ΔU = q+w The system does work, which gives a negative value: -77kJ
The heat absorbed is q, which is 115J = 0.115kJ
Change of internal energy= 0.115kJ + (-77kJ) = -76.885kJ
Taking two sig figs: -77kJ
What is internal energy and an illustration?
The term "internal energy" describes the power contained in all of the chemical bonds that hold a system's molecules together as well as the kinetic energy of the molecules themselves. Every time heat, work, and internal energy interact, there is a transfer of energy and a conversion.
What makes it internal energy?
W. Thomson first used the word in thermodynamics in 1852. (the later Lord Kelvin). Because certain energy contributions are ignored, the adverb "internal" is used. For instance, the entire system possesses kinetic energy when it is moving uniformly.
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g what is the magnitude of the tension ta in rope a? a. 500 n b. 3200 n c. 370 n d. 130 n e. 100 n f. 400 n value: 10 if the axis of rotation is placed on rope a, then the torques of f
The torque of rope F = 500 N * 3 m * sin(30 degrees) = 800 Nm.
What is torque?
Torque seems to be the rotational equivalent of force in physics and mechanics. Depending on the area of study, it is also known as that of the moment, instant of force, rotational force, or turning effect. It illustrates how a force can cause a change in the body's rotational motion. In his famous adage, "Give me a lever as well as a place to stand, and I'll move the Earth," Archimedes, who studied the use of levers, is credited with developing the idea. A torque could be thought as a twist to the an object around a particular axis, similar to how a linear force is indeed a push or a pull.
The torque of rope F is equal to the product of the force (F) and the lever arm (r). The lever arm is equal to the length of the rope multiplied by the sine of the angle between the rope and the axis of rotation.
Therefore, the torque of rope F = F * r = F * (length of rope) * sin(angle between rope and axis of rotation).
For example, if F = 500 N, the length of the rope = 3 m, and the angle between the rope and the axis of rotation is 30 degrees, then the torque of rope F = 500 N * 3 m * sin(30 degrees) = 800 Nm.
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A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure.
Which of the following free-body diagrams could be used to analyze the forces exerted on the moon when it is at the position indicated in the figure?
The correct diagram is option F where GRAVITY arrow pointed to the right.
Explain how the moon orbits a planet ?A planet's gravitational influence on a moon is felt. The moon is dragged into a slightly extended shape because the near side of the moon experiences a stronger pull than the far side. We have ocean tides because the moon has a similar differential attraction on the Earth.
This specific instance of tidal locking was brought on by the gravitational pull of the Moon and Earth (called synchronous rotation).
The Earth takes 365 1/4 days, or one year, to complete one orbit of the Sun. The Moon revolves around the Earth as it revolves around the Sun. The orbit of the Moon lasts 27 1/2 days.
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a player catches a ball. consider the action force to the ball against the player's glove. the reaction is the
The reaction is the force applied by the player's glove on the ball.
What is Newton's third law of motion?Newton's third law of motion states that when one body exerts a force on the other body, the first body experiences a force which is equal in magnitude in the opposite direction of the force which is exerted”.
The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.
The direction of the force on the first object is opposite to the direction of the force on the second object.
According to this question, a player catches a ball. The action is the force to the ball against the player's glove while the reaction or opposite force will be the player's glove against the ball.
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A golfer making a putt gives the ball an initial velocity of v0, but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole?
[tex]2v_{0}[/tex] speed should he have given the ball.
here,
initial speed of the ball is v₀
let the resistive force be f and the distance of the hole be d
when it cover distance d/4
using work energy theorem
work done grass force = change in kinetic energy
F × d/4 = 0.5 × m × [tex]v_{0} ^{2}[/tex]
F = 2 ×m×[tex]\frac{v_{0} ^{2} }{d}[/tex] (1)
for covering the distance d
let the velocity be v
work done grass force = change in kinetic energy
F ×d = 0.5 × m × [tex]v^{2}[/tex]
putting F from (1)
2 ×m× [tex]\frac{v^{2} _{0} }{d}[/tex]×d = 0.5 ×m × [tex]v^{2}[/tex]
4 × [tex]v_{0} ^{2}[/tex] = [tex]v^{2}[/tex]
v = [tex]2v_{0}[/tex]
What is work-energy theory and how is it supported?
