1/9 of the total mechanical energy is the system's potential energy x=1/3.A .
Exactly how is energy defined?Energy is the capacity to perform labor, according to scientists. Due to the sheer capacity to convert energy from one medium to some other and use it to achieve things, human civilisation is attainable.
Which energy kinds are there?Chemical, electrical, radiant, mechanical, thermal, nuclear, and other six main types of energy exist. Additional kinds, such as electrochemical, acoustic, electromagnetic, and others, may be discussed in other studies.
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let a, b, c, and d be the vertices of a regular tetrahedron each of whose edges measures 1 meter. a bug, starting from vertex a, observes the following rule: at each vertex it chooses one of the three edges meeting at that vertex, each edge being equally likely to be chosen, and crawls along that edge to the vertex at its opposite end. let p
It picks one of the three edges that meet at each vertex, each of which has an equal chance of being chosen, and crawls along that edge to the vertex at its opposite end is p=182/729 and n is 182.
Let[tex]$V_k$[/tex] crawl exactly [tex]$k$[/tex] meters starting from vertex [tex]$V$[/tex] and ending at vertex A, where [tex]$V\in\{A,B,C,D\}$[/tex] and k is a positive integer. We wish to find [tex]$A_7.$[/tex]
Since the bug must crawl to vertex [tex]$B,C,$ or $D$[/tex]
on the first move, we have
[tex]where $S_k=A_k+B_k+C_k+D_k.$[/tex]
More generally, we get
[tex]\[A_{k+2}=A_k+2S_k. \qquad\qquad (\spadesuit)\]\[/tex]
The requested probability is
[tex]\[p=\frac{A_7}{3^7}=\frac{2(3)+2\left(3^3\right)+2\left(3^5\right)}[/tex]
[tex]{3^7}=\frac{2(1)+2\left(3^2\right)+2\left(3^4\right)}{3^6}=\frac{182}{729},\]from which $n=\boxed{182}.$[/tex]
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A uniform solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal. How fast is it moving after it has rolled 2.2 m down the plane? O 3.0 m/s O 4.3 m/s O 5.2 m/s O 3.7 m/s O 2.6 m/s
A uniform solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal. fast is it moving after it has rolled 2.2 m down the plane =O 2.6 m/s
Definition: This type of uniform is defined as the movement of an item in which the object travels in a direct line, and its velocity stays steady along that line because it covers identical distances in the same intervals of time, irrespective of the period of time.
If the velocity of an object transferring alongside an instant line maintains changing, its movement is referred to as non–uniform. An item shifting alongside an immediate line with a steady speed is stated to be in uniform motion.
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a 4 kg ball is thrown straight up in the air. what is the net force acting on the ball when it reaches its maximum height? g
A 4 kg ball is launched vertically into the air. The net force exerted on the ball at its highest point is 39.24N.
Given data
Ball mass m=4 kilogram
Gravitational acceleration is [tex]9.81 m/sec^{2}[/tex] , or g.
The location of the ball has no bearing on the net force applied to it in vertical projectile motion. As a result, the ball experiences a net downward force throughout its travel, and the size of this force is equal to the mass times the acceleration caused by gravity.
[tex]F_{net} = mg\\F= 4*9.81\\F= 39.24 N[/tex]
Therefore, the ball is subject to a net force of 39.24 N.
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a 0.20 m long metal wire has a radius of 1 cm and a resistance of 3.2x10-5 ω. what is the resistivity of the metal?
The metal has a resistance of 5.0x10-8 ohm x m.
Given: radius=1cm , resistance=3.2x10¬⁵ω .
What does circuit resistance mean?Using ohms () as the unit, resistance acts as a gauge to quantify how easily current will flow through a circuit. When resistance falls, current rises, and when resistance rises, current falls. In order to make sure that current is flowing in circuits at the proper rate, resistors are crucial.
Why does resistance exist?When electricity flows through with a conducting, such a metal wire, an electric current occurs. The electrons in the metal may clash with the travelling electrons. Resistance is created as a result, making it harder for current to flow.
