To solve for the current I3 in wire 3, we can apply the principle of conservation of charge, which states that the total current flowing into a junction must equal the total current flowing out of the junction. This can be expressed mathematically as:
I1 + I2 = I3
where I1 and I2 are the currents in wires 1 and 2, respectively, and I3 is the current in wire 3.
To find I1 and I2, we can use the formulas for current (I = J x A), where J is the current density and A is the cross-sectional area of the wire. The cross-sectional area can be calculated from the diameter using the formula A = π/4 x d^2, where d is the diameter.
For wire 1:
I1 = J1 x A1 = 2.1 A/mm^2 x π/4 x (1.7 mm)^2 = 4.52 A
For wire 2:
I2 = J2 x A2 = 3.9 A/mm^2 x π/4 x (2.4 mm)^2 = 13.21 A
Substituting these values into the conservation of charge equation, we get:
4.52 A + 13.21 A = I3
Simplifying, we get:
I3 = 17.73 A
Therefore, the current I3 in wire 3 is approximately 17.73 amperes (or amps) to two significant figures.
What is a current ?Current can be thought of as the rate at which electric charges flow through a circuit. It is caused by the movement of electrons, which are negatively charged particles, in response to an electric field. In a metallic conductor, such as a wire, electrons can move freely through the material, which allows current to flow easily.
Current can be either direct current (DC) or alternating current (AC). DC flows in one direction, whereas AC changes direction periodically. DC is commonly used in batteries and electronic devices, while AC is used for power transmission over long distances.
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A photodetector has three polarizing films between it and a source of
unpolarized light. The first film is oriented vertically. At what angle should the
second polarizing film be oriented so that 37.5 percent of the original light
intensity reaches the detector?
Investigation 12 Electromagnetic Radiation
The angle between the polarization direction of the second film and the vertical direction should be approximately 51.4° so that 37.5% of the original light intensity reaches the detector.
Steps
Let's denote the angle between the vertical polarization direction of the first film and the polarization direction of the second film by θ. The transmitted intensity of the light after passing through the two films is given by Malus's law:
I = I₀ cos²θ
where I₀ is the initial intensity of the unpolarized light.
We want to find the angle θ that will result in 37.5% of the original light intensity reaching the detector. This means that we want to solve the equation:
I/I₀ = 0.375
Substituting the expression for I into this equation, we get:
cos²θ = 0.375 / I₀
Taking the square root of both sides and using the fact that cosθ is positive when 0 ≤ θ ≤ π/2, we get:
cosθ = √(0.375 / I₀)
θ = arccos(√(0.375 / I₀))
Now we need to substitute the values of I₀ and evaluate the expression for θ. Let's assume that the intensity of the original light is I₀ = 1 W/m². Then we get:
θ = arccos(√(0.375 / 1)) = arccos(0.6124) = 51.4°
Therefore, the angle between the polarization direction of the second film and the vertical direction should be approximately 51.4° so that 37.5% of the original light intensity reaches the detector.
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Problem 3 For the shaft below, calculate factors of safety based on the distortion energy theory for stress elements A and B when F 0.55 kN, P 4 kN, and T = 25 N.m. The shaft is made of AISI 1006 cold-drawn (CD) steel 15-mm D
The factor of safety based on the distortion energy theory for stress elements A and B of the shaft when F = 0.55 kN, P = 4 kN, and T = 25 N.m and made of AISI 1006 cold-drawn (CD) steel 15-mm D is 66.67 and 26.66, respectively.
The factor of safety based on the distortion energy theory for stress elements A and B of the shaft when F = 0.55 kN, P = 4 kN, and T = 25 N.m and made of AISI 1006 cold-drawn (CD) steel 15-mm D can be calculated as follows:
For stress element A:
Factor of Safety = [tex](2τ_allowable\times L)/(F\times d)[/tex]
Where τ_allowable is the allowable shear stress for the material, L is the length of the element, F is the force acting on the element, and d is the diameter of the element.
For this example, τ_allowable = 55 MPa (from AISI 1006 CD steel data), L = 0.15 m, F = 0.55 kN, and d = 0.015 m.
