The speed of the coaster at position B is 12mvB2. The value of the coaster speed at point B 3.016 m.
What is speed?Speed is the rate in which something is traveling.
The speed of the coaster at position B can be determined using the work-energy theorem. According to the theorem, the work done by the gravitational force is equal to the change in kinetic energy. Therefore, the kinetic energy of the roller coaster at point B is equal to the potential energy at point A.
The potential energy at point A is equal to mghA, where m is the mass of the roller coaster, g is the acceleration due to gravity, and hA is the height of point A. Similarly, the kinetic energy at point B is equal to 12mvB2, where vB is the speed of the roller coaster at point B.
Therefore, the speed of the roller coaster at point B can be calculated as follows:
vB = √(2ghA/m) = √(2*9.8*30/m) = 5.48 m/s.
b) The efficiency of the roller coaster is 55%, so the actual speed of the roller coaster at point B would be 55% of the calculated speed. Therefore, the actual speed of the roller coaster at point B would be 5.48 * 0.55 = 3.016 m
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what can you conclude about the time it takes a hollow cylinder and a solid cylinder to roll down an incline?
The fact that a solid cylinder rolls down a hill more quickly than a hollow one has been demonstrated above. This is as a result of their inertial moments.
What is hollow cylinder?A cylinder that is hollow from the inside out and has a discrepancy between its internal and external radii is referred to as a hollow cylinder. The base of the hollow cylinder is shaped like an annular ring.. So the hollow cylinder's bottom resembles a zone enclosed by two concentric rings.
What Is the Volume of a Hollow Cylinder and its formula?The area encircled by the shape in a three-dimensional plane is referred to as the volume of a hollow cylinder. A hollow cylinder is one that has a discrepancy between the internal and external radius and is empty on the inside. In other terms, it is a cylindrical shape with some thickness at the edges and no inside.
Because the formulas for calculating the total surface area (TSA) of a cylinder and a hollow cylinder are almost identical, use caution. TSA of a cylinder is equal to 2 rh plus 2 r2, or the surface area of the cylinder plus the area of 2 circles.
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Answer: 6.0 m/s/s
Explanation: If the net force acting on an object is halved, the acceleration of the object will also be halved. Therefore, if the object has an acceleration of 12.0 m/s/s and the net force acting on it is halved, the new acceleration of the object would be 12.0 m/s/s / 2 = 6.0 m/s/s.
A kid with a mass of 30 kg slides down a slide 2.5 meters high from rest.
What was his speed at the bottom?
If his speed was only 1 m/s at the bottom, how much energy was lost due to friction?
The amount of energy lost due to friction is 735 J
What is kinetic energy?The energy an object has as a result of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force. After the work is finished, energy is transferred to the item, which then moves at a new, constant speed.
Given mass of the kid is 30 kg
The length of the slide from the ground is 2.5 meters
the speed given is 1 m/s
Energy lost is PE-KE = M*g*h - 0.5M*V^2
= 30 × 10 × 2.5 - 0.5 × 30 × 1²
= 750 - 15
= 735 J
Thus the energy lost is 735 J
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A child who weighs 30 kg descends a slide that is 2.5 meters high. Friction results in an energy loss of 735 J.
What gives rise to friction?A force called friction opposes the relative motion of two materials or objects. These resistive forces are brought on by elastic deformation, surface roughness, and molecule adhesion. The force that prevents one solid item from moving across another is known as friction. Friction force, kinetic friction, tumbling friction, and kinetic friction are the four main categories of friction.
What outcomes does friction produce?It generates heat, which is useful for warming our bodies or specific areas of any object. Power is also lost as a result. It makes noise during every operation. We are able to just walk, jump, play, etc. due to friction.
Briefing:Energy lost = PE-KE
= M*g*h - 0.5M*V^2
= 30 × 10 × 2.5 - 0.5 × 30 × 1²
= 750 - 15
= 735 J.
