Answer:
- Elevated temperatures.
- Elevated pressures.
Explanation:
In the manufacture of plastic products are used:
Raw material (pellets) which are the monomers that promote the chemical reaction.
To these are added the charges, in order to reduce the cost of the final product and improve some properties. These charges can be fiberglass, paper, metal structures.
Additives are also added whose mission is to improve or achieve certain properties, such as reducing friction, reducing chemical degradation, increasing electrical conductivity, coloring the product, and all this happens in the presence of a catalyst that is responsible for initiating and accelerating the chemical reaction process.
There are different methods of production of plastics, one of the most frequent is by injection.
Injection is a process that is carried out on machines similar to extrusion machines, in which the spindle, in addition to rotating, has an axial displacement.
In the injection, once the mold is filled, it is separated from the nozzle of the machine, breaking the feed channel. After a certain time, the piece already cooled is demoulded.
High pressures and temperatures are necessary, but parts of good finish and at high production speeds are obtained
The correct answer is: Elevated temperatures.
During fabrication processes, polymeric materials are often subjected to elevated temperatures. This is because many polymers are thermoplastic, meaning they soften and can be reshaped when heated. The elevated temperatures allow the polymer chains to move more freely, enabling the material to be molded, extruded, or otherwise formed into the desired shape or structure.
While ambient temperature and pressure can also affect polymeric materials, the key condition for shaping and fabricating these materials is typically elevated temperature. Ambient temperature is usually not sufficient to induce the necessary molecular mobility for fabrication. Ambient pressure is generally constant and does not play a significant role in the fabrication process unless specific pressure conditions are required for certain molding techniques, such as injection molding or compression molding, where controlled pressure is applied to ensure the polymer fills the mold properly.
Suppose a piece of dust finds itself on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)
Answer:
405.3m
Explanation:
Since the CD spin rate is 500 rpm, or revolution per minutes, its angular speed in rad per second is
[tex]\omega = 500 rev/min * 2\pi rad/rev * 1/60 min/sec = 52.36 rad/s[/tex]
The dusk is 4.3 cm from center, so its velocity must be
[tex]v = R\omega = 4.3 * 52.36 = 225.14 cm/s[/tex]
Then the distance traveled by the dusk after 3 minutes, or 180 seconds is
[tex]d = v*t = 225.14 * 180 = 40526.54 cm[/tex] or 405.3m
The force required to stretch a Hooke’s-law spring varies from 0 N to 63.5 N as we stretch the spring by moving one end 5.31 cm from its unstressed position. Find the force constant of the spring. Answer in units of N/m. Find the work done in stretching the spring. Answer in units of J.
Answer:
Force constant will be 1195.85 N/m
Work done will be 1.6859 J
Explanation:
We have given the force, F = 63.5 N
Spring is stretched by 5.31 cm
So x = 0.0531 m
Force is given , F = 63.5 N
We know that force is given by [tex]F=kx[/tex]
So [tex]63.5=k\times 0.0531[/tex]
k = 1195.85 N/m
Now we have to find the work done
We know that work done is given by
[tex]W=\frac{1}{2}kx^2=\frac{1}{2}\times 1195.85\times 0.0531^2=1.6859J[/tex]
A long pipe of outer radius ????1=3.50 cm and inner radius ????2=2.98 cm carries a uniform charge density of 9.22 mC/m3. Assuming that the pipe is sufficiently long to consider it infinitely long, use Gauss's law to calculate the electric field ???? at a distance ????=7.35 cm from the centerline of the pipe. Use ????0=8.85×10−12 C/N·m2 for the the permittivity of free space.
Answer:
2388078.86544 N/C
Explanation:
[tex]\rho[/tex] = Charge density = 9.22 mC/m³
r = Distance = 7.35 cm
[tex]r_o[/tex] = Outer radius = 3.5 cm
[tex]r_i[/tex] = Inner radius = 2.98 cm
l = Length of cylinder
[tex]\epsilon_0[/tex] = Permittivity of free space = [tex]8.85\times 10^{-12}\ F/m[/tex]
V = Volume
E = Electric field
Charge is given by
[tex]Q=\rho V\\\Rightarrow Q=\rho\pi l(r_o^2-r_i^2)[/tex]
Area
[tex]A=2\pi rl[/tex]
From Gauss law the flux through a cylindrical surface is given by
[tex]EA=\frac{Q}{\epsilon_0}\\\Rightarrow E=\frac{Q}{\epsilon_0A}\\\Rightarrow E=\frac{\rho\pi l(r_o^2-r_i^2)}{\epsilon_02\pi rl}\\\Rightarrow E=\frac{\rho(r_o^2-r_i^2)}{\epsilon_02r}\\\Rightarrow E=\frac{9.22\times 10^{-3}(0.035^2-0.0298^2)}{8.85\times 10^{-12}\times 2\times 0.0735}\\\Rightarrow E=2388078.86544\ N/C[/tex]
The electric at the given distance is 2388078.86544 N/C
Early on in the story the narrator mentions the sound of wind through the wires strung overhead: "The wind in the wires took up the story . . ."Taking the plot's rising action at this point into account, which of the following literary devices is the author most likely using?