According to the work-energy theorem, the work done by the net force exerted on a body equals the change in kinetic energy. W = kf - ki is the simplest way to express it. The work energy theorem equation is the one shown above. If the body's kinetic energy declines, the net work done W becomes negative.
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an mri technician moves his hand from a region of very low (almost negligible) magnetic field strength into an mri scanner’s 2.00 t field with his fingers pointing in the direction of the field. (a) find the average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) what current is induced in the ring if its resistance is 0.0100 ω? (c) what average power is dissipated?
The average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field is 3mV.
What is magnetic field?
The magnetic impact on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it while the charge is travelling through a magnetic field.
Given:
[tex]- $B=2 T$[/tex] is the magnetic field strength
[tex]- $d=2.2 \mathrm{~cm}=0.022 \mathrm{~m}$[/tex] is the ring diameter
[tex]- $t=0.25 \mathrm{~s}$[/tex] is the time needed to move the ring
(a) The electromotive force (emf) can be calculated using Faraday's law as:
[tex]$$\epsilon=-\frac{d \phi}{d t}$$[/tex]
We can expand the magnetic flux term here:
[tex]$$\epsilon=-\frac{d}{d t}[B A]$$[/tex]
The magnetic field here is constant so it is the area that is changing:
[tex]$$\epsilon=-B\left(\frac{d A}{d t}\right)$$[/tex]
Since we have no actual functions and just the initial area exposed to the magnetic field (zero) and the final area (entire ring area), we can re-write this as:
[tex]$$\epsilon=-B\left(\frac{0-\pi r^2}{t}\right)$$[/tex]
We substitute and recall that the radius is half the diameter:
[tex]$$\epsilon=-(2 T)\left(\frac{0-\pi\left(\frac{0.022 \mathrm{~m}}{2}\right)^2}{0.25 \mathrm{~s}}\right)$$[/tex]
We thus get:
[tex]$$\epsilon=0.003 \mathrm{~V} \approx 3 \mathrm{mV}$$[/tex]
(b) Wedding rings are usually made of metals like gold or silver, which means they are conducting. This means that the resistance of a wedding ring should be low. So here if we use Ohm's law:
[tex]$\epsilon=I R$[/tex]
We can assume that the current is also small here since the emf is fairly small and the resistance is expected to be small. With a small current, the temperature of the wedding ring shouldn't change much.
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what is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to i0/2?
Complete Question:
Two slits spaced 0.260 mm apart are placed 0.700 m from a screen and illuminated by coherent light with a wavelength of 660 nm. The intensity at the center of the central maximum ( = 0°) is [tex]I_{0}[/tex].
What is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to [tex]I_{0}/2[/tex]
The distance on the screen from the center of the central maximum 0.44 mm where the intensity has fallen to [tex]I_{0}/2[/tex]
The two slits are separated by 0.260 mm.
The screen's distance from the slits is 0.700 meters.
The coherent light has a wavelength of 660 nm.
The value of the path difference will equal to [tex]\pi /2[/tex] because the intensity has decreased to [tex]I_{0}/2[/tex].
This path difference's above formula can be expressed as,
[tex]y_{n} = \frac{(2n-1)D\alpha }{2d}[/tex]
D is the distance of the screen to the slits.
[tex]\alpha[/tex] is the wavelength of the light
d is the distance between slits.
The intensity at the center of the central maximum is [tex]I_{0}[/tex]
Now,
[tex]y = \frac{(2*1)D}{d} *\frac{\alpha }{2\pi } *\frac{\pi }{2}[/tex]
Putting all the values in the formula, we get:
y = 0.44 m
Thus, the distance on the screen from the center of the central maximum 0.44 mm.
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An object is thrown horizontally off a cliff with an initial velocity of 5. 0 m/s.
The vertical speed is 29.4 m/s.
What is vertical speed?
In aeronautics, the rate of climb is an aircraft's vertical speed, that is the positive or negative rate of altitude change with respect to time. In most ICAO member countries, even in otherwise metric countries, this is usually expressed in feet per minute; elsewhere, it is commonly expressed in meters per second.
