The electric field due to a charged rod of length 2a with total charge q uniformly distributed along its length, placed along the z axis with its center at the origin.
Through the application of Coulomb's equation and the concept of superposition, we can determine the electric field everywhere caused by the charged rod. The electric field due to a tiny piece of the rod at a point P in space is given by:
dE = k dq / r²
where
k = Coulomb's constant,
dq i= the segment's charge,
r = the segment's distance from point P, and
dE = the segment's contribution to the electric field.
We integrate this formula along the entire length of the rod, from -a to +a, to determine the total electric field at P as follows:
E = ∫ dE = k ∫ dq / r²
where the rod's length is used as the integral. The charge per unit length of the rod, or dq, can be expressed in terms of the charge density as dq = ds, where ds is an element along the rod with an infinitesimal length. r = √(s² + z²) where z is the segment's distance from the z axis, we can also describe r in terms of the distance s from the origin to the segment.
E = k ∫ dq / r^2 = k ∫ λ ds / (s² + z²)
E = k λ z ∫_{-arctan(a/z)}^{arctan(a/z)} dθ / (1 + (a/z)² tan² θ)
E = k λ z / (2πε_0) ∫_{-a/z}^{a/z} du / (1 + u²)
E = k λ z / (2πε_0) [arctan(a/z) - arctan(-a/z)]
E = k λ a / (2πε_0 z√(a² + z²))
This is the equation for the electric field produced by a charged rod of length 2a, arranged along the z axis with its center at the origin, and with total charge q evenly distributed throughout its length. The electric field radiates outward from the rod, and as you move away from the rod, its strength diminishes as 1/r².
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1/1 For the 3500-lb car, determine (a) its mass in slugs, (6) its weight in newtons, and (c) its mass in kilograms. W = 3500 lb Problem 1/1 1/2 Determine your mass in slugs. Convert your weight to newtons and calculate the corresponding mass in kilograms. 1/3 For the given vectors V, and V2, determine V1 + V2, Vi + VV-V, V, V, V, X V1, and V.V. Consider the vectors to be nondimensional. у V2 = 12 V1 = 15 3 60° x
1/1. For the 3500-lb car, its mass in slugs is 108.7 slug, its weight in newtons 15540 N, and its mass in kilograms is 1584 kg. 1/2. For my weight, mass in slug is 3.421 slug, weight in newton is 488.4 N, and corresponding mass in kg is 49.786 kg. 1/3. Based on the given vectors\vec{V1}+\ \vec{V2}=18i+\left(9+6\sqrt3\right)j, \vec{V1}-\ \vec{V2}=6i+\left(9-6\sqrt3\right)j, \vec{V1}\ast\ \vec{V2}=165.53\ units, \vec{V1}\ x\ \ \vec{V2}=\left(72\sqrt3-54\right)k, and \vec{V2}\ x\ \ \vec{V1}=\left(54-\ 72\sqrt3\right)k.