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at what rate must the potential difference between the plates of a parallel-plate capacitor with a 2.0uF capacitance be changed to produce a displacement current of 1. 5A?
The International Systems of Units' standard unit measuring capacitance (C) is the rate of change of the capacitor's potential difference, which is equal to 0.75 MV/s (SI). It a substance reacts to the an electric charge.
What purpose serves a capacitor?Two electrodes that seem to be close to one another but still separated from one another make up a capacitor, a device used to store electrical energy. The parallel-plate capacitor is one simple but effective instance of this type of storage devices.
dt
dV
=
ϵ
0
A
i
d
d
=
C
i
d
=
2.0×10
−6
F
1.5A
=7.5×10
5
V/s
Therefore, we need to change the voltage difference across the capacitor at the rate of 7.5×10
5
V/s.
What underlies a capacitor's fundamental workings?When an earthing system conductor is moved close to a conductor, its capacitance increases, which is how capacitors operate. The capacitor therefore contains two parallel plates that are spaced apart by a certain amount or gap and oriented in opposing directions.
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true or false?: the manual instrument grip release wrench can be used when the system is not in a fault state.
No, the manual instrument grip release wrench can't be used when the system is not in a fault state. The given statement is false. Using manual instrument grip release comes under da vinci si syatem.
Faults can be of two types, recoverable faults and non recoverable faults. a recoverable fault is one that the da Vinci SI system can recover from and does not require a system restart in order to resolve the fault.
Non recoverable fault is a system fault associated with red arm LEDs and requires a system restart.
Manual instrument grip release is used in the event that normal instrument removal is not possible or when Surgeon Console control of the instrument is not practical or available.
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Rudolph launches himself into the sky! If his mass is 300 kg and his acceleration is -9. 8 m/s^2, what is the force that gravity exerts on Rudolph?
The force that gravity exerts on Rudolph is -2940 N.
Newton's second law states that the acceleration of an object depends upon two variables. They are the net force acting on the object and the mass of the object. The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the mass of the object. This means that, if force acting upon an object is increased, the acceleration of the object also increases. If mass of an object is increased, the acceleration of that object decreases.
It is given by the formula, F = ma
where, F is the net force
m is the mass
a is the acceleration
Given that, m = 300 kg
a = -9.8 m/s²
F = ?
Substituting in the above formula, we have
F = m * a
⇒ 300 * (-9.8)
⇒ 30 * (-98)
⇒ -2940 N
Thus, the force that gravity exerts on Rudolph is -2940 N.
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When you check your credit score for incorrect information what are you checking?
a. velocity
b. variety
c. veracity
d. volume
When you check your credit score for incorrect information, you are checking the veracity of the information.
option C is the correct answer.
What is veracity?Veracity is a word that describes the quality of being true, honest, or accurate.
Veracity also entails the conformity with truth or fact. It shows the validity of information or fact.
From the given question, when you check your credit score for incorrect information you are checking the veracity of such information or the conformity with truth or fact about the credit score.
Thus, we can conclude that veracity entails the truth, validity or conformity of information with proven truth.
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1) you are riding your bike on a track that forms a vertical circular loop. if the diameter of the loop is 10.0 m, what is the minimum speed required for you to make it around the loop?
You must travel around the loop at a minimum speed of 7 m/s.
what is speed?
Speed is defined as the rate at which a distance changes over time. It has a distance by time dimension. The basic unit of distance with the basic unit of time are combined to form the SI unit of speed. The metric system uses metres per second as the unit of speed.
A body is being affected by FN.
Fc is the centripetal force. m = mass, v = speed, and r = radius. the "centripetal" force required to maintain the motion of a mass m object around a circle of radius r at speed v.
Fnet= Fc=Fg+FN
mv^2/r=mg
v=√(5.0)(9.8)
=7.0m/s
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write the balanced nuclear equation for formation of 81kr through electron capture.
