Velocity of golf ball after collision with golf club using law of conservation of momentum is 65.21 m/s
What is momentum ?
Momentum seem to be directly dependent on the value of mass as well as velocity of the object in the direction of motion. it is quantified by "mass velocity". Since mass is a scalar quantity but velocity is a vector, momentum is a vector quantity.
From the given information-
mass of golf club = 200 g
mass golf ball = 46 g
velocity of club before collision = 55 m/s
velocity club after collision =40 m/s
velocity of golf ball before collision = 0 m/s
You need to use conservation of momentum here.
momentum = mass x velocity
Prior to impact, the golf club has a momentum of 0.200 kg * 55 m/s = 11.00 kg m/s.
The ball's not moving before impact, so it has a momentum of zero. Therefore the total momentum before impact will be 11.00 kg m/s. Conservation of momentum dictates the total momentum of the two objects after impact will also be 11.00 kg m/s.
We know the speed of the club after the impact, so the momentum of the club after impqact is 0.200 kg * 40 m/s =8 kg m/s.
So the momentum of the ball must be 11.00 kg m/s - 8 kg m/s = 3 kg m/s, and dividing by the mass of the ball (0.046 kg) gives the speed of the ball, 65.217 m/s
Velocity of golf ball after collision wit golf club is 65.21 m/s
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A circular loop of wire with a radius of 13.0 cm and oriented in the horizontal xy-plane is located in a region of uniform magnetic field. A field of 1.5 T is directed along the positive z-direction, which is upward.part.aIf the loop is removed from the field region in a time interval of 2.7 msms , find the average emf that will be induced in the wire loop during the extraction process.
A circular loop of wire with a radius of 13.0 cm and oriented in the horizontal XY-plane is located in a region of the uniform magnetic field. A field of 1.7 T is directed along the positive z-direction, which is upward. A) If the loop is removed from the field region in a time interval of 2.9 ms,
The average emf that will be induced in the wire loop during the extraction process=
e =(pi) r^2B/t
e = pi*169*10^-4*1.7/(2.9*10^-3) = 31.12 V
In classical geometry, a radius of a circle or sphere is any of the line segments from its middle to its perimeter, and in greater present-day usage, it is also their length. The call comes from the latin radius, which means ray but additionally, the spoke of a chariot wheel.
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When wind speeds up as it blows over the top of a hill, atmospheric pressure there.
When wind speeds up as it blows over the top of a hill, atmospheric pressure there increases.
Atmospheric pressure is defined as the force per unit area exerted against a surface by the weight of the air molecules above the earth surface.The atmospheric pressure is not distributed uniformly over the earth. The amount of pressure increases or decreases, according to the amount of molecules, that exerts the force on the surface.When temperature of the air increases, the air expands and reduces the number of molecules over the unit area. It leads to reduction in pressure.Similarly, when the temperature falls, the air contracts and the pressure increase. Therefore, the temperature and atmospheric pressure are inversely related.
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An elastic cord is 61 cm long when a weight of 75 N hangs from it but is 85 cm long when a weight of 210 N hangs from it. What is the "spring" constant k of this elastic cord? also, find the frequency of the motion with the 210N object hanging on it (Physics 'Algebra base')
The spring constant of this elastic cord is 562.64 Nm.The frequency of the motion with the 210 N is 0.817Hz.
Elastic cord is a fairly versatile stretchy rope. it is small diameter makes it ideal for indoor craft makes use of and light duty strapping. Use this elastic string for sewing initiatives, scrapbooking, and kids' crafts.
Calculation:-
Spring constant K = f/x
= 75/0.61 - L
= 75/0.61 - 0.4767
= 562.64 Nm
Frequency when 210 N is hanging is
extension X = 0.85 -L
= 0.87 - 0.4767
= 0.3733
Frequency = 1/2π√g/X
= 1/2π √9.8/0.3733
= 0.816 Hz.
The free movement of a frame with appreciate to time is called motion. for example-the fan, the dirt falling from the carpet, the water that flows from the tap, a ball rolling around, a shifting car etc. Even the universe is in chronic motion.
