Torque is defined as the cross product of the force and the distance from the center to the point of application (force = r * F * sin) (theta)
Where is the maximum torque?Keep in mind that at 90 degrees, the torque is at its highest level. Finding the lever arm and multiplying it by the applied force is a useful method for calculating the amount of torque. The distance that separates the force's line of action from its rotational axis is known as the lever arm.
Why does a 90-degree angle matter?Perpendicular describes two straight lines that meet at a 90-degree angle. When it comes to geometric proofs and examining various vertices and angles, perpendicular lines can be used in a variety of ways. They are helpful for making sure things are straight and aligned properly when painting or building.
to know more about torque here:
brainly.com/question/25708791
#SPJ4
In the above situation, what is the net torque on wire 2 due to wire 1?
a. Up b. Down
c. Into the screen d. Out of the screen e. Zero
In the above situation the net torque on wire 2 due to wire 1 is Zero.
Which way is the force acting on the wire?Fleming's left-hand rule identifies the force's direction on a current-carrying wire when it is placed in a magnetic field. It always runs counter to how the magnetic field and electric current are moving.
Directional torque: what is it?Torque is a vector quantity by definition. The direction is determined as part of the torque computation. The direction is parallel to both the force and the radius from the axis. It is customary to choose it along the rotational axis in the right-hand rule direction.
When rotating clockwise, is torque negative?a force that is applied that results in a positive counterclockwise torque A negative torque rotates an object in a clockwise direction.
To know more about torque visit:
https://brainly.com/question/20691242
#SPJ4
Like the Kelvin scale, the Rankine scale is an absolute temperature scale: Absolute zero is zero degrees Rankine (0∘R). However, the units of this scale are the same size as those on the Fahrenheit scale (∘F) rather than the Celsius scale (∘C).
A) Given that water at standard pressure freezes at 0∘C, which corresponds to 32∘F, and that it boils at 100∘C, which corresponds to 212∘F, calculate the temperature difference ΔT in degrees Fahrenheit that corresponds to a temperature difference of 1 K on the Kelvin scale.
B) What is the numerical value of the triple-point temperature Ttriple of water on the Rankine scale?
The temperature difference of 1 K on the Kelvin scale is equivalent to the temperature difference of (5/9)°F on the Fahrenheit scale. Triple-point temperature of water is approximately 491 degrees Rankine.
The unit of scales on the Rankine scale is the same as those on the Fahrenheit scale. Hence, from the freezing point of water (0⁰C) to the boiling point of water(100⁰C) , Rankine scale is divided into 180 scales.
The absolute zero is zero degrees Rankine. In Celsius scale, absolute zero is −273 °C.
A). A unit scale on the Kelvin scale is the same size as a unit scale in the Celsius scale. Hence,
ΔT 1 K = ΔT 1°C
The ratio of Celsius and Fahrenheit scale is 5/9, therefore:
K/F = C/F = 5/9
Hence,
ΔT 1 K = ΔT (5/9)°F
B) Triple-point temperature of water is approximately 0 °C. Since zero degrees Rankine is equivalent to −273 °C, hence:
0 °C = 0 - (9/5)(-273) = 491 degrees Rankine.
Learn more about Rankine scale here:
https://brainly.com/question/13294139
#SPJ4
A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with vertical, what must this angle be if the tension in each wire is equal to 0.75 of the weight of the frame?
(Neglect any friction betweem the wall and the picture fame)
The angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰.
By using the parallelogram law of vector addition, it is possible to calculate the angle between the two wires.
a² + b² - 2abcosθ = R²
Where;
R = is the outcome vector = the frame's weight ⇒ W
Angle between the two wires equals 0.75W for the first wire's tension and 0.75W for the second wire's tension.
(0.75W)² + (0.75W)² - 2(0.75W x 0.75W) cosθ = W²
1.125W² - 1.125W² cosθ = W²
= 1.125W²(1 - cosθ)
W²/1.125W² = 1 - cosθ
0.8889 = 1 - cosθ
cosθ = 1 - 0.8889
cos θ = 0.1111
θ = arc cos(0.1111)
θ = 83.6⁰
So, the angle must be formed if the tension in each cable is equal to 0.75 of the frame weight is 83.6⁰
Learn more about tension here: https://brainly.com/question/13258922
#SPJ4
Three loops of wire move near a long straight wire carrying a current as in the following figure. (a) What is the direction of the induced current, if any, in loop A? O clockwise O counterclockwise
O No current is induced. (b) What is the direction of the induced current, if any, in loop B? O clockwise O counterclockwise O No current is induced. (c) What is the direction of the induced current, if any, in loop C? O clockwise O counterclockwise O No current is induced.
