From the first law of thermodynamics, we have 100 J of heat that we would dump in the hot reservoir.
What is the first law of thermodynamics?We know that thermodynamics has to do with the area of science that studies the exchange of heat. Heat is that which could cause the temperature of an object to rise. Thus heat can also be defined as a form of energy that owes to the difference in temperature between the objects.
From the first law of thermodynamics, we have been told that energy is neither created nor destroyed but we can convert it from one form to another in the system. Here we are told that you perform 100 J of work on a refrigerator that extracts heat from a cold reservoir and dumps heat into a hot reservoir.
This implies that the same amount of heat is dumped.
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A car is sitting at a traffic light. When the light turns green, the car begins moving, accelerating at a constant rate. After 14.9 seconds the car has moved 266 meters. What is the acceleration of the car?
Answer:
The acceleration 2.4 m/s²
Explanation:
Given:
V₀ = 0 m/s - Initial vehicle speed
t = 14.9 s - Time
D = 266 m - Distance traveled by car
__________
a - ? - the acceleration
D = V₀·t + a·t² / 2;
V₀ = 0
D = a·t² / 2;
a = 2·D / t² = 2·266 / 14.9² ≈ 2.4 m/s²
a planet with a radius of 6.00 x 107 m has a gravitational field of magnitude 30.0 m/s? at the surface. what is the escape speed from the planet?
The escape speed of the planet is 756.60 m/s
How to calculate escape speed from the planet ?The earth's surface escape speed is roughly 11.2 km/s. This means that an object must have a minimum beginning velocity of 11.2 km/s in order to escape the gravity of the earth and journey into limitless space.
The minimum speed required for a free, unpropelled object to be able to escape the gravitational pull of a primary body and travel an infinite distance from it is known as the escape velocity or escape speed in celestial mechanics. Typically, it is expressed as an ideal speed that disregards atmospheric friction.
Given ,
Gravitational magnitude = 30.00m/s
Escape speed from planet = √[2×30/6*107][
√[2×30.00] /6 ×107
= 756.60 m/s
Therefore Escape speed from planet is 42.4264
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The average kinetic energy of gas molecules is ________ proportional to the absolute temperature.
The absolute temperature of the gas determines the average kinetic energy of the gas particles, and all gases with the same temperature have had the same average kinetic energy.
What exactly is kinetic energy?A sort of energy that such an item or particle possesses as a result of its mobility is known as kinetic energy. An item accelerates and gains kinetic energy when work, which transfers the heat, is done on it by exerting a net force.
What makes kinetic energy so special?Thermal energy also goes by the term of heat energy. It is kinetic because the atoms and molecules in the thing are constantly moving. The temperature of an object can be transferred to another object by means of the atoms and molecules that are in motion.
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an object is suspended by a string from the ceiling of an elevator. if the tension in the string is equal to 25 n at an instant when the elevator is accelerating downward at a rate of 2.0 , what is the mass of the suspended object? (your answer should have one decimal place)
The mass of the suspended object is 3.2 kg.
Solution:
25 N - m (9.8 m/s²) = - m (2.0 m/s²)
= m = (25 N) / (9.8 m/s² - 2.0 m/s²) ≈ 3.2 kg
When suspending an object freely from one point and with a stable balance, hang it so that the center of gravity is directly below the mounting point. In this sketch, the object is suspended at point A and its center of gravity G is directly below point A.
Objects can be hung by strings from a fixed point and can be freely hung and balanced. This is either informed in the question statement or previously determined using previous calculations. Mass must be specified in kilograms.
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a brass cube, 10 cm on a side, is raised in temperature by 200oc. the coefficient of volume expansion of brass is 57x10-6/oc. by what percentage does its volume increase?
A brass cube with a side measurement of 10 cm increases in volume by 22.5% when the temperature is increased by 200°C. Brass has a volume expansion coefficient of 57x10-6/oc.
A device's ability to enable fluid flow is relative measured by the flow coefficient of volume of the device. In more concrete terms, the flow coefficient Cv is the amount of water (measured in US gallons) that will pass through a valve at 60 °F and a pressure drop of 1 psi per minute. The concept of temperature is used to convey quantitatively how hot and cold something is. Using a thermometer, one can gauge temperature. Thermometers are calibrated using different temperature scales that traditionally relied on different reference points and thermometric materials for definition.