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when the barrel is full it has a much blank moment of inertia and resistance to changes in its rotation, so it will be a blank stable moving platform than the empty barrel.
It will be a more stable moving platform than the empty barrel when the barrel is full because it has significantly more moment of inertia and resistance to variations in rotation.
The moment of inertia of a rigid body—also referred to as the mass moment of inertia, angular mass, second moment of mass, or—most precisely—rotational inertia—determines the torque required for a desired angular acceleration about a rotational axis, much like mass determines the force required for a desired acceleration. The term "rotation" refers to an object moving in a circle around its centre. A rotation around the centre point is conceivable for various shapes. A rotation in mathematics corresponds to a map.
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the pendulum consists of a 14-kgkg uniform disk and a 3-kgkg uniform slender rod. it is released from rest in the position shown. suppose that lll
The angular velocity of the pendulum at the bottom is 2.82 rad/s.
The length of the pendulum rod is 1.5ma nd the radius of the pendulum is 0.8m. The mass of the pendulum bob is 14kg and the mass of the rod is 3 kg.
When the pendulum is dropped,
Rotational kinetic energy = Potential energy
Iw²/2 = Mg(L+R) + mgL
Where,
L is the length of the rod and the R is the radius of the bob and I is the moment of inertia of the system while W is the angular speed,
[mL²/3 + MR² + M(L+R)²]W²/2 = Mg(L+R) + mgL
Now, solving the above complex equation,
W = 2.82 rad/s.
So, the angular speed of the pendulum is 2.82 rad/s.
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Complete question- The pendulum consists of a 14 kg uniform disk and a 3 kg uniform slender rod. It is released from rest in the position shown. Suppose that L = 1.5 m. Determine the angular velocity, measured clockwise, when it rotates clockwise 90 degrees.
Three identical rods are welded together to form a Y- shaped figure. The cross-sectional area of each rod is A, and they have length L and thermal conductivity k. The free end of rod 1 is maintained at T1 and the free ends of rods 2 and 3 are maintained at a lower temperature T0. You may assume that there is no heat loss from the surfaces of the rods What is TJ, the temperature of the junction point?
The temperature of the junction point = [tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
What is Temperature ?Temperature is a unit used to describe hotness or coldness. It can be stated in terms of any number of arbitrary scales and shows the direction in which heat energy will naturally flow, i.e., from a hotter body to a colder body (one at a lower temperature). Temperature does not equal the energy of a thermodynamic system; for instance, an iceberg has a far larger total thermal energy than a match, despite the fact that a match is burning at a much higher temperature.
According to the given information
[tex]T_{1} - T_{j} = 2 ( T_{j} - T_{0})[/tex]
Q/t = K × A ×([tex]T_{1} - T_{j}[/tex] )/L
However you have the Y shape so that half the heat transfer goes into each part of the Y. So you need a factor of 2 when you add in the Y parts.
(Q/t)bottom = 2x(Q/t)top
[tex]T_{1} - T_{j} = 2 ( T_{j} - T_{0})[/tex]
[tex]T_{1} + 2T_{0} = 3T_{j}[/tex]
[tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
The temperature of the junction point = [tex]T_{j} = \frac{(T_{1}+2T_{0} ) }{3}[/tex]
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A passenger weighing 500N is inside an elevator weighing 24500 N that rises 30 m every minute. How much power is needed for the elevator’s trip?
A passenger weighing 500N is inside an elevator weighing 24500 N that rises 30 m every minute is 12500 W (12.5 kW).
What is Power?
Power is the amount of work that is done per unit of time. It can be associated with the speed of a change of energy within a system, or the time it takes to perform a job.
There are different types of power,
Mechanical power: is that work performed by an individual or a machine in a certain period of time.
Electric power: which is the result of the multiplication of the potential difference between the ends of a load and the current flowing there.
P= W/t
Where, P- Power,
W- Work
T- Time
The total weight of the passenger + elevator is
Fg = 500+24500
= 25000
The total work done to rise the elevator + passenger is equal to the product between the total weight and the distance covered during the trip (d = 30 m):
W = Fgd
= 25000×30
=7,50,000 J.