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What is the voltage drop across resistors r2 in volts
The voltage drop across resistors r2 in volts is 6.6 volts.
What is resistor?Resistor is defined as an electrical component that regulates voltage and temperature. Resistors are frequently employed in electronic circuits to reduce current flow, divide voltages, impede transmission signals, and bias active parts. The resistor controls the electron flow to prevent overly rapid current from damaging the breadboard, wires, battery,
The Voltage drop can be calculated as
Give voltage of battery = 113 V
R2 has current = 1.9 A
And resistance = 4.7 ohms
Voltage = 1.9 + 4.7
= 6.6 V
Thus, the voltage drop across resistors r2 in volts is 6.6 volts.
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an emerald has an index of refraction of 1.57. the light from a red laser of wavelength 633nm in vacuum travels within the emerald. what is the maximum angle with respect to the normal that this light can strike the emerald/air interface such that the light wave exits into the air?
The maximum angle with respect to the normal that this light can strike the emerald/air interface such that the light wave exits into the air is: 39.34.
Total Internal Reflection
[tex]M_{1}[/tex] sin(∅[tex]_{c}[/tex]) = M[tex]_{2}[/tex] Sin(90)
sin(∅[tex]_{c}[/tex])= M[tex]{2}[/tex]/M[tex]_{1}[/tex] = 1/1.57 = 0.636
∅[tex]_{c}[/tex]= 39.49
∅ = 39.34
v = c/λ
c = 1000/5.56e - 6 = 1.798 × [tex]10^{8}[/tex] m/s
v = 1.798 × [tex]10^{8}[/tex]/400e-9 = 4.496 × [tex]10^{14}[/tex] Hz
What is refraction index?
In optics, the refractive index (or refractive index) of an optical medium is a dimensionless number that indicates the ability of the medium to diffract light.
The index of refraction determines how much a light path bends or refracts as it enters a material. This is described by Snell's law of refraction n1 sin θ1 = n2 sin θ2. where θ1 and θ2 are the angles of incidence and refraction, respectively, for a ray that crosses the interface between two media with indices of refraction n1 and n2. The index of refraction also determines the amount of light reflected upon reaching an interface, the critical angle for total internal reflection, its intensity (Fresnel equation), and Brewster's angle.
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with what initial velocity must an object be thrown upward from ground level to reach the top of the washington monument
Beginning velocity is required for a projectile to be launched from the ground up to the Washington Monument's 555-feet summit.
The Washington Monument is 555 feet 5 inches tall, so why?Casey was convinced to make the height of the tower 10 times the width of the base, which meant that the Washington Monument's ideal height was 555 feet rather than the 600 feet that Mills had originally envisioned.
The Washington Monument is not a memorial, so why?When compared to a memorial, why is the Washington Monument a "monument"? A memorial honors or pays tribute to a person who has passed away. A monument has a crucial distinction: it is created to honor or remember a living person.
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how many times larger in diameter of the smallest jovian planet than the diameter of the largest terrestrial planet
The diameter of the smallest jovian planet is 3.96 times larger than the diameter of the largest terrestrial planet.
What are the jovian and terrestrial planets?The jovian planets or also called giant gaseous planets are those that are far away in the solar system, which includes Jupiter, Saturn, Uranus, and Neptune, while terrestrial rocky planets include Mercury, Venus, the Earth planet and Mars.
Therefore, with this data, we can see that the jovian and terrestrial planets are different based on the composition of their surfaces and also due to the distance to the Sun.
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consider a tall, skinny pine tree, initially upright, that falls over in a forest. as it is falling, its base remains in contact with the ground and does not move from side to side. what sort of path does the tree's center of mass follow as it falls?
The tree will fall along quarter circular path by virtue of centre of mass.