1/1. The weight of the car in pounds is given as 3500 lb. According to the unit conversion, as 1 lb is equal to 0.0311, the mass of the car in slugs is:
Mass = 3500 x 0.0311 = 108.7 slug
As 1 lb is equal to 4.44 N, the weight of car in newtons is:
Weight = 3500 x 4.44 = 15540 N
The equation for weight is given by:
W = mg where m is mass in kg and g is the gravity equal to 9.81 m/s^2
Hence, the mass is given by:
m= W/g=15540/9.81=1584 kg
1/2. My weight in pounds = 110 pounds
Mass in slug = 110 x 0.0311 = 3.421 slug
Weight in newton = 110 x 4.44 = 488.4 N
Corresponding mass in kg is:
m=488.4/9.81=49.786 kg
1/3. The magnitude of vector 1 = 15 units
The magnitude of vector 2 = 12 units
The angle of inclination of vector 2 from the horizontal θ = 60∘
The vector 1 is given by:
\vec{V1}=V1\ast\left(\frac{4}{5}\right)i+V1\ast\left(\frac{3}{5}\right)j=15\ast\left(\frac{4}{5}\right)i+15\ast\left(\frac{3}{5}\right)j=12i+9j
The vector 2 is given by:
\vec{V2}=V2\ cos\theta i+V2sin\theta j=12cos60i+12sin60j=6i+6\sqrt3j
Sum of the two vectors is:
\vec{V}=\ \vec{V1}+\ \vec{V2}
\vec{V}=(12i+9j)+(6i+6\sqrt3j)
\vec{V}=\ 18i+(9+6\sqrt3)j)
Difference of the two vectors is:
\vec{V}=\ \vec{V1}-\ \vec{V2}
\vec{V}=\left(12i+9j\right)-(6i+6\sqrt3j)
\vec{V}=\ 6i+(9-6\sqrt3)j)
The dot product of the two vectors is:
\vec{V}=\ \vec{V1}\ast\ \vec{V2}
\vec{V}=\left(12i+9j\right)\ast(6i+6\sqrt3j)
\vec{V}=\ 165.530\ unit
The cross product of the two vectors is:
\vec{V}=\ \vec{V1}\ x\ \vec{V2}
\vec{V}=\left(12i+9j\right)x(6i+6\sqrt3j)
\vec{V}=\ 72\sqrt3k-54k=(72\sqrt3-54)k
The cross product of the two vectors is:
\vec{V}=\ \vec{V2}\ x\ \vec{V1}\
\vec{V}=(6i+6\sqrt3j) x \left(12i+9j\right)
\vec{V}=\ 54k-\ 72\sqrt3k=(54-\ 72\sqrt3)k
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The measured total pressure for each trial is the sum of the vapor pressure of the liquid and the pressure due to any air trapped in the flask (see equation 1 in the introduction) a) What happens to the air pressure in higher temperature flasks? Explain in terms of molecular motion. b) Calculate corrected air pressures for any of the trials that were not performed at the same temperature as the atmospheric pressure data. Hint: P1/T1 = P2/T2
As the temperature of the flask increases, the molecules in the air become more energetic, resulting in an increase in air pressure.
Given the total pressure measured for the each trail = vapor pressure of liquid + pressure due to any air trapped in the flask.
a) The pressure of the gas rises because the molecules collide with the container walls more frequently as a result of the faster collisions between the molecules and the walls. This is because the molecules are moving faster and collide more often with the walls of the flask, creating a greater force.
b) To calculate the corrected air pressure, the ideal gas law can be used (P1/T1 = P2/T2). The atmospheric pressure (P1) and temperature (T1) must be known for the trial and the temperature (T2) of the flask must be known. The corrected air pressure (P2) can then be calculated.
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assuming you start at the top of the ramp that is 10 m tall with velocity of 10 m/s and your car has a mass of 1000 kg, what is your pe g
The gravitational potential energy of the car at the top of the ramp is 98,000 Joules.
How to calculate the potential energy?The gravitational potential energy (PE) of an object of mass m at ground level h is given by
PE = mgh
where g is the acceleration due to gravity, approximately 9.8 m/s^2 near the surface.
In this case, the car has a mass of 1000 kg and a height of 10 m above the ground. Therefore, the gravitational potential energy (PEg) is:
PEg = mgh = 1000kg * 9.8m/s^2 * 10m = 98,000J
Therefore, the gravitational potential energy of the car at the top of the ramp is 98,000 Joules.
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suppose that the apparatus used in the demonstration is placed on a moving cart. the cart moves with a constant acceleration a, and the spring is activated when the cart crosses point p. which ball will hit the ground first?a. Ball A and Ball B hit the ground simultaneously b. Ball Ac. Ball B
The ball will hit the ground first if the cart moves with a constant acceleration a, and the spring is activated when the cart crosses point P as Ball A and Ball B hit the ground simultaneously.
Thus, the correct option is A.