The power needed for the trip is equal to the ratio between the work done (W) and the time taken (t):
P = W/t
Since the time taken is t = 1 min = 60 s, the power needed is
P = 750000 / 60
= 12,500 W
P = 12.5 kW
Thus, Power was calculated as P = 12.5 kW.
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The shaft has an outer diameter of 100 mm and an inner diameter of 80 mm. It is subjected to the three torques T1=4 kN⋅m, T2=19 kN⋅m, T3=15 kN⋅m. The smooth bearings A and B do not resist torque.
Shaft C E has gears at C D and E, with bearing B between C and D and bearing A between D and E. The gears exert the following torques in kilo Newton meters: C, T1 clockwise; D, T2 counterclockwise; E, T3 clockwise.
Determine the absolute maximum shear stress in the shaft.
Express your answer to three significant figures and include appropriate units.
The absolute maximum shear stress in the shaft are Tmax = 129.4 MPa for the shaft that has an outer diameter of 100 mm and an inner diameter of 80 mm.
The shaft constitutes an important aspect of the hole shaft motor, that's utilized in electrically powered vehicles, along with trains. Hollow shafts also are appropriate for the development of jigs and furnishings in addition to computerized machines.
Here we have diameter of 80 mm and outer diameter of 100 mm .
[tex]T = π / 16 × T × (D^4 -d^4)/D\\15×1000 = π/16 × T × 0.1^4 - 0.08^4 /0.1\\Tmax = 129.4 × 10 ^6 N/m^2\\Tmax = 129.4 MPa.[/tex]
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a large bird drops a coconut as it flies horizontally at a constant speed. when the coconut hits the beach below, where will the bird be in relation to the coconut?
Since the bird is traveling at a constant horizontal velocity, the coconut hits the beach below, the bird will be in a position that is directly above the coconut in relation to the coconut.
What is the free fall of an object?The free fall of an object refers to the motion of an object that is released from a certain height above the ground and allowed to fall freely under acceleration by the force of gravity alone.
Objects that are experiencing free fall, are accelerated by a constant value that is equal to the value of acceleration due to gravity.
Examples of objects experiencing free fall include:
a coconut fruit that falls off the treea mango fruit that drops off the treea person that jumps off the roof of a tall buildingFor the coconut dropped by a bird flying at a constant horizontal velocity, the initial horizontal velocity of the coconut is the velocity of the bird in the horizontal direction.
When the bird drops the object, the object will fall with a vertical velocity that is accelerated by g. The object will fall at a distance equal to the horizontal distance traveled by the bird.
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rewrite your result for g(r) in terms of gp , the gravitational acceleration at the surface of the planet, times a function of r. express your answer in terms of gp , r , and rp
The gravitational acceleration at the surface of the planet, times a function of r is g = mG/r².
Gravitational acceleration is described as an object receiving acceleration due to the gravitational force acting on it.
It is represented by 'g' and its unit is m/s². Gravitational acceleration is a vector quantity, that is, it has both magnitude and direction.From Newton's second law of motion we can write
F=ma
Here, F is the force acting on the object.
m is its mass and
"a" is the acceleration.
Also according to Newton's law of gravity we can write,
Fg = GmM / (r+h)²
Also a = Fg/M
a = g = {GmM / (r+h)²} / M
g = Gm/r²
The gravitational acceleration at the surface of the planet, times a function of r is g = mG/r².
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A 1,800 kg car is parked on a road that has an elevation angle of 7°. Suppose the coefficient of static friction of the kinds of rubber and asphalt involved is 0.65. Which is approximately the force of static friction between the tires and the road?
A 1,800 kg car is parked on a road that has an elevation angle of 7°. Suppose the coefficient of static friction of the kinds of rubber and asphalt involved is 0.65.The force of static friction between the tires and the road is 2149.8 N
To find the force, the given data can be,
m = mass of the car = 1800 kg
g = acceleration due to gravity
= 9.8 m/s²
Fg = force of gravity on the car
What is static friction?