The acceleration of gravity is 9.8 m/s². This simply means that when anything falls, its downward speed keeps increasing, and it falls 9.8 m/s faster every second than it fell 1 second earlier.
After 3 seconds of falling, the object is falling at (3 x 9.8 m/s) = 29.4 m/s faster than at the beginning of the 3 seconds. If it had no vertical speed at the beginning of the 3 seconds, then THAT's its speed after 3 seconds . . . . . 29.4 m/s downward.
As far as being thrown horizontally off the cliff . . . that has no effect on its vertical speed. Horizontally, it doesn't matter whether it rolls gently over the edge, or somebody throws it horizontally, or it gets shot horizontally out of a high power rifle. It hits the ground at the same time and at the same speed in every case.
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what does the resulting slope imply about the relation between the heat lost by the warm water and the heat gained by the cold water?
The outcome was a slope that was upwards. Heat is received at a rate that is inversely proportional to the quantity of heat lost.
Describe heat using an example.Simply said, temperature is an object's heat or cold, and heat is the energy that moves from a hotter to a cooler thing. If you stick your thumb around a cup of coffee, it might feel warm to the touch, for instance. It is warm because the coffee's heat has been transmitted to the cup.
Why do we use the term "heat"?The transfer of energy at a high pace from an energy source to a medium or an object, or the opposite, is known as heat. These three techniques for transferring energy include radiation, conduction, and convection.
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which planet detection method would work best for a massive planet that's close to its host star but doesn't pass between us and the star?
The Doppler method is most frequently employed to find extrasolar planets, however it works best for finding extremely large planets that are near to their host star.
Which planet is the hottest?Venus is the hottest planet within our solar system, with average global temperatures hot enough even to melt lead due to the runaway greenhouse effect caused by its thick atmosphere, which traps heat. Venus is around 700°F (390°C) hotter that it would be in the absence of the greenhouse effect.
Is it 8 or 9 planets?Our solar system is made up of ten planetary systems, 146 moons, countless comets, meteorites, and other space objects, as well as Pluto and several dwarf planets. In the system, there is just the Sun. The eight planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and finally Neptune.
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calculate the theoretical magnetic field at the center of the solenoid calculate the percent difference between the theoretical and experimental values for the magnetic field at the center of the solenoid.
The Theoretical Magnetic field at center of solenoid will be ηNi/L with a percentage difference of 50%.
A solenoid is a long wire that has been wound in a helix shape. Using this arrangement, we can create a magnetic field that is reasonably uniform. When the turns are closely spaced, we can think of the solenoid as having a single circular loop for each turn, and the net magnetic field is the vector sum of all the magnetic fields produced by the turns. As the solenoid's length increases, the interior field becomes more consistent.We can think of it as the ideal solenoid when the turns are closely spaced and the length is significantly greater than the turn radius. In this instance, the interior field is uniform over a sizable volume, and the external field is zero. An expression for the magnetic field in a hypothetical solenoid is obtained using Ampere's law.[tex]B=uNi/L[/tex]
[tex]\beta =\int\limits^ {} B\, dx[/tex]
[tex]\beta =Bsin[2\pi -wt]\\\\k=2\pi /y\\\\\frac{B}{e}=c[/tex]
[tex]\int\limits^a_b {B} \, dx =UIc= Flux[/tex]
where u is permeability , N is number of turns , i is current and L is the length of solenoid.
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If the sun mysteriously gets twice as massive as it is right now, what effect will it have on its pull on mars?.
If the sun mysteriously gets twice as massive as it is right now, it's gravitational pull on Mars will be twice as much.
How are masses and gravitational pull of sun are related?The mass of the object also affects how strong the gravitational attraction is. The sun is very large and very powerful. It weighs somewhere between 2 times 10 raised to the 30th power kilos. More than 99 percent of the mass of the solar system is made up of the Sun. Because of its size, the Sun pulls the planets in with its strong gravity, which causes them to orbit it. Gravity is stronger for heavier objects. With distance, gravity also becomes weaker. Therefore, the gravitational pull of things increases with their proximity to one another. All of the mass on Earth contributes to gravity.To learn more about gravitational pull, refer:
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a negatively charged particle has a velocity in the negative z direction at point p. the magnetic force on the particle at this point is in the negative y direction. what is the direction of the magnetic field at point p from this information?