What is constant acceleration?Аccelerаtion is the rаte of chаnge in velocity, which is а vector, therefore, chаnges in this quаntity cаn influence its mаgnitude аnd/or direction. Аlthough аccelerаtion cаn be null, positive, or negаtive, it is, often, misunderstood аs а synonym for speeding up. This is true when аccelerаtion is positive for а strаight-line motion. In this type of motion, а negаtive аccelerаtion meаns thаt the object is slowing down, аnd а null аccelerаtion meаns thаt the speed does not chаnge.
Thus, when the cart moves with a constant acceleration a, and the spring is activated when the cart crosses point P, Ball A and Ball B hit the ground simultaneously.
Your question is incomplete, but most probably your full question can be seen in the Attachment.
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What is the answer to question which statement correctly describes a characteristic that a scientific measuring tool should have ?
To be accurate, a scientific measuring instrument needs to be able to provide repeatable observations of a quantity.
How can you be scientific?of, pertaining to, or showing the scientific concepts or procedures. conducted scientifically or in accordance with findings of scientific investigation: by practicing or employing comprehensive or orderly procedures. advertising using science.
Who is referred to as scientific?A scientist is a person who methodically acquires data and uses it to form hypotheses, test those assumptions and further knowledge and understanding. Additional characteristics of a scientist include: their methodology, such as their use of statistics.
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What is the current flowing through this circuit?
A) 1.3 A
B) 6.7 A
C) 15 A
D) 0.15 A
Answer:
see below
Explanation:
the given circuit comprises of a 10V battery and 2Ω and 6Ω resistance. The resistances are connected in parallel, so we can find the net resistance as ,
[tex]\implies \dfrac{1}{R_n}=\dfrac{1}{R_1}+\dfrac{1}{R_2} \\[/tex]
[tex]\implies R_n =\dfrac{R_1R_2}{R_1+R_2} \\[/tex]
[tex]\implies R_n =\dfrac{2\times 6 }{2+6}\Omega \\[/tex]
[tex]\implies R_n =\dfrac{12}{8}\Omega\\[/tex]
[tex]\implies R_n = 1.5\Omega \\[/tex]
Now from Ohm's law, we have,
[tex]\implies V = iR \\[/tex]
where ,
V is potential differencei is currentR is resistance[tex]\implies 10V = i \times 1.25\Omega \\[/tex]
[tex]\implies i =\dfrac{10}{1.25} A \\[/tex]
[tex]\implies \underline{\underline{ i = 8A }}\\[/tex]
and we are done!
A 66 kg student traveling in a car with a constant velocity has a kinetic energy of 1.1 104 J. What is the speedometer reading of the car in km/h?
Answer:
The speedometer reading of the car in km/h is 100.1 km/h. This can be calculated by using the formula K = 0.5mv2, where K is the kinetic energy, m is the mass, and v is the velocity. Rearranging this equation to solve for v yields v = √(2K/m). In this case, m = 66 kg and K = 1.1 x 104 J, so v = √(2 x 1.1 x 104 J/ 66 kg) = 100.1 km/h.
A ball is thrown straight up. It reaches its highest point and then falls back. Which of the following is the correct statement?(a) Throughout its motion, the ball's velocity is zero(b) At the highest point in its motion, the ball's acceleration is zero(c) At the highest point in its motion, the ball's velocity is zero(d) Throughout its motion, the ball's acceleration is zero(e) At the highest point in its motion, the ball's velocity and acceleration.
The correct statement is (c): At the highest point in its motion, the ball's velocity is zero.
This is due to the fact that when anything is thrown straight up, it has a starting velocity and then accelerates as it descends towards the Earth. Its velocity is equal to zero as it reaches its highest point (due to the gravitational pull of the Earth). The ball's acceleration varies continuously as it travels because it accelerates towards the Earth when it is travelling upward and decelerates when it is travelling downward.
The ball is briefly at rest, and the only force acting on it is the gravitational pull of the Earth, therefore at its fastest point in motion, the acceleration is equal to zero.