Given:
length of the cube, l = 10cm
change in temperature of the cube, T = 200
coefficient of volume expansion, beta = 57*10^-6
delta L = delta L/L *100
delta L = 0.0225/0.1 *100
delta L = 22.5%
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The abundance of __________________ _________________( H, He, Li) in the universe is almost exactly as what The Big Bang predicts. Elements were first fused within the _______________________ after the Big Bang
The abundance of light elements such as Hydrogen (H), Helium (He), and Lithium (Li) in the universe is almost exactly as what the Big Bang predicts. Elements were first fused within the protons and neutrons after the Big Bang.
What is Big bang theory?Light elements like hydrogen (H), helium (He), and lithium (Li) are abundant throughout the cosmos, almost exactly as predicted by the Big Bang theory. After the Big Bang, protons and neutrons were the first to combine elements. The most popular theory for how the universe came into being is called the Big Bang Theory. Simply put, it asserts that the universe as we currently understand it originated from a single point that was infinitely hot and dense and that it first expanded and contracted at unfathomable speeds before slowing down and expanding over the course of 13.7 billion years to become the universe that we see today.
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a mass m on a frictionless table is attached to a hanging mass m by a cord through a hole in the table. find the speed with which m must move for m to stay at rest.
The speed with which m must move from M to stay at rest is √Mgr/m m/sec .Centripetal Force is responsible for the speed of mass m.
We are given that final state of mass M is rest. It means its velocity is zero. If velocity is zero it means that force acts on the mass M is balanced. When forces are balanced ,body will remain at rest as component of force and gravity cancel each other.
So, if mass M is at rest we need to identify what force are acting on the mass M.
Since mass M is directly perpendicular to acceleration due to gravity, therefore gravity will act some force on it.
Since mass M is moving in circle, due to its movement mass M feels centripetal force.
Therefore, centripetal force due to mass m=Force due to gravity
=>m×(v²)/r=Mg
=>v² = (Mg×r)/m
=>v=√Mgr/m
Hence, speed of mass m is √Mgr/m,
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(Complete question) is:
a mass m on a frictionless table is attached to a hanging mass M by a cord through a hole in the table. find the speed with which m must move for M to stay at rest.
a disk of mass 7 kg and radius 0.6m hangs in the xy plane from a horizontal low friction axle. the axle is 0.06m from the center of the disk. what is the frequency of f of small - angle oscillations of the disk ?
The frequency of of small - angle oscillations of the disk is 1.99/sec. Frequency is converse of time period.
We know very well that,
T=2π√I/mgh
where T is the time period,
I is the moment of inertia of body
m is the mass of the body
g is the acceleration due to gravity
and h is the height of the point from center of body
Now, we know very well that moment of inertia of disk is given by=(1/2)mr² where m is the mass of the body and r is the radius of the body
So, putting the values of mass and radius of disk, we get
=>I=(1/2)×7×(0.6)²
=>I=3.5×0.36
=>I= 1.26kg-m²
Now, h is given as 0.06m,value of g is 9.8m/sec² and value of m is 7kg
So, mgh=7×9.8×0.06=4.116kgm²/sec²
Therefore, T=2π√1.26/4.116
=>T=2π√0.306
=>T=2π×0.55sec
=>T=6.28×0.55sec
=>T=3.454sec
=>Frequency(ω)=2π/T
=>Frequency(ω)=2π/3.454
=>ω=6.28/3.454
=>ω=1.99/sec
Hence, frequency is 1.99/sec.
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328-kg car moving at 19.1 m/s in the x direction hits from behind a second car moving at in the same direction. if the second car has a mass of and a speed of right after the collision, what is the velocity of the first car after this sudden collision?
The velocity of the first car after this sudden collision is +14 m/s.
What is velocity?
Velocity can be defined as the rate of change of position of object with respect to time or a specific frame of reference. it can also be defined as the speed of an object in a specific direction, this means that the value of velocity changes as the direction of the the movement of the object changes. this makes velocity a vector quantity.
Its SI unit is [tex]m/s^{-1}[/tex].