Physics defines the center of mass as the location where the weighted position of a body's mass in relation to other points is equal to zero, creating a point of balance. Any distribution of mass within an object is possible. In essence, it is a hypothetical position defined in the laws of physics themselves in relation to any object at all, or even a system of objects based on the distribution of masses. The body can now be forced to experience some linear acceleration without experiencing any angular acceleration. Only rotation's effects are visible when a body is rotated through its center of mass.The tree's center of mass will be affected by the weight of the entire tree because the base is fixed in place at its initial location.To know more center of mass -
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a cannon sits on a stationary railroad flatcar with a mass of 1000 kg. when a 10-kg cannonball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? the recoil speed of the flatcar is m/s.
The recoil speed of the flatcar is0.5 m/s.
Step by Step Explanation:The cannon's momentum equals the flatcar's momentum according to Newton's third law of motion.
mv = MV........................ Equation 1:
where m is the cannon's mass, v is its velocity, and m is the flatcar's mass, v is its velocity.
Assign V as the subject of the equation V = mv/M... Equation 2
Given: M = 1000 kg
m = 10 kg,
and v = 50 m/s
Replace with V = 1050/1000 V = 500/1000
V = 0.5 m/s in equation 2.
Consequently, the flatcar's speed is equal to 0.5 meters per second.
What is Newton's Third Law of Momentum?An object interacts with another object when a push or pull is applied to it. A product of an interaction is force. Frictional force, for example, falls into the category of contact force. Non-contact force, on the other hand, includes gravitational force. Newton's third rule of motion explains that when two bodies interact, they exert force on one another. This force is referred to as an action and reaction pair.According to Newton's third law of motion,The first body receives a force that is equivalent in magnitude to the force applied in the opposite direction when one body exerts a force on another.To learn more about Newton's Third Law of Momentum refer to:
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An automobile moves on a level horizontal road in a circle of radius 30 m. The coefficient of friction between tires and road is 0. 50. The maximum speed with which this car can round this curve is:.
The maximum speed with which the car can round the curve is 12.1 m/s
What is Frictional force ?The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction.
The force produced between surfaces that slide against one another is known as the frictional force. Because frictional force develops when two surfaces come into contact with one another, it is referred to be a contact force. Walking on the road is an illustration of frictional force.
According to the given information
radius, [tex]$r=30 \mathrm{~m}$[/tex]
coefficient of friction, [tex]$\mu_k=0.50$[/tex]
Here friction : force will balance centripetal force.
[tex]$\begin{aligned} &\left(F_k=\text { Friction force })\right. \\ & F_k=\frac{m v^2}{r} \\ & \mu m_g=\frac{m v^2}{r} \\ & \mu g=\frac{v^2}{r} \\ & v^2=r \mu g=30 \times 0.5 \times 9.8 \\ & v=12.1 \mathrm{~m} / \mathrm{s}\end{aligned}$[/tex]
The maximum speed with which the car can round the curve is 12.1 m/s
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as a copper wire is heated, its length increases by 0.1%. what is the change in temperature of the wire? (copper
The change in temperature of the wire is 60.2°C.
What is the change in the temperature of the copper?Near room temperature, the temperature coefficient of copper is +0.393% per degree C. It follows that the resistance will rise by 0.393% if the temperature rises by 1°C.The only way to do so would be to attach a copper plate to the wire and take its temperature in order to use an infrared thermometer to measure it (the laser only shows where you are pointing it). That would provide results almost instantly because copper is such a good heat conductor.Increasing temperature causes silicon's resistance to decrease, whereas doing so causes copper's resistance to rise. As copper warms up, the vibrations of the atoms scatter more conduction electrons.Learn more about change in the temperature refer to :
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while checking out the front end of a vehicle, the technician grabs the driver’s side tire and steers the wheels manually left and right. while he does this, he notices that the center link moves up and down. what component is most likely at fault?
The worn idler arm is the component that is most likely at fault.
What occurs when a wheel hits a dip or home and moves downward?
When you hit any bump or dip in a road, your vehicle's suspension and springs move so the tire can stay in contact with the road and absorb the energy. The shock absorbers dampen the movement of the springs by converting the spring's kinetic energy into thermal (heat) energy.