A moving object has a negative velocity when it is moving in the wrong direction. If an object is slowing down, its acceleration vector is pointing away from the direction in which it is moving.
Positive and negative charges move in the polar opposite directions. The positive charges will flow counterclockwise and the negative charges will travel clockwise, for instance, if the field is into this page. Positive charges are subject to an electric force that travels with the electric field. Additionally, negative charges are subject to an electric force that runs counter to the direction of the electric field. When a car is speeding up, the acceleration points in the same direction as the velocity; when it is slowing down, it points in the opposite direction.
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if the distance between two charges is doubled, what will happen to the force between the charges? (4 points) to answer this question, perform the calculation first with a r value of 1 and then a second calculation with a r value of 2.
If the distance between two charged particles is doubled, the force between them changes by a factor of 1/4.
What is force?
A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Force between two charge particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Therefore, if the distance between two charged particles is doubled, the force between them changes by a factor of 1/4.
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what is the acceleration due to gravity at the surface of this planet? express your answer in meters per second squared.
The gravitational acceleration symbol is G. The standard value of the g is 9.8 m/s2 at sea level.
What respond with a square meter per second estimate?The magnitude of g, or Earth's gravitational acceleration, is 9.8 m/s2. The acceleration of a free falling object on Earth would be 9.8 meters per second, according to this. This acceleration is due to the Earth's gravitational pull.
Which of the following statements about the acceleration of Earth's gravitation is true?The acceleration that every thing experiences as it moves toward or away from the earth is due to gravity, and the average acceleration is the same for all objects. The object's mass has no bearing on i.
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A man walks toward Carrefour beginning at his home. It takes him 2 hours to cover the 7 kilometers. He spends 1 hour in the store. He then walks 2 km in 1 hour in the same direction to drop the toys off to his niece.
a) What is the man's average speed for the whole journey?
b) What is the man's average velocity for the whole journey?
The average speed of the man for the whole journey is 2.25 km/hr.
The average velocity of the man for the whole journey is 2.25 km/hr.
What is the average speed of an object?The average speed of an object is the ratio of the total distance traveled by an object and the time taken for the journey.
The average speed of an object is given mathematically as follows:
Average speed = tota; distance / total time taken
From the data given:
Total distance traveled = 7 km + 2 km
Total distance traveled = 9 km
Total time taken = 2 + 1 + 1
Total time taken = 4 hours
Average speed = 9 km / 4 hrs
Average speed = 2.25 km/hr
The average velocity of the man for the journey is calculated as follows:
average velocity = change in displacement/change in time
The journey took place in the same direction, hence, the displacement is 9 km.
Average velocity = 9 km / 4 hrs
Average velocity = 2.25 km/hr
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Nasa’s orion spacecraft, which left earth last week, flew within 81 miles of the surface of which celestial body on monday?.
Nasa’s Orion spacecraft, which left earth last week, flew within 81 miles of the surface of the moon.
What is the Orion spacecraft mission?The NASA Artemis 1 mission uses the crewed spaceship Orion, which is largely reusable. On Monday, NASA's Orion spacecraft flew by the moon's far side, coming 81 miles from the surface. There are no people on board the spacecraft. A lunar landing is the goal of the third Artemis 1 mission, which will use the Orion spacecraft and a SpaceX vehicle. Orion's systems will be tested extensively during the spacecraft's six-day stay, giving mission commanders plenty of time to do so.One of the primary goals of the trip is to test that the Orion spacecraft functions as intended .Its goal is also to provide NASA the opportunity to make any necessary modifications and repairs before astronauts embark for the Artemis II mission, which won't launch until at least 2024.To learn more about Orion spacecraft, refer:
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which component of an ideal vapor-compression refrigeration cycle is modeled as having internal reversibilities
The heat exchangers, evaporator and condenser, which are where the most irreversibilities are seen, are the most important parts of the VCR system.