What are vector quantities?
Vector quantities are those quantities that have both the direction and the magnitude, eg: velocity, displacement, force etc.
According to the given information:
we know, mV + Mv = mU + Mu
where m = 320kg, M = 720 kg, v = 13m/s, V = 19 m/s, u = 15.1 m/s
U = (mV + Mv - Mu)/m
= (328 x 19.1 + 790 x 13 - 790 x 15.1)/328
= +14 m/s
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I understood the question to be:
A 328-kg car moving at 19.1 m/s in the + x direction hits from behind a second car moving at 13.0 m/s in the same direction. If the second car has a mass of 790 kg and a speed of 15.1 m/s right after the collision, what is the velocity of the first car after this sudden collision?
An object moving in a straight line has a velocity v in meters per second that varies with time t in seconds according to the following function.
v = 4 + 0.5t^2
The instantaneous acceleration of the object at t = 2 seconds is
2 m/s2
The instantaneous acceleration of the object at t = 2 seconds is:
2 m/s2.
In mechanics, acceleration is the charge of change of the velocity of an item with respect to time. Accelerations are vector portions. The orientation of an object's acceleration is given via the orientation of the internet pressure appearing on that object.
Acceleration, charge at which velocity adjustments with time, in terms of both speed and direction. A point or an object moving in a directly line is accelerated if it hastens or slows down.
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how long ago (in seconds) was that galaxy right next door to our own galaxy if it has always been receding at its present rate? since the universe began when all galaxies were very close together, this number is a rough estimate for the age of the universe.
According to the Statement it always was receding at its current rate, that galaxy was just next to our own galaxy, moving at 8000 km/s.
Which galaxy contains Earth?Astronomy The Universe The Nebula Galaxy. Did you know that, in conjunction to our light, the Sun, the Milky Way Cluster, a large expanse of space, includes millions and billions of other stars? Its Milky Way is distinguished by a phenomenal number of stars, infinitesimal particles, and gas.
Briefing :Since V = H x d, the velocity of a galaxy at a distance of 400 x 10⁶ light-years = 8000 km/s
For H = 20 km/s per million light-years. The time required to travel
4 x 10⁸ light - years at 8000 km/s is given by :
T = (4x10⁸ light - years ) (9.46 x 10¹² km /light-year) ÷ 8 x 10³
= 4.7 x 10¹⁷ = 15 billion year
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Complete question : Consider a galaxy at a distance of 400 million light-years receding from us at a velocity, v. If the Hubble constant is 20 km/s per million light-years, what is its velocity? How long ago was that galaxy right next door to our own Galaxy if it has always been receding at its present rate?
calculate the rms speed of carbon atoms near the surface of the sun at a temperature of about 6000 k .
Root mean square speed of the carbon atom near the surface of sun is 32233.52 m/sec.
Root mean square speed is defined as the the square root of the average of the square of the velocity and given as [tex]\sqrt{3}[/tex]RT/M
Where R =8.3145J/mol.k
M molar mass of the molecule in kg/mol
Carbon atom has the element number as 6 and has a molecular mass of 12 au. molar mass of the molecule can be given as:
Carbon = C = 12g/mol = 0.012kg/mol
T= Temperature = 6000K
Vrms = [tex]\sqrt{3}[/tex]RT/M
Vrms = ( [tex]\sqrt{3 * 8.315 * 6000}[/tex] ) / 0.012
Vrms = 32233.52 m/sec
The rms speed of carbon atoms near the surface of the sun at a temperature of about 6000 k is 32233.52 m/sec.
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at the instant that the mass passes through the position where the spring is unstretched, what can be said about its instantaneous acceleration?
The instantaneous acceleration is maximum.
What is instantaneous acceleration?The main definition of instantaneous acceleration is. The ratio of velocity change during a given time interval such that the time interval equals zero.The velocity of an object at a specific point in time or along its path is referred to as instantaneous velocity. Acceleration that occurs instantly. It is defined as the limiting value of the average acceleration when the time interval t becomes very small.The result is the instantaneous acceleration expressed mathematically as a(t)=ddtv, which is the derivative of the velocity function v(t) (t). Thus, instantaneous acceleration is the derivative of the velocity function, just as velocity is the derivative of the position function.
