Mass of the heaviest book is 0.733 kg.
Heaviest book has weight
= (6 + 6) * 0.6 N
= 7.2 N
If m = mass of the heaviest book in kg
m = 7.2/9.81 kg
= 0.733 kg.
Children often bring a well-established "life-view" of friction with them because of their experiences with slippery surfaces like frozen ponds (low friction) and "gripping" surfaces like deep pile carpets (high friction) and the effects they have on movement. This way of existence needs to be expanded and understood in the perspective of science.
The force that modifies movement as a result of surface/surface interaction is known scientifically as friction (all changes of movement require the action of a force). When using diagrams to portray forces in action, the direction of the frictional force should be depicted as being opposed to that of the movement.
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A sample of gas has a pressure of .87atm at 25 ˚C. What is its pressure when the temperature is increased to 50˚C?
It states that: "At constant volume the pressure of a gas sample is directly proportional to the absolute temperature."
This means that doubling the pressure of the gas will cause its absolute temperature to double.
Mathematically this law is expressed as:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{P_{1}}{T_{1}}=\frac{P_{2}}{T_2} \iff \ P_1T_2=P_2T1 } \end{gathered}$} }[/tex]
We have that the data is:
P₁ = 0.87 atm
T₁ = 25 °C + 273 = 298 K
T₂ = 50 °C + 273 = 323 K
P₂ = ?
We clear for the final pressure:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{P_{2}=\frac{P_1T_2}{T_{1}} } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{P_{2}=\frac{(0.87 \ atm)\cdot(323\not{k})}{298\not{k}} } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{P_{2}=0.94 \ atm } \end{gathered}$}}}[/tex]
If the temperature increases to 50°C, its new pressure will be 0.94 atm.Hydropower is the production of electrical energy through the use of
A. gravitational force
B. stored energy
C. water flowing upwards
D. water resistance
Answer:
gravitational force .. .. .
Explanation:
hope it helps^o^A dog pulls on a pillow with a force of 5.6 N at an angle of 39 degrees above the horizontal. Assume the x-axis of a reference frame is along the horizontal and the y-axis is along the vertical. Find the x and y components of the force.
1. The x component of the force is 4.4 N
2. The y component of the force is 3.5 N
How do I determine the components of the force?The following data were obtained from the question:
Force applied (F) = 5.6 NAngle (θ) = 39 degreesx component =?y component =?1. How to determine the x component
Force applied (F) = 5.6 NAngle (θ) = 39 degreesx component =?x component = FCosθ
x component = 5.6 × Cos 39
x component = 4.4 N
2. How to determine the y component
Force applied (F) = 5.6 NAngle (θ) = 39 degreesy component =?y component = FSineθ
y component = 5.6 × Sine 39
y component = 3.5 N
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A ball is thrown from a 10 m high cliff at the velocity 20 ms-¹ with an angle of 30° to the horizontal plane as shown in the picture below. 40 m from the edge of the cliff is a 10 m high wall. a) Will the ball pass over the wall? b) If not, where will it hit the wall and with what velocity?
(a) The ball will not pass over the wall
(b) The velocity is 21.45m/s
It is the amount of change in velocity per unit time. The velocity change can be calculated using the formula: velocity change = final velocity - initial velocity. This is the time when: The rate of change in velocity is expressed in
Given
A ball is thrown from a 10 m high cliff at the velocity 20 ms-¹ with an angle of 30° to the horizontal plane as shown in the picture below. 40 m from the edge of the cliff is a 10 m high wall.
We have to determine
a) Will the ball pass over the wall?
b) If not, where will it hit the wall and with what velocity?