(A) The current in the long straight wire produces a magnetic field that is perpendicular to its direction of flow.
What is Counter clockwise ?
Counter clockwise is a direction opposite to the usual clockwise direction. It is often used to describe the direction of rotation or movement, such as the turning of a wheel, the orbits of planets, or the hands of a clock. Counterclockwise motion can also be referred to as "widdershins" or "anticlockwise."
This magnetic field interacts with the loops of wire, inducing a current in them. The direction of the current in loop A is clockwise due to the right hand rule.
(B) No current is induced. Since the flux through loop B is not changing, no induced current is created.
(C) No current is induced. Since loop C is not moving, the changing magnetic field will not induce any current in it.
To learn about Counter clockwise
https://brainly.com/question/28354740
#SPJ4
Complete Questions:
(a) What is the direction of the induced current, if any, in loop A?
A) clockwise
B) counterclockwise
C) No current is induced.
(b) What is the direction of the induced current, if any, in loop B?
A clockwise
B counterclockwise
C No current is induced.
(c) What is the direction of the induced current, if any, in loop C?
A clockwise
B counterclockwise
C No current is induced.
An object is dropped from a height of 8 m. At what height will its kinetic energy and its potential energy be equal
At the peak it has the same potential and kinetic energy.
How is kinetic energy calculated?Kinetic energy (K.E.) is inversely proportional to the square of an object's velocity and its mass: K.E. = 1/2 m v2. When a mass is measured in kilograms and a speed is measured in meters per second, the kinetic energy is measured in kilogram-meters squared per second squared.
Kinetic energy and potential energy are equivalent at what height?The velocity will be zero and the ball's displacement will be at its maximum at the highest point of the trajectory. We might state that the energy present is equivalent to the sum of the potential energy.
To know more about kinetic energy visit:-
https://brainly.com/question/15764612
#SPJ4
Describe a method that can be used to open a tight lid of bottle without damaging it
Answer:
But the safest way to loosen a tight cap may be to run hot water on it so that it expands slightly.
Explanation:
You and your friend, who weighs the same as you want to go to the top of the Eiffel Tower Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy of you and your friend, after you both reach the top. Your gravitational potential energy is greater than that of your friend, because you traveled a greater distance in getting to the top. Your friend's gravitational potential energy is greater than yours, because he got to the top faster Both of you have the same amount of gravitational potential energy at the top. Dit is impossible to tell, since the times you both took are unknown Impossible to tell since the distances you both traveled are unknown
You and your friend will have the same potential energy at the top of the tower because gravitational potential only depends on height and not on how an object got there.
What does potential energy mean?The power that a substance retains as a result of its position in relation to other things, internal pressures, electric charge, or other substances is known as potential energy in physics. Potential energy is a form of energy that is stored but is dependent on the interactions of different system components.
A steel ball has more potential energy if it is raised above the ground as opposed to dropping to it. The energy that is present in everything that is raised from rest and has the potential to be released at a later time is known as potential energy.
To learn more about potential energy visit:
brainly.com/question/24284560
#SPJ4
The____of a conductor is defined as the diameter of the conductor in mils, squared.
The cross-sectional area of a conductor is defined as the diameter of the conductor in mils, squared.
What is conductor?
A conductor is a material or object that allows the flow of electric current. It is a material that has a large number of free electrons which can move freely between atoms, allowing for the current to flow through the material. Conductors can be either solid or liquid, and can be used to create electrical circuits and systems. Common conductors used in electrical systems include copper, aluminum, silver, and gold. These materials have high electrical conductivity, meaning they have low resistance and allow for large amounts of electric current to pass through them. Conductors are essential in many electronics and electrical devices, as they are responsible for carrying the electric current from one component to another.
To learn more about conductor
https://brainly.com/question/492289
#SPJ4
Running at 2. 0 m/s, Burce, the 45. 0 kg quarterback, collides with Max, the 90. 0 kg tackle, who is traveling at 7. 0 m/s in the other direction. Upon collision, Max continues to travel forward at 1. 0 m/s.