What are the symptoms of a bad idler arm?
What are the warning signs of a bad idler arm? If you notice your steering wheel feels loose or has extra play before the tires respond, this may be a sign of an issue with your idler arm or pitman's arm. If these arms fail completely, you will lose all steering in your vehicle.
Can a worn idler arms cause play?
A steering wheel with too much play that shimmies, shakes, or vibrates too loosely can be a symptom of a bad idler arm. Poor steering likely means the ball joints are worn.
How important is an idler arm?
Idler's arms are particularly important for two reasons. First, as mentioned, the idler arm supports the right end of the track rod. Without it, the track rod would not hold the right wheel in place or turn it effectively, if at all. Second, the idler arm maintains proper toe angle.
Thus, a worn idler arm is a correct answer.
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A car is moving east at 28.8 m/s before applying it’s breaks. The car comes to a stop after 74 meters. How long does it take for the car to stop?
Answer:
Below
Explanation:
AVERAGE velocity = ( 28.8 - 0 ) / 2 = 14.4 m/s
74 m / 14.4 m/s = 5.14 s
Barium-131 is used in the detection of bone tumors. The half-life of barium-131 is approximately 12 days. How long will it take for the radiation level of barium-131 to drop to 1/4 of its original level?.
It will take 24 days for the radiation level of barium-131 to drop to 1/4 of its original level.
We know that radioactive reactions are 1st order reactions.
Given half life of Barium-131 is approximately 12 days.
So to drop to 1/4 of it's original level it will take more 12 days i.e. one more half life.
Total days are : 12+12=24 days
So it will take 24 days for the radiation level of barium-131 to drop to 1/4 of its original level.
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he mass of a bugatti veyron car is 1834 kg. the shape of the car is such that the aerodynamic drag coefficient c is 0.342 kg/m for quatratic drag. neglecting all other sources of friction, calculate the maximum speed in m/s if the veyron's engine can impart a force of 4522 n on the road.
To calculate the maximum speed of the Bugatti Veyron, we can use the equation $F_d = \frac{1}{2} \rho v^2 c A$,
which relates the drag force $F_d$ acting on an object to the density of the fluid $\rho$, the speed $v$ of the object, the drag coefficient $c$, and the cross-sectional area $A$ of the object.
In this case, we are given the mass of the car, the drag coefficient, and the force that the engine can impart on the road, so we can solve for the maximum speed.
First, we need to convert the mass of the car to its weight, which is the force of gravity acting on the car. The weight of the car is given by the equation $W = mg$, where $m$ is the mass of the car and $g$ is the acceleration due to gravity.
We can convert the mass of the car from kilograms to newtons by multiplying it by $g$, which is approximately 9.8 m/s$^2$. This gives us a weight of $W = 1834 \text{ kg} \times 9.8 \text{ m/s}^2 = 17983.2 \text{ N}$.
Next, we need to calculate the cross-sectional area of the car. Since we are given the shape of the car and the drag coefficient, we can assume that the car has a streamlined shape with a length $L$ that is much greater than its width or height.
In this case, the cross-sectional area of the car is approximately equal to its width $w$ times its height $h$, or $A \approx wh$. If we assume that the width of the car is $w = 1.8$ meters and the height is $h = 1.2$ meters, then the cross-sectional area is $A \approx 2.16 \text{ m}^2$.
Now that we have all of the required information, we can solve for the maximum speed of the car. The maximum speed is achieved when the drag force acting on the car is equal to the force that the engine can impart on the road. This means that the maximum speed $v_\text{max}$ is given by the equation
$$F_d = \frac{1}{2} \rho v_\text{max}^2 c A = F_\text{engine}$$
where $\rho$ is the density of the air, $c$ is the drag coefficient, $A$ is the cross-sectional area of the car, and $F_\text{engine}$ is the maximum force that the engine can impart on the road.