From the given information
Initial velocity v =20m/s
Initial velocity along x direction vx = vcos300
= 20 cos300
= 20 x 0.866
= 17.32m/s
Initial velocity along y direction vy = v sin300
= 20 sin300
= 20 x 0.5
= 10m/s
Displacement along +ve x = 40m
Time required to travel t = x/vx
= 40/17.32
= 2.31seconds
At this time displacement of the ball along the y direction
Sy = vyt – 1/2gdt2
= 10x2.31 – ½ x 9.81 x (2.31)2
= 23.10 – 26.17
= - 3.07m
Since displacement is in a negative value, it will hit the wall and will not pass over the wall
The ball will hit at d distance from the ground
H = (10 – 3.07)
= 6.93m
Final velocity along +ve y = v’y = vy –gt
= 10 – 9.81 x 2.31
= 10 – 22.66
=-12.66m/s
velocity along +ve x = v’y = vx
= 17.32m/s
So-net velocity of the ball v’= √((v^' x)^2+(v^' y)^2 )
= √(〖(17.32)〗^2+〖(-12.66)〗^2 )
= 21.45m/s
Therefore
(a) The ball will not pass over the wall
(b) The velocity is 21.45m/s
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Light passes straight through two vertical polarizers. The axes of the filters are aligned parallel to each other. How does the light that passes through the second filter compare to the light that passed through the first filter?.
When light passes through the first filter then it will also pass through the second filter. All of the light will pass through both filters.
Polarization:
Polarization is a property applied to transverse waves that specify the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave.
When the axes of the first and second filters are aligned (parallel), then all of the polarized light passed by the first filter is also passed by the second. If the second polarizing filter is rotated, only the component of the light parallel to the second filter's axis is passed.
Therefore all the light will pass through both filters.
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how did eratosthenes estimate the size of earth in 240 b.c.? how did eratosthenes estimate the size of earth in 240 b.c.? by measuring the size of earth's shadow on the moon in a lunar eclipse by comparing the maximum altitude of the sun in two cities at different latitudes on the summer solstice by sending fleets of ships around earth by observing the duration of a solar eclipse we don't know how he did it since all his writings were destroyed.
By analyzing the Sun's position information at two separate sites on the earth's surface, Eratosthenes, a Greek library in Alexandria, Egypt, discovered the moon's gravity in the third century BCE.
What is the meaning of the solstice?The solstice marks the time of year when the Sun appears to be at either its lowest or highest point in the sky. Because of this, ancients came to refer to this day as one when the Sun popped up to stand still. The word solstice is derived from the Latin words sol, which means "Sun," and sistere, which means "To Stand Still."
What takes place on the solstice?The Earth's axis tilts most nearly toward the sun twice a year during what are known as the solstices. The longest day is experienced in the hemisphere that is inclined closest toward our star.
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This is the third time I’m asking, please, On a wet road, is a higher coefficient of friction on the tires safer or a lower one and pls explain I don’t get it
Answer:
higher is safer
Explanation:
because it is a wet slippery surface, you would need more friction on the tires, to get more traction in the slippery wet road, if you had low friction you would not move anywhere and or could swerve off somewhere
A candle 3.0 cm high is placed 30 cm from a converging mirror with a focal length of 20 cm.
I hate to leave you without an answer, but there isn't enough information to be able to answer your problem.
An inclined plane make an angle of 30 degree with the horizontal. Find the contant force applied parallel to the plane required to caue a 15kg box to lide up the plane with anm acceleration of 1. 2m/^2 and down thge incline with an acceleration o1. 2m/^2. Neglect friction force
The constant force applied parallel to the plane required to cause a 15kg box to line up is 127.31 N.
Acceleration is the rate of change of the velocity of an item with appreciation to time. Accelerations are vector portions. The orientation of an item's acceleration is given by the orientation of the net pressure appearing on that object.
Calculation:-
mass =15 kg
Normal force = mgCos30°
parallel force = mgsin30°
acceleration required = 1.2 m/s²
Contact force = 15 × 9.8 × √3/2
= 127.31 N
Acceleration is the charge at which velocity modifications with time, in terms of each speed and route. A factor or an object moving in a straight line is accelerated if it quickens or slows down. Movement on a circle is extended despite the fact that the rate is consistent because the course is continually changing.
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Physical science please help me I really need help I’m begging
all of the following statements are correct except group of answer choices resistance tests may not reflect the actual performance conditions of an ignition coil. current ramping can be used to test for current limits and charging rise time of the ignition circuit. testing an ignition coil for resistance will always indicate its condition. a digital storage oscilloscope is used to perform current ramping tests.
Given statements are correct according to ignition coil resistance.
Resistance testing could not accurately represent how an ignition coil performs in practice. Testing the current limits and charging rise time of the ignition circuit can be done using current ramping. A coil's state may always be determined by measuring the resistance of the coil. Testing of current ramping is done using a digital storage oscilloscope.