The balanced nuclear equations for formation of ⁸¹ Kr through electron capture is (81,37)Rb + (0,-1)e > (81,36)Kr
Nuclear equations represent the reactants and products in radioactive decay, nuclear fission, or nuclear fusion. Instead of chemical equations showing that different numbers of elements are conserved in a reaction, atomic mass and proton number are conserved in a nuclear reaction.
A nuclear reaction is generally expressed by a nuclear equation, which has the general form, where T is the target nucleus, B is the bombarding particle, R is the residual product nucleus, and E is the ejected particle, and Ai and Zi (where I = 1, 2, 3, 4) are the mass number and atomic number, respectively. Finding a well balanced equation is critical for understanding nuclear reactions. Balanced nuclear equations provide excellent information about the energy released in nuclear reactions. Balancing the nuclear equation requires equating the total atomic number as well as the total mass number before and after the reaction using the rules of atomic number and mass number conservation in a nuclear reaction.To know more about nuclear equations,
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suppose nasa wants a satellite to revolve around earth 6 times a day. what should be the radius of its orbit if we neglect the presence of the moon? (g
If we ignore the moon's presence and assume that NASA wants a satellite to orbit the planet six times per day, its orbital radius is 1.44 x 10⁷.
What is satellite?A constructed item or spacecraft designed to circle the earth, the moon, or another celestial body. A celestial body orbiting another of greater size. An object that has been placed into orbit in space on purpose is known as a satellite or artificial satellite. Most spacecraft, with the exception of passive satellites, contain a means of generating electricity for the electronics they carry, such as solar cells or radioisotope thermoelectric generators.
How many satellites are in space right now and why it used for?As of the end of December 2021, just 4,852 of the 8,261 satellites circling the Earth were active, according to UNOOSA data, which were corroborated by the Union of Concerned Scientists (UCS), which keeps track of the functioning satellites.
There are several satellites in operation. They are used for a number of purposes, including as the weather forecasting, amateur radio, television broadcasting, and the Global Positioning System. They use telescopes to look outward at the solar system in order to conduct research and collect data.
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an accelerator laboratory is considering using a solid-state detector as part of a high-energy experiment. what would be an advantage of using a solid-state detector?
The accelerator lab is considering using a solid-state detector as part of a high-energy experiment, converting some of the particle energy directly into an electrical current, which would be an advantage of using a solid-state detector.
Solid-state detector, also called Semiconductor Radiation Detector, is a radiation detector in which a semiconductor material such as silicon or germanium crystal forms the detection medium.
One such device consists of a p - n junction through which a pulse of current is developed when a particle of ionizing radiation passes through it.They require no window to admit charged particles into the detector.These have very good energy resolution.Also they converts part of the particles energy directly into electric current, this would be an advantage of using a solid-state detector.
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Which trait is solely dependent on its environment?
Answer:
The tendency of a dog to bark defines entirely on the type of environment and the situation the dog looks at. Hence the correct answer is option.
a projectile is launched at 50 m/s at 37 degrees from the horizontal. how long will it be in the air if it returns to the same level it was launched
The projectile will take 6 seconds to return to the same level it was launched if it is launched at 50 m/s at 37 degrees from the horizontal.
Time taken by projectile to cover entire trajectory is called "Time of flight".
Suppose the initial velocity is u = [tex]v_{0[/tex] sin Ф
Let the Time of flight is T
As the projectile is reaching the same level of projection, vertical displacement is y=0
we have, s= u t +1/2 a[tex]t^{2}[/tex]
0= [tex]v_{0[/tex] sinФT- 1/2 g[tex]T^{2}[/tex]
0= [tex]v_{0[/tex] sinФ- 1/2 gt
so, T = 2[tex]v_{0[/tex] sinФ/g
Putting values in this formula, we have
T= 2×30/10
T= 6 s
So, Time of flight is 6 seconds.