A.creative license
B.irony
C.extended metaphor
D.personification
Answer:
option D.
Explanation:
The correct answer is option D.
The irony is the figure of speech which represents the contradiction between what is stated and what actually the scenario is.
the statement by the poet does not have any contradictory statements.
The extended metaphor is a part of speech which is used when there is a comparison between two unlike things in the paragraph.
in the given statement of the poem, there is no comparison.
Personification is the part of speech where human quality are given to non-living things.
in the give statement wind in the wire took up the story can be taken as the human quality.
so, the statement part of speech is personification.
A small bolt with a mass of 33.0 g sits on top of a piston. The piston is undergoing simple harmonic motion in the vertical direction with a frequency of 3.05 Hz. What is the maximum amplitude that the piston can oscillate without the bolt losing contact with the piston's surface?
Answer:
0.027m
Explanation:
the bolt loses contact with the piston only when acceleration due to gravity equals acceleration of piston
ω² * A = g where ω is angular velocity, A amplitude, g acceleration due to gravity
ω is given by 2πf, ω² is 4π²f²
A= g/4π²f² depending on the value of g used either 10m/s² or 9.8m/s²,
i used 10m/s² in this answer
name one situation in which you might notice the reflection of a wave
Answer:
A perfect example of wave reflection is an echo.
Explanation:
A wave reflection takes place when waves cannot pass through a surface and in turn they bounce back. It is not necessary that wave reflections can only happen with sound waves, they can also take place in light waves. Also, the waves which are reflected have the same frequency as the original wave, but their direction is different. When a wave strikes an object in the same angle, they bounce back straight but when they hit an object with different angle, their direction changes.
A satellite has a mass of 5850 kg and is in a circular orbit 4.1 x10 to the 5th power m above the surface of a planet. The period of the orbit is two hours. The radius of the planet is 4.15 x 10 to the 6th power m. What is the true weight of the satellite when itis at rest on the planet's surface?
Answer:
W = 24.28 kN
Explanation:
given,
Mass of satellite = 5850 Kg
height , h = 4.1 x 10⁵ m
Radius of planet = 4.15 x 10⁶ m
Time period = 2 h
= 2 x 3600 = 7200 s
Time period of satellite
[tex]T = \dfrac{2\pi}{R}\sqrt{\dfrac{(R+h)^3}{g}}[/tex]
R is the radius of planet
h is the height of satellite
[tex]T^2 = \dfrac{4\pi^2}{R^2}\ {\dfrac{(R+h)^3}{g}}[/tex]
now calculation of acceleration due to gravity
[tex]g = \dfrac{4\pi^2}{R^2}\ {\dfrac{(R+h)^3}{T^2}}[/tex]
[tex]g = \dfrac{4\pi^2}{(4.15\times 10^6)^2}\ {\dfrac{(4.15\times 10^6+4.1\times 10^5)^3}{(7200)^2}}[/tex]
g = 4.15 m/s²
True weight of satellite
W = m g
W = 5850 x 4.15
W = 24277.5 N
W = 24.28 kN
True weight of the satellite is W = 24.28 kN
The true weight of the satellite, when the satellite is at rest on the surface of the planet, is 24.28 kN.
What is the time period of satellites?Time period of satellites is the total time taken by a satellite to complete a full orbit around a body. It can be given as,
[tex]T=\dfrac{2\pi}{R}\sqrt{\dfrac{(R+h)^3}{g}}[/tex]
Here, (R) is the radius of the body, and (g) is the gravitational acceleration force.
In a circular orbit 4.1 x10 to the 5th power m above the surface of a planet. The period of the orbit is 2 hours and the radius of the planet is 4.15 x 10 to the 6th power m.
To find the weight of the satellite, first find the value of gravitation acceleration using the time period formula as,
[tex]2=\dfrac{4\pi^2}{4.15\times10^6}\sqrt{\dfrac{(4.15\times10^6+4.1\times10^5)^3}{g}}\\g=4.15\rm m/s^2[/tex]
The weight of the body is mass time gravity. As the satellite has a mass of 5850 kg and value of g is 4.15 m/s². Thus, the weight of it is,
[tex]W=5850\times4.15\\W=24277.5\rm N\\W=24.28\rm \; kN[/tex]
Thus, the true weight of the satellite, when the satellite is at rest on the surface of the planet, is 24.28 kN.
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Are wind-driven currents found near the surface of the oceans or in the deep waters of the ocean?
Wind-driven currents are found NEAR THE SURFACE of the oceans
Explanation:
Surface currents are at the interphase between the hydrosphere and atmosphere. Therefore the feel the greatest effect of drag by wind currents, especially prevailing winds (that blow predominantly in one direction like westerlies and easterlies) within the lower atmosphere. The deep currents, on the other hand, are more influenced by Coriolis effect of the earth’s rotation. It is these differences in influences of surface and deeper currents that cause Ekman transport in oceans.