Therefore, Factor of Safety = [tex](2 \times 55 \times 0.15) / (0.55 \times 0.015) = 66.67[/tex]
For stress element B:
Factor of Safety =[tex](τ_allowable\times L^2)/(T\times d^3)[/tex]
Where τ_allowable is the allowable shear stress for the material, L is the length of the element, T is the torque acting on the element, and d is the diameter of the element.
For this example, τ_allowable = 55 MPa (from AISI 1006 CD steel data), L = 0.15 m, T = 25 N.m, and d = 0.015 m.
Therefore, Factor of Safety =[tex](55 \times 0.15^2) / (25 \times 0.015^3) = 26.66[/tex]
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Estimat the number and wattage of lamps. which would be required to illuminate a workshop space 60x1.5 meteres by means of lamps mounted 5 metres above the working Plane The average illumination required is about 100 wt. coefficient of utilisation = 0.4 luminous efficiency 16 lumens per watt. Assume a space-height ratio of unity and a cundle Power depreciation of 20%
The number and wattage of lamps required to illuminate the workshop would be approximately 8 lamps and 70 watts respectively.
Wattage calculationTo estimate the number and wattage of lamps required to illuminate a workshop space of 60x1.5 meters, we can follow these steps:
Calculate the area of the workshop:
Area = length x widthArea = 60m x 1.5mArea = 90 square metersDetermine the total lumens required:
Lumens = area x average illuminationLumens = 90 sq m x 100 luxLumens = 9000 lumensAdjust for the coefficient of utilization and luminous efficiency:
Effective lumens = lumens / (coefficient of utilization x luminous efficiency)Effective lumens = 9000 / (0.4 x 16)Effective lumens = 1406.25 lumensAdjust for space-height ratio and candle power depreciation:
Effective lumens per lamp = effective lumens x space-height ratio x (1 - depreciation)Effective lumens per lamp = 1406.25 x 1 x (1 - 0.2)Effective lumens per lamp = 1125 lumensDetermine the number of lamps required:
Number of lamps = total lumens required / effective lumens per lampNumber of lamps = 9000 / 1125Number of lamps = 8 lamps (rounded up)Determine the wattage of each lamp:
Wattage per lamp = effective lumens per lamp / luminous efficiencyWattage per lamp = 1125 / 16Wattage per lamp = 70.3 watts (rounded up)Therefore, approximately 8 lamps with a wattage of 70 watts each would be required to illuminate the workshop space.
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5.32 calculate ix and vo in the circuit of fig. 5.70. find the power dissipated by the 60-k resisto
The power dissipated by the 60-k Ohm resistor is 3 mv and 24mv.
[tex]=V_1=V =4mv\\=I_{iN}=\frac{4mv}{10k}=0.4\mu A\\= \frac{V_1 - V+}{50k}=0.4\mu A\\V_1 - 4m= 20m\\V_1 = 24mv[/tex]
[tex]i_x=\frac{V_1}{20+(6 || 3)} =\frac{24*10^{-3}}{(20+2.857)*10^{3}}\\i_x=1.05\mu A\\i_0=\frac{i_x*60}{60+3}=1\mu A\\V_0=3k*1\mu=3mv\\V_0=3mv[/tex]
An Ohm resistor is a passive electrical component that restricts the flow of current in an electrical circuit. It is named after Georg Simon Ohm, a German physicist who discovered Ohm's law which states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points.
An Ohm resistor has a resistance value measured in ohms, which determines how much it restricts the flow of current. The higher the resistance value, the more it restricts the current flow. Ohm resistors are commonly used in electronic circuits to control the voltage and current levels, and to protect sensitive electronic components from damage. They can also be used to divide voltages, as voltage dividers, or as current limiting devices.
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Complete Question: -
Calculate i_x and v_o in the circuit of Fig. 5.70. Find the power dissipated by the 60-k Ohm resistor.
is the equation a=v^2/r dimensionally correct?
Answer:
No, the equation a=v^2/r is not dimensionally correct. This can be seen by breaking down the dimensions of each term in the equation.