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consider the following circuit. after leaving the switch at the position a for a long time, move the switch from a to b. there will be current oscillations.
Switch the switch from position a to position b after leaving it in position a for a while. Current oscillations are expected to be zero.
What defines oscillation?The regular to-and-fro oscillation of a Simple pendulum is referred to as its oscillatory motion. One oscillation of the a pendulum is defined as the motion of a bob starting from one end and returning to the other.
What is oscillation of a wave?An oscillating wave is one that moves back and forth on a regular, repeated basis. This oscillation may occur between extremes of force, amount, or position. Oscillations in waves can take many distinct forms.
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Cynthia constructed a small device called a catapult shown below.
Catapult
tip of
spoon
small toy
The catapult is able to accelerate objects in order to propel them in a certain direction. After placing a small toy in the end of the
spoon, she pulls back with her finger on the tip of the spoon to a point and releases.
She uses toys of the same shape and size, but different masses and compares how much each travels when released. Which of
the following is Cynthia most likely trying to demonstrate with her device?
It is to be noted that Cynthia with her device, is most likely trying to demonstrate "Newton's second law of motion" (Option D).
What is the rationale for the above answer?Note that Cyntia is carrying out a sort of experiment that involves various items with different masses while comparing them to how fast they can travel.
Recall that Newton's Second Law of Motion (Force) indicates that the acceleration of an entity depends on the mass of the object and the amount of force applied.
Given that Cyntia's experiment is in this line, it is therefore correct to state that Cynthia, using her device, is most likely trying to demonstrate "Newton's second law of motion"
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Full Question:
Cynthia constructed a small device called a catapult shown below.
The catapult is able to accelerate objects in order to propel them in a certain direction. After placing a small toy in the end of the spoon, she pulls back with her finger on the tip of the spoon to a point and releases.
She uses toys of the same shape and size, but different masses and compares how much each travels when released. Which of the following is Cynthia most likely trying to demonstrate with her device?
A. Newton's universal law of gravitation
B. Newton's third law of motion
C. Newton's first law of motion
D. Newton's second law of motion
based on counting the number of galaxies in a small patch of the sky and multiplying by the number of such patches needed to cover the entire sky, the total number of galaxies in the observable universe is estimated to be approximately:_____.
Answer:
two trillion galaxies
Explanation:
If we made the most straightforward estimate using today's best technology, we'd state there are 170 billion galaxies in our Universe. But we know more than that, and our modern estimate is even grander
ppA hollow plastic ball is projected into the air.
There is significant air resistance opposing the
ball's motion, so the magnitude of the ball's
acceleration is not equal to g. At time t, the ball is
moving up and to the right at an angle of 45° to
the horizontal, as shown above. Which of the
following best shows the magnitude a and the
direction of the ball's acceleration at time/?
a > g , is the best shows the magnitude a and the direction of the ball's acceleration at time.
What is acceleration?Acceleration is the rate at which the speed and direction of a moving object change over time. A point or object travelling in a straight path is accelerated if it accelerates or decelerates. Even if the speed is constant, motion on a circle is accelerated because the direction is always changing.
Given data
The velocity of the ball is: V
The angle of velocity with the horizontal is (θ) = 45
The acceleration of the ball is: a
The acceleration due to gravity is: g
When the hollow ball is projected into the air, air resistance will act on the ball that will slow down the ball's motion. Therefore the velocity direction is opposite to the reducing force. The reducing force relates to the opposite to the acceleration of the hollow ball.
F(delaying) ∝ -VF(delaying) ∝ m×a(r)×F(delaying) ∝ a(r)
Here m is the mass of the hollow ball.
The force of gravity on the ball which is acting downward given as:
F(gravity) ∝ g
So, a > g
Correct option: (B)
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A box is on the floor. The box is not moving.
Draw a labelled force diagram to show all the forces acting on the box.
Answer: The floor has more friction than the force given to the box for movement.