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I need help answering these questions on this worksheet
The density measures the compactness of a substance. Here the density of an object of mass 60 g and volume 150 cm³ is 0.4 g/cm³.
What is density?The mass of an object contained per unit volume is defined as the density. The SI unit of density is kg / m³. The equation used to calculate density is:
Density = Mass / Volume
= 60 / 150 = 0.4 g/cm³
The objects which have same volume, but different masses have different densities. If greater the mass, more dense will be the object.
Thus the density of the object is 0.4 g/cm³.
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What is the maximum distance we can shoot a dart, provided our toy dart gun gives a maximum initial velocity of 9.12m/s?
The distance that is covered is 8.5 m.
What is the maximum distance?We have to note that the movement of the dart would be the movement of a parabola. We would need to know that in this case, the first thing that we should find is the time that has been taken;
t = u sin 45/0.5 * 9.8
t = 9.12 sin 45/0.5 * 9.8
t = 1.32 s
Then we have that;
R = Vxt
Thus the distance that is covered is;
R = 9.12 cos45 * 1.32
R = 8.5 m
We can see that the projectile movement of the dart would cover a horizontal distance of about 8.5 m
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Momentum is defined as mass times velocity. You find the mass of a car to be 2014.88 kg and the velocity of the car to be 7.85 m/s, giving you a momentum of 15816.808 kg-m/s.
Round this momentum to the correct number of significant digits.
The momentum is 15817 kg-m/s rounded to the nearest whole number.
What is momentum?Momentum is a measure of an object's motion. It is defined as the product of an object's mass and its velocity. In mathematical terms, momentum (p) is equal to the mass (m) of an object times its velocity (v): p = m × v.
The unit of momentum is kilogram-meter per second (kg-m/s). The concept of momentum is important in physics, particularly in the study of motion, forces, and collisions. It provides a useful way of understanding and describing the motion of objects in the real world.
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How can you show respect of others intellectual property?
Answer:
You can show respect for others' intellectual property by:
Acknowledging the source of the material and giving credit to the original creator or owner.Obtaining permission before using or reproducing any protected material, such as patents, trademarks, copyrights, or trade secrets.Following all laws and regulations related to intellectual property, such as the Digital Millennium Copyright Act (DMCA).Not infringing on others' intellectual property rights by creating or distributing counterfeit or fake products.Being mindful of others' rights and taking steps to protect their intellectual property, just as you would want others to respect your own.A person pushes a 16.0-kg shopping cart at a constant velocity for a distance of 22.0 m. She pushes in a direction 29.0� below the horizontal. A 48.0-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.
The force that the shopper exerts is equal to the frictional force of 48.0 N in the opposite direction.
The work done by the pushing force is equal to the force multiplied by the distance, W = Fd = (48.0 N)(22.0 m) = 1056 J. The work done by the frictional force is equal to the opposite of the work done by the pushing force, W = -1056 J.
The work done by the gravitational force is zero since the gravitational force is in the opposite direction of the displacement and the object is not moving up or down, it is moving horizontally.
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A person standing at the edge of a cliff throws one rock straight up and another rock straight down at the same initial speed. The rock that was thrown ______ has less speed at impact
The rock thrown straight up will have less speed at impact compared to the rock thrown straight down.
The rock that was thrown straight up will experience slower speed at impact due to the effect of gravity. As the rock rises, gravity will slow its velocity and increase its potential energy. At the highest point, its velocity will be zero and its potential energy will be at a maximum.
As the rock falls back down, it will convert potential energy back into kinetic energy, reaching its maximum speed just before impact. The rock thrown straight down, on the other hand, will not experience any change in velocity as it falls due to gravity, leading to a higher speed at impact.
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Compare the force of gravity on the Moon due to the Earth, and the force of gravity on the Earth due to the Moon.
A. The force on the Moon is greater than the force on the Earth.
B. The forces are equal and opposite.
C. The force on the Earth is greater than the force on the Moon.
After comparing the force of gravity on the Moon due to the Earth, and the force of gravity on the Earth due to the Moon, we find that The forces are equal and opposite. Thus, option B is correct.