We are given that the drag coefficient is 0.342 kg/m and the maximum force that the engine can impart on the road is 4522 N. The density of the air is approximately 1.225 kg/m$^3$ at sea level. Plugging these values into the equation, we get
$$\frac{1}{2} \times 1.225 \text{ kg/m}^3 \times v_\text{max}^2 \times 0.342 \text{ kg/m} \times 2.16 \text{ m}^2 = 4522 \text{ N}$$
Solving for the maximum speed, we get $v_\text{max} \approx 242.5$ m/s. This is the maximum speed of the Bugatti Veyron if we neglect all other sources of friction and assume that the car has a streamlined.
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To make the pattern bigger and easier to see, should you move the slide closer tothe screen or closer to the laser? Explain. Be sure to comment on what variableschange (e.g. wavelength, angles to the minima, distance to the screen, position ofthe minima, etc.)
So, by moving the slit towards the laser will increase the slit and screen distance and the screen and the fringe will be bigger, angle of diffraction, wavelength will remain unaltered in this case
What is diffraction?
When waves flow through an aperture or around objects, they spread out, which is referred to as diffraction. It happens when the wavelength of the incident wave and the size of the aperture or obstruction are on the same order of magnitude. The majority of the wave is blocked at extremely small aperture diameters. Large apertures prevent severe diffraction from occurring as the wave passes past or through the obstruction.
What is wavelength?
Wavelength is the separation between the corresponding points of two successive waves. When two points or particles are referred to be "corresponding points," it means that they are both in the same phase means, points that have completed identical fractions of their periodic motion.
Hence, by moving the slit towards the laser will increase the slit and screen distance, and the screen and the fringe will be bigger, angle of diffraction, wavelength will remain unaltered in this case.
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step 2 of 2 : suppose a sample of 1350 floppy disks is drawn. of these disks, 67 were defective. using the data, construct the 85% confidence interval for the population proportion of disks which are defective. round your answers to three decimal places.
The 85% confidence interval estimate of the true population proportion of disks which are defective is 0.100 +/- 0.010
= (0.095, 0.110),Lower: 0.095 ,Upper: 0.110
Confidence intervals are a set of values with a known probability that the value of a parameter will fall within them.
The confidence interval of statistical data can be written as.
p+/-z√(p(1-p)/n)
We are given that,
Proportion of disks that are not defective = p' = 1283/1475 = 0.950
Proportion of disks that are defective = p = 1 - p' = 1 - 0.950 = 0.05
Thus , p = 0.05
Number of samples= n = 1350
Confidence interval = 85%
z value(at 85% confidence) = 1.28
Substituting the values we have;
0.100 +/- 1.28√(0.100(1-0.05)/1350)
0.100 +/- 1.28(0.00703703)
0.100 +/- 0.0090073984
0.100 +/- 0.010
= (0.095, 0.110)
According to the 85% confidence interval, the actual population percentage of defective discs is 0.100 +/- 0.010
Therefore, interval = (0.095, 0.110), Lower: 0.095, Upper: 0.110 can be used to describe the population portion.
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an ideal gas is compressed from 900 cm3 to 425 cm3 while 125 j of heat energy is removed from it. if the gas's pressure remains constant at 400 kpa during the compression, how much work was done by the gas?
The work done by the gas is 190,000 J.
What is work?
Work in physics is the energy that is transferred to or from a object when a force is applied along a displacement. In its simplest form, it equals the product of the force's magnitude and the distance travelled for a constant force directed in the same direction as the motion. When a force is applied, it is said to have a component that moves the point of application, or it is said to have positive work. If the component of a force at the point of application is in the opposite direction of the displacement, the force is said to do negative work.
The work done by the gas can be calculated using the equation W = P∆V. In this equation, P represents the constant pressure of 400 kPa, ∆V is the change in volume, and W is the work done by the gas.
Since the volume of the gas changed from 900 cm3 to 425 cm3, the change in volume is ∆V = 900 cm3 - 425 cm3 = 475 cm3. Plugging this into the equation above, we get W = 400 kPa x 475 cm3 = 190,000 J.
Therefore, the work done by the gas is 190,000 J.
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if a particle undergoes shm with amplitude 0.23 m , what is the total distance it travels in one period?