Explanation:
The labeled diagram is given below.
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The forces acting on the block at rest are the normal force (N), weight of the block (W) and the force of friction (F).
What are the forces acting on the block?When a block is at rest on a horizontal floor, several forces are acting on it.
These forces are in equilibrium, meaning they balance each other out and result in zero net force, allowing the block to remain stationary.
The main forces acting on the block are:
Weight: The force of gravity pulls the block downward toward the center of the Earth.
Normal Force: The normal force is the force exerted by a surface to support the weight of an object resting on it.
Frictional Force: If the block is not on a perfectly frictionless surface, there will be a frictional force opposing the tendency of the block to slide.
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Working as a seismologist, you find the epicenter of many earthquakes in a region. What features of earth's crust would you expect to find in this region?
Answer:
Explanation:
As a seismologist studying earthquakes in a particular region, you might expect to find certain features of the earth's crust in that region that are indicative of tectonic activity. Some examples of these features include:
Fault lines: These are fractures in the earth's crust where two tectonic plates have moved relative to each other, often resulting in earthquakes when the movement is sudden and violent.
Folded mountain ranges: When tectonic plates collide, the resulting pressure can cause the earth's crust to fold and form mountain ranges.
Volcanoes: Many earthquakes occur in regions with volcanic activity, as the movement of magma beneath the earth's surface can cause the ground to shake.
Plate boundaries: The boundary between two tectonic plates is often a zone of high seismic activity, as the plates grind against each other and cause earthquakes.
Seismic gaps: Some areas along a fault line may have experienced few or no earthquakes in recent history, and are therefore considered "seismic gaps." These areas may be more prone to earthquakes in the future as the pressure builds up.
By studying these and other features of the earth's crust, you can gain a better understanding of the underlying tectonic processes that contribute to earthquakes in the region.
5. Bill is swimming and drops his swim goggles in the pool. He looks from above the top of the water to see where they fell and positions himself directly above the goggles. He dives down to the bottom of the pool with his eyes closed so that the chlorine doesn't burn his eyes. He tries several times to retrieve his goggles but comes up empty handed each time. Which interaction of light is distorting the image of where his goggles appear to be?
The interaction of light that distorted the image of where Bill's goggles appear to be is Refraction.
What happens to the speed of light when it hits water in a swimming pool?
The light slows down when it passes from the less dense air into the water, this slow down of the ray of light which causes the ray of light to change direction and then the changes the speed of the light that causes refraction.
The swimming pool appears shallow than it appear to be because the rays of light coming from the bottom of the swimming pool that is refracted by the water making the height of the swimming pool to be above the actual swimming pool bed and there by misleading the observer(Bill).
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1. Can you use the change in temperature to predict how long it will take for thermal equilibrium to be reached? What equation would you use? What other variables would you need?
2. How does temperature affect the time it takes to reach thermal equilibrium?
3. Explain why it takes different amounts of time for thermal equilibrium to occur in each case.
PLEASE HElP I URGENTLY NEED THIS!!!!
A body is said to be in thermal equilibrium where all the system temperatures are the same.
What is thermal equilibrium?Take a well insulated beaker and pour water of known mass in it. Record its initial temperature.Place heated metal into the beaker and make sure that the beaker is tightly packed so that no heat escapes from the beaker.Record temperature of the beaker at different intervals and after temperature has become constant ( No heat is being gained) , note the final temperature In end we will check whether thermal equilibrium is established or not.heat lost by the metal = heat gained by water + heat gained by the beaker If you are working with closed systems, you need to know the mass of water, its initial temperature, the specific heat of the water (which is 1 cal / g °C), the mass of the environment with which the water is in contact, its initial temperature and the specific heat.A body is said to be in thermal equilibrium where all the system temperatures are the same. In this case, there will be no temperature gradient between the system and the environment.While, A body is said to be in thermodynamic equilibrium if all three requirements of equilibrium are met, i.e. mechanical equilibrium, chemical equilibrium and thermal equilibrium.To learn more about thermal equilibrium refer to:
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What will be the period of oscillation of a 12kg metallic bob attached to a spring, where the same pendulum takes 4 seconds for a bob of
mass 8kg attached to the spring?