What is the new velocity of Bruce?(list unknown variable and known variables, write an equation, plug in numbers, and get answer with unit. )
Burce, a 45-kg quarterback, collides with Max, a 90-kg tackle, who is moving at 7.0 m/s in the opposite direction, as he runs at 2.0 m/s. This results in Bruce's new speed being 14 m/s.
Max hits the ground moving forward at a speed of 1.0 m/s. A moving object's velocity is a function of time and measures how quickly its position changes in relation to a frame of reference. When an object is moving, its speed and direction are specified by its velocity. A collision in physics is referred to as an elastic collision when the combined kinetic energy of the two bodies stays constant. A collision that is ideal and absolutely elastic
V1 = (720 - (90)(1))/45
V1 = 14m/s
Learn more about speed here
https://brainly.com/question/28224010
#SPJ4
How does dynamic stretching help an individual prepare for an activity brainly?
Dynamic stretching helps to prepare the body for an activity by increasing:
body temperatureimproving range of motionactivating the muscles and nervous system for the activity. also helps to reduce the risk of injury by improving the body's ability to move through a full range of motion.improving coordination and balance.What is dynamic stretching?Dynamic stretching is a form of stretching that involves active, controlled movements such as swinging, bouncing, and twisting. The goal of dynamic stretching is to improve range of motion and flexibility while preparing the body for physical activity.
Learn more about dynamic stretching:
https://brainly.com/question/24842019
#SPJ4
A box is released from the top of a frictionless track. It starts from rest and has a speed of 14 m/s at the bottom. What is the height of the track
If we use the aceleration equation, we can calculate the height value: The height of the track is: 98.04 m,
The height of the track can be calculated using the equation:
h = (v^2)/(2g)
Where h is the height, v is the velocity, and g is the acceleration due to gravity (9.8 m/s^2).
Therefore, the height of the track is:
h = (14^2)/(2*9.8) = 98.04 m
The equation h = (v^2)/(2g) is derived from the equation of motion for an object moving in a uniform gravitational field. This equation states that the change in potential energy is equal to the kinetic energy of an object. The potential energy of an object is determined by its height in the gravitational field, and the kinetic energy of an object is determined by its velocity. Therefore, the equation of motion can be used to calculate the height of an object, given its velocity.
Learn more about potencial energy :
https://brainly.com/question/23979653
#SPJ4
You're in the back of a friend's pickup truck when it stalls on a hill. You jump out, get behind the truck and push with all your might (300 N) in a vain attempt to keep the truck from accelerating down the hill. The force the truck exerts on you is: less than 300 N 300 N greater than 300 N
The force the truck exerts on you is 300 N.
What is meant by force?
A force in physics is an effect that has the power to alter an object's motion.Intuitively, a push or a pull can also be used to describe force.Being a vector quantity, a force has both magnitude and direction. The SI unit of newton is used to measure it (N). The letter F stands for force (formerly P).According to Newton's second law's original formulation, an object's net force is equal to the speed at which its momentum is changing over time. According to this law, an object's acceleration is inversely proportional to the net force acting on it, is in the direction of the net force, and is directly proportional to the mass of the object if its mass is constant.To learn more about force refer to
https://brainly.com/question/12970081
#SPJ4
N a circuit, when the two conductors leading from the power source touch metal-to-metal, this is called a _____ circuit
In a circuit, when the two conductors leading from the power source touch metal-to-metal, this is called a short circuit
Types of short circuitThere are two types of short circuits, short-to-power and short-to-ground, where electricity takes an unintentional shortcut without going through the intended sensor or actuator.
Short to ground - When there is a short to ground, it refers to the current flowing from the circuit to the car body. Wires can tear and strip their insulation, contacting the body or engine. A short path to ground can result in blown fuses, malfunctioning lights or motors, or “missing” sensors. For example, a scuffed wire might be short to ground, which could cause the headlight fuse to blow, protecting the circuit from overheating, but killing the headlights. Short power - In a wire harness, with many circuits in close proximity, there is a possibility of a short power fault. In this case, wires that are wound or cut can interconnect with each other, allowing current to flow where it is not intended. For example, someone installing an aftermarket device might push a screw through a wire harness, accidentally puncturing and "connecting" some of the wires. Turning on the headlights might send current into the horn, or hitting the brakes might illuminate the taillights.Learn more about short circuit at https://brainly.com/question/18207608.
