.
Train Car A has a velocity of 10 m/s and Train Car B has a velocity of 5 m/s. What is their total
momentum after the collision? Make sure to show all your work and include proper units.
Answers
Answer:
25
Explanation:
I just did this
A student picks up four books from the floor, walks across the room through some distance with the book
at the same height and then keeps these books at the new place. In which of these sequence of actions
work is said to be performed ?
Answers
Work is performed while initially lifting books off the floor. The work is due to gravity.
what important discovery did physicists michael faraday and joseph henry make? group of answer choices electromagnetic induction electromagnetic relativity electromagnetic waves electromagnetic deduction
Answers
In 1831, Michael Faraday and Joseph Henry independently and almost simultaneously made the discovery of electromagnetic induction therefore, option A is the right choice.
Electromagnetic induction refers to the production of an electromotive force (EMF) by the use of a moving magnetic field that is encircling an electric conductor, as well as the production of current by means of the movement of an electric conductor through a static magnetic field.
Electromagnetic interference (EMI) is also known as electric current and electromagnetic induction. It may also be referred to as magnetic induction due to the fact that the underlying concept is the same regardless of whether the procedure is carried out using an electromagnet or a static magnet.
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a cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in
Answers
This is an interesting scenario! When a cube is balanced with one edge in contact with a table top and with its center of gravity directly above the edge, it is said to be in a state of unstable equilibrium. This means that even a slight disturbance could cause the cube to fall over.
To understand this concept, it is important to first understand what center of gravity means. The center of gravity is the point where the weight of an object is evenly distributed in all directions. In a cube, this point is located at the geometric center of the cube.
Now, in the scenario described, the cube is resting on one of its edges. This edge is acting as a pivot point or fulcrum. When the cube is in this position, its center of gravity is located directly above the pivot point. This means that the weight of the cube is evenly distributed on either side of the pivot point.
However, since the cube is in a state of unstable equilibrium, any slight disturbance could cause the weight distribution to shift. For example, if the table were to vibrate or if there were a gust of wind, the weight distribution could shift slightly, causing the cube to fall over.
When a cube is balanced with one edge in contact with a table top and with its center of gravity directly above the edge, it is in a state of unstable equilibrium. This means that even a slight disturbance could cause the cube to fall over.
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The magnitude of the Poynting vector of a planar electromagnetic wave has an average value of 0.939 W/m2. The wave is incident upon a rectangular area, 1.5 m by 2.0 m, at right angles. How much total electromagnetic energy falls on the area during 1.0 minute? (c = 3.0 × 108 m/s, μ0 = 4π × 10-7 T ∙ m/A, ε0 = 8.85 × 10-12 C2/N ∙ m2)
Answers
The total electromagnetic energy that falls on the rectangular area during 1.0 minute is approximately 3.54 × 10⁴ J.
To calculate the total electromagnetic energy that falls on the rectangular area, we need to find the energy flux density (S) incident on the area and then multiply it by the area and time.
Given that the magnitude of the Poynting vector (S) is 0.939 W/m², we know that S = c * ε₀ * E₀², where c is the speed of light, ε₀ is the vacuum permittivity, and E₀ is the electric field amplitude.
Since the wave is incident at right angles to the rectangular area, the energy flux density incident on the area is equal to the magnitude of the Poynting vector. Therefore, S = 0.939 W/m².
The electric field amplitude (E₀) can be found by rearranging the equation S = c * ε₀ * E₀² and solving for E₀.
E₀ = √(S / (c * ε₀))
E₀ = √(0.939 W/m² / (3.0 × 10⁸ m/s * 8.85 × 10⁻¹² C²/N * m²))
Substituting the given values, we can calculate E₀:
E₀ ≈ 1.82 × 10⁻⁵ V/m
Now, we can calculate the total electromagnetic energy (W) incident on the area by multiplying the energy flux density (S) by the area (A = length × width) and the time (t):
W = S * A * t
W = 0.939 W/m² * 1.5 m * 2.0 m * 60 s
Calculating this expression gives us:
W ≈ 3.54 × 10⁴ J
Therefore, the total electromagnetic energy that falls on the rectangular area during 1.0 minute is approximately 3.54 × 10⁴ J.
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state the term used to describe the turning force exerted by the man pushing down on a lever to lift one end of a heavy log
Answers
The way levers work is by multiplying the effort exerted by the user. Specifically, to lift and balance an object, the effort force the user applies multiplied by its distance to the fulcrum must equal the load force multiplied by its distance to the fulcrum. Consequently, the greater the distance between the effort force and the fulcrum, the heavier a load can be lifted with the same effort force.