What is ignition coil resistance?Although most ignition coils' primary resistance should range from 0.4 to 2 ohms, you should check the manufacturer's specifications for the exact value. If the reading is zero, the ignition coil needs to be changed since the primary windings have internally shorted.
The resistance of an ignition coil can always be used to assess its condition.
The actual operating conditions of an ignition coil might not be captured by a resistance test.
Current ramping can be used to test the current limitations and charging rise time of the ignition circuit.
A digital storage oscilloscope is used for the ramping tests that are currently being done.
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a hockey puck of mass 150.0 g is sliding due east on a frictionless table with a speed of 10.0 m/s. suddenly, a constant force of magnitude 5.0 n and direction due north is applied to the puck for 1.5 s. find the momentum at the end of the 1.5s in component form.
The momentum at the end of the 1.5s in component form a speed of 1.23 m/sec.
mgh=1/2mv²
v=√2gh
v=3.7 m/s
elastic collision
V=(m₁-m₂/m₁+m₂)v
=0.5-2.5/.5+2.5(3.7)
V₁=-2.47 m/sec
V₂=(2m₁/m₁+m₂)V
=2(0.5)/0.5+2.5
V₂=1.23 m/sec
In Newtonian mechanics, momentum is calculated as the sum of an object's mass and velocity. It has both a magnitude and a direction, making it a vector quantity. The momentum of an object is determined by its mass (m) and its velocity (v). Since velocity is a vector and mass is a scalar, momentum is a vector quantity. Momentum can be viewed as a body's "power" while it is moving, or the amount of force it can exert on another body. For instance, a baseball (small mass) thrown quickly can have the same momentum as a bowling ball (big mass) going extremely slowly (low velocity) (high velocity).
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What are the forces applied?
The forces applied on the bucket are tension and gravitational.
What is the gravitational force?
According to Newton’s gravitational law, it is the force exerted due to attraction between two objects that is directly proportional to the product of their masses and is inversely proportional to the square of distance between them.
The force applied to the bucket containing water is gravitational force. The gravitational force acts in downward direction and there is no change in the state of motion. There is another force as well which is the muscular force by which we hold the bucket in the upward direction with the help of our muscles. Tension is also exerted on the bucket as this force is seen in existence when any object is being pulled up with the help of string or rope. It is always seen in the direction which is parallel to the rope.
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the only force acting on a 3.5 kg canister that is moving in an xy plane has a magnitude of 7.2 n. the canister initially has a velocity of 3.2 m/s in the positive x direction, and some time later has a velocity of 4.5 m/s in the positive y direction. how much work is done on the canister by the 7.2 n force during this time?
Answer:
17.5175J
Explanation:
By the work-kinetic energy theorem,
[tex]W=\frac{1}{2} m{v_{f} }^{2} -\frac{1}{2} m{v_{i} }^{2}[/tex]
where [tex]v_{i}[/tex] is initial velocity and [tex]v_{f}[/tex] is final velocity. Note that their directions make no impact on the problem.
We can simplify this to:
[tex]W=\frac{1}{2} m({v_{f} }^{2} -{v_{i} }^{2})[/tex]
Now sub in our values:
[tex]W=\frac{1}{2} (3.5)({4.5 }^{2} -{3.2 }^{2})[/tex]
W= (1.75)(20.25-10.24)=17.5175J
the weight of the builder and new roof tiles is 640N. draw a diagram to calculate the components of the total weight parallel and perpendicular to the slope of the roof
Answer:
Explanation:
is there a diagram of the question?
The parallel component of the total weight is 320 N and the perpendicular component of the total weight is 554.3 N.
What are the components of the Total weight?The components of the total weight of the builder and the new roof tile which may be of two types, i.e. parallel components or perpendicular components.
The parallel component and new roof tiles can be calculated as;
Fn ( parallel ) = W sin ( θ )
where;
W is the total weight
θ is the slope or angle of inclination of the total weight
So,
Fn ( parallel ) = 640 sin ( 30 )
Fn ( parallel ) = 320 N
The perpendicular component and new roof tiles is calculated as follows;
Fn ( parallel ) = W cos ( θ )
where;
W is the total weight
θ is the slope or angle of inclination of the total weight
So,
Fn ( perpendicular ) = 640 cos ( 30 )
Fn ( perpendicular ) = 554.3 N
Thus, the parallel component of the total weight is 320 N and the perpendicular component of the total weight is 554.3 N.