#SPJ4
Suppose a molecule has neutrons, a Coulomb total electric charge, and electrons. About how many protons must it have
molecule possesses neutrons and a total electric charge of one Coulomb. e is the electronic value, 1.60 x 10-19 Coulombs, and the proton has a cost of +e while the electron has a fee of -e.
How much is one coulomb?The quantity of charge carried by a present of one amp for one second is measured in coulombs, which is the unit of measurement used in the SI for electric charge. It may also be a quality of a substance that causes magnetic and electric effects to occur. The symbol for it is C. According to math, 1 Coulomb equals 1 Ampere x 1/sec.
A coulomb quizlet: what is it?A coulomb is an unit of power charge that represents the charge that is transmitted over one ampere of current in one second. Colomb's rule. depending on the charged items, electric force.
To know more about Coulomb visit :
https://brainly.com/question/12498766
#SPJ4
This problem contains several examples of this.Consider an object sliding on a frictionless ramp as depicted here. (Figure 1) The object is already moving along the ramp toward position 2 when it is at position 1. The following questions concern the direction of the object's acceleration vector a_vec. In this problem, you should find the direction of the acceleration vector by drawing the velocity vector at two points near to the position you are asked about. Note that since the object moves along the track, its velocity vector at a point will be tangent to the track at that point. The acceleration vector will point in the same direction as the vector difference of the two velocities.
Which direction best approximates the direction of a_vec when the object is at position 2?
a. straight up b. upward to the right c. straight down d. downward to the right
This problem contains several examples of this.Consider an object sliding on a ramp as depicted here.Downward to the right.
What is the sliding ?
Sliding is a type of motion that involves the movement of an object relative to a surface while keeping contact with it. This type of motion is often used in everyday activities such as walking, running, and skiing. Sliding can also refer to the movement of two or more objects in contact with each other, such as a car door sliding open or a sheet of paper sliding across a table. In physics, sliding is considered to be a type of frictional motion, in which the frictional force between the object and the surface it is sliding on causes the object to move.
To learn more about sliding
https://brainly.com/question/17140804
#SPJ4
The internal energy within a system associated with the motion of particles and that can be added to a substance is called _____.(1 point) electrostatic forces electrostatic forces temperature temperature thermal energy thermal energy kinetic energy
Thermal energy is the internal energy that exists in a system and is connected to the movement of the particles and can be contributed to a substance.
Describe thermal energy.The energy in such a system that regulates its temperature is referred to as thermal energy. The exchange of thermal energy is referred to as "heating." Thermodynamics, a whole field of physics, is the study of how heat is transmitted between various systems and how work is performed in the process.
Describe motion.In physics, motion is a variation in an object's position with respect to its surroundings over a predetermined amount of time. To describe how an object travelling with a specific mass moves, use the terms below: Distance. Displacement. Speed.
So-called thermal energy is the internal energy present in a system that is connected to particle motion that can be given to a substance.
Learn more about thermal energy from the given link.
https://brainly.com/question/19666326
#SPJ4
A crate of eggs is located in the middle of a pickup truck as the truck rounds a corner in the road. The curve has a radius of 35 m. If the coefficient of static friction between the crate and the truck is 0.600, how fast can the truck move without the crate sliding
The speed of the truck is 14.3m/s without the crate sliding.
What is the equation for static friction?The resistive friction force (Fr) multiplied by the usual or horizontal pressure (N) pushing the things together yields the frictional coefficient (fr), which is a numerical value. The formula fr = Fr/N serves as a representation of it.
Calculation -:Call the mass of the egg crate m. The forces on it are its weight Fg =mg vertically down, the normal force n of the truck bed vertically up, and static friction (fs) directed to oppose relative sliding motion of the crate on the truck bed. The friction force is directed radially inward. It is the only horizontal force on the crate, so it must provide the centripetal acceleration. When the truck has maximum speed, friction fs will have its maximum value with fs=μn.
Newton’s second law in component form becomes
∑Fy=ma(y) giving n−mg = 0 or n = mg
∑F(x)=ma(x) giving f(s)= ma(r)
From these equations
μ(s)n ≤ mv²/r and μ(s)mg ≤ mv²/r
The mass divides out. The maximum speed is then
v≤[tex]\sqrt{}[/tex]μrg =[tex]\sqrt{}[/tex]0.600(35.0m)(9.80 m/s²) = v ≤1 4.3m/s.