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Two technicians are discussing the need for the history of the vehicle. Technician A says that an accident could cause faults due to hidden damage. Technician B says that some faults could be related to a previous repair. Which technician is correct?a. Tech A onlyb. Tech B onlyc. Both a and bd. Neither a and b
Answer:
(C) both tech A and tech B
Explanation:
both technicians are correct because an accident could cause faults due to hidden damages which might not have been detected at the time of the accident and some faults could be related to previous repair probable due to human error from the repair man or even improper repair due to lack of adequate knowledge on the vehicle.
A 1.0-m long wire is carrying a certain amount of current. The wire is placed perpendicular to a magnetic field of strength.20 T. If the wire experiences a force of 0.60 N, what is themagnitude of the current moving through the wire?
A) 1A
B) 5A
C) 4A
D) 2A
E) 3A
Answer:
Current, I = 3 A
Explanation:
It is given that,
Length of the wire, l = 1 m
Magnetic field acting on the wire, B = 0.2 T
The magnetic force acting on the wire, F = 0.6 N
Let the current flowing through the wire is given by I. The magnetic force acting on an object in the uniform magnetic field is given by :
[tex]F=ILB\ sin\theta[/tex]
Here, [tex]\theta=90^{\circ}[/tex]
[tex]F=ILB[/tex]
[tex]I=\dfrac{F}{LB}[/tex]
[tex]I=\dfrac{0.6\ N}{1\ m\times 0.2\ T}[/tex]
I = 3 A
So, the current flowing through the rod 3 A.
Write the answer to this question. Energy is measured in units called joules(J). Suppose a roller coaster car starts with 78,000 J of potential energy. In a few seconds, it converts two-thirds of this energy into kinetic energy. As it takes a curve, the car doubles its kinetic energy. How much mechanical energy does the car now have?
The rollercoaster initially had 78,000 J of energy. It converted two-thirds of the energy into kinetic energy and later doubled it on a curve. Therefore, the coaster's new total mechanical energy is 182,000 J.
Explanation:In this energy problem, the roller coaster car starts out with 78,000 J of potential energy. It then converts two-thirds of its energy into kinetic energy, which is 2/3 * 78,000 J = 52,000 J. However, this isn't the end of the energy conversion. As the roller coaster car takes a curve, it doubles its kinetic energy to become 2 * 52,000 J = 104,000 J. Therefore, the new total mechanical energy of the car, considering both its remaining potential and newly gained kinetic energy, is its original potential energy (78,000 J) minus the potential energy converted to kinetic and then doubled (2/3 * 78,000 J * 2), which gives us 78,000 J - (2/3 * 78,000 J * 2) = 78,000 J - 104,000 J = -26,000 J. However, energy can't be negative, so it means the question might be flawed or we need to ignore the energy conservation law in this case and simply sum up potential and kinetic energies getting 78,000 J + 104,000 J = 182,000 J.
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To find the mechanical energy of the roller coaster car, we calculate the converted kinetic energy and then account for it being doubled during the ride. The car's total mechanical energy remains at 78,000 J due to conservation of energy.
The problem involves calculating the mechanical energy of a roller coaster car after it has converted some of its initial potential energy into kinetic energy and then doubled that kinetic energy. Initially, the car starts with 78,000 J of potential energy. As the problem states, the car converts two-thirds of this energy into kinetic energy. This conversion can be calculated as (2/3) × 78,000 J = 52,000 J of kinetic energy. Then, as the car takes a curve, it doubles this kinetic energy, resulting in 2 × 52,000 J = 104,000 J of kinetic energy. Due to the conservation of mechanical energy, and considering that no energy is lost to friction or other forces, the total mechanical energy of the car will be the same as the initial potential energy it had at the top of the first rise. Therefore, the car now has a total mechanical energy of 78,000 J.
Suppose that two objects attract each other with a gravitational force of 16 units. if the mass of object one was doubled, and if the distance between the objects was tripled, then what would be the new force of attraction?
Answer: 3.5units
Explanation:
Gravitational force existing between the two masses is directly proportional to the product of their masses and inversely proportional to the square of the distances between the masses.
Mathematically, F = GMm/r^2
G is the gravitational constant
M and m are the masses
r is the distance between the masses.
If the force of attraction between the masses is 16units, it becomes,
16 = GMm/r^2... (1)
If the mass of object 1 is doubled and distance tripled, we will have
F= G(2M)m/(3r)^2
F=2GMm/9r^2... (2)
Solving eqn 1 and 2 to get the new Force
Dividing eqn 1 by 2, we have
16/F = GMm/r^2 ÷ 2GMm/9r^2
16/F = GMm×9r^2/r^2×2GMm
16/F = 9/2(upon cancelation)
Cross multiplying we have
9F=32
F= 32/9
F= 3.5units
Answer:
Answer: F = 4 units
Explanation:
If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (22). The new force is then 1/4 of the original 16 units.
F = (16 units ) / 4 = 4 units
The work function of titanium metal is 6.93 × 10⁻¹⁹ J. Calculate the kinetic energy of the ejected electrons if light of frequency 1.216 × 10¹⁵ s⁻¹ is used to irradiate the metal.