What is gravity?The force that unites all matter is called gravity (which is anything you can physically touch). The gravitational pull of objects with a lot of matter, such as planets, moons, and stars, increases with their mass.
The quantity of matter in something is determined by its mass. Everything has a gravitational pull, and this pull increases with mass. The Earth pulls on us as we walk on its surface, and we yank back in response. The Earth's pull can cause us to fall to the ground, whereas our pull is insufficient to move the Earth because it is so much heavier than we are.
In this system both the objects have mass so the gravitational force between them is,
[tex]$\mathrm{F = \frac{GM_1M_2}{R_2} }[/tex]
For the earth moon system,
[tex]$\mathrm{F_{e/m} = \frac{GM_eM_m}{R_2} }[/tex] and [tex]$\mathrm{-F_{m/e} = \frac{GM_eM_m}{R_2} }[/tex]here negative sign stands for opposite direction.
According to Newton's third law of motion, gravitational forces from the earth to the moon are equal but opposite in direction. Because the gravitational force formula is based on the masses of both objects, the formula applies to both objects.
Therefore, B. The forces are equal and opposite is correct.
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A 0.600-kg ball traveling at 4.00 m/s to the right collides with a 1.00-kg ball traveling at 5.00 m/s to the left. After the collision, the lighter ball is traveling 7.25 m/s to the left. What is the velocity of the heavier ball after the collision?
Answer:
Explanation:
The velocity of each ball after the collision can be determined using the law of conservation of momentum. The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces are acting on the system. In this case, the two balls form an isolated system before and after the collision, so their total momentum must be conserved.
Let's call the velocity of the heavier ball after the collision "v". The total momentum before the collision is given by:
p_i = (0.600 kg)(4.00 m/s) + (1.00 kg)(-5.00 m/s) = -2.00 kg m/s
The total momentum after the collision is given by:
p_f = (0.600 kg)(v) + (1.00 kg)(-7.25 m/s) = 0.600 kg v - 7.25 kg m/s
Since the total momentum is conserved, we can set the initial momentum equal to the final momentum and solve for v:
p_i = p_f
-2.00 kg m/s = 0.600 kg v - 7.25 kg m/s
Adding 7.25 kg m/s to both sides and dividing both sides by 0.600 kg, we get:
v = (2.00 kg m/s + 7.25 kg m/s) / 0.600 kg = 9.25 m/s
So, the velocity of the heavier ball after the collision is 9.25 m/s.
Answer:
The velocity of the heavier ball after the collision is 3.05 m/s
Explanation:
This is an example of partially elastic collision. In a partially elastic collision, momentum is conserved and the objects move at different speeds. A portion of the initial kinetic energy is still retained by the colliding objects after the impact.
The conservation of momentum states that the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.
The formula for momentum is
[tex]p=mv[/tex]
We can conclude that
[tex]m_1v_{1i} +m_2v_{2i}=m_1v_{1f} +m_2v_{2f}[/tex]
Let object 1 be the 0.600 kg ball.
Let object 2 be the 1.00 kg ball.
We are given
[tex]m_1=0.600\\v_{1i} =4.00\\m_2=1.00\\v_{2i} =5.00\\v_{1f} =7.25[/tex]
Inserting our given values into the equation gives us
[tex](0.600*4.00)+(1.00*5.00)=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]
Lets solve for [tex]v_{2f}[/tex].
Evaluate each set of parenthesis.
[tex]2.4+(1.00*5.00)=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]
[tex]2.4+5=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]
[tex]2.4+5=4.35+\left(1.00*v_{2f}\right)[/tex]
Anything multiplied by 1 stays the same.
[tex]2.4+5=4.35+v_{2f}[/tex]
Add 2.4 and 5.
[tex]7.4=4.35+v_{2f}[/tex]
Subtract 4.35 from both sides of the equation.