Evaporator: What is it?The evaporator operates in opposition to the condenser; here, refrigerant liquid is transformed into gas while absorbing heat from compartment's air. The pressure of the liquid refrigerant has decreased by the time it reaches the evaporator, losing its heat content thus causing it to become significantly colder than the fan air circulating around it.
what are they Condenser and evaporator: what are they?Condenser coils discharge heat into outdoor air while evaporator coils absorb heat from indoor air. When heated refrigerant vapor cycles into the coil and condenses to liquid, it quickly releases the load of heat energy that has been collected from your home and compacted in it.
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an aluminum rod with a initial length of 15 m and a diameter of 37 mm is subjected to an axial tensile load of 65 kn. calculate its elongation (mm). 0.2390.02390.0023923.9
The elongation of the aluminium rod subjected to an axial tensile load is 0.00239 mm. So, the 3rd option is correct.
It is given to us that -
Initial length of the aluminium rod = 15 mm
Diameter of the aluminium rod = 37 mm
Axial tensile load on the aluminium rod = 65 kN
We have to find out the elongation of the aluminium rod in mm.
The deformation (in this case, elongation) of an aluminium rod with specific length and diameter which is subjected to an axial tensile load can be represented in the form of an equation given by -
δ = [tex]\frac{P*L}{A*E}[/tex] ----- (1)
where,
δ = Deformation of the rod
P = Axial tensile load
L = Length of the rod
A = Area of the rod
E = [tex]2*10^{5}[/tex] [tex]N/mm^{2}[/tex]
According to the given information, we have
P = 65kN = [tex]65*10^{3}[/tex] N
L = 15 mm
A = [tex]\frac{\pi }{2} d^{2}[/tex] where d is diameter of rod
Substituting these values in equation (1), we have
δ = [tex]\frac{P*L}{A*E}[/tex]
=> δ = [tex]\frac{65*10^{3}*15}{\frac{\pi }{2} (37)^{2}*2*10^{5}}[/tex]
=> δ = 0.00239 mm
Thus, the elongation of the aluminium rod subjected to an axial tensile load is 0.00239 mm. So, the 3rd option is correct.
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What must an object be doing in order to have kinetic energy?
Answer:
An object must be in motion
Explanation:
In order for an object to have kinetic energey it must be moving. However, if it has potential energy, it hasn't started moving yet, but it has the potential to move.
a swimmer is floating on his back on the sea surface. if his density is 980 kg/m3 and he has a volume of 0.060 m3, what is the buoyant force that supports him in the sea water of density 1025 kg/m3?
The buoyant force that supports him in the sea water of density is 3931.613N.
On the water's surface, a swimmer is lying on his back. if his volume is 0.060 m, and his density is 980 kg/m³.
When an object floats, a force called buoyancy is responsible for this. It is specifically the external force that an object that is partially or completely submerged in water or any other fluid experiences. A body or object is said to be buoyant when it is placed in or submerged in a fluid.
We can also define buoyancy as the upward force applied by the fluid on a body or object in this way. The pressure on two sides of a body submerged in a static fluid causes the buoyancy phenomenon.
The Buoyant Force is measured in Newtons (N), which is also the unit of Force (F).
F=hpg
h=∛0.060
=0.3914m
F=0.3914 x 1025 x 9.8
F=3931.613N
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Help me please!!
Label the 3 forms of heat transfer. Conduction,
convection, or radiation.
Answer:
a. radiation
b. convention
c. conduction
Explanation:
An electromagnetic wave of wavelength 435nm is traveling in vacuum in the − z-direction. The electric field has amplitude 2. 70×10−3v/m and is parallel to the x-axis.
The frequency of wave generated is [tex]6.9 * 10^{14} Hz[/tex].
The electromagnetic wave travels at the speed of light.
Speed of light (c) = [tex]3 * 10^{8} m/s[/tex]
Given wavelength is 435nm = [tex]435 * 10^{-9} m[/tex]
We can find the frequency(f) of the wave by using the relationship between f and c:
Frequency = speed of light/ wavelength
= [tex]3 * 10^{8} / 435 * 10^{-9}[/tex]
= [tex]6.9 * 10^{14} Hz[/tex]
So the frequency of wave generated is [tex]6.9 * 10^{14} Hz[/tex].