We can calculate the kinetic energy of the ejected electrons in the photoelectric effect by applying the equation KE = hf - BE, where 'KE' is kinetic energy, 'h' is Planck's constant, 'f' is the frequency of the light, and 'BE' is the binding energy or work function of a metal (in this case, titanium).
Explanation:The photoelectric effect is the process where light of sufficient energy (in this case, frequency) shone on a metal surface can release electrons (photoelectrons). Kinetic energy of these ejected electrons can be calculated according to the equation: KE = hf - BE. Here, 'KE' is the kinetic energy we're striving to find, 'h' is Planck's constant, 'f' is the frequency of the incident light, and 'BE' is the binding energy or work function of the electron.
For titanium metal, you've provided that the work function (BE) is 6.93 × 10⁻¹⁹ J. The frequency ('f') of the light used is 1.216 × 10¹⁵ s⁻¹. And, Planck's constant ('h') approximately equals 6.63 × 10⁻³⁴ Js.
To execute the calculation: KE = (6.63 × 10⁻³⁴ Js x 1.216 × 10¹⁵ s⁻¹) - 6.93 × 10⁻¹⁹ J. The solution will provide your kinetic energy in Joules
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A light horizontal spring has a spring constant of 138 N/m. A 3.85 kg block is pressed against one end of the spring, compressing the spring 0.103 m. After the block is released, the block moves 0.290 m to the right before coming to rest. The acceleration of gravity is 9.81 m/s 2 . What is the coefficient of kinetic friction between the horizontal surface and the block?
Answer:
0.06683
Explanation:
m = Mass of block = 3.85 kg
g = Acceleration due to gravity = 9.81 m/s²
[tex]\mu[/tex] = Coefficient of kinetic friction
x = Compression of spring = 0.103 m
k = Spring constant = 138 N/m
Work done against friction is given by
[tex]W=m\mu gs\\\Rightarrow W=\mu 3.85\times 9.81\times 0.29\\\Rightarrow W=10.952865\mu[/tex]
The potential energy of the spring is given by
[tex]P=\frac{1}{2}kx^2\\\Rightarrow P=\frac{1}{2}\times 138\times 0.103^2\\\Rightarrow P=0.732021\ J[/tex]
The potential energy and the work done against friction will balance the system
[tex]0.732021=10.952865\mu\\\Rightarrow \mu=\frac{0.732021}{10.952865}\\\Rightarrow \mu=0.06683[/tex]
The coefficient of kinetic friction between the horizontal surface and the block is 0.06683
Technician A says that maintenance-free batteries use a large amount of water. Technician B says that maintenance-free batteries use materials that reduce the amount of water used by the battery. Which technician is correct
a. Technician A
b. Technician B
c. Both A and B
d. Neither A nor B
Answer:
Option B
Explanation:
Maintenance-free battery uses Recombination Electrolyte in order to limit the oxygen and hydrogen formation during charging.
Each plate of the battery uses a glass micro-fiber separator that absorbs the whole liquid electrolyte in its pore thus resulting in no free acid.
As the battery charges to its fullest, the oxygen produced at the positive plate moves via the pores of the separator to the negative plate.
Initially it reacts and forms [tex]PbSO_{4}[/tex], i.e., Lead Sulphate, then on further charging it gets converted to Pb, i.e., lead.
Due to this, the negative plate is not able to reach the correct potential in order to liberate hydrogen, and hence no water formation takes place.
Thus technician B is correct.
A coin with a diameter of 2.11 cm is dropped onto a horizontal surface. The coin starts out with an initial angular speed of 19.0 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular deceleration of 1.26 rad/s2 , how far does the coin roll before coming to rest?
Answer:
9.49596 m
Explanation:
[tex]\omega_f[/tex] = Final angular velocity = 0
[tex]\omega_i[/tex] = Initial angular velocity = 19 rad/s
[tex]\alpha[/tex] = Angular acceleration = -1.26 rad/s²
[tex]\theta[/tex] = Angle of rotation
Equation of rotational motion
[tex]\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \theta=\frac{\omega_f^2-\omega_i^2^2}{2\alpha}\\\Rightarrow \theta=\frac{0^2-19^2}{2\times -1.26}\\\Rightarrow \theta=143.25396\ rad[/tex]
Converting to m
[tex]143.25396\times \pi d=143.25396\times \pi\times 0.0211=9.49596\ m[/tex]
The distance the coin rolls before it stops is 9.49596 m
In the two-slit experiment, for the condition of bright fringes, the value of m = +2 corresponds to a path difference of λ.
True or False?
Answer:
False
Explanation:
We know that if path difference is even multiple of wavelength then bright fringes are formed and if path difference is odd multiple of wavelength then dark fringes are formed .
For bright fringes
Path difference Δx = m λ
m = 0 , 2 , 4 , 6.......
If m = 2 then the path difference will be
Δx = 2 λ
therefore the above statement if false.
False
When is an electron in an atom likely to move from one energy level to another
Explanation:
When a electron is collided with a photon with exactly the same energy it would require to get to any of the farther orbits,electron transition takes place to an orbit depending on the energy of the photon.
When electrons emit exactly the same amount energy that is difference between the current energy level and the new level,then the electron makes a transition to the new level.