The total distance is 0.92 m
How to calculate total distance it travels in one period ?In physics, amplitude refers to the greatest displacement or distance that a point on a vibrating body or wave can move relative to its equilibrium position. It is equivalent to the vibration path's half-length.
A particle can move up to 0.23 meters from its resting position if it experiences simple harmonic motion with an amplitude of 0.23 meters.
It moved twice as far from its beginning place to its original position during one period, then returned after travelling a further twice as far distance.
Given ,
A total distance of
2*amplitude + 2*amplitude
= 2*0.23 + 2*0.23
= 0.42 + 0.46
= 0.92 meters
Therefore the total distance is 0.92 m
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Stars emit different wavelengths of visible light due to their different temperatures. How does this phenomenon support the particle model of light?.
The particle model of light states that light is composed of discrete particles called photons.
What is photon?
The electromagnetic force is carried by a photon, an elementary particle which is a quantum of a electromagnetic field and includes electromagnetic radiation like light and radio waves. Due to their lack of mass, photons always travel at the speed of light in a vacuum, which is 299792458 m/s (or 186,282 mi/s). The photon is a member of the boson family. Photons exhibit wave-particle duality, with their behaviour exhibiting characteristics of both waves and particles. Like other subatomic particles, photons have been best explained by quantum mechanics. In the first two decades of the twentieth century, Albert Einstein developed the modern photon theory, building on the work of Max Planck.
The varying wavelengths of visible light emitted by stars are evidence of the particle nature of light, since different temperatures of stars result in different amounts of energy being released in the form of photons, which each have a different frequency and energy level. This phenomenon supports the particle model of light because it demonstrates that light is composed of distinct particles with different energies.
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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.
Loftiest to smallest temperature
Mercury
Earth
Mars
Jupiter
Neptune
What's the average face temperature?
Planetary face temperatures range from over 400 °C on Mercury and Venus to below-200 °C on distant globes. The factors that determine temperature are the complex balance of heat entered and lost.
Thus, for these five globes, temperature correlates with distance from the Sun. The near to the sun, the hotter the earth. Note, still, that this isn't always the case, as the earth's temperature also depends on its reflectance and the strength of the greenhouse effect( if present). For illustration, although Venus is nearly doubly as far from the Sun, the average temperature on Venus is advanced than on Mercury due to the greenhouse effect.
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what is the magnetic field at a distance x from the center of the axis of a circular loop of a radius r carrying current i ?
The magnetic field at a distance x from the center of the axis of a circular loop of a radius r carrying current is µI/2R
Think about a loop that is R in diameter and I in current. The axis of the loop OX is located in the plane of the paper, while the Y-Z plane of the coil is perpendicular to the plane of the paper. Consider breaking up the circular loop into a large number of current elements, I*dl
Then, the Magnetic field due to the whole current loop will be:
B = µI[tex]R^{2}[/tex]/2[tex]2(x^{2} +R^{2} )^{3/2}[/tex]
When x =0, we get the correct results for the field at the center of a current loop.
B = µI/2R
When x exceeds R by a significant amount, the magnetic field diminishes as [tex]1/x^{3}[/tex]
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Which description is true for the following situation? As you are taking a shower, water vapor in the humidified air strikes the mirror and turns into a water droplet.
Alright, the answer is A.
Endothermic means that the source requires absorption of heat. Exothermic means that the source is accompanied by the release of heat.
B and D are incorrect, as they mean the opposite of the term associated.
So between A and C, when you lose heat in water vapor, the water VAPOR turns into regular water. Therefore:
A is correct.
(Logically, anyways.)
Let me know if this helped.
by what factor would the torsion constant need to be changed to make the smaller balance wheel oscillate at the original frequency? express your answer using three significant figures.