The dimension of acceleration (a) is length/time^2 (L/T^2).
The dimension of velocity (v) is length/time (L/T).
The dimension of radius (r) is length (L).
Substituting these dimensions into the equation, we get:
L/T^2 = (L/T)^2 / L
Simplifying this expression, we get:
L/T^2 = L/T^2
This means that the dimensions on both sides of the equation are equal and therefore the equation is dimensionally correct.
Answer:
Yes, the equation a=v^2/r is dimensionally correct.
Explanation:
The dimensions of acceleration (a) are distance/time^2, the dimensions of velocity (v) are distance/time, and the dimensions of radius (r) are distance.
When we substitute these dimensions into the equation a=v^2/r, we get:
a = (distance/time)^2 / distance
Simplifying, we get:
a = distance^2 / time^2 / distance
a = 1 / time^2
Therefore, the dimensions of both sides of the equation are the same, which confirms that the equation is dimensionally correct.
What is the magnitude of the total charge of all the electrons in 2.6 L
of liquid water?
A certain Tesla car has a 400 V battery which stores 2.9x108 J. The car can travel 402 km (250 miles) at 105 km/hr (65 mph = 29 m/s) on just the battery before it is depleted. The steps below will let you determine the current delivered by the battery.A. How long does it take to deplete the battery?B. What is the power delivered by the battery (P=E/dt)?C. Power in a circuit is related to the potential difference, current and resistance in the circuit. What is the current delivered by the battery?D. What is the resistance of the circuit?
A. Baterry takes time = 2.9x[tex]10^{8}[/tex] J / power to deplete.
What is time taken?
To determine how long it takes to deplete the battery, we can use the formula:
time = energy / power
where energy is the energy stored in the battery (2.9x[tex]10^{8}[/tex] J) and power is the power delivered by the battery (which we will determine in part B).
time = 2.9x[tex]10^{8}[/tex] J / power
B. Power delivered by the baterry is 20864.5 W
What is the power?
To determine the power delivered by the battery, we can use the formula:
power = energy / time
where energy is the energy stored in the battery (2.9x[tex]10^{8}[/tex] J) and time is the time it takes to deplete the battery (which we will determine in part A).
First, let's convert the distance traveled from kilometers to meters:
402 km = 402,000 m
Now, we can use the formula:
time = distance / speed
where distance is the distance traveled (402,000 m) and speed is the speed of the car (105 km/hr = 29 m/s).
time = 402,000 m / 29 m/s = 13896.6 s
Now we can calculate the power delivered by the battery:
power = 2.9x[tex]10^{8}[/tex] J / 13896.6 s = 20864.5 W
C. The current delivered by the battery is 52.2 A.
What is current?
The power delivered by the battery is related to the current and potential difference in the circuit by the formula:
power = potential difference x current
The potential difference in the circuit is given as 400 V. Therefore, we can rearrange the formula to solve for the current:
current = power / potential difference
current = 20864.5 W / 400 V = 52.2 A
Therefore, the current delivered by the battery is 52.2 A.
D. We cannot directly determine the resistance of the circuit from the given information.
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a tennis ball is dropped from a height of 1.21 m above the ground. calcualte its velocity when it is 0.27m from the ground
The velocity of the tennis ball when it is 0.27m from the ground is approximately 3.39 m/s.
What is velocity?
To calculate the velocity of the tennis ball when it is 0.27m from the ground, we can use the principle of conservation of mechanical energy, which states that the total mechanical energy of an object is conserved when it moves through a conservative force field, such as gravity.
At the initial position, the ball has potential energy due to its position above the ground, but no kinetic energy as it is at rest. At the final position, the ball has no potential energy (since it is at the same height as the ground), but it has kinetic energy due to its motion. Assuming that air resistance is negligible, the initial potential energy is converted into final kinetic energy, so we can equate these energies:
mgh = (1/2)mv²
where m is the mass of the ball, g is the acceleration due to gravity, h is the initial height of the ball above the ground, and v is the velocity of the ball when it is 0.27m from the ground.