The term used to describe the turning force exerted when pushing an object is effort.
What is effort?The is the input force or force applied at one point of a lever in order to overcome a load.
The relationship between effort, load and mechanical advantage of a lever is given as;
M.A = L/E
where;
M.A is mechanical advantageL is the loadE is the applied force or effortThus, the term used to describe the turning force exerted when pushing an object is effort.
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A fluid (rho = 0.07088lbm/ft3, μ = 0.04615 lbm/ft-hr) is to be transported through a 400 ft long circular plastic pipe at a rate of 12ft3/s. If the head loss must not exceed 50ft, determine the minimum required diameter of the pipe.
Answers
The minimum required diameter of the pipe is 7.93 ft.
Density of the fluid, ρ = 0.07088 lbm/ft³
μ = 0.04615 lbm/ft-hr
Length of the plastic pipe, L = 400 ft
Rate of flow of the fluid, Q = 12 ft³/s
Head loss, h(L) = 50 ft
The expression for the rate of flow of the fluid is given by,
Q = AV
V = Q/A
h(L) = 32μVL/γD²
50 = 32 x 0.04615 x 12 x 400 x 4/3.14 x D² x 0.07088 x 32.17x D²
D⁴ = 28.4 x 10³/7.15
D⁴ = 3972 ft
Therefore, the diameter of the pipe is,
D = (3972)¹/₄
D = 7.93 ft
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A stone thrown from the top of a tall building follows a path that is
a. circular...
b. made of two line segments..
c. hyperbolic..
d. parabolic..
Answers
A stone thrown from the top of a tall building follows a parabolic path due to the effects of gravity on its motion. The correct answer is D.
A stone thrown from the top of a tall building follows a parabolic path. This is because the stone is initially moving in a straight line, but it is also being pulled downward by gravity. As a result, the stone follows a curved path that is shaped like a parabola. In mathematical terms, the path of the stone can be described by a quadratic equation, which is a type of equation that produces a parabolic graph. The equation for the path of the stone will include terms for the initial velocity of the stone, the acceleration due to gravity, and the initial height of the stone.
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What are some exercise for 3 opposing muscle pairs that covers Arms,
Legs, and Core,
Answers
Arms: Bicep curls (biceps) and tricep dips (triceps).
Legs: Squats (quadriceps) and hamstring curls (hamstrings).
Core: Plank (abdominals) and back extensions (lower back).
1. Bicep curls target the biceps, which are responsible for flexing the arm, while tricep dips work the triceps, which are responsible for extending the arm. These exercises help build strength and definition in the arm muscles.
2. Squats target the quadriceps, which are the large muscles in the front of the thighs, while hamstring curls focus on the hamstrings, which are the muscles at the back of the thighs. These exercises help strengthen the leg muscles, improve stability, and enhance overall lower body strength.
3. Planks engage the abdominals, including the rectus abdominis and transverse abdominis, which provide core stability. Back extensions target the muscles of the lower back, including the erector spinae, helping to improve posture and strengthen the back muscles. These exercises contribute to core strength and stability, which is essential for overall functional fitness and preventing injuries.
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find the total (resultant) force and the total (resultant) moment about point a of the given forcing system note that in statics study the original complex forcing system can be replaced by this simple system of a single point force and a single moment about a only.
Answers
In order to calculate the total force and moment around point A, we must first simplify the system into a single point force and a single moment around point A. This point force is determined by adding all individual forces in the system using vector addition. The resultant force has both magnitude and direction.
The single moment about point a is the sum of all the moments of the individual forces in the system about point a. We can add the moments using the right-hand rule to get the resultant moment. The resultant moment will have a magnitude and direction.
Once we have the single point force and single moment, we can find the total (resultant) force and moment about point a using the following equations:
Resultant force = single point force
Resultant moment about point a = single moment about point a
By simplifying the forcing system to a single point force and a single moment about point a, we can easily calculate the total force and moment about point a.
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which layer of the earth contains convection currents
Answers
a 0.25 kg ball is thrown with an initial velocity of 32 m/s at an angle of 30o. determine its total energy at the top of its flight path.
Answers
The total energy of the ball at the top of its flight path is 224.2 Joules.
What is the total energy?To determine the total energy of the ball at the top of its flight path, we need to consider the ball's kinetic energy and potential energy.