When an object is static these irregularities get more time to be interlocked as compared to when an object is in motion thus the coefficient of static friction is more than the coefficient of sliding friction.
Force of gravity on the car is given as
Fg= mg
Substituting the values,
Fg= (1800) (9.8)
= 17640 N
Fs= static frictional force acting on the car
From the force diagram of the car, the static frictional force is opposite to the parallel component of force of gravity on the car . hence static frictional force must balance the component of force of gravity parallel to inclined surface.
Fs = Sin7°
= (17640) Sin7°
= 2149.8 N
Hence, the force of static friction between the tires and the road is 2149.8 N.
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In addition to science courses like physics and chemistry, what other types of courses are becoming increasingly relevant to space science careers?.
Structural engineering is the other course that are increasingly becoming relevant to space science careers
What are Space science careers ?Investigating how gravity affects the human body, building the telescopes of the future. providing accessible explanations of solar system discoveries. These are just a few examples of the projects that people involved in space exploration employment work on.
Learning how to repair space stations, aircraft, or even make space shuttles or items you'll need in space requires knowledge in civil engineering, which is the notion of designing large transportation projects.
Structural engineering is the other course that are increasingly becoming relevant to space science careers
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when two carts of equal mass collide in an elastic collision, which cart has a negative velocity after the collision?
Similar to a head-on shot with the cue ball on a pool table, the projectile will come to rest and the target will move off with an equal velocity for a head-on impact with a stationary object of equal mass.
What is meant by elastic collision ?A collision is considered elastic if it does not result in a net loss of kinetic energy for the system. Momentum and kinetic energy are both conserved in elastic collisions.
Elastic collisions occur when there is no net loss of kinetic energy in the system as a result of the collision. Accidental crashes. Inelastic collisions are the kind of collisions when there is a loss of kinetic energy.
Elastic collisions preserve both kinetic and momentum energy. The total kinetic energy of the system prior to the collision is equal to the total kinetic energy of the system following the collision.
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how will the momentum of the blocks after the collision compare to the momentum of the blocks before the collision? *
Momentum is conserved for any collision in an isolated system. Before and after the collision, the collection of items in the system had an equal amount of total momentum.
What does physics define as momentum?
Momentum is characterized as the intensity of a body's motion.
As momentum relies on both velocity and the direction of the body's motion, it is quantified by "mass velocity".
What is the connection between collision and momentum?
During collisions between objects, momentum is a relevant concept. The total momentum before a collision between two objects equals the total momentum after the impact (in the absence of external forces). The law of conservation of momentum is this. It holds true in every collision.
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given the mass of the rubber in the balloon is 1.10 g, what is the net vertical force (in n) on the balloon if it is let go? you can neglect the volume of the rubber. n (upward)
The vertical component of force is 10.78N
The need is to find what would be the net vertical force (in n) on the balloon if it were released, given that the rubber in the balloon weighs 1.10g.The relationship between an object's mass and the amount of force required to accelerate it is outlined in Newton's second law of motion. F=ma, or the force acting on an object is equal to its mass times acceleration, is a common way to express Newton's second law. Therefore, more force is required to accelerate an object with more mass. Neglecting the volume of rubber , additionally, an object accelerates more quickly the more force it is under.[tex]F=ma\\\\F=1.10 * 9.81\\\\F=10.78N[/tex]To learn more about Newton's second law of motion-
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if a jumper falls for one minute through upper winds averaging 30 knots from the west, how far will the jumper drift? in what direction?
A jumper will drift half a mile if they fall for one minute through winds that are blowing from the west at an average speed of 30 knots.
Explain about the Distance?Distance is an object's overall movement, regardless of direction. Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has travelled.
The distance between two objects, points, lines, etc., in any direction. the condition or occurrence of being away from another object or person in space; distance. an area that is linear: Seven miles is too far to go in an hour of walking.
The entire path an object has taken can be used to define the distance of an object. an illustration If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the car must be 13 km.