To know more about static friction visit :
brainly.com/question/13000653
#SPJ4
Can nuclei of the same element have different values of Z? Of N? Of A?
Check all that apply.
O 1 Nuclei of the same element must have the same values of Z, N, and A.
O 2 Nuclei of the same element can have different values of Z.3
O 3 Nuclei of the same element can have different values of A.
O 4 Nuclei of the same element can have different values of N.
Nuclei of the same element can have different values of Z, N, and A, as these values are all related to the number of protons, neutrons, and nucleons in the nucleus, respectively. Therefore, option 2, 3, and 4 are correct.
Nuclei of the same element can have different values of Z, N, and A due to the number of protons, neutrons, and nucleons they contain, respectively. This is because the number of these particles in the nucleus can vary, although they all will still be the same element. Therefore, option 2, 3, and 4 are correct and option 1 is incorrect.
Nuclei of the same element can have different values of Z, N, and A, as these values are all related to the number of protons, neutrons, and nucleons in the nucleus, respectively. Therefore, option 2, 3, and 4 are correct.
learn more about proton here
https://brainly.com/question/12535409
#SPJ4
Caffeine dosage causes a change in the time to finish a maze and it isn't possible for that the time to finish a maze could cause a change in
caffeine dosage.
Caffeine dosage and time to finish a maze are independent variables, meaning that a change in one does not cause a change in the other. It is possible that caffeine dosage may have an effect on the time it takes to finish a maze, but the time it takes to finish a maze would not cause a change in caffeine dosage.
Caffeine Maze Time ImpactCaffeine is a stimulant that can affect the central nervous system and can have a range of effects on the body, including increased alertness, focus, and energy. When it comes to completing a maze, the time it takes to finish it could be affected by the person's level of alertness, focus, and energy. Therefore, if a person ingests a certain dosage of caffeine, it could affect the time it takes for them to finish the maze because of the effect caffeine has on the body.
On the other hand, the time it takes to finish a maze does not affect the caffeine dosage, in other words, caffeine dosage is an independent variable, it does not depend on other variables, and does not change based on the time it takes to complete a maze. It is determined by the amount of caffeine consumed.
So, in short, caffeine dosage can have an effect on the time it takes to finish a maze, but the time it takes to finish a maze does not have an effect on caffeine dosage.
Learn more about Caffeine Dosage here:
https://brainly.com/question/8554538
#SPJ4
define visible light radiation
How do you calculate the speed of an object rolling down a ramp?
We can calculate the speed of an object rolling motion a ramp by using the equation of motion in which we consider rolling and a tangential force acting on it.
Rolling motion occurs when an object rolls down over a height from the ramp or from any other sloppy or rough surface. the surface can be both smooth or rough, depending on it the friction acts on the object that is rolling over the ramp. we also consider the rolling tangential force in our calculation along with other forces when we tend to calculate the rest of the things. We can calculate the speed of an object rolling motion a ramp by using the equation of motion in which we consider rolling and a tangential force acting on it. Hence by this we can consider that we can calculate the rolling of any object by the equation of motion.
Learn more about Rolling motion:
brainly.com/question/29568301
#SPJ4
Under certain circumstances, the grounded (neutral) conductors of a residential service ____ permitted to be sized smaller than the phase conductors.
Under certain circumstances, the grounded (neutral) conductors of a residential service are permitted to be sized smaller than the phase conductors.
What is conductors?
A material that easily permits the flow of electricity is referred to as an electrical conductor. Conductivity is the quality of conductors that enables them to conduct electricity.
Electric current is the name given to the movement of electrons through a conductor. Voltage is the amount of power necessary to cause that current to flow through the conductor.
What is phase ?
Phases are parts of a system that are mechanically separable from other parts of the system and are physically distinct from other parts of the system. types of substance. Solid, liquid, or gaseous phases can exist in a system. Strong atomic bonding and high viscosity, which produce a hard form in solids, are their distinguishing characteristics.
Therefore, Under certain circumstances, the grounded (neutral) conductors of a residential service are permitted to be sized smaller than the phase conductors.