First, let's find the maximum height the ball will reach. At the top of its flight path, the ball will have no vertical velocity, so we can use the equation:
\(v_f^2 = v_i^2 + 2ad\)
where\(v_f\)is the final velocity (0 m/s), \(v_i\) is the initial velocity (32 m/s), a is the acceleration due to gravity \((-9.8 m/s^2)\), and d is the maximum height. Solving for d, we get:
\(d = (v_f^2 - v_i^2)/(2a) = (0 - (32 m/s)^2)/(2*(-9.8 m/s^2)) = 51.8 m\)
Next, let's find the kinetic energy of the ball at the top of its flight path. Since the ball has no vertical velocity at this point, we can use the horizontal velocity to find the kinetic energy. The horizontal velocity is:
\(v_x = v_i cos(30o) = 27.7 m/s\)
The kinetic energy is:
\(K = (1/2)mv_x^2 = (1/2)(0.25 kg)(27.7 m/s)^2 = 96.4 J\)
Finally, let's find the potential energy of the ball at the top of its flight path. The potential energy is:
U = mgh = \((0.25 kg)(9.8 m/s^2)(51.8 m)\) = 127.8 J
The total energy at the top of the ball's flight path is the sum of the kinetic and potential energy:
E = K + U = 96.4 J + 127.8 J = 224.2 J
Therefore, the total energy of the ball at the top of its flight path is 224.2 Joules.
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An object travels 8 meters in the first second of travel, 8 meters again during the second second of travel, and 8 meters again during the third second. Its VELOCITY in meters per second is O 0 0 5 O 8 O 10 O more than 10 MARE
Answers
Answer:
V = (S2 - S1) / t
V = 8 m / 1 s = 8 meters /second
How does occluded fronts form.
Answers
Answer:
when a cold front catches up to a warm front
Explanation:
cold fronts moving along much faster than warm fronts do. the cold front over takes the warm front and cold air moves into cooling air ahead of the warm front
A bomb, originally sitting at rest, explodes and during the
explosion breaks into four pieces of exactly 0.25 kg each.
One piece flies due south at 10 m/s while another piece flies
due north at 10 m/s. The other two pieces travel in
directions.
Answers
Answer:
opposite
Explanation:
codys motorboat took 3 hours to make a trip downstream with a 6mph current. the return trip against the same current took 5 hours. find the speed of the boat in still water.
Answers
A boat can move at 12.5 km/h on calm water and 2.5 km/h in a stream, respectively.
How quickly does still water move?Motionless water is defined as water that is still, not flowing, and has no current, such as in ponds. Therefore, a boat's relative speed on calm water is equal to 12 (a + b) km/hr. The stream is moving at a pace of 1/2 (a - b) km/hr.
codys motorboat took = 3 hour
current trip downstream = 6mph
the return trip against the same current = 5 hour
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According to the question, the speed of the boat in still water is 6 mph.
What is speed?
Speed is a measure of how quickly an object or person moves or travels. It is typically measured in units of distance per unit of time, such as meters per second, miles per hour, or kilometers per hour. Speed can also be expressed as the time it takes to cover a given distance, such as the time it takes to travel one mile or one kilometer.
The speed of the boat in still water can be calculated using the formula V = (D1 + D2) / (T1 + T2), where V is the speed of the boat in still water, D1 is the distance traveled downstream, D2 is the distance traveled upstream, T1 is the time it took to travel downstream, and T2 is the time it took to travel upstream.
In this case, D1 = 6 mph × 3 hours = 18 miles, D2 = 6 mph × 5 hours = 30 miles, T1 = 3 hours, and T2 = 5 hours.
Plugging the values into the formula, we get V = (18 + 30) / (3 + 5) = 48 / 8 = 6 mph.
Therefore, the speed of the boat in still water is 6 mph.
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Verify that the Divergence Theorem is true for the vector field F(x,y,z)=3xi+xyj+3xzk on the region E which is the cube bounded by the planes x=0,x=3,y=0,y=3,z=0,z=3
Answers
The Divergence Theorem is true for the vector field F(x,y,z)=3xi+xyj+3xzk on the region E, which is the cube bounded by the planes x=0,x=3,y=0,y=3,z=0,z=3.
Explanation: The Divergence Theorem states that the flux of a vector field across a closed surface is equal to the volume integral of the divergence of the vector field over the enclosed volume. In this case, the cube is a closed surface, and the vector field F has a constant divergence of 6. Therefore, by the Divergence Theorem, the flux of F across the cube is equal to 6 times the volume of the cube. The volume of the cube is (3^3)=27, so the flux of F across the cube is 6 times 27, which is equal to 162.