Complete question:
An electromagnetic wave of wavelength 435nm is traveling in vacuum in the − z-direction. The electric field has amplitude 2. 70×10−3v/m and is parallel to the x-axis. Find frequency of wave generated.
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A force of 25 newtons east and a force of 25 newtons west act concurrently on a 5. 0-kilogram cart. What is the acceleration of the cart?.
The acceleration of the 5. 0-kilogram cart on applying two equal and opposite force be 0 m/s².
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
Given parameters:
One force: F₁ = 25 Newtons acted eastwards.
Another force: F₂ = 25 Newtons acted westwards.
Magnitude of net force acting on the object = (25N -25N) = 0 Newton.
Hence, acceleration of the 5. 0-kilogram cart. be 0 m/s².
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what is the maximum speed with which a 1200- kg car can round a turn of radius 87.0 m on a flat road if the coefficient of static friction between tires and road is 0.55?
The value of speed will be 21.67 m/s
It is given that,
Mass of the car = m=1200 kg
Radius of the round road = r=87.0 m,
Coefficient of static friction= 0.55
As we know,
The value of friction can be determined by using the relationship:
Friction = mCfg
Where, Cf = centripetal force, which can be calculated by relationship:
centripetal force = mv^2/r
As we know,
The point at which the speed is maximum
Then,
Ff = Fc
So, we can write it as:
[tex]mC_fg = \frac{mv^2}{r}\\v^2=\frac{rmC_fg}{m}\\v={\sqrt{C_fgr}[/tex]
So, the value of speed will be:
[tex]v = \sqrt{0.55 \times 9.81 \times 87)}\\v = 21.6658 \approx 21.67\: m/s[/tex]
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The following images show five planets in our solar system. Rank these planets from left to right based on their average surface (or cloud-top) temperature, from highest to lowest. (Not to scale.)
Highest -- Mercury, Earth, Mars, Jupiter, Neptune -- Lowest
Notice that, for these five planets, temperature correlates with distance from the Sun: the closer to the Sun, the hotter the planet. Remember, however, that this is not always the case, because a planet’s temperature also depends on its reflectivity and on the strength of its greenhouse effect (if any). For example, the greenhouse effect gives Venus a higher average temperature than Mercury, even though Venus is nearly twice as far from the Sun.
Highest to Lowest temperature:
Mercury
Earth
Mars
Jupiter
Neptune
What is average surface temperature?
Planetary surface temperatures range from over 400°C on Mercury and Venus to below -200°C on distant planets. The factors that determine temperature are the complex balance of heat received and lost.
For these five planets, temperature correlates with distance from the Sun. The closer to the sun, the hotter the earth. Note, however, that this is not always the case, as the planet's temperature also depends on its reflectance and the strength of the greenhouse effect (if present). For example, although Venus is almost twice as far from the Sun, the average temperature on Venus is higher than on Mercury due to the greenhouse effect.
Therefore, the temperature on each planet is according to the composition of that planet and the surrounding atmospheric gases.
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a railroad car of mass 2.00 3 104 kg moving at 3.00 m/s col- lides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) what is the speed of the three coupled cars after the collision? (b) how much kinetic energy is lost in the collision?
The speed of the three couple car after the collision is 1.8 m/s and the total loss in kinetic energy of the system during the collision is 2.16 x 10⁴ J.
The mass M of the each railroad car is given to be 2 x 10³ kg and the speed U of the each railroad car is 3m/s. The speed V of the coupled car is given to be 1.20 m/s.
(a) According to the law Conservation of Linear Momentum, the linear momentum before and after the collision is always conserved.
So, we can write here,
MU + 2MV = (M+2M)V'
Where,
V' is the speed after collision.
U + 2V = 3V'
V' = (U+2V)/3
V' = (3+2.4)/3
V' = 1.8m/s.
(b) The loss in kinetic energy of the system can be calculated as,
∆K = final kinetic energy - initial kinetic energy
∆K = (1/2MU²+1/2×2MV²) - 1/2 × 3MV'²
Putting values,
∆K = (0.5×2.00×10⁴×(3.00)2+0.5×2(2.00×10⁴)(1.20)2)−0.5×3(2.00×10⁴)(1.8)2
∆K = 2.16 x 10⁴ J.