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if the moon rises around 3 a.m., its phase must be a) full. b) first quarter. c) third quarter. d) waning crescent. e) waxing crescent.
if the moon rises around 3 a.m., its phase must be Waning crescent .
What is meant by Waning crescent?The moon will look as a half moon, or third quarter moon, when the light level drops. The shadow cast by a third quarter moon will increase until it resembles a crescent form, which is known as a fading crescent.
A fading crescent moon has an illuminated area of less than 50% but is still growing.
You'll notice that the energy is waning as the moon begins to move back into the new phase, allowing you to calm down and devote more attention to your inner thoughts.
When the moon is transitioning from a full moon to a new moon, it is said to be in its declining phase. The declining moon, keep in mind sympathetic magick, is wonderful for banishing work, or cutting ,
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how are solar power plants help humans harness
energy.
Answer:
by collecting the sun's heat. Solar thermal power plants use heat from the sun to create steam, which can then be used to make electricity. On a smaller scale, solar panels that harness thermal energy can be used for heating water in homes, other buildings, and swimming pools.
Explanation:
A boy is watching his grandfather fire an old cannon. He notices that whenever the cannonball is fired, it moves with a very high velocity to the right. He also notices that when the cannonball is fired, the cannon moves very slowly to the left. How does conservation of momentum explain these observations?.
Since the system's total momentum was zero before the cannon was fired, the momentum of the projectile and the cannon must be equal and opposing. The cannon will have a lower velocity since it has a lot greater mass.
Law of conservation of momentum states that total momentum of system remains conserved in the absence of external force.
As we know that know external no force is acting in the on the system therefore momentum should be conserved according to the law of the conservation of momentum.
As we know that momentum is given by the formula
momentum = mass × velocity
initially momentum of the system is equal to zero because the velocity of the system is zero.
After fire ball move with high velocity means we have some momentum in the direction of the ball's motion but according to the law of the conservation there should be some momentum in the opposite direction which will cancel out the momentum of the ball therefore cannon will also move in opposite direction.
But as we know that momentum = mass × velocity
As the mass of the cannon is much higher than the mass of the ball therefore less velocity can generate the same amount of the momentum that is required to the cancel the momentum of the ball .
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a solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius b and outer radius c in the following figure. the central conductor and tube carry equal currents i in opposite directions. the currents are distributed uniformly over the cross sections of each conductor.
We can determine the magnetic field at two different distances from a system made up of two conductors using Ampere's law:
a) The system's magnetic field is:
b) The magnetic field for the system's exterior is b = 0.
Ampere's Rule.
According to Ampere's law, the magnetic field's dot product times a closed path is proportional to the current flowing through the path.
∫ B. ds = μ₀ I
Here, B is the magnetic field, S is the closed path, μ₀ is the vacuum permittivity, and I is the current where bold indicates vectors.
Ask about the magnetic fields within the two conductors (optional).
Fixing the associated circular path will cause I, the current that stops inside the path, to flow through the system.
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Wave action works to straighten a coast as wave energy focuses around headlands and tends to disperse energy in coves and bays in a process called.
As wave energy concentrates at headlands and tends to disperse in coves and bays through a process known as wave refraction, wave activity helps to straighten a coastline.
What does physics define as a wave?A disruption or fluctuation that causes energy to be transferred gradually from one place to another in a medium. It might be in the form of an elastic deformation or a change in pressure, electrical or magnetic intensity, electric potential, or temperature.
What are the characteristics of a wave?Waves are the organized movement of disturbance from one location to another. There are two types of waves: mechanical and non-mechanical. Like sound waves, mechanical waves need a medium to travel.
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A diverging lens has a focal length of magnitude 21.8 cm.
(a) Locate the images for each of the following object distances.
43.6 cm
distance cm
location ---Select--- in front of the lens behind the lens
21.8 cm
distance cm
location ---Select--- in front of the lens behind the lens
10.9 cm
distance cm
location ---Select--- in front of the lens behind the lens
(b) Is the image for the object at distance 43.6 real or virtual?
realvirtual
Is the image for the object at distance 21.8 real or virtual?
realvirtual
Is the image for the object at distance 10.9 real or virtual?
realvirtual
(c) Is the image for the object at distance 43.6 upright or inverted?
uprightinverted
Is the image for the object at distance 21.8 upright or inverted?
uprightinverted
Is the image for the object at distance 10.9 upright or inverted?
uprightinverted
(d) Find the magnification for the object at distance 43.6 cm.