An electron in an atom is likely to move from one energy level to another when it gains or loses energy.
Explanation:
The change in an electron’s position with respect to energy levels is termed as Atomic electron transition. In spite of having similar charge and mass, the energy level of any electron in an atom, surrounding the nucleus, differs depending on its orbital position from the nucleus.
Electrons positioned nearest to the atomic nucleus carry least energy. To move an electron from its original ground state energy level to a higher level; energize the atom and it will excite the electrons thus making it move from its lower energy stable state to an unstable state with higher energy level. Releasing energy of an atom decreases the energy level of its excited electrons, de-energizing it and thus stabilizing the atom.
A 1.60-kg object is held 1.05 m above a relaxed, massless vertical spring with a force constant of 330 N/m. The object is dropped onto the spring.
(a) How far does the object compress the spring?
m
(b) Repeat part (a), but this time assume a constant air-resistance force of 0.750 N acts on the object during its motion.
m
(c) How far does the object compress the spring if the same experiment is performed on the Moon, where g = 1.63 m/s2 and air resistance is neglected?
m
Answer:
(A) l = 0.39 m
(B) l =0.38 m
(C) l = 0.14 m
Explanation:
Answer:
Explanation:
Answer:
Explanation:
from the question we are given the following values:
mass (m) = 1.6 kg
height (h) = 1.05 m
compression of spring (l) = ?
spring constant (k) = 330 N/m
acceleration due to gravity (g) = 9.8 m/s^{2}
(A) initial potential energy of the object = final potential energy of the spring
potential energy of the object = mg(1.05 + l)
potential energy of the spring = 0.5 x k x l^{2} (k= spring constant)
therefore we now have
mg(1.05 + l) = 0.5 x k x l^{2}
1.6 x 9.8 x (1.05 + l) = 0.5 x 300 x l^{2}
15.68 (1.05 + l) = 150 x l^{2}
16.5 + 15.68l = 150l^{2}
l = 0.39 m
(B) with constant air resistance the equation applied in part A above becomes
initial P.E of the object - air resistance = final P.E of the spring
mg(1.05 + l) - 0.750(1.05 + l) = 0.5 x k x l^{2}
1.6 x 9.8 x (1.05 + l) - 0.750(1.05 + l) = 0.5 x 300 x l^{2}
(16.5 + 15.68l) - (0.788 + 0.75l) = 150l^{2}
16.5 + 15.68l - 0.788 - 0.75l = 150l^{2}
15.71 + 14.93l = 150^{2}
l =0.38 m
(C) where g = 1.63 m/s^{2} and neglecting air resistance
the equation mg(1.05 + l) = 0.5 x k x l^{2} now becomes
1.6 x 1.63 x (1.05 + l) = 0.5 x 300 x l^{2}
2.608 (1.05 +l) = 0.5 x 300 x l^{2}
2.74 + 2.608l = 150 x l^{2}
l = 0.14 m
The compression of the spring when it is dropped from 1.05 m is 0.37 m.
The compression of the spring when air resistance is considered 0.36 m.
The compression of the spring when air resistance is neglected and gravity is 1.63 is 0.14 m.
The given parameters;
mass of the object, m = 1.6 kginitial position of the object, h₀ = 1.05 mspring constant, k = 330 N/mThe compression of the spring is determined by applying the principle of conservation of energy;
[tex]\frac{1}{2} kx^2 = mgh\\\\\frac{1}{2} kx^2 = mg(1.05 + x)\\\\kx^2 = 2mg(1.05 + x)\\\\330x^2 = 2\times 1.6 \times 9.8(1.05 + x)\\\\330x^2 = 32.93 + 31.36x\\\\330x^2 - 31.36x - 32.93 = 0\\\\a = 330, \ b = -31.36, \ c = -32.93\\\\x = \frac{-b \ \ +/- \ \sqrt{b^2 -4ac} }{2a} \\\\x = \frac{-(-31.36) \ \ +/- \ \sqrt{(-31.36)^2 -4(330\times -32.93)} }{2(330)}\\\\x = 0.37 \ m[/tex]
Considering air resistance, the compression of the spring is calculated as follows;
[tex]\frac{1}{2} kx^2 = mg(1.05+ x) - F(1.05+ x)\\\\\frac{1}{2} \times 330 x^2 = 1.6\times 9.8(1.05 + x) - 0.75(1.05 + x)\\\\165x^2 = 16.46 + 15.68x - 0.79 - 0.75x \\\\165x^2 -14.93x - 15.67 = 0\\\\a = 165, \ \ b = -14.93 \ \ c = -15.67 = 0\\\\x = \frac{-b \ \ +/- \ \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-(-14.93) \ \ +/- \ \sqrt{(-14.93)^2 - 4(15.67)} }{2(165)}\\\\x = 0.36 \ m[/tex]
The compression of the spring when air resistance is neglected and gravity is 1.63;
[tex]\frac{1}{2} kx^2 = mg(1.05 + x)\\\\\frac{1}{2} \times 330 x^2 = 1.6 \times 1.63(1.05 + x)\\\\165 x^2 = 2.74 + 2.61x \\\\165 x^2 - 2.61x- 2.74 = 0\\\\a = 165, \ \ b = -2.61, \ c = \ -2.74\\\\x = \frac{-b \ \ +/- \ \ \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-(-2.61) \ \ +/- \ \ \sqrt{(-2.61) ^2 - 4(165\times -2.74)} }{2(165)}\\\\x = 0.14 \ m[/tex]
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Circle the letter of the sentence that tells how Bohr' model of the atom differed from Rutherford's model A. Bohr's model focused on the nucleus B. Bohr's model focused on the protons C. Bohr's model focused on the neutrons D. Bohr's model focused on the electrons
Answer:
A. Bohr's model focused on the nucleus
Lenses are described as convergent or divergent depending on how they refract light. What is the difference between these two types of lenses?