So, the loss in kinetic energy of the system after the collision is 2.16x10⁴ J.
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A cooling tower is 120 meters tall. The sides of the tower are in the shape of a hyperbola defined by the equation x^2/500 - y^2/900 = 1 with units in meters. The center of the tower is at the origin. How wide is the tower at the top?50 m92 m100 m184 m
The width of the tower at the top will be 92 m. Then the correct option is B.
Hyperbola-
The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
A cooling tower is 120 meters tall.
The sides of the tower are in the shape of a hyperbola defined by the equation x²/500 – y²/900 = 1 with units in meters.
The center of the tower is at the origin.
Then the width of the tower at the top will be
x²/500 – (120)²/900 = 1
x²/500 – 14400/900 = 1
x²/500 – 16 = 1
x²/500 = 1 + 16
x²/500 = 17
x² = 8500
x = 92.19 ≈ 92 m
Then the correct option is B.
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You measure 48 turtles' weights, and find they have a mean weight of 34 ounces. Assume the population standard deviation is 4.4 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight.
The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is +- 0.634
Given:
The sample size, [tex]n=48\\[/tex]
The mean of the given sample, [tex]x=34\\[/tex]
Population standard deviation[tex]=4.4\\[/tex]
Significance level[tex]=1- confidence \\[/tex]
[tex]=1-0.90\\=0.1[/tex]
The critical value, [tex]z=(n-x)/deviation=\frac{48-34}{4.4}=3.181[/tex]
The closest z value from the z table corresponding to z=3.181 is [tex]z=.99926[/tex]
The margin of error, [tex]E=z* deviation/\sqrt{n} =0.99926*\frac{4.4}{\sqrt{48} }= 0.634[/tex]
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a weight of mass 1.09 kg is suspended by a string wrapped around a pulley wheel, which consists of a solid disk of mass 4.22 kg and radius 1.04 m. the system is released from rest. over what vertical distance does the hanging mass move in 3.0 seconds? ignore friction and drag forces, and assume that the string does not slip.
a weight of mass 1.09 kg is suspended by a string wrapped around a pulley wheel, which consists of a solid disk of mass 4.22 kg and radius 1.04 m. the system is released from rest. vertical distance does the hanging mass move in 3.0 seconds is 18.27 m
distance can be calculate as follows:
Suspended mass, m = 1.09 kg
Pulley mass, M=4.22 kg
pulley radius, r = 1.04 m
now,
Let's put some tension on the "T" string
For this,
vertical net force
mg - T = ma …………(1)
Where,
g is the gravitational acceleration
a is the acceleration of the suspended mass.
Pulley torque = Iα
I is the moment of inertia of the pulley
α is the angular acceleration
Pulley torque is due to string movement
therefore,
Torque = T x r
Also
α = a/r
and I = (Mr²/2) (for circular discs)
Substituting the values of the above relationship for torque, we get
T × r = (Mr²/2) × (a/r)
T = (Ma)/2 …………(2)
from 1 and 2
mg - [(Ma)/2] = ra
mg= a(M + r)
2
(1.09x9.8) = a( 4.22 + 1.04)
2
a= 4.06
now we know that
s= ut+1/2 at²
where s is the distance traveled
u is the initial velocity = 0 (in this case)
t is time = 3 seconds
So if you replace the value
s= (0x3)+ 1/2 4.06 (3)²
s = 18.27 m
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A force of 10. Newtons toward the right is exerted on a wooden crate initially moving to the right on a horizontal wooden floor. The crate weighs 25 newtons. Calculate the magnitude of the force of friction between the crate and the floor.
The magnitude of the force of friction between the crate and the floor is calculated to be 5 N.
What is force of friction?Force generated by two surfaces that contact and slide against each other is referred to as frictional force.
Given: A force of 10 N towards right is exerted on a wooden crate initially moving to the right on horizontal wooden floor and weight of crate is 25 N
The magnitude of the force of friction between the crate and the floor is given as ;
F= μ* m * g
= 0.2 * 25
= 5N
The magnitude of the force of friction between the crate and the floor is 5 N.
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