The factor through which the constant would have to change is given as 0.00412
How to solve for the oscillation frequencyThe moment of inertia is expressed as I = mr²
mass and volume has the relationship that is written as:
m = pV
m α V
mass is directly proportional to volume
m∝r³
m ∝ (1/3)³ = 1 / 27
the moment of inertia can be decreased by: 1 / 27 * (1 / 3)²
= 1 / 243
a. The angular frequency is gotten by
√1 / I
[tex]\sqrt{\frac{1}{1/243} }[/tex]
= 243
The factor through which the torsion constant would have to be reduced is given as 1 / 243
= 0.00412
There was a decrease of 0.00412
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Your boss at the Cut-Rate Cuckoo Clock Company asks you whatwould happen to the frequency of the angular SHM of the balancewheel if it had the same density and the same coil spring (thus thesame torsion constant), but all the balance wheel dimensions weremade one-third as great to save material.
By what factor would the torsion constant need to be changedto make the smaller balance wheel oscillate at the originalfrequency?
Thermodynamics deals with the macroscopic properties ofmaterials. Scientists can make quantitative predictions about thesemacroscopic properties by thinking on a microscopic scale. Kinetictheory and statistical mechanics provide a way to relate molecularmodels to thermodynamics. Predicting the heat capacities of gasesat a constant volume from the number of degrees of freedom of a gasmolecule is one example of the predictive power of molecularmodels.
The molar specific heat C_v of a gas at a constant volume is thequantity of energy required to raise the temperature T of one mole of gas by one degree while thevolume remains the same. Mathematically,
C_{\rm v}= \frac{1}{n}\,\frac{dU}{dT},
where n is the number of moles of gas, dU is the change in internal energy, anddT is the change in temperature.
Kinetic theory tells us that the temperature of a gas isdirectly proportional to the total kinetic energy of the moleculesin the gas. The equipartition theorem says that each degree offreedom of a molecule has an average kinetic energy equal to\frac{1}{2}k_{\rm B}T, wherek_B is Boltzmann's constant1.38 \times 10^{-23} \rm {J/K}. Whensummed over the entire gas, this gives \frac{1}{2}nRT, where R=8.314\;{\rm \frac{J}{mol\cdot K}}is the ideal gas constant, for each molecular degree offreedom.
Part A
Using the equipartition theorem, determine the molar specific heat,C_v, of a gas in which eachmolecule has s degrees of freedom.
Express your answer in terms ofR and s.
Part B
Given the molar specific heat C_v of a gas at constant volume, you candetermine the number of degrees of freedom s that are energetically accessible.
For example, at room temperature cis-2-butene,\rm C_4 H_8, has molar specific heatC_v=70.6\;{\rm \frac{J}{mol \cdot K}}. How many degrees of freedom of cis-2-butene areenergetically accessible?
Express your answer numerically tothe nearest integer.
Mathematically, the answer to the following question's a part is: [tex]C_{v} = \frac{Rs}{2}[/tex] and b part is: s=17.
a) Using the equipartition theorem,
U = [tex]\frac{1}{2} k_{b} T[/tex]
= [tex]\frac{1}{2} n_{R} T[/tex]
Degree of freedom for 's'
= [tex]\frac{1}{2} sn R T[/tex]
Then, molar specific heat [tex]C_{v} = \frac{1}{n} \frac{dU}{dT}[/tex]
Mentioning it in terms of R and s;
[tex]C_{v} = \frac{1}{n} \frac{dU}{dT} (\frac{1}{2} sn RT)[/tex]
[tex]C_{v} = \frac{Rs}{2}[/tex]
b) As per question,
[tex]C_{v}[/tex] = 70.6 J/mol.K and R = 8.314 J/mol.K
Using the formula, [tex]C_{v} = \frac{Rs}{2}[/tex]
70.6 J/mol.K = [tex]\frac{(8.314 J/mol.K) X s}{2}[/tex]
taking 2 on the left side by moving it from the division
70.6 J/mol.K x 2 = 8.314 J/mol.K x s
= [tex]\frac{70.6 J/mol.K X 2}{8.314 J/mol.K}[/tex]
s = 16.983 then we round it off to the nearest figure
We get, s = 17
Each degree of freedom that only appears quadratically in the total energy has an average energy of 1/2 kBT in thermal equilibrium, which increases the system's heat capacity by 1/2 kB, according to the equipartition theorem, also known as the law of equipartition, the equipartition of energy, or simply equipartition. The classical physics presumption that this concept holds true in all situation is refuted by the quantum theory.