Answer:
Explanation:
Convergent lens is the lens which converges the rays of light falling on it. It is thicker at the middle and thinner at the edges. It is also known as convex lens.
Divergent lens is the lens which diverge the rays of light falling on it. It is thinner at the middle and thicker at the edges. It is also called as concave lens.
Convergent lenses, or convex lenses, thicken in the middle and focus light rays to a point, forming real or virtual images; divergent lenses, or concave lenses, are thinner in the middle, causing the light rays to spread out and only form virtual images. Snell’s law describes the refraction process in both lens types as being influenced by differences in the index of refraction.
Explanation:Difference Between Convergent and Divergent Lenses
Lenses are often categorized as either convergent (convex) or divergent (concave) depending on how they refract light. A converging lens is thicker at the middle and causes parallel light rays entering the lens to converge, or come together, at a single point known as the focal point. This lens can create both real and virtual images, the nature of which depends on the position of the object relative to the lens. In contrast, a divergent lens is thinner at the middle and causes parallel light rays to spread apart or diverge after passing through the lens. Divergent lenses only form virtual images.
Snell's law helps explain the refraction in both types of lenses, considering the difference in the index of refraction between the lens material and the surrounding air. The lens power is determined by its ability to bend light, described by the lens's focal length, with more powerful lenses having shorter focal lengths.
Advantages of outsourcing project work may likely include all of the following EXCEPT:
a. Increased flexibility.
b. Higher level of expertise.
c. Shortened project duration.
d. Reduced costs.
e. Reduced conflict.
Answer:
e. Reduced conflict.
Explanation:
Outsourcing is a tool that allows you to hire a provider outside the company for the execution of secondary activities, such as cleaning or mail, or covering other areas of the company, such as financial or accounting systems or the human resources area
- Advantages of Outsourcing
- Cost reduction
- Focus on the main activity
- Transformation of fixed costs into variables
- Reduce risk
- Improve quality
- Productivity increase
- Improve innovation processes
- Greater flexibility
- Access to the latest technologies
- Increase in competitiveness
Advantages of outsourcing project work include increased flexibility, higher level of expertise, and reduced costs.
Explanation:The advantages of outsourcing project work may likely include increased flexibility because organizations can access a global talent pool and adapt to changing markets. Outsourcing can also provide a higher level of expertise as specialized firms or individuals with specific skills can be hired. Additionally, outsourcing can lead to reduced costs by eliminating the need for in-house resources and infrastructure.
However, one advantage that is unlikely to be associated with outsourcing project work is reduced conflict. When different parties are involved in a project, conflicts may arise due to differences in goals, perspectives, or communication barriers. Outsourcing does not automatically guarantee a reduction in conflict.
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An object of mass m is dropped from a height h above the surface of a planet of mass M and radius R. Find the speed of the object when it hits the planet surface. Enter your answer as an expression in terms of m, M, R, h and the universal constant of gravity G.
Final answer:
The speed of an object of mass m when it hits the planet's surface after being dropped from height h is found by using the conservation of energy, yielding the formula v = √[2GM(1/R - 1/(R+h))] where G is the gravitational constant, M the planet's mass, and R its radius.
Explanation:
To find the speed v of an object of mass m when it hits the surface of a planet, we will use the principles of energy conservation in the context of gravitational fields. The total mechanical energy (potential plus kinetic) at the beginning and at the end must be equal since we are ignoring air resistance and any other non-conservative forces.
The initial potential energy when the object is at height h above the planet is given by the gravitational potential energy formula U = -G(Mm)/(R+h) and the initial kinetic energy is zero as the object is initially at rest. When the object reaches the surface of the planet, its potential energy is U = -G(Mm)/R and its kinetic energy is K = (1/2)m*v^2. Conservation of energy dictates that the initial total energy equals the final total energy:
-G(Mm)/(R+h) = -G(Mm)/R + (1/2)m*v^2
Solving for v, the speed of the object at the planetary surface, we get:
v = √[2GM(1/R - 1/(R+h))]
This expression shows that the object's speed increases with a greater initial height h, a more massive planet M, and decreases with a larger planetary radius R.
Two waves are traveling in the same direction along a stretched string. The waves are 45.0° out of phase. Each wave has an amplitude of 9.00 cm. Find the amplitude of the resultant wave.