The pendulum swings in one direction for 4 seconds in each direction, making a 15.9 m swing in one second.
What purposes serve pendulums?Instruments utilized in science, such as seismometers and accelerometers, also employ pendulums. They have a history of being used as length standards and gravimeters for measure an acceleration of gravity in geophysical surveys. The word "pendulum" is derived from the Latin word "pendulus," which means "hanging."
When you swing a pendulum, what happens?The gravity force will cause the swing to freely swing back and forth when it has been hoisted and released. The swing keeps swinging back and forth on its own until frictional (between the swing and the air, and between chains and the connection points) slows it down and ultimately causes it to stop.
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if the average force of friction is equal to 0.15 of its weight, with what speed will it reach point 2? the distance traveled is 40 m .
At reach point 2, the speed V is equal to 24.9 m/s if the average friction force is equivalent to 0.15 of the its weight.
Describe friction.A force that opposes the rolling or sliding of three stationary surfaces over one another. Although frictional forces, such the traction required to walk without falling, may be advantageous, they can provide a significant amount of resistance to motion. the physical contact of two bodies.
What 3 forms of friction are there?The interaction of a car's tires with the road causes friction, specifically three types of friction: rolled friction, starting turbulence, and sliding friction. This friction is what allows humans to operate cars at all.
Briefing:speed= 1.5m/s
The Initial speed u = 1.5m/s.
point 1 $ point 2 is (39-13) =26m
40 meters is equivalent to an altitude of(40/6) =6.7
kinematics equation v^2 =u^2 + 2as
V^2 = 1.5^2 + 2*9.8 (26 + 6.7)
V = 24.9 m/s
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Scallops use muscles to close their shells. Opening the shell is another story--muscles can only pull, they can't push. Instead of muscles, the shell is opened by a spring, a pad of a very elastic biological material called abductin. When the shell closes, the pad compresses; a restoring force then pushes the shell back open. The energy to open the shell comes from the elastic energy that was stored when the shell was closed. (Figure 1) shows smoothed data for the restoring force of an abductin pad versus the compression. When the shell closes, the pad compresses by 0.15 mm.
How much elastic potential energy is stored?
The elastic potential energy stored is 0.9375 J.
The elastic potential energy stored in a spring can be calculated using the following formula:
Elastic potential energy = 0.5 × k × x²
where:
k is the spring constant
x is the distance the spring is compressed or stretched
In this case, the spring constant is given as 12.5 N/mm and the compression is 0.15 mm. Plugging these values into the formula, we get the following:
Elastic potential energy = 0.5 × 12.5 N/mm × (0.15 mm)²
= 0.9375 J
Therefore, the elastic potential energy stored is 0.9375 J.
The elastic potential energy stored in the abductin pad is used to open the shell when the muscles relax. The muscles close the shell by contracting, which compresses the pad. When the muscles relax, the pad expands, pushing the shell open. The energy to do this comes from the elastic potential energy that was stored in the pad when it was compressed.
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a sinusoidal wave with wavelength 0.400 m trav- els along a string. the maximum transverse speed of a point on the string is 3.00 m>s and the maximum transverse acceleration is 8.50 * 104 m>s 2 . what are the
The distance from one crest to the next or from one dip to the next may be used to calculate the wavelength.
In actuality, the distance between a wave's point and its equivalent point in the following cycle may be used to calculate a wave's wavelength.
What is a sinusoidal wave's equation?The equation I = I sin t, where I is the current at time t and I is the maximum current, can be used to describe a sinusoidal alternating current.
For a sinusoidal alternating voltage, we may express it similarly by writing v = V sin t, where v is the voltage at time t and V is the maximum value.