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1. Herbivores, who have a diet high in tough plant fibers, tend to have a much longer digestive tract than carnivores. Apply your knowledge of digestion to discuss why you think this is the case.
2. The lower esophageal sphincter forms a barrier to prevent stomach acid and digestive enzymes from entering the esophagus. Apply your knowledge of these compounds to explain why dysfunction of the lower esophageal sphincter would be harmful to the esophagus, pharynx, and mouth.
The majority of nutrients and minerals are absorbed from food by the small intestine, also referred to as the small bowel, which is an organ in the digestive system, Food that has been swallowed cannot pass back up the lower esophagus due to a ring of muscle fibers.
1) Because they consume plant and grass-based meals that are high in cellulose, which takes a while to digest, herbivores have longer small intestines than carnivores. Bile, a digestive fluid released by the liver, is kept in the gallbladder.
2) The lower esophageal sphincter, a ring of muscle fibers, separates the esophagus from the stomach. Heartburn and other gastric disease symptoms can result from food and fluids moving backward into the esophagus if the sphincter does not seal completely (GERD).
Regular overeating and being overweight cause the stomach to enlarge and significantly increase the strain on the LES.
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he purpose of low beam headlights is to provide better visibility to a driver driving in fog, rain and smoke. a) true b) false
It is true that the aim of low beam headlamps is to increase a driver's visibility while they are driving in the rain, fog, or smoke.
What brings on fog?When cold air passes over warm water, steam fog is created. The warm moist breath and over lake cools when it comes in contact with the cool air, reaching a humidity level of 100% and forming fog.
How does morning fog develop?Southerly winds bring in warm, moist air, and they will come into contact with any snow or cool wetness on the ground. The fans going in will cool down as a result of this air-ground contact. Dew point then rises, resulting in high humidity and also the formation of fog.
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The complete question is-
The purpose of low beam headlights is to provide better visibility to a driver driving in fog, rain, and smoke.
(a). True
(b). False
Why does the closed top of a convertible bulge when the car is riding along a highway?.
Inside the automobile, the air pressure is higher than outside.
What is air pressure?Everything you touch is pressed upon by the weighty air that surrounds you. This pressure is referred to as air pressure or atmospheric pressure. It is the force that the air above a surface applies to it while gravity pulls the surface toward Earth. A barometer is frequently used to measure atmospheric pressure.
Now
According to Bernoulli's equation, regions of airflow with greater velocities have lower pressure than regions with lower velocities when considering airflow over and around a surface.
The air inside the convertible is moving more quickly than the air outside. As a result, there is a greater pressure zone immediately inside the roof's surface.
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an opaque horizontal plate is well insulated on the edges and the lower surface. the irradiation on the plate is 3000 w/m2, of which 500 w/m2 is reflected. the plate has a uniform temperature of 700 k and has an emissive power of 5000 w/m2. determine the total emissivity and absorptivity of the plate. add: repeat assuming material is semitransparent with transmissivity of 0.10, the same reflectivity and the same emissive power.
Total emmisivity is 0.3706
and absorptivity is 0.833
Irradiation, I = 3000W / m2
reflection, Ir = 500W / m2
uniform temperature, T = 700 k
emissive power E = 5045 W / m2
Total emmisivity,
e = E / 5.67 x 10^-8 (T^4)
e= 5045 / 5.67 x 10^-8 x 700^4
e= 0.3706
absorptivity,
∝ = Iabs / I = I -Ir / I
∝ = 3000-500 / 3000
= 1 - 500 / 3000
∝ = 1 - 1/6
∝ = 0.833
Emissivity is described as the ratio of the energy radiated from a material's surface to that radiated from an ideal emitter, referred to as a blackbody, on the identical temperature and wavelength and underneath the equal viewing conditions.
It's miles a dimensionless range among zero (for an excellent reflector) and 1 (for an ideal emitter).
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a circular coil of wire has a radius of 7 cm and contains 40 turns. a field of 0.900 t passing through the coil collapses at a uniform rate to zero in 0.200 seconds. what emf is generated in the wire?
The EMF generated by the coil is 2.772 V.