[tex]3.05=v_{2f}[/tex]
a researcher interested in identifying common patterns of traits that characterize whole persons will likely use a approach.
A researcher interested in identifying common patterns of trait variation that characterize whole persons is using an essential-trait. approach
What is an essential-trait?In the context of this article, an essential quality is a component that could not be left out of a concept's primary definition. When something is excluded, the definition is changed, and it might no longer be a definition at all or it might refer to another idea.
Qualitative traits, like eye color, can also be quantitative (such as height or blood pressure). A specific characteristic is a component of a person's overall phenotype.
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A parachute is used to decelerate a skydiver from an initial velocity of vo = 83 m/s to a velocity of vf = 9 m/s. The deceleration produced by the parachute is a = (-0.0302) m/s2. Determine the distance in [m], As, required to reach its final speed. As = number (3 significant figures) [m]
The distance required to be covered by the skydiver to reach the final speed is found to be 378.22m.
The deceleration produced by the parachute is -0.0302m/s². The final and the initial velocity of the skydiver are 9m/s and 83m/s respectively.
Now, we know the equation of motion,
V² - U² = 2as
Where,
V and U are the final and the initial velocity,
a is the net acceleration,
s is the distance covered by the parachute.
Now, putting all the values,
(9)²-(83)² = 2(-0.0320)s
s = 378.22 m.
So, distance that should be travelled by the skydiver is 378.22m.
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true/false. relationship between the strength of the attractions between particles and the number of particles you expect to be in the gas phase at a given temperature.
suppose that vehicles taking a particular freeway exit can turn right (r), turn left (l), or go straight (s). consider observing the direction for each of three successive vehicles.
the direction for each of three successive vehicles. A = {RRR,LLL,SSS} , B = {RLS, RSL, LSR, LRS, SRL, SLR} C = {RRS, RRL, RSR, RLR, LRR, SRR}
What is the best definition of direction?Direction is defined as the path that something takes, the path that must be taken to reach a specific place, the way in which something is starting to develop or the way you are facing. An example of direction is when you go right instead of left.
What is direction in a sentence?the course or path on which something is moving or pointing. The army attacked from three different directions. Down the road, he could see a bus coming from the opposite direction. The wind changed direction and started blowing in faces.
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How do you convert a proton into an electron. Answer in words and math.
Answer:
The ability of a substance to be reused depends on various factors such as its chemical and physical properties, how it is processed and used, and the environmental conditions it is exposed to. Some substances can be easily purified or restored to their original state, while others may undergo chemical changes or deteriorate during use, making it difficult or impossible to reuse them. Additionally, the cost and availability of alternative materials, as well as regulations and policies, can also impact the decision to reuse a substance.
A car is stopped at a traffic light. It then travels along a straight road so that its distance from the traffic light is given by x(t)=bt2−ct 3, where b=2.40ms −2 and c=0.120ms −3.The instantaneous velocity of the car at t=5.0s is?
The instantaneous velocity of the car at t = 5.0 s is -3 m/s. The negative sign indicates that the car is moving in the opposite direction from the traffic light at that moment.
What is instantaneous velocity ?Instantaneous velocity is the velocity of an object at a specific point in time. It is the rate of change of the object's position at that particular moment, and it is represented by the derivative of the object's position with respect to time. Instantaneous velocity is a vector quantity, meaning it has both magnitude and direction. It can be determined by taking the limit of the average velocity as the time interval approaches zero. It is also the limit of the average acceleration when the time interval approaches zero.
This can be found by taking the derivative of the equation [tex]x(t) = bt2 − ct3[/tex]with respect to t. The derivative of this equation is [tex]v(t) = 2bt - 3ct^2.[/tex]Plugging in the given values of b and c, and evaluating the equation at t=5.0s gives the instantaneous velocity of the car.