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Your question is incomplete, most probably the complete question is :
The weight of the builder and new roof tiles is 640 N. The slope is at 30 degrees on the given diagram. Draw a diagram to calculate the components of the total weight parallel and perpendicular to the slope of the roof.
An 0.8 kg cart rolls down a frictionless hill of height 0.32m. At the bottom of the holl the cart rolls on a flat surface., which exerts a frictional force if 2 n on the cart. How far does the cart roll on the flat surface before it comes to a stop
The distance travelled by the cart on the flat surface before it comes to a stop is 1.25 m.
What is the acceleration of the cart?
The acceleration of the cart is determined by applying Newton's second law of motion as shown below.
F = ma
a = F/m
a = 2 N / 0.8 kg
a = 2.5 m/s²
The velocity of the cart at the bottom of the hill is calculated as;
u = √2gh
u = √(2 x 9.8 x 0.32)
u = 2.5 m/s
The distance travelled by the cart before stopping;
v² = u² - 2as
where;
v is the final velocity of the cart = 0u is the initial velocity = 2.5 m/sa is the accelerations is the distance travelled2as = u²
s = u²/2a
s = (2.5²) / (2 x 2.5)
s = 1.25 m
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a car of mass 1689 kg collides head-on with a parked truck of mass 2000 kg. spring mounted bumpers ensure that the collision is essentially elastic. if the velocity of the truck is (in the same direction as the car's initial velocity) after the collision, what was the initial speed of the car?
If the velocity of the truck is (in the same direction as the car's initial velocity) after the collision, The initial speed of the car is 18.565 km/h.
Let the initial velocity of the car be uc
the truck is parked it implies ut = 0
for a head on elastic collision the final velocities are given by
[tex]vc = - (mt - mc/mt + mc) uc[/tex]
[tex]vt = (2mc/mt + mc)uc[/tex]
Velocity (vt) = 17 Km/hr
uc = 18.565 Km/hr
In physics, a collision, which is also known as an impact, is the abrupt, violent coming together in close proximity of two bodies, such as two pool cues, The force and the amount of time the objects are in touch, in addition to the materials the two objects are made of, have an impact on the outcome of the impact. It is generally knowledge that a hard steel ball dropped on a steel plate would rebound almost to the original position from where it was dropped, while a ball made of putty or lead will not.
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What is the term of a Living to Serve project? four years one year six months one month
Answer:
six months
Explanation:
Trust me on this i just answer it yesterday
you launch a projectile horizontally from a height of 0.85 m. the projectile travels a horizontal distance 1.8 m. with what speed (m/s) did you launch the projectile?
Speed (m/s) required to launch the projectile is 5.94m/s.
What constitutes speed?Speed is defined as the product of distance and the amount of time it took to cover that distance.
Equations,
Vx = Vxo
x = Vx × t
Vy = Vyo + gt
Vyo = 0
Vy = gt
y = yo - Vyo - gt² / 2
yo - y = gt²/ 2
time to get to the ground,
0.85 = g t² / 2
t² = 0.85m × 2 / 9.81 m/s²
t² =0.1732 s²
t = 0.416s.
initial velocity,
Vxo = x / t = 1.8m/ 0.416s =4.32m/s
speed before it strikes the ground,
Vy = g*t = 9.81 m/s × 0.416 = 4.08m/s
V² = Vy² + Vx² = (4.32 m/s)² + (4.08 m/s)² = 35.3064m²/s²
V = [tex]\sqrt{35.3064}[/tex]= 5.94m/s.
Speed required to launch the projectile is 5.94m/s.
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. you have requested helicopter transportation of a critical burn patient. the remote nature of the accident will force the helicopter to land on an incline. from which direction should you approach the helicopter?
The direction should approach the helicopter is the downhill side.
The Federal Communications Commission controls and regulates all interstate and international radio television wire satellite and cable communications within the United States. Typically the helicopter is approached from the front or sometimes from the side, within the pilot's line of sight. Never approach from behind. Never approach a downhill helicopter. Main he could step into the rotor.
Choose your way to the machine on level ground or uphill. Always approach helicopters from the downhill side. Rotor separation is greatly affected by slopes. To avoid the main rotor and other components of the described communication system taking off by approaching the sloping side of the sloping landing site.