We can rearrange this equation to solve for v:
v = √(2gh)
Substituting the given values, we get:
v = √(2 x 9.81 m/s² x (1.21 m - 0.27 m)) = 3.39 m/s
Therefore, the velocity of the tennis ball when it is 0.27m from the ground is approximately 3.39 m/s.
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by how much should lower the pressure at the top of the straw to have the lemonade rise 5 cm above the surface
The lemonade rise 5 cm above the surface, you must lower the pressure at the top of the straw by [tex]49 N/m^2[/tex] (or Pascals).
Let's assume that atmospheric pressure is 1 atm, and we want to raise the water to a height of 5 cm. Pressure in a fluid increases with depth, and the pressure at the bottom of the fluid is greater than the pressure at the top. Consider a horizontal straw filled with water that is open at both ends.
The pressure of the water in the straw is determined by atmospheric pressure at the open end of the straw. At the bottom of the straw, the pressure is the same as the pressure of the surrounding water (P0).
Let us consider a horizontal straw in which the water level rises to a height of 5 cm above the surrounding water when the pressure at the top of the straw is lowered by an amount of P.
As a result, the pressure of the water at the top of the straw is now (P + 1 atm), and the pressure at the bottom of the straw is (P0 + P).
Because the pressure at the bottom of the straw (P0 + P) is equal to the pressure of the surrounding water (P0), we have:
P0 + P = P0 + ρgh.
Solving for P, we get:
P = ρgh
In this case, h = 5 cm,
ρ is the density of lemonade, and
g is the acceleration due to gravity.
The value of g is [tex]9.8 m/s^2[/tex] on average.
[tex]ρgh = (1000 kg/m^3) × (9.8 m/s^2) × (0.05 m) = 49 N/m^2[/tex] (or Pascals).
So, to have the lemonade rise 5 cm above the surface, you must lower the pressure at the top of the straw by [tex]49 N/m^2[/tex] (or Pascals).
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Check the correctness of the following equation , a=v^2/r, where a=acceleration, v=velocity, r= radius
Answer:
check
Explanation:
Sam drives 20 miles North, 10 miles East, 20 miles South and 10 miles West.
Distance:
Displacement:
Sam traveled a total distance of 60 miles, but his displacement is zero, as he ended up back at his starting point after all of his movements.
How to measure the distance?
The distance that Sam has traveled is the total length of the path he took, regardless of the direction. In this case, the distance can be calculated as follows:
Distance = 20 miles (North) + 10 miles (East) + 20 miles (South) + 10 miles (West)
Distance = 60 miles
Therefore, Sam has traveled a total of 60 miles.
The displacement, on the other hand, is the shortest distance between the starting point and the ending point. It is the distance between the initial and final position of an object, measured in a straight line. To calculate the displacement, we need to find the net vector sum of all the individual movements.
Starting from the origin, Sam moved 20 miles to the north and then 20 miles to the south, which means he ended up back at the starting point. Next, he moved 10 miles to the east and then 10 miles to the west, which also means he ended up back at the starting point.
Therefore, the displacement of Sam's journey is zero.
In summary, Sam traveled a total distance of 60 miles, but his displacement is zero, as he ended up back at his starting point after all of his movements.
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A proton moves along the x-axis with v_x=1.0×10^7m/s. As it passes the origin, what are the strength and direction of the magnetic field at the (0 cm, 1 cm, 0 cm) position? Give your answer using unit vectors.
Here ya go! i think this will help!
jason weighs 150 n and sits on his big brother's shoulders. his big brother weighs 400 n. the support force supplied by the floor must be
Jason weighs 150 N and sits on his big brother's shoulders. Big brother weighs 400 N. the support force supplied by the floor must be 500N.
Force can be defined as any influence that causes an object to undergo a change in motion, direction, or shape. In physics, force is represented as a vector quantity, which means it has both magnitude and direction. The standard unit of force is the newton, which is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
Force can be categorized into two types: contact force and non-contact force. Contact force is a force that is exerted through direct contact between two objects, while non-contact force is a force that is exerted without any physical contact between two objects, such as gravity or electromagnetic force. Force plays a crucial role in the study of physics, as it governs the behavior of all objects in the universe.