Learn more about conductors from the given link.
https://brainly.com/question/492289
#SPJ4
Justin throws a 10. 0-g ball straight
down from a height of 2. 0 m. The ball
strikes the floor at a speed of 7. 5m/s.
What was the initial speed of the ball?
The ball's initial speed as it descended straight down from a height was 17.5 miles per hour.
The starting velocity is the speed at time t = 0. (u). It is the speed at which motion first becomes apparent. Four equations can be used to calculate initial velocity: (1) If time, acceleration, and end velocity are known, the initial velocity can be calculated using the formula u = v - at.
Calculation:We can simply use the following equation of motion to solve this:v² - u² = 2 × a × s
here, v = final velocity = 7.5 m/s
a = 9.81 m/s^2
s = 2.0 m
Solving for u (initial velocity) we get:
(7.5)² - u² = 2 × 9.8 × 2
56.25 - u² = 39.2
u² = 56.25 - 39.2
u² = 17.05
To know more about velocity visit:-
https://brainly.com/question/18084516
#SPJ4
It is known that a damped oscillator has a maximum displacment that is 13.5% of the original amplitude after 0.60 s. What is the value of the time constant
The value of the time constant is = 0.2996 s. Due to the fluid's dampening effect, the oscillations' amplitudes reduce. ma=−bv−kx.
How long does it take for the damped oscillations' amplitude to decrease to half of what it was initially?Its amplitude decreases by half after every ten oscillations. Find the starting time at which the amplitude becomes 11000 times as large as it was initially: Q. A damped harmonic oscillator's displacement is determined by the equation x(t)=e01.
How do amplitude and oscillation relate to one another?In an oscillating system, the amplitude is the amount by which the oscillating variable changes with each oscillation. For instance, sound waves in the air oscillate the atmospheric pressure, and the amplitude of each oscillation is proportional to the variation in the pressure.
to know more about time constant visits:
brainly.com/question/13860412
#SPJ4
In general, how can you calculate the distance of object B from the fulcrum so that it balances object A
The formulas F(A)×R(A) = F(B)×R(B) should be used to determine the distance of item B from the fulcrum such that it balances object A. where F is the object's force and R is the object's distance from the fulcrum.
What does "force" actually mean?The push or pull that causes a massed body to change its speed is the definition of force. An agent with the ability to change a body's rest or moving condition is known as an external force. It has a magnitude as well as direction.
How come forces occur?Forces are created by the interactions between two (or more) objects. There is a similar but opposing force acting on each individual on the other. External forces are what cause the item to move.
To know more about force visit :
https://brainly.com/question/13191643
#SPJ4
Find the interaction energy for two point charges, q1 and q2, a distance a apart. [Hint: Put q1 at the origin and q2 on the z axis; use spherical coordinates, and do the r integral first.]
The interaction energy for two point charges, q₁ and q₂, a distance 'a' apart is q₁q₂/4πε₀a.
In physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being evaluated. The interaction energy generally depends on the relative position of the objects.
For example q₁q₂/4πε₀Δr is the electrostatic interaction energy between two objects with charges q₁ and q₂.
[tex]W_{tot}[/tex] = ε₀/2(∫E²dτ)
= ε₀/2{(∫E₁ + E₂)²dτ}
= ε₀/2(∫E₁² + E₂² + 2E₁E₂)dτ
= W₁ + W₂ + ε₀(∫E₁ × E₂)²dτ
E₁ = 1/4πε₀(q₁/r²)r
E₂ = 1/4πε₀(q₂/ᴫ²)ᴫ
[tex]W_{i}[/tex] = ε₀q₁q₂/(4πε₀)²[∫{(1/r²ᴫ²)cosβr²sinθdrdθdφ}]
Where (from the figure)
ᴫ = √(r² + a² - 2ra cosθ), cosβ = (r - a cosθ)/ᴫ
Therefore
[tex]W_{i}[/tex] = {q₁q₂/(4π)²ε₀} 2π∫{(r - acosθ)/ᴫ³} sinθ drdθ
First do the r integral first, changing variables to ᴫ:
2ᴫdᴫ = (2r - 2a cosθ)
⇒(r - a cosθ)dr = ᴫdᴫ
As r : 0→∞, ᴫ : a→∞, so
[tex]W_{i}[/tex] = {q₁q₂/8πε₀a} [tex]\int\limits^\pi _0[/tex](∫limit 0 to ∞ 1/ᴫ² dᴫ) sinθ dθ
The ᴫ integral is 1/a, so
[tex]W_{i}[/tex] = {q₁q₂/8πε₀a} [tex]\int\limits^\pi _0[/tex] sinθ dθ
[tex]W_{i}[/tex] = q₁q₂/4πε₀a
This is the exact interaction energy of two-point charges.