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Destructive interference in a standing wave produces points with zero amplitude called?.
Destructive interference causes nodes—points with no amplitude—to form in a standing wave.
What do you call a point of destructive interference on a standing wave?
The nodes are areas of no displacement brought on by the two waves' destructive interaction. The two waves' constructive interference causes the antinodes to move maximally from their resting position.
Is there zero destructive interference amplitude?
The amplitude is 0 and resembles a node at a point of destructive interference. So, if we consider the aforementioned point to be nodes and antinodes, we can observe that the pattern of nodes and antinodes exactly matches that of a standing wave.
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If a roller coaster car increased its mass to twice its original value, then by what factor would its kinetic energy change? the roller coaster car's kinetic energy would?
The object's kinetic energy is proportional to its mass.
By doubling the mass kinetic energy the roller coaster car's kinetic energy is also doubled.
What is meant by kinetic energy?In physics, an object's kinetic energy is the energy it has as a result of its motion. It is defined as the amount of work required to accelerate a body of a given mass from rest to a given velocity. Unless the body's speed changes, it retains its kinetic energy after gaining it during acceleration. The body does the same amount of work when slowing down from its current speed to rest. Formally, kinetic energy is any term in a system's Lagrangian that includes a time derivative.
Gottfried Leibniz and Johann Bernoulli established the principle in classical mechanics that by describing kinetic energy as the living force, vis viva. The Netherlands' Willem's Gravesande provided experimental evidence of this relationship.
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what force plays the role of centripetal force causing the electrons to follow a circular path? does this force alter the kinetic energy of the electrons? briefly explain.
The electron and nucleus interact electrostatically, acting as a centripetal force. As the electron's velocity is tangential and this force is radial, it is perpendicular to the electron's motion and consequently has no effect on the electrons' kinetic energy.
The electron is a subatomic particle with the symbol or an electric charge of one elementary negative charge. Due to their lack of known components or substructure, electrons, which are part of the lepton particle family's first generation, are typically considered elementary particles. The mass of an electron is around 1/1836 that of a proton. In terms of the decreased Planck constant, the electron intrinsic angular momentum (spin) has a half-integer value. The Pauli exclusion principle states that because electrons are fermions, they cannot share the same quantum state. Electrons, like all elementary particles, have characteristics of both particles and waves: they can collide with other particles and can be diffracted like light.
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what is the moment of inertia for a disk with mass of 500g and radius of 12 cm rotated about its diameter? group of answer choices
The moment of inertia for a disk with mass of 500g and radius of 12cm rotated about its diameter is 7.2 × 10-³kgm².
How to calculate moment of inertia?Moment of inertia is a measure of a rigid body's resistance to change in its angular velocity around a given axis.
The formula for the moment of inertia is the “sum of the product of mass” of each particle with the “square of its distance from the axis of the rotation”. The formula of Moment of Inertia is expressed as follows:
I = mr²
Where;
I = moment of inertiam = mass r = radiusAccording to this question, a disk with mass of 500g and radius of 12 cm rotated about its diameter. The moment of inertia can be calculated as follows:
I = 0.5kg × 0.12²m
I = 7.2 × 10-³kgm²
Therefore, 7.2 × 10-³kgm² is the moment of inertia of the disk.
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Help Please! would really appreciate it! THANK YOU!
The time taken for the orange to return is 0.96 s.
How long does it take to return?We know that if an object is thrown up or down that we have to look at the equations of kinematics under gravity so as to be able to obtain the velocity of the object or the time taken.
Now;
v = u - gt
v = final velocity
u = initial velocity
g = acceleration due to gravity
t = time taken.
Thus;
v = 0 m/s at the maximum height so;
u = gt
t = u/g
t = 4.73/9.8 m/s^2
t = 0.48 s
In order to go up and return;
2( 0.48 s) = 0.96 s
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Car a with mass 1,783 kg collides with stationary 1600 kg car b. they become locked together after the collision and move with speed 8 m/s. what was the initial speed of car a?
The initial speed of car A is 15.18 m/s.