The separation between peaks in a sine wave is known as the wavelength.
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by which primary heat transfer mechanism does one end of a steel rod become hot when the other end is placed in a flame?
Heat transfer by convection occurs when a fluid (such as air or water) is moving. The movement of a material carrier distinguishes conduction from convection, which is the transfer of thermal energy by the movement of hot fluid (as opposed to making other material hot by wiggling atoms).
Usually, changes in density cause this motion to happen. Because warmer particles are less dense, they will travel to areas where it is cooler because they are less dense, whereas cooler particles will move to areas where it is warmer. Until balance is attained, the fluid will continue to move.Thermal energy can be exchanged between objects by a variety of techniques, all of which are based on the fundamental idea that heat and kinetic energy both prefer equilibrium and similar energy states. Conduction, convection, and radiant heat (commonly referred to as radiation, but it's a more comprehensive phrase that includes many other processes) are the three main ways that heat can transfer.
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what is the primary function of a refrigerant distributor at the outlet of a thermostatic expansion valve? what is the primary function of a refrigerant distributor at the outlet of a thermostatic expansion valve? allow the evaporator to operate with a proper superheat feed the evaporator sufficient liquid to control the leaving air temperature decrease the pressure drop across the evaporator coil evenly feed each evaporator circuit
The distributor's job is to distribute refrigerant equally throughout the circuiting of the evaporator. As the expansion valve's larger nozzle opens, the distributor maintains a constant flow rate.
What is the thermostatic expansion valve's main purpose?An essential piece of machinery in the HVAC sector is the Thermal Expansion Valve (TXV). The valve's function is to regulate the flow of refrigerant into the evaporator section. In this manner, it regulates the discrepancy between superheat and the refrigerant temperature that is currently present at the evaporator outlet.
What is the operation of a thermal expansion relief valve?The thermal expansion relief valve works similarly to an expansion tank by taking up the extra pressure that thermal expansion causes in the plumbing system.
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1. a car is traveling with a velocity of 65km/h around a turn with a radius of 85m. what angle would be required to bank the turn so that no friction is required?
The angle that will be required to bank the turn so that friction will not be required is 21.4°
What is centripetal force?A centripetal force is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.
Centripetal force = Mv²/r, Where r is the radius of the curvature and v is the speed.
For a turning car to be banked without friction, the angle of the curvature is given as tan(phi)= v²/rg
where (phi) is the angle.
phi = tan^-1(v²/rg)
v = 65km/h = 65×1000m/3600s= 18.06m/s
phi = tan^-1(18.06²/(85×9.8)
phi = tan^-1(0.392)
phi = 21.4°
therefore the angle required to bank the turn so that no friction will be required is 21.4°
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A car travels 500 m in 20 seconds what is the speed
Average speed of the car be 25 meter/second.
What is speed?Speed is characterized as the rate at which an object's position changes in any direction.
The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity. SI unit of speed be meter/second.
Given parameters:
Distance travelled by the car: s = 500 m.
Time taken by the car: T = 20 second.
So, speed of the car be = distance travelled/time taken
= 500/20 meter/second
= 25 meter/second.
Hence, its average speed be 25 meter/second.
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A regular pentagonal garden plot has centre symmetry o and an area of 338 m2. Find the distance oa
The distance is 9.65 m.
Area of each triangular sector = 338/5
Angle subtended at center = 360° / 5 = 72°
Let, circumradius of pentagon = r
Side of pentagon = 2r sin36°
Apothem = rcos36°
Area of each sector = 1/2 (2r sin 36°)(rcos36°)
= [tex]r^{2}[/tex]/2 sin72° = 338/5
[tex]r^{2}[/tex] = 338/5 × 2/sin72° = 142.16
r = 11.9 m
Apothem = rcos36° = 9.65 m
Hence, the distance is 9.65 m.
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