To know more about electrostatic, here
https://brainly.com/question/14889552
#SPJ4
How far up a wall will a 25 ft ladder reach if the base of the ladder is 7 feet from the wall?
The height formed by this 25-foot ladder that leans against a wall is 24 feet.
To find out how far up a wall a ladder will reach, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the ladder forms one side of the triangle, the wall forms another side, and the distance between the base of the ladder and the wall forms the hypotenuse.
Let's call the height of the wall h. Using the Pythagorean theorem, we can set up the following equation:
(25 ft)^2 = h^2 + (7 ft)^2
625 = h^2 + 49
576 = h^2
h = sqrt(576) = 24 ft
Therefore, a 25 ft ladder that is 7 feet from the wall will reach 24 feet up the wall.
Learn more about determining the height of a ladder based on its length and the distance of its base from a wall here: https://brainly.com/question/13734303
#SPJ4
An engine with a power output of 110 hp has a thermal efficiency of 28%. Determine the rate of fuel consumption (in kg/hr) if heating valve of the fuel is 44,200kj/kg
The rate of fuel consumption is 6.69 kg/hr.
Solution:
To determine the rate of fuel consumption, we need to calculate the amount of energy required by the engine and divide that by the thermal efficiency.
From the question:
W = 110 hp
η = 28%.
r = ?
First, we can convert the power output from horsepower to watts:
1hp = 746 W
power output = 110 hp x 746 W/hp
= 82016 W
Then, we can calculate the energy required by the engine by multiplying the power output by the time the engine is running:
Energy = Power x time
Without knowing the time the engine runs, we cannot calculate the energy required.
We can calculate the fuel consumption by using the heating value of the fuel and the thermal efficiency.
Fuel consumption = ( Power )
(heating value * thermal efficiency))
So in this case:
Fuel consumption = (82016)
(44200*0.28)
= (82016)
12276
Fuel consumption = 6.69 kg/hr
Hence, the rate of fuel consumption is 6.69 kg/hr.
Learn more about rate of fuel consumption on
https://brainly.com/question/28809733
#SPJ1
ethe earth takes 1 day to rotate once about its axis. what is the angular v elocity of a point on the surface of the earth studentroom physics ocr a
The angular velocity of a point on the surface of the earth is [tex]7.3 * 10^{-5} rad/s[/tex]
What is angular velocity?
Angular velocity is a vector quantity and is described as the rate of change of angular displacement which specifies the angular speed or rotational speed of an object and the axis about which the object is rotating.
What is angular velocity and write its formula?
Angular velocity is the rate of change of the position angle of an object with respect to time, so w = theta / t, where w = angular velocity, theta = position angle, and t = time.
Every point on the earth's surface completes one circular orbit (centered at a point on the axis) in 1 day
1 day = 24x60x60
1 day=86400s
Angular velocity is given by :
[tex]w =2\pi /86400\\ w =7.3*10^{-5} rad/s[/tex]
Thus, [tex]7.3 * 10^{-5} rad/s[/tex] is the correct answer.
To know more about angular velocity :
https://brainly.com/question/20432894
#SPJ4
A car accelerates uniformly from 20mph to 50mph in 3 seconds. What is its acceleration during this time
A = (v-u)/t, where an is acceleration, v is final speed, u is initial speed, and t is time, is the equation for acceleration. When the values are filled in, we obtain a = (60-20)/5 or an is 8 m/s2.
How is acceleration determined?The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t). This enables you to calculate the change in velocity in meters per second squared (m/s2).
How quickly does the time go from 0 to 2 seconds?+2 m/s2
If there is no change in velocity between 2 and 3 seconds, the acceleration is 0 m/s2. The acceleration is +2 m/s2 over the first 0 to the second interval. The acceleration is zero between seconds two and three. The acceleration is -3 m/s2 throughout the three to six-second period.
to know more about accelerates here:
brainly.com/question/12550364
#SPJ4