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Complete Question:-
Jason weighs 150 N and sits on his big brother's shoulders. Big brother weighs 400 N. the support force supplied by the floor must be
In the circuit in the figure, a 20-ohm resistor sits inside 104 g of pure water that is surrounded by insulating Styrofoam.
If the water is initially at temperature 11.8 C, how long will it take for its temperature to rise to 57.1 C?
Use 4190 J/kg.C as the heat capacity of water, and express your answer in seconds using three significant figures.
The time taken for the water to raise its temperature from 11.8[tex]C^o[/tex] to 57.1[tex]C^o[/tex] is 987 s.
[tex]t = \frac{mc(\theta_1 - \theta_2)}{I^2R_1}\\= \frac{(0.104kg)(4190/kg.C^o [(5.71C^o) - (11.8C^o)])}{(1.0A)^2(20.0)}[/tex]
=987s
Temperature is a measure of the average kinetic energy of the particles in a substance or system. In simpler terms, it is a way of measuring how hot or cold something is. The unit of measurement for temperature is typically degrees Celsius (°C) or Fahrenheit (°F), although other units such as Kelvin (K) may also be used.
Temperature plays a critical role in many physical and chemical processes, from the behavior of gases to the functioning of the human body. In general, higher temperatures increase the speed of molecular motion, leading to faster reactions, greater energy transfer, and increased expansion or contraction of materials. Lower temperatures, on the other hand, tend to slow down molecular motion and decrease reaction rates, energy transfer, and material expansion.
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Two balls collide and bounce off of each other. Ball A has a mass of 4.00kg and an initial velocity of 10.0m/s. Ball B has a mass of 6.00kg and an initial velocity of
-5.00m/s.
A. What is the initial momentum of the system?
B. Ball B bounces off with a velocity of 7.00m/s. What is the velocity of Ball A?
C. Prove if this is a perfectly elastic collision or not.
why big tractor can plough many fields than small tractor
A big tractor is more efficient and productive than a small tractor, allowing it to plow through more fields and cover more ground with less time and effort.
A big tractor can plow many fields than a small tractor due to several reasons:Engine Power: Big tractors have larger and more powerful engines than small tractors, which allow them to generate more torque and power to pull heavy loads and work for longer periods of time without overheating or breaking down. This means they can work more efficiently and cover more ground than small tractors.
Size and Weight: Big tractors are usually larger and heavier than small tractors, which gives them more stability and traction on the ground. This allows them to plow through tough and uneven terrain with less effort and more control, reducing the time and effort needed to complete the task.
Implements: Big tractors can accommodate larger and more advanced implements, such as wider plows, cultivators, and seeders, which allow them to cover more ground with each pass. These implements can also be customized to match the specific needs of the soil and crops, increasing the efficiency and productivity of the tractor.
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S18-MP4 roblem 26.23 K) 8 of 10 How far does the proton travel before reaching its turning point? Express your answer with the appropriate units. View Available Hint(s) Constants | Periodic Table on an infinite charged plane is -1.60x10-6 C/m2 . A proton is shot straight away from the plane at 2.30x106 m/s Hint 1. How to approach this problem When the proton has reached its farthest point, it is standing still. This means that the work done on the proton by the electric field of the infinite sheet has exactly canceled the original kinetic energy of the proton. Hint 2. What is the work done by the sheet Recall that the electric field near an infinite sheet of charge density ? is given by E Since the electric field strength is independent of the distance from the sheet, the force is constant along the path of the proton and the work done is simply equal to the force times the distance traveled. Value Units Submit
Eating disorders that go untreated can lead to serious illness, unhappiness, depression, and even death.
A.
True
B.
False
A. Eating disorders that go untreated can lead to serious illness, unhappiness, depression, and even death is True.
Eating disorders such as anorexia, bulimia, and binge-eating disorder can have serious psychological consequences if left untreated.
What is depression?