Answer:
Amplitude of the resultant wave = 15.72 cm
Explanation:
If two identical waves are traveling in the same direction, with the same frequency, wavelength and amplitude; BUT differ in phase the waves add together.
A = 9cm (amplitude)
φ = 45 (phase angle)
The two waves are y1 and y2
y = y1 + y2
where y1 = 9 sin (kx - ωt)
and y2 = 9 sin (kx - ωt + 45)
y = 9 sin(kx - ωt) + 9 sin(kx - ωt + 45) = 9 sin (a) + 9 sin (b)
where a = (kx - ωt)
abd b = (kx - ωt + 45)
Apply trig identity: sin a + sin b = 2 cos((a-b)/2) sin((a+b)/2)
A sin ( a ) + A sin ( b ) = 2A cos((a-b)/2) sin((a+b)/2)
We have that
9 sin ( a ) + 9 sin ( b ) = 2(9) cos((a-b)/2) sin((a+b)/2)
= 2(9) cos[(kx - wt -(kx - wt + 45))/2] sin[(kx - wt +(kx -wt +45)/2]
y = 2(9) cos (φ /2) sin (kx - ωt + 45/2)
The resultant sinusoidal wave has the same frequency and wavelength as the original waves, but the amplitude has changed:
Amplitude equals 2(9) cos (45/2) = 18 cos (22.5°) = 18 * -0.87330464009
= -15.7194835217 cm ≅ 15.72 cm
since amplitudes cannot be negative our answer is 15.72 cm
A stamping machine begins turning out components that are out of tolerance. The manager removes the machine from service to ensure that more defective components are not produced and notifies maintenance to repair the machine. This is an example of ________. A. immediate corrective action B. benchmarking C. corporate governance D. disciplinary action E. basic corrective action
Answer:
Option A
Explanation:
Immediate corrective measure happens at the instant as it triggers a reaction according to a particular situation.
The time period of the solution is also on the same pattern and is not sustainable.
Thus the case where the stamping machine malfunctions and there is immediate removal of the machine from the service in order to reduce the production of the defective components is an example of immediate corrective measure.
A pulley system is used to lift a 2,000 newton engine up a distance of 3 meters. The operator must apply a force of 250 newtons to the chain of the pulley system to lift the motor. To lift the engine 3 meters, the operator must pull a total of 30 meters of chain through the pulley system. What is the value of do?
To calculate the value of 'do' in the given pulley system, we need to know the efficiency.
Explanation:In order to calculate the value of 'do' in the given pulley system, we need to understand the concepts of actual mechanical advantage (AMA) and ideal mechanical advantage (IMA).
AMA is the ratio of the output force (load) to the input force (effort). In this case, the load is the engine with a weight of 2,000 newtons and the effort force is 250 newtons. So, AMA = Load/Effort = 2000 N/250 N = 8.
IMA is the theoretical mechanical advantage calculated by counting the number of ropes supporting the load. In this case, since there is only one rope supporting the load, IMA = 1.
The relationship between AMA and IMA is given by the equation: AMA = IMA x efficiency.
Since the efficiency is not provided in the question, we cannot directly calculate the value of 'do' without this information.
Why is it important to develop alternative energy sources
Answer:
The alternative energy sources are defined as those resources that are used in place of the natural and non-renewable resources. This resources plays an important role in the conservation of natural resources.
The fossil fuels are the resources on which the people are directly dependent. Burning up of these fossils leads to the emission of carbon, which has a direct impact on earth. A small increase in the amount of carbon dioxide can lead to the increase in the surface temperature of earth.
In addition to this, these fossil fuels such as coal, petroleum, oil and natural gases are found to be present in a limited proportion, and it is a very expensive process to obtain these resources, so sustainable development method must be adopted in order to save this natural resources for the future generation.
Some of the examples of alternative resources that are widely used in place of fossil fuels are wind energy, solar energy, tidal energy, biomass energy and bio-fuels.
Thus, it is very important to develop and use alternative resources.
Final answer:
Developing alternative energy sources is vital for mitigating climate change, reducing reliance on finite fossil fuels, and enhancing economic opportunity and security. Renewable energy such as solar, wind, and hydropower are crucial for the sustainable transition.
Explanation:
Developing alternative energy sources is crucial for a number of reasons. First, as renewable energy sources like solar and wind become more technically superior and cost-effective compared to fossil fuels, market forces will naturally encourage a transition away from non-renewable resources. This helps prevent dependency on finite resources that will eventually deplete.
Second, climate change concerns necessitate the development of alternative energy sources. Political measures may impose financial penalties on fossil fuel use to mitigate harmful ecological impacts, prompting a migration towards more sustainable energy choices.
Lastly, alternative energy sources like solar, wind, and hydropower can provide increased economic opportunity, job creation, and energy security. Especially in light of climate-related disasters that reveal the vulnerabilities of fossil-fuel-dependent energy systems, diversification is key. It is also critical to plan now for a transition to sustainable energy to avoid the potential "energy trap" where too much energy is consumed in building new infrastructure, leaving insufficient resources for society's needs.