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how much force should be applied on the piston (radius 0.012 meter ) so that a car of 1500 kg is completely supported by a piston of radius 0.15 meter.
Answer:
Force = 93 N
Explanation:
Given:
m₁ = 1500 kg
R₁ = 0.15 m
R₂ = 0.012 m
g = 9.8 m/s²
_____________
F₂ - ?
1)
Piston area:
S₁ = π·R₁² = 3.14·0.15² ≈ 71·10⁻³ m²
S₂ = π·R₂² = 3.14·0.012² ≈ 0.45·10⁻³ m²
2)
Force:
F₁ = m₁·g = 1500·9.8 = 14 700 N
F₂ = F₁· (S₂ / S₁)
F₂ = 14 700· (0.45·10⁻³ / (71·10⁻³) ≈ 93 N
Light having a wavelength in vacuum of 600 nm enters a liquid of refractive index 2. 0. In this liquid, its wavelength will be
The frequency is 5 x 10^14 Hz, the speed of light in the medium is 2 x 10 m/s and the wavelength is
4 x 10^-7 m
Given that,
Wavelength X = 600 nm
Refractive index n = 1.5
We know that,
The frequency is the ratio of the speed of light and wavelength of the light.
f = c/λ
f = 3 x 10^8/600 × 10^-9
f = 5 x 10^14 Hz
The speed in the medium is the ratio of the speed of the light in the vacuum and the refractive index.
n = c/v
1.5 = 3 x 10^8/υ
v = 2 × 10^8 m/s
The wave length is the ratio of the speed of the light in the medium and frequency.
λ = v/f
λ = 2 × 10^8/5 x 10^14
λ = 4 × 10^-7 m
Hence, The frequency is 5 x 10^14 Hz, the speed of light in the medium is 2 x 10^8 m/s and the wavelength is 4 x 10^-7 m
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another pendulum swings to and fro at a regular rate of 2 times per second. what is its period? (in s)
Five times per second is the typical frequency at which another pendulum swings back and forth. 2S
Describe the pendulum ?The back-and-forth motion of a pendulum can be used to demonstrate how potential energy transforms into kinetic energy and vice versa.Another pendulum swings back and forth with a normal frequency of five times per second. 2SThe formula for the period is T = t N.Time it takes for things to happen. Number of occurrences tAn oscillation of a pendulum takes a certain amount of time, or simply "period," to complete.It is obvious that the pendulum's mass or weight have nothing to do with the time period.To learn more about pendulum refer to:
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to date, we've found few planets orbiting their stars at distances comparable to the distances of the jovian planets in our solar system. why do astronomers think this is the case?
The answer is (b), meaning that we haven't been looking for planets so at distances for long enough.
What are the definitions of the 12 planets?(Astronomy) The solar system is made up of the sun and the objects gravitationally attracted to it, such as the planets Mercury, Venus, Mars, Mars, Octavian, Saturn, Uranus, and Neptune, as well as the minor planets Eris, Pluto, and Ceres.
What are the planets' roles?The world sustains us and gives us the resources we require. Last but not least, experts claim that if our planet disappeared, we and everything else on the world would have died. The one and only planet capable of supporting life is Earth.
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which component within an absorption refrigeration system requires heat transfer from a high temperature aource
Generator component within an absorption refrigeration system requires heat transfer from a high temperature source.
The evaporator "buckets" or collects heat from the chilled area. Low pressure causes the "bucket" to undergo a state shift (latent heat transfer) as it takes in heat. The "bucket" of low pressure and heat is then transported to the compressor by the evaporator. The component of the refrigeration system that actually cools things down is called the evaporator. The evaporator is situated in the region to be cooled because its purpose is to absorb heat into the refrigeration system (from where you don't want it to).
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