Find the magnification for the object at distance 21.8 cm.
Find the magnification for the object at distance 10.9 c
A diverging lens has a focal length of magnitude 21.8 cm and the images are located behind the lens.
(a) u = -10.9 cm
1/v= 1/10.9 - 1/21.9
v= 21.8cm
Behind the lens.
(b) 1. Virtual
2. Virtual
3. Real
(c) m = v/u
1. Erect/ Upright
2. Upright
3. Inverted
(d) m = v/u
1. m = -43.6/-43.6 = 1. Magnification = 1.
2. infinity.
3. m = 21.8 / -10.9 = -2. Magnification = -2.
Therefore, these are the answers for above given question.
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FOR CHEMISTRY:
A small package of Reese's Pieces candy contains 234 calories and 12 grams of fat. Assuming the package contains 36 pieces, what is the maximum number of pieces I could eat without exceeding 150 calories?
The maximum number of 23 pieces a person could eat without exceeding 150 calories.
What are calories?A calorie can be described as unit of energy. The large calorie, food calorie was originally described as the amount of heat required to raise the temperature of 1 Kg of water by one degree Celsius.
The small calorie was defined as the amount of heat required to cause the same increase in one gram of water. In physics and chemistry, the calorie usually refers to a small unit of energy. One calorie is equal to exactly 4.184 Joules.
Given, the 234 calories contained in pieces of candy = 36
Then 150 calories contain by pieces of candy = (36/234) ×150 = 23
Therefore, a maximum number of 23 pieces someone could eat without exceeding 150 calories.
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three 4.0-pf capacitors are connected in parallel across the terminals of a 60.0-hz generator. what is the capacitive reactance of the circuit?
The Capacitive reactance of the circuit is 221 ohms. The capacitor draws a charging current from the supply and charges up to a value equal to the applied voltage.
From the question, we have
Capacitors connected in parallel
Cequ = 4 + 4 + 4 = 12 muF
Xc = 1 / 2 pi f C = 1 / (2 pi * 60 * 12 * 10-6)
Capacitive reactance = 221 ohms
Capacitive reactance :
When a DC voltage is supplied to a capacitor, as we saw in the RC Network tutorial, the capacitor draws a charging current from the supply and charges up to a value equal to the applied voltage. The charge stored in the capacitor also decreases and discharges as the supply voltage is lowered. The internal impedance of the capacitor limits the current that can travel through it when it charges or discharges. This internal impedance is frequently referred to as capacitive reactance and is represented by the Ohms symbol XC.
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Four identical blocks are moving on a surface for which the coefficient of kinetic friction between each block and the surface is Hk. The velocity of each block is indicated by the vector on the block.for which block is the force of friction between the surface and the block greatest?
The maximum friction pressure that can act at the block is given with the aid of fax = muS*N, in which muS is the coefficient of static friction.
In physics, pressure is a power that could alternate the movement of an object. A force can motivate an item with mass to alternate its velocity, i.e, to boost up pressure also can be defined intuitively as a push or a pull. A pressure has both significance and path, making it a vector quantity.
Exceptional kinds of pressure are contact forces and non-forces. a few examples of pressure are Nuclear force, gravitational force, Frictional pressure, magnetic pressure, electrostatic force, spring pressure, and so on.
In physics, a force is a push or pull between gadgets. it is called an interplay because if one object acts on another, its action is matched by using a response from the alternative item. This idea is called Newton's 0.33 regulation, wherein movement and reaction are identical and opposite.
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a ball is shot from the ground straight up into the air with initial velocity of 48 ft/sec. assuming that the air resistance can be ignored, how high does it go?
The ball goes up to 35.83 ft high. The result is obtained by using the formula of motion with constant acceleration.