Depression is a mental health disorder characterized by persistent feelings of sadness, hopelessness, and a loss of interest in activities that were once enjoyable. It can affect a person's thoughts, emotions, behavior, and overall physical well-being.
What is anorexia?
Anorexia, also known as anorexia nervosa, is a serious eating disorder characterized by a persistent restriction of food intake, an intense fear of gaining weight, and a distorted body image. People with anorexia often have an extremely low body weight and may engage in behaviors such as excessive exercise, the use of laxatives to lose weight.
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Complete question is: Eating disorders that go untreated can lead to serious illness, unhappiness, depression, and even death is True.
if the speed increase and wavelength stays the same what will happen to energy?
Answer:
If frequency is constant, wavelength will get longer as speed increases. Here is an animation of a wave changing speed. The green dots and line show that frequency is constant on both mediums, but the speed and wavelength both change.
what observations can you make if the string are released in the trolley
Without more specific details, it is difficult to determine exactly what observations might be made if strings are released in a trolley.
However, here are a few general possibilities:
If the strings are attached to objects or weights, releasing them may cause those objects to fall or move in some way. The motion of the objects could be observed.If the trolley is on a slope or incline, releasing the strings could cause the trolley to roll or slide down the slope. The speed and direction of the trolley's motion could be observed.If the strings are attached to other parts of the trolley itself, releasing them could cause some part of the trolley to move or shift. This could be observed visually or by measuring any changes in the trolley's position or orientation.To know more about motion , visit :
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Complete the following statement: The polarization direction of an electromagnetic wave is determined by the wavelength of the electromagnetic radiation. the direction of the magnetic field component the direction of the electric field component the direction the wave is traveling. the frequency of the electromagnetic radiation.
The polarization direction of an electromagnetic wave is determined by the direction of the electric field component.
What is an electric field ?
Electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of the wave's propagation. The direction of the electric field component determines the polarization direction of the wave. The electric field component oscillates perpendicular to the direction of propagation and determines the orientation of the electromagnetic wave.
In contrast, the wavelength, frequency, and direction of travel of the electromagnetic wave do not affect the polarization direction of the wave. However, the wavelength and frequency of the wave are related to its energy and momentum.
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Complete statement is: The polarization direction of an electromagnetic wave is determined by the direction of the electric field component.
when a ray of light hits a surface, the angles made by the reflection and refraction of the ray must all be measured from the normal, which is
When a ray of light hits a surface, the angles made by the reflection and refraction of the ray must all be measured from the normal, which is perpendicular to the surface at the point where the light ray hits it.
Reflection occurs when light rays hit a surface and bounce back whereas Refraction, occurs when light travels through a medium of a different density or refractive index.
The laws of reflection and refraction states that the angle of incidence is equal to the angle of reflection, and the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This ratio is known as the refractive index of the material from where the light is passing through.
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calculate the GPE of a 15 kg wooden block 6m above the ground
потенциальная енергия - E=mgh, g = ускорение свободного падения, всегда равна 9.81, примерно 10: g=10. Единица измерения енергии - Джоул: [E] = Дж
от этого, E=15×10×6=900 J
ответ: 900 Дж
what is the voltage reading vr(t) given by the voltmeter across the resistor (figure 2) at time t after t
The voltage reading V,(t) across the resistor at time t after t = 0 is equal to the current I(t) multiplied by the resistance R, since V = IR. Therefore, V,(t) = RI(t).
What is resistor?A resistor is an electrical component that reduces the flow of current in a given circuit. It is made from a conductive material, generally either carbon or metal, that has been treated to produce a specific resistance value. The resistance value of a resistor is measured in ohms, and is generally marked on the component itself. Resistors are used to limit the amount of current flowing through a circuit, which in turn can control the voltage and power levels in the circuit. They can also be used to create voltage dividers which divide the voltage of a circuit into different levels, or to provide stability to a circuit by providing a fixed current. Resistors are a fundamental component of all electronic circuits and are used in a wide range of applications.
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Complete Question:
true/false.if you were standing directly at the earth's north magnetic pole, in what directino would a compass point if it were free to swivel in any direction
True. The compass would point south, towards the Magnetic South Pole, if it were free to swivel in any direction.