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A negative charge, which is free to move is released from rest in an electric field Neglect non-electrical forces. It will always move to a position with O higher potential O lower potential O electric field with higher magnitude. O electric field with lower magnitude. O larger electrical force O smaller electrical force
The correct option is A. A negative charge, which is free to move is released from rest in an electric field Neglecting non-electrical forces. It will always move to a position with higher potential.
The ability difference between any points inside the electric-powered field is defined as the quantity of labor done in transferring a unit of fantastic charge without acceleration from one point to another alongside any route among the 2 factors. The distinction in price between higher capability and lower capacity is known as a voltage or capacity distinction.
The voltage between points can be a result of the build-up of electric rate (e.g., a capacitor), and from an electromotive pressure (e.g., electromagnetic induction in generators, inductors, and transformers).On a macroscopic scale, a potential distinction can be due to electrochemical methods (e.g., cells and batteries), the stress-induced piezoelectric effect, and the thermoelectric effect.
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what concept in the video of the Big Bang Theory show which demonstrated operant conditioning that is incorrect?
Answer:
getting chocolate is a positive reinforcement
Explanation:
A 5.0 Ω, 10.0 Ω, 12.0 Ω, and 16.0 Ω resistor are connected in series to a 120 V voltage source. What is the current of the circuit?
A) 2.8 A
B) 4.4 A
C) 44 mA
C) 28 mA
Answer:
2.8 A
Explanation:
since the resistances are in series, the net resistance will be,
R = R1 + R2 + R3 + .....
R = ( 5+10+12+16)Ω
R = 43Ω
From Ohm's law,
V = iR
120 = i * 43
i = 120/43 A
i = 2.8A
an investor is building a hydropower station. it's 5 megawatt capacity and utility is paying 26 cents per kilowatt hour. how much revenue will the hydropower station make per year? PLEASE TRY TO SOLVE
Answer:
1,300dollars
Explanation:
5megawatt= 5*10^6watts=5,000,000W
26cents/1000watts (10^3=kilo)
total amount=26cents/1000watts*5,000,000W
=130000cents
=1300 dollars
Might be wrong but you can try this
body a of mass 4m moving with speech u colldes with another body b of mass 2m, at rest the collisn on and elastic nature. after collision the fracyion of energy lost by the colding body a is
a.1/9
b.8/9
c.4/9
d.5/9
The fraction of energy lost by the colliding body is 8/9.
In an elastic collision, the total kinetic energy of the system before the collision is equal to the total kinetic energy of the system after the collision.
Before the collision, the total kinetic energy of the system is given by:
[tex]K1 = 0.5 * m1 * u^2[/tex]
After the collision, the total kinetic energy of the system is given by:
[tex]K2 = 0.5 * m_{1} * v_{1} ^2 + 0.5 * m_{2} * v_{2}^2[/tex]
where m1 is the mass of body A, u is its initial velocity, v1 is its final velocity, m2 is the mass of body B, and v2 is its final velocity.
Conservation of momentum also applies in this case. The momentum of the system before the collision is equal to the momentum of the system after the collision.
Before the collision, the momentum of the system is given by:
[tex]p_{1} = m_{1} * u[/tex]
After the collision, the momentum of the system is given by:
[tex]p_{2} = m_{1} * v_{1} + m_{2} * v_{2}[/tex]
From the conservation of momentum, we have:
[tex]m_{1} * u = m_{1} * v_{} + m_{2} * v_{2}[/tex]
Solving for v1 and v2, we find:
[tex]v_{1} = u * (m_{1} - m_{2}) / (m_{1} + m_{2})[/tex]
[tex]v_{2} = 2 * u * m_{1} / (m_{1} + m_{2})[/tex]
Substituting these values into the equation for K2, we find:
[tex]K_{2} = 0.5 * m_{1} * u^2 * (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2[/tex]
The fraction of energy lost by body A is given by:
[tex](K_{1} - K_{2}) / K_{1} = 1 - K_{2} / K_{1}[/tex]
= [tex]1 - 0.5 * m_{1} * u^2 * (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2 / (0.5 * m_{1} * u^2)[/tex]
= [tex]1 - (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2[/tex]
= 1 - (4 - 2)^2 / (4 + 2)^2
= 1 - (2)^2 / (6)^2
= 1 - 4/36 = 1 - 1/9 = 8/9
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Three blocks in contact with each other are pushed across a rough horizontal surface by 63 N force as shown. The acceleration of gravity is 9.8 m/s 2 kg kg 2.5 kg K = 0.1 If the coefficient of kinetic friction between each of the blocks and the surface is 0.1, find the magnitude of the force exerted on the 9 kg block by the 2.5 kg block_ Answer in units of N.