Radius of the coil = R = 7 cm = 0.07 m
Number of turns = N = 40
Initial Magnetic Field = B₁ = 0.900 T
Final Magnetic Field = B₂ = 0
Time = 0.2 s
Change in the Magnetic field of the coil =
= dB/dt = (0.9 - 0) / 0.2
= dB/dt = 9/2 T/s
Area of the coil = A = πR²
The total flux related to the circular coil = ∅
= ∅ = NBA
EMF induced by the coil =
= E = d∅/dt
= E = NA dB/dt
= E =40 X π X (0.07)² X (9/2)
= E =2.772 V
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A gray kangaroo can bound across a flat stretch of ground with each jump carrying it 8 m from the takeoff point. part a if the kangaroo leaves the ground at a 19 ∘ angle, what is its takeoff speed
The take-off speed of the gray kangaroo is 11.28 m/s.
How to calculate the takeoff speed?The kangaroo's final speed is zero when it is at its highest point above the ground, and the time it spends there is halved from the time it will take it to hit the earth again.
To calculate the horizontal distance (S) travelled by the kangaroo we need the equation,
[tex]S=v_{0} cos\theta t[/tex]
Here,
v₀ = takeoff speed
[tex]\theta[/tex] = the angle of projection
t = total time taken by the kangaroo.
Given,
The take-off distance for each jump attained by the kangaroo = 8 m
The angle of projection = 19°
Substituting the above values in the above equation,
[tex]8 = v_{0} cos19t[/tex]
[tex]t=\frac{8}{v_{0}cos19 }[/tex]
[tex]t=\frac{8}{0.9455v_{0} }[/tex]
The following equation can be used to determine the kangaroo's final speed when it reaches its highest point above the ground:
[tex]v=v_{0} sin\theta-\frac{gt}{2}[/tex]
Now, Substitute 0 for the value of v we get,
[tex]0=v_{0} sin\theta \frac{g}{2} ( \frac{8}{0.9455v_{0} })\\v_{0} = \sqrt{\frac{8g}{2*0.9455*sin\theta} } \\[/tex]
[tex]v_{0} = \sqrt{\frac{8g}{2*0.9455*sin\theta} } \\\\v_{0} = \sqrt{\frac{8*9.80}{2*0.9455*sin19} }\\v_{0}= 11.28 m/s[/tex]
Hence, the take-off speed of the gray kangaroo is 11.28 m/s.
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A ball is initially moving at 12 m/s up a ramp. The acceleration of the ball is -2 m/s/s down the ramp. What is the balls velocity after 8 seconds? (frame of reference + is up the ramp)
The ball is moving with a velocity of 28 m/s after 8 seconds.
What is the equation of motion?The equations of motion can be used to set up the relationship between the initial velocity and final velocity, acceleration, time, and displacement of a moving object.
The three equations of motion for a moving object can be represented:
[tex]v = u +at\\S = ut +\frac{1}{2} at^2\\v^2 - u^2 = 2aS[/tex]
Give, the initial velocity of the ball moving up, u = 12 m/s
The acceleration of the ball up the ramp, a = + 2m/s²
The final velocity can be calculated from the first equation of motion:
v = u + at
v = 12 + (2) (8)
v = 12 + 16
v = 28 m/s
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Why does the skateboarder continue to move forward when he hits the trash? what is the unbalanced force?.
According to Newton's first law: An item at relaxation will continue to be at relaxation until acted on with the aid of using an unbalanced force.
What are newton's laws of motion?
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
According to Newton's first law: An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
There is a force that moves the skater and his skate forward, after the hit, his speed is reduced, but this force is not completely counteracted, and that's why he continues moving forward.
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What is the formula for the compound that forms between magnesium and phosphorous?
Answer:
Magnesium phosphate | Mg3(PO4)2
Explanation:
The formula for the compound that forms between magnesium and phosphorous is Mg3(PO4)2
at what speed does the rock strike the water if it is thrown with the same initial speed but at an angle 24 degrees below the horizontal?
The offered statement states that the rock hits the water at various times and with equal velocity.
What is a speed set of questions?The number of kilometers reached to the time needed to travel that distance is known as speed. Since speed simply has a part and no magnitude, it is a proportionality constant.