If you were standing directly at the Earth's North Magnetic Pole, a compass would point towards the Magnetic South Pole. A compass is a simple instrument used to determine direction. It is based on the principle that Earth has a magnetic field that attracts certain metals, such as iron. The needle on a compass is a small magnet that is suspended so that it can rotate freely. When the compass is held level, the needle is able to rotate until it comes to rest along the magnetic lines of force, indicating the direction of the magnetic north. However, the magnetic North Pole is not the same as the geographic North Pole, which is the point where the Earth's axis of rotation intersects with the surface of the planet.
The Earth's magnetic field is generated by the motion of molten iron in the outer core. As a result, the magnetic field is not perfectly aligned with the axis of rotation. It is tilted at an angle of approximately 11.5 degrees. This means that the magnetic North Pole is not located at the same point as the geographic North Pole. If you were standing directly at the Earth's North Magnetic Pole, a compass would point towards the Magnetic South Pole. This is because the North and South Poles of a magnet are opposite. When the north-seeking pole of a compass needle is placed near the North Magnetic Pole, it will be attracted to the south-seeking pole of the Earth's magnetic field, which is located in the vicinity of the Magnetic South Pole.
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This hair-dryer has a plastic case. It is connected to a mains socket by a 3-pin plug.
The cable connecting the hair-dryer to the plug contains only two wires.
Write down the colour of the insulation on the wires.
Wire 1
Wire 2
(ii)
Which of the usual three wires is not needed?
=
This hair-dryer is safe to use without the third wire. Explain why.
Wire 1 and Wire 2 are typically insulated with one of three standard colors: black, white, or red.
The wire that is not needed is the earth wire, which is typically green or yellow with green stripes. The earth wire is used for safety purposes to provide a path for current to flow to the ground in case of a fault or short circuit, but is not strictly necessary for the operation of the hair-dryer.
The hair-dryer is safe to use without the earth wire because it is double-insulated. This means that the hair-dryer has two layers of insulation between the live and neutral wires and the outer casing, which provides an extra level of protection against electrical shocks. Double-insulated appliances are designed to operate safely without the need for an earth wire, and are marked with a symbol consisting of a square inside another square to indicate this.
What is an earth wire?
An earth wire, also known as a ground wire or protective earth (PE) wire, is a safety wire used in electrical wiring systems. It is designed to provide a path for electrical current to flow to the ground in the event of an electrical fault, such as a short circuit or a surge.
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You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 1515
lb and was traveling eastward. Car B weighs 1125
lb and was traveling westward at 41.0
mph. The cars locked bumpers and slid eastward with their wheels locked for 18.5
ft before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750
.
What speed
(in miles per hour) was car A traveling just before the collision? (This problem uses English units because they would be used in a U.S. legal proceeding.)
Answer:
Solve for force:
Ff = UFn
Ff = 0.75(Fn)
Ff = 0.75(1515 + 1225 * g)
Ff = 20550N
Solve for acceleration:
F= ma
20550N = (1515 + 1225) a
a = 7.5m/s^2
solve for time:
a = d / t^2 ---> 7.5m/s^2 = 18.5/ t^2 ----> t = 0.85s
solve for velocity final
Impulse = F * t = 20550N * 0.85s
mv^2 = Impulse = 17467.5
(1515 + 1125)v^2 = 17467.5
vf = 2.5m/s
Plug in stuff:
1515 * v1 + 1125 * (-18.3m/s) = (1515 + 1125) * 2.5m/s
v1 = 9.23
Note: I converted 41mph(v2) to 18.3m/s, which is negative because "westward" is in the negative direction.
Explanation: Inelastic collision
I'm not sure but my guess is we can solve for the force of friction using the coefficient of friction. With that, we can solve for the acceleration in F = ma, and use that to solve for the time the two cars slide. And using that we can solve for the impulse, which is just the Force of friction times that time, which is also our momentum. Since we know the momentum, we can solve for the velocity of the two objects after the collision. Using that velocity, we can use the equation( m1v1 + m2v2 = (m1+m2)vf ), plug in the known quantities and solve for v1.(Note: don't forget to convert mph to mps and 18.5ft to meters)
Extra: I'm guessing because the two cars slide, the only force acting on them is the force of friction(so it's our net force), hence the Fnet = ma.