The 2.5 kg block pulls on the 9 kg block with an 87.2 N force.
Newton's Third Law, often known as the law of action and reaction, can be used to determine the force that the 2.5 kg block exerts on the 9 kg block. The force applied to the 9 kg block is equivalent to, but applied in the opposite direction from, the force applied to the 2.5 kg block. Since they are in touch, the force of friction operating on the 9 kg block is equal to the force of friction acting on the 2.5 kg block.
Calculating the friction force is as simple as multiplying the normal force, or weight of the object, by the coefficient of friction:
Step 1: Determine the normal force or weight of the object. The weight of a 9 kg object can be calculated as 9 kg x 9.8 N/kg = 87.2 N.
Step 2: Determine the coefficient of friction. In this case, the coefficient of friction is 0.1.
Step 3: Calculate the friction force by multiplying the normal force by the coefficient of friction.
Friction force = Normal force x Coefficient of friction
= 87.2 N x 0.1 = 8.72 N.
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a star with 0.5 apparent magnitude would appear how many times brighter than a star with 5.5 apparent magnitude? Therefore the star with apparent magnitude 0.5 must be how many times farther away?
The star with an apparent magnitude of 0.5 appears approximately 100.06 times brighter than the star with an apparent magnitude of 5.5. It is approximately 10 times closer to us.
The magnitude scale used in astronomy is logarithmic, which means that each whole number increase or decrease in magnitude represents a difference in brightness by a factor of approximately 2.512. Therefore, to determine the relative brightness between two stars, we can calculate the difference in magnitude and then use this factor.In this case, the difference in apparent magnitude between the two stars is 5.5 - 0.5 = 5 magnitudes. Using the factor of 2.512, we can calculate the relative brightness:Brightness factor = 2.512^(difference in magnitude) = 2.512^5 ≈ 100.06So, the star with an apparent magnitude of 0.5 would appear approximately 100.06 times brighter than the star with an apparent magnitude of 5.5.To determine the distance between the two stars, we can use the inverse square law of light. Since brightness decreases with distance squared, if one star appears 100.06 times brighter, it must be approximately [tex]\sqrt{ 100.06}[/tex] ≈ 10 times closer to us than the star with apparent magnitude 5.5.For more questions on magnitude
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1. An object was launched from the ground to the top of a building at a
distance of 65 m from its foot on a horizontal plane at an angle of 60
degrees. Using SOHCAHTOA, find the height of the building the
projectile was launched to from the ground.
Using SOH,CAH,TOA, we can calculate the height of the building by taking the sine of the launch angle (60°) and the distance traveled (65 m). The height of the building is 56.9 m.
What is SOH,CAH,TOA?SOH,CAH,TOA stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse and Tangent = Opposite/Adjacent. This is a set of trigonometric ratios that can be used to solve for angles and lengths of sides of a right triangle. It is used when the angle and length of two sides of a right triangle are known, but the length of the third side needs to be calculated.
Calculation using SOH, CAH, TOA
The distance from the ground to the top of the building is 65 m and the angle is 60 degrees. the height (h) of the building.has to be found
Using the trigonometric ratio of Sine, calculate the height of the building:
Sin(60°) = Opposite/Hypotenuse
h/65 = sin(60°)
h = 65sin(60°)
h = 65(0.866)
h = 56.59 m
Therefore, the height of the building the projectile was launched to from the ground is 56.59 m.
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