Briefing:
If we ignore air resistance due to the energy conservation, then the velocity of both stones would have to be equal because energy is a finite resource. They will each have the same sum of kinetic and potential energies at the beginning, hence the potential and the kinetic energies must be identical at the end, this happens when they reach the ground. Potential energy will change into kinetic energy.
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for a parallel flow double pipe heat exchanger insulated from its surroundings, the mean outlet temperature of the initially cold fluid can exceed the mean outlet temperature of the initially hot fluid.
Heat flows from the hot fluid to the cold fluid, and the amount of heat transferred is directly dependent on the temperature difference between the two sides.
What is heat exchange?
In a heat exchanger, heat flows from the hot fluid to the cold fluid, and the amount of heat transferred is directly dependent on the temperature difference between the two sides.
In a parallel flow arrangement, the cold inlet and hot inlet are interacting with each other. At that entry point, the temperature difference is wide, and heat transfers quickly.
As the streams pass through the parallel-flow exchanger, they start to approach each other’s temperature. The heat transfer rate drops in line with the reduction in temperature difference.
Now we have the answer to your question. It is impossible for the exit temperature of the cold liquid to exceed the exit temperature of the hot liquid. This is because once the same temperature is reached, all heat transfer stops because there is no temperature difference.
This limitation of parallel flow heat exchangers is the reason most heat exchangers are arranged in counterflow. The counter-flow design results in a higher average temperature difference and greater heat transfer.
Therefore, heat flows from the hot fluid to the cold fluid, and the amount of heat transferred is directly dependent on the temperature difference between the two sides.
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write an expression for the gravitational potential energy of the falling mass in terms of the angular displacement
The potential energy of a falling mass is [tex]PE=-m g R \theta[/tex] and [tex]g=9.8 \mathrm{~m} / \mathrm{s}^2.[/tex]
As we know,
The expression that relates linear displacement and angular displacement is given below:
[tex]s=r \theta[/tex]
Now we will replace s with h and r with R in the above expression.
[tex]h=R\theta[/tex]
Here, the height is h and the radius is R.
The initial potential energy is as follows:
[tex]P E_{\mathrm{i}}=m g h[/tex]
Now, replace h with R[tex]\theta[/tex].
We will get it as: [tex]P E_{\mathrm{i}}=m g R \theta[/tex]
Now, substituting [tex]$0^{\circ}$[/tex] for [tex]\theta[/tex]
[tex]P E_{\mathrm{i}} & =m g R\left(0^{\circ}\right) \\=0 \mathrm{~J}[/tex]
The expression for the final potential energy will become:
[tex]P E_{\mathrm{f}}=m g R \theta[/tex]
The potential energy of the falling mass will become:
[tex]P E=P E_{\mathrm{i}}-P E_{\mathrm{f}}[/tex]
From Expressions (1) and (2), the following expression can be obtained:
[tex]P E =0 \mathrm{~J}-m g R \theta \\=-m g R \theta[/tex]
The value of g is as follows: g=9.8 [tex]\mathrm{~m} / \mathrm{s}^2[/tex]
The potential energy of a falling mass is [tex]PE=-m g R \theta[/tex] and [tex]g=9.8 \mathrm{~m} / \mathrm{s}^2.[/tex]
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if the number of sulfate aerosols inside a cloud should increase, the cloud would have to share its available moisture with the added nuclei, and cloud droplets would be produced.
According to collision- coalescence proposition, conformation of droplet from pall clouds occurs when pall clouds collide and coalesce or stick together.
The only significant difference between a droplet and a pall drop is that a droplet correspond of a haste that's non-negligible during the fall.
Larger driblets having advanced terminal rapidity fall briskly and collide with lower clouds. frequently the pall driblets stick together and coalesce to form a larger drop.
This starts a chain response where these bigger driblets fall indeed fleetly, collide with the other clouds in their path and combine with these driblets.
As drop and ice demitasse size increase, the probability increases that the clouds will burst in the pall. This is the medium behind rush. When the shadows come heavy enough due to these clouds or ice chargers, rain or snow is produced that falls to the ground.
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a 150-g block connected to a light spring for which the force constant is 3.2 n/m oscillates on a frictionless, horizontal surface. the block is displaced 3.0 cm from equilibrium and released from rest as in the figure.