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A 0.145 kg baseball is thrown with a velocity of 25.0 m/s. How much work was done on the baseball to bring it from rest to 25.0 m/s? [Neglect air resistance]
Answers
Answer:
45.31 J
Explanation:
We are given that
Mass of baseball , m=0.145 kg
Initial velocity, u=0
Final velocity, v=25 m/s
We have to find the work done on the baseball to bring it from rest to 25 m/s
We know that
Work done = Change in kinetic energy
Work done, W=\(\frac{1}{2}m(v^2-u^2)\)
Using the formula
Work done, W\(=\frac{1}{2}(0.145)((25)^2-0)\)
Work done=\(\frac{1}{2}(0.145)(625)\)
Work done, W=45.31 J
Hence, the work done on the baseball to bring it from rest to 25 m/s
=45.31 J
Listen When the reflection of an object is seen in a flat mirror, the distance from the mirror to the image depends on the distance of both the observer and the object to the mirror. the distance from the object to the mirror. the size of the object. the wavelength of light used for viewing. Question 22 (2 points) Listen Which is an example of refraction? A fish appears closer to the surface of the water than it really is when observed from a riverbank. A parabolic mirror in a headlight focuses light into a beam. Light is bent slightly around corners. In a mirror, when you lift your right arm, the left arm of your image is raised. 1
Answers
A fish appears closer to the surface of the water than it really is when observed from a riverbank. Refraction is the bending of light as it passes from one medium to another with a different optical density. In the case of the fish appearing closer to the surface of the water, this is an example of refraction because the light rays coming from the fish underwater undergo bending at the air-water interface.
When light passes from water (a denser medium) to air (a less dense medium), it changes its direction due to the difference in optical density. This bending of light causes the fish to appear higher or closer to the surface of the water than its actual position.
The other options mentioned in the question are not examples of refraction:
A parabolic mirror in a headlight focusing light into a beam is an example of reflection and focusing of light using a curved surface.
Light bending slightly around corners is an example of diffraction, not refraction.
In a mirror, when you lift your right arm, the left arm of your image is raised. This is an example of lateral inversion due to reflection, not refraction.
Therefore, the correct example of refraction from the given options is when a fish appears closer to the surface of the water than it really is when observed from a riverbank.
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describe the energy changes in mass-spring system that is oscilating horizontally.
Answers
Answer:
Explanation:
l etme y lo saoc apr aotarsy r dealkten dpo
How to find resultant of all vectors?
Answers
Answer:
To draw the resultant vector, join the tail of the first vector with the second vector's head and put the arrowhead. To determine the magnitude, measure the length of resultant R, and to find out the direction, measure the angle of the resultant with the x-axis.
A car of mass 500 kg travelling at 36 km/hr brought to
rest over a distance of 40m find the average retraldation and
average braking force
Answers
Answer:
Explanation:
mass, m = 500 kg
initial velocity, u = 36 km/h = 10 m/s
final velocity, v = 0
distance, s = 40 m
\(v^{2} = u^{2} + 2as\)
\(0^{2} = 10 ^{2} +\) 2 × a × 40
0 = 100 + 80 a
- 80a = 100 - 0
-80a = 100
a = -100 / 80
a = -1.25 m/\(s^{2}\)
force, f = ?
mass = 500 kg
acceleration = -1.25 m/s^2
f = ma
= 500 × -1.25
= -625 N
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Why are some forces considered to be noncontact forces? A. Objects must be far apart in order to exert a force. B. Objects do not have to touch each other to experience a force. C. Objects push each other apart to increase the distance between them. D. Objects must be large in size in order to exert a force that is strong enough to notice. is it a,b,c or d?
Answers
Answer:
B. Objects do not have to touch each other to experience a force.
Explanation:
For example ..One of the noncontact forces is magnetic force whereby a magnetic object will be attracted to another magnetic object of oppsite charged particles, through waves called electromagnetic waves. On the other hand, the two magnetic objects of similar charged particles can repel through electromagnetic waves..
Student A states that when she sits down on a chair, she is exerting a force on the chair and that is all that happens. Student B states that when she sits on a chair, the chair is actually exerting a force back on her in reaction to her force exerted upon the chair. Which student is correct and why?
A.
Student A is correct because Newton’s 1st Law of Motion states that if the chair exerted a force on the student, her motion would change.
B.
Student A is correct because Newton’s 3rd Law of Motion states that for every action there is an equal and opposite action and the chair does not show any action.
C.
Student B is correct because Newton’s 1st Law of Motion states that if the chair were to be exerting a force on the student, her motion would change.
D.
Student B is correct because Newton’s 3rd Law of Motion states that for every action there is an equal and opposite action and the chair’s action counteracts the student’s so that neither move.
Answers
Answer:
C
Explanation:
I got it right on the test !!
The student that is correct is C. Student B is correct because Newton’s 1st Law of Motion states that if the chair were to be exerting a force on the student, her motion would change.