Two pop cans are at rest on a stand. A firecracker is placed between the cans and lit. The firecracker explodes and exerts equal and opposite forces on the two cans. Assuming the system of two cans to be isolated, the post-explosion momentum of the system ____.
a. is dependent upon the mass and velocities of the two cans
b. is dependent upon the velocities of the two cans (but not their mass)
c. is typically a very large value
d. can be a positive, negative or zero value
e. is definitely zero
Answer:
e. is definitely zero
Explanation:
Given that
At initial condition the speed of the pop cans is zero.
We know that linear momentum
P = Mass x velocity
P = m v
At initial condition v = 0
P= 0
If there is no any external force then the linear momentum of the system will be conserve.And given that ,consider the system isolated.
Therefore the answer is e.
A platinum sphere with radius 1.21 cm is totally immersed in mercury. Find the weight of the sphere, the buoyant force acting on the sphere, and the sphere's apparent weight. The densities of platinum and mercury are 2.14 × 104 kg/m3 and 1.36 × 104 kg/m3, respectively.
Answer:
1.556 N , 0.989 N, 0.567 N
Explanation:
Radius of sphere, r = 1.21 cm = 0.0121 m
density of platinum , d = 2.14 x 10^4 kg/m^3
density of mercury, d' = 13.6 x 10^3 kg/m^3
Volume of sphere, [tex]\frac{4}{3}\pi \times r^{3}= \frac{4}{3}\times 1.34\times \left (0.0121 \right )^{3}[/tex]
V = 7.42 x 10^-6 m^3
Weight of sphere = volume of sphere x density of platinum x gravity
W = V x d x g = 7.42 x 10^-6 x 2.14 x 10^4 x 9.8 = 1.556 N
Buoyant force, B = Volume x density of mercury x gravity
B = 7.42 x 10^-6 x 13.6 x 10^3 x 9.8 = 0.989 N
Apparent weight = True weight - Buoyant force
Apparent weight = 1.556 - 0.989 = 0.567 N
To find the weight of the platinum sphere, calculate the mass of the sphere using its density and volume. Then, use the formula weight = mass × gravitational acceleration. The buoyant force acting on the sphere is equal to the weight of the fluid displaced, which in this case is the weight of an equivalent volume of mercury. The sphere's apparent weight can be calculated by subtracting the buoyant force from its actual weight.
Explanation:To find the weight of the platinum sphere, we can use the formula:
Weight = Mass × Gravitational acceleration
Given the density of platinum and the radius of the sphere, we can calculate the mass of the sphere using the formula:
Mass = Density × Volume
Using the volume of a sphere formula, we can determine the volume of the sphere. Once we have the mass, we can calculate the weight of the sphere.
The buoyant force acting on the sphere can be calculated using Archimedes' principle, which states that the buoyant force equals the weight of the fluid displaced. In this case, the fluid is mercury. Since the sphere is totally immersed in mercury, the buoyant force would be the weight of an equivalent volume of mercury.
The sphere's apparent weight can be calculated by subtracting the buoyant force from the weight of the sphere. This gives us the net force acting on the sphere when it is immersed in mercury.
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A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 15 kg piston. The piston is 90 cm above the bottom when the gas temperature is 315 ∘C. The air above the piston is at 1.00 atm pressure.
A) What is the gas pressure inside the cylinder?B) What will the height of the piston be if the temperature is lowered to18 ∘C?
Considering the gasses law and all the parameters, 1) the pressure inside the cylinder is 3249.4 Pa, 2) the height of the piston at 18ºC is 0.4452 m.
What is the Law of gasses?
The law of gasses is a group of chemical and physical laws that allows understanding the behavior of gasses in a close system.
The law of gasses considers different parameters, such as
Pressure, P: the amount of force applied on a surface. It is expressed in Pascals (Pa) or atmospheres (atm). 1 atm = 101325 Pa.
Volume, V: spaces occupied by a certain amount of mass. It is expressed in litters (L).
Temperature, T: it is a measure of the particles' internal agitation. It is expressed in kelvins (K). One centigrade = 1 + 273 kelvins.
When talking about standard conditions in gas, we refer to 1 atm pressure, 273 K of temperature (0ºC), and 22.4 L/mol of volume.
The different laws are,
Boyle law ⇒ P₁V₁ = P₂V₂ ⇒ P and V are inversely proportional. T is constant.Charles law ⇒ V₁/T₁ = V₂/T₂ ⇒ V and T are directily porportional. P is constant.Gay-Lussac law ⇒ P₁/T₁ = P₂/T₂ ⇒ T and P are directily porportional. V is constant.The relationship between these three laws and the variables is as follows,
(P₁V₁) / T₁ = (P₂V₂) / T₂
According to this framework, we can answer the questions in this porblem.
Available data:
D = 24-cm² = 0.0024 m²m = 15 kgh = 90 cm = 0.9 mT₀ = 315ºC ⇒ 315 + 273 = 588 K.Pair = 1atmA) What is the gas pressure inside the cylinder?
We know that P is defined by the relationship between force and area.
P = F/A
So, let us define Force and Area.
FORCE
F is the force applied by the piston. So we need to get the F of the piston.
To do it, we will use the following formula,
W