The block will oscillate back and forth along the horizontal surface with a period given by the equation $T = 2\pi\sqrt{\frac{m}{k}}$,
where $m$ is the mass of the block, $k$ is the force constant of the spring, and $T$ is the period of the oscillation. In this case,
the mass of the block is 150 g, which is equivalent to 0.15 kg, and the force constant of the spring is 3.2 N/m.
Plugging these values into the equation, we get
$$T = 2\pi\sqrt{\frac{0.15}{3.2}} \approx 0.3268\text{ s}$$
The amplitude of the oscillation is equal to the maximum displacement of the block from its equilibrium position, which in this case is 3.0 cm. The block will oscillate back and forth with this amplitude and with a period of approximately 0.3268 seconds.
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An athlete at the gym holds a 3.0 kg steel ball in his hand. His arm is 70 cm long and has a mass of 4.0 kg. Assume, a bit unrealistically, that the athlete's arm is uniform.
What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor? Include the torque due to the steel ball, as well as the torque due to the arm's weight.
What is the magnitude of the torque about his shoulder if he holds his arm straight, but 40 ∘ below horizontal?
The magnitude of the torque about his shoulder if he holds his arm straight, but 40 ∘ below horizontal is 40 Nm.
Arm Weight: 4 kilogram
Ball weight: 4 kilogram
arm span: 70 cm
You must first determine the weights of the arm and the ball. Add the gravity factor to them.
Arm weight: 4 kg times 9.8 equals 39.2 Ball weight: 4 kg times 9.8 equals 39.2
In order to find the torque, = r1 F1 sin + r2 F2 sin,
We must determine r1 and r2, where r1 = 70/2 = 35 cm or.35 m. (arm: to find the center of gravity, divide by 2)
r2 = 70 cm, or.70 m (ball)
The angle is 180° since the arms are extended straight out, which equals m1g(L/2) + m2gL.
The system's length is L.
τ =4 * 9.8 *(0.7/2) + 4 * 9.8 * 0.7 \s
= 40 Nm
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a simple harmonic oscillator with an amplitude of 2.0\;\mathrm{cm}2.0cm passes through its equilibrium position once every 0.0300.030 seconds, what is the frequency of the oscillator?
The frequency of the oscillator is 33.33 Hz.
What is the frequency of the oscillator?
Frequency describes the number of waves that pass a fixed place in a given amount of time
The frequency of the oscillator is determined from the number of times or period taken for the wave to make one complete cycle.
Mathematically, the formula for frequency of oscillatory motion is given as;
F = 1/T
where;
F is the frequency of the oscillatorT is the period of the oscillationF = (1) / (0.03 s)
F = 33.33 Hz
Thus, the frequency of the oscillator is a function of the period of the motion.
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you have been hired to design a spring-launched roller coaster that will carry two passengers per car. the car goes up a 13-m-high hill, then descends 20 m to the track's lowest point. you've determined that the spring can be compressed a maximum of 2.5 m and that a loaded car will have a maximum mass of 420 kg. for safety reasons, the spring constant should be 14 % larger than the minimum needed for the car to just make it over the top.
a) what spring constant (k) should you specify ?
b) What is the maximum speed of a 350 kg car if the spring iscompressed the full amount.
Based on safety considerations, the spring constant to be provided is computed to be k = 1661.4N/m. The speed of a 370 kg car when the spring is fully compressed is computed to be v = 14.6 m/s.
Where F = applied force and x = spring displacement, the formula for the spring constant is provided. The absence of a positive sign indicates that the restorative force opposes the speed.
In common use and kinematics, an object's speed (often abbreviated as v) is defined as the size of the change in position per unit of time or over time for an object.
These calculations are used to determine the car's weight:
W = mg W = 420* 9.8 = 4116 N
F = k(spring constant)
K = f=F/x = 4116/2.5 = 1646.4N/m is the formula for the spring constant.
Given the need for safety, the spring constant to be used is determined as follows: k = 1646.4N/m + 15 = 1661.4N/m.
When the spring is fully compressed, the 370 kg automobile will move at a speed of 14.6 m/s because 1/2 mv^2 = 1/2kx^2
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