What is motion with a constant acceleration?A motion along a straight line with a constant acceleration is a motion which the initial and final velocity change. There are 3 important formulas in this case for vertical motion.
v₁ = v₀ + gt
v₁² = v₀² + 2gh
h = v₀t + 1/2 gt²
Where
v₀ = initial velocity (m/s)v₁ = final velocity (m/sg = acceleration due to gravity (9.8 m/s²)t = time (s)h = height (m)Note: If the object goes up, the value of g is (-).
A ball moves from the ground straight up with a velocity of 48 ft/sec. Find the height of the ball!
First, we change the unit of initial velocity.
v₀ = 48 ft/sec
v₀ = 48 × 0.3048 m/s
v₀ = 14.63 m/s
The ball will go up to a certain height. At the maximum height, the velocity of the ball is 0. Thus, we can use the following formula to find h.
v₁² = v₀² - 2gh
0 = (14.63)² - 2(9.8)h
214.04 = 19.6h
h = 10.92 m
h = 10.92/0.3048 ft
h = 35.83 ft
Hence, the ball will go straight up to a height of 35.83 ft.
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if a spinning star gets larger in diameter, what happens to its rotation rate? if a spinning star gets larger in diameter, what happens to its rotation rate? it will not change. it decreases. it increases.
If a spinning star gets larger in diameter its rotation rate is decreases.
As the radius of a spinning star decreases, some of its rotational inertia is lost, which results in a rise in rotational speed owing to the conservation of angular momentum. Because stars gradually slow down over time, much like a top spinning on a table, a star's spin rate depends on its age. The mass of a star also influences its spin; astronomers have discovered that larger, heavier stars have a tendency to spin more quickly than smaller, lighter ones. As the radius of a rotating star decreases, some of its rotational inertia is lost, which results in a rise in rotational speed due to the conservation of angular momentum.
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how fast (in rpm ) must a centrifuge rotate if a particle 3.1 cm from the axis of rotation is to experience an acceleration of 200000 g 's?
The value of the speed will be [tex]2.7\times 10^4rm[/tex]
We have,
Radius of particle = 3.1 cm
Acceleration of particle = 20000 g's
As we know,
The value of acceleration can be determined by using the formula:
[tex]a & =v^2 / r \\v & =\sqrt{a r}{ }^2=a r \\[/tex], where, v = velocity, a = acclreation, and r = radius of particle
So, putting the value of "a" and 'r" in the above formula:
[tex]$$\begin{aligned}& =\sqrt{(200000 \mathrm{~g})\left(3.1 \times 10^2 \mathrm{~m}\right)} \\v & =\sqrt{(200000)\left(9.8 \mathrm{~m} / \mathrm{s}^2\right)\left(3.1 \times 10^{-2} \mathrm{~m}\right)} \\v & =1.745 \times 10^2 \mathrm{~m} / \mathrm{s} \\& =\left(1.745 \times 10^2 \mathrm{~m} / \mathrm{s}\right) \frac{1 \mathrm{rev}}{(2 \pi)\left(6.2 \times 10^{-2} \mathrm{~m}\right)}\left(\frac{60 \mathrm{~m}}{1 \mathrm{~min}}\right) \\& =2.7 \times 10^4 \mathrm{rm}\end{aligned}$$[/tex]
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the area of a typical eardrum is about 5.0 10-5 m2. (a) calculate the sound power (the energy per second) incident on an eardrum at the threshold of hearing
The sound power at the threshold of hearing is 5* 10⁻¹⁷ W.
The sound power at the threshold of hearing:
Given that,
Area of the eardrum = 5* 10⁻⁵ m²
We know that, I = power/area
Threshold of hearing I = 1* 10⁻¹² W/m²
Form the above formula, we can write
Power = I* area = 1* 10⁻¹² * 5* 10⁻⁵ = 5* 10⁻¹⁷ W
The sound power incident on an eardrum at the threshold of pain is
We know that, I = power/area
Threshold of pain = 1 W
Power = I* area = 1* 5* 10⁻⁵ W
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