An applied frictional force on this wheel (not shown) causes it to slow down until it comes to a complete stop after a time interval Δt, where: |ωo| = 34.28 rad/s, R = 0.29 m, |α| = 1.77 rad/s2.
a) Solve for the time interval needed for the wheel to come to a complete stop.
19.37s
b) Solve for total angular distance traveled (in radians, not meters) by the wheel during this time interval.
We can use the formula for angular deceleration to find the time interval needed for the wheel to come to a complete stop:
α = (ωf - ωo) / Δt
where ωf is the final angular velocity, ωo is the initial angular velocity, and Δt is the time interval. Rearranging the formula, we get:
Δt = (ωf - ωo) / α
Since the wheel comes to a complete stop, the final angular velocity is zero:
ωf = 0
Substituting the given values, we get:
Δt = (0 - 34.28) / (-1.77) ≈ 19.37 s
What is the r total angular distance traveled?The formula for angular displacement is:
θ = ωo t + (1/2) α t^2
where θ is the angular displacement, ωo is the initial angular velocity, α is the angular acceleration, and t is the time interval. When the wheel comes to a complete stop, the final angular velocity is zero, so the formula simplifies to:
θ = ωo t + (1/2) α t^2
Substituting the given values, we get:
θ = (34.28 rad/s)(19.37 s) + (1/2)(-1.77 rad/s^2)(19.37 s)^2 ≈ -2003.9 rad
The negative sign indicates that the wheel has rotated in the opposite direction of its initial motion.
To get the total angular distance traveled by the wheel during this time interval, we take the absolute value of θ:
|θ| = |-2003.9 rad| = 2003.9 rad
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Question 1
11) You are driving a vehicle at 55 mph on dry pavement, about how much total stopping distance do you need
to bring it to a stop?
The total stopping distance required to bring it to a stop is 300 metres.
What exactly is stopping distance?
The stopping distance is the distance travelled between the time a moving vehicle's body decides to stop and the time the vehicle completely stops.
Bringing a moving vehicle to a stop involves three critical factors.
1.Distance of perception
2. Distance between reactions
3.Distance between the brakes
1. Perception distance is the amount of time that a vehicle travels while your brain perceives the need to apply the brakes.
An alert driver must react in about 0.75 seconds. This time represents approximately 60 feet of travel.
2. Reaction distance is the distance travelled before the driver applies the brakes. This takes about 0.75 seconds for a cautious
driver. This adds an additional 60 feet of travel.
3. Braking distance is the distance travelled by a vehicle before coming to a complete stop on dry ground. This distance is longer on slick ground (after snow or rain). The skidding distance on dry ground is approximately 170 feet.
This means that a cautious driver needs 60+60+170 = 290 feet (approximately 300 feet) to come to a complete stop.
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Determine the magnitude of force at the pin A and in the cable BC needed to support the 500-lb load. Neglect the weight of the boom AB
The magnitude of the force at pin A and in cable BC needed to support the 500-lb load is 2,000 lbs, since the cable BC supports 1/4 of the load. The force in the cable is transferred to the pin A and distributed along the boom AB. The weight of the boom AB can be neglected in this calculation.
Load = 500 lb Boom AB = Neglected To determine :Magnitude of force at the pin A and in the cable BC needed to support the 500-lb load Formula used:ΣFx = 0ΣFy = 0
Considering point AΣFy = 0ΣFy = Ay - 500Ay = 500 lb Considering point CΣFx = 0∴T cos 45° = 0T = 0 lbΣFy = 0∴T sin 45° - B = 0B = T sin 45°B = T / √2By substituting the value of T in the above equation we get B = 0 lb Therefore, force required at pin A is 500 lb and force required in the cable BC is 0 lb to support the 500-lb load.
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