According to Newton's third law of motion, there's an equal and opposite reaction force for every action force. It should be noted that when an individual sits on a chair, the chair is actually exerting a force back on her in reaction to the force exerted upon the chair.
Student A is incorrect because when she sits down on a chair, the force that she's exerting on the chair is not the only thing that happens because the chair exerts a force back. Therefore, as the chair were to be exerting a force on the student, her motion would change.
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convert the following Celsius temperatures to Kelvin
a} the boiling point of liquid hydrogen -252.87C
b} the temperature of a winter day in the north pole -40.0C
c} the melting point of gold 1064C
Answers
The following Celsius temperatures to Kelvin
a} The boiling point of liquid hydrogen -252.87C is 20.28K
b} The temperature of a winter day in the north pole -40.0C is 233.15K
c} The melting point of gold 1064C is 1337.15K
What is Temperature?
Temperature is defined as the physical quantity that quantitatively expresses the perception of hotness and coldness which is measured with a thermometer.
For the conversion of Celsius to Kelvin, the following formula is used
Kelvin = Celsius + 273.15.
For above given example,
Conversion of Liquid hydrogen into Kelvin= -252.87+273.15= 20.28K
Conversion of temperature of a winter day into Kelvin= -40+273.15= 233.15K
Conversion of Melting point of Gold into Kelvin= 1064+273.15= 1337.15K
Thus, following are the conversion:
a} The boiling point of liquid hydrogen -252.87C is 20.28K
b} The temperature of a winter day in the north pole -40.0C is 233.15K
c} The melting point of gold 1064C is 1337.15K
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: Prove that the following paraboloid coordinate system (u, v, ϕ):
x = u.v cosϕ
y = u.v sinϕ
z = 1/2 (u2 - v2)
is orthogonal, and then find the following:
1. The scale factors
2. Gradient
3. Divergent
4. Curl
5. Laplacian
Answers
The given paraboloid coordinate system (u, v, ϕ) with x = u.v cosϕ,
y = u.v sinϕ , z = 1/2 (u2 - v2) is orthogonal. The gradient is ∇f = (∂f/∂u) e_u + (∂f/∂v) e_v + (∂f/∂ϕ) e_ϕ ; divergent is ∇²f = ∇ · (∇f) ; curl is (∇ x) and laplacian is (∇²).
We can prove that the paraboloid coordinate system (u, v, ϕ) is orthogonal, by computing the dot products of the basis vectors. The basis vectors in this coordinate system are given by:
e_u = (∂x/∂u, ∂y/∂u, ∂z/∂u) = (v cosϕ, v sinϕ, u)
e_v = (∂x/∂v, ∂y/∂v, ∂z/∂v) = (u cosϕ, u sinϕ, -v)
e_ϕ = (∂x/∂ϕ, ∂y/∂ϕ, ∂z/∂ϕ) = (-u.v sinϕ, u.v cosϕ, 0)
By Taking the dot products, we find that e_u · e_v = 0, e_v · e_ϕ = 0, and e_ϕ · e_u = 0. This proves that the basis vectors are mutually perpendicular, and therefore, the coordinate system is orthogonal.
Next, we can calculate the gradient (∇) in this coordinate system. The gradient of a scalar function f(u, v, ϕ) is given by:
∇f = (∂f/∂u) e_u + (∂f/∂v) e_v + (∂f/∂ϕ) e_ϕ
The divergence (∇ ·) and curl (∇ x) can be computed using the standard formulas in terms of the basis vectors. Finally, the Laplacian (∇²) can be obtained by taking the divergence of the gradient:
∇²f = ∇ · (∇f)
Thus, By evaluating these operations in the given coordinate system using the appropriate partial derivatives, we can determine the gradient, divergent, curl, and Laplacian for any scalar function in the (u, v, ϕ) coordinates.
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An un-stretched spring that is initially 20 centimeters long has a spring constant of 3.5 x 103 newtons per meter. What is the total length of the spring in centimeters when it is stretched to the point where 2.8 joules are stored in it?
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Answer:
30
Explanation:
30
the total length of the spring in centimeters when it is stretched to the point where 2.8 joules are stored in it is 30.
What are the unit of length ?length can be defined as the measurement which is an act for the identification of the object's length in some standard or non-standard units.
The most common units of length are U.S. customary units and the metric units include SI and non-SI units, others are British Imperial units are also still used in some countries.
Other units of length include kilometres, nanometre, millimetres, centimetres, metres, decimetres where as the Imperial and U.S. customary systems, basic unit of length is the yard.
other units are thou (1⁄1000 of an inch), line (1⁄12 of an inch), inch (25.4 mm), foot (12 inches, 0.3048 m)
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