Momentum is defined as mass in motion. If there are two objects (the two objects in motion or only one object in motion and the other in stationary) that collide and no other forces work in the system, the law of momentum conservation applies in the system.
p=p'
pa+pb = pa'+pb'
(ma×va) + (mb×vb) = (ma×va') + (mb×vb')
ma = mass of object A (kg) = 1,783 kgmb = mass of object B (kg) = 1,600 kgva = speed of object A before collides (m/s)va' = speed of object A after collides (m/s) = 8 m/svb = speed of object B before collides (m/s) = 0 m/svb' = speed of object B after collides (m/s) = 8 m/sp = momentum before collision (Ns)p' = momentum after collision (Ns)(ma×va) + (mb×vb) = (ma×va') + (mb×vb')
(1,783×va) + (1,600×0) = (1,783×8) + (1,600×8)
(1,783×va) + 0 = 14,264+12,800
(1,783×va) = 27,064
[tex]va \:=\: \frac{27,064}{1.783}[/tex]
va = 15.18 m/s
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A train is running smoothly along a curved track at the rate of 50 m/s. a passenger standing on a set of scales observes that his weight is 10% greater than when the train is at rest, the track is banked so that the force acting on the passenger is normal to the floor of the train. what is the radius of the curvature of the track?
By using components of the centripetal force, it can be calculated as Radius of the curvature of the track is 557.5 m
According to the centripetal force, the force is
[tex]F_{c} = \frac{mv^{2} }{r}[/tex]
where m is the mass of the object , v is the velocity and r is the radius of the curvature.
This Fc will have two components, FccosФ and FcsinФ.
FccosФ = mg
1.1 mgcosФ = mg
cosФ = [tex]\frac{1}{1.1}[/tex]
so, sinФ = 0.416
Now, FcsinФ = [tex]\frac{mv^{2} }{r}[/tex]
1.1mgsinФ = [tex]\frac{mv^{2} }{r}[/tex]
r = 557.478
r = 557.5 m
Hence the radius of the curvature is 557.5 m.
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in our study of magnetism we learned that an energized conductor will build a magnetic field around it, is this field the same with both ac and dc circuits?
we learned that an energized conductor will build a magnetic field around it.this field is not same with both ac and dc circuits
what is magnetic field?A magnetic field is an invisible field that exerts a magnetic force on substances that are sensitive to magnetism. A classic example of one is the field created by an iron magnet; to see how the energy in such a field works, a small magnet can be placed under a piece of paper and iron filings sprinkled on it.
This important relationship between electricity and magnetism is known as electromagnetism, or the magnetic effect of current.
When DC current flows, the magnetic field will act in one direction.
when AC current flow will produce a magnetic field that varies in direction with the direction of the electron current flow.
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a multimeter is used for? select one: a. frequency testing of coaxial cable b. general electrical measurements c. testing the bandwidth of all types of cables d. testing continuity of fiber optic cable
A multimeter is used for general electrical measurements. So, the correct option is (b)
What is a multimeter?A multimeter is an electronic measuring device that combines multiple measurement functions into one device. A typical multimeter include features such as the ability to measure voltage, current, and resistance.
Most multimeters have the ability to test circuit continuity. This makes it easier to find faults such as bad cables. It also helps to see if two points in the circuit are connected.
The typical multimeter can measure voltage, resistance, and current. In this case, the device is also called a Volt-Ohm Milliammeter (VOM), since it has the functions of a voltmeter, an ammeter, and an ohmmeter. Some of them even offer measurements of additional properties such as temperature and capacitance.
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calculate the height (in m) of a cliff if it takes 2.21 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.01 m/s. (enter a number.) (b) how long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (enter a number.)
The height of the cliff is 6.22 meters and the time taken by the rock to hit the ground if thrown with same speed is 0.81 seconds.
The time taken by the rock to hit the ground when it is thrown up from the the cliff with an initial velocity of 8.01 m/s.
(a) From the equation of motion,
H = ut+1/2at²
H is the height of the cliff,
u is the the initial velocity,
t is the time taken by the rock,
g is the acceleration due to gravity.
Putting values,
H = (8.01)(2.21) + 1/2(-9.8)(2.21)²
H = -6.22m.
The height of the cliff is 6.22 m.
(b) If the rock is thrown down with the same speed,
Then the time taken by it to reach the ground is,
t = u/g
Putting values,
t = 8.01/9.8
t = 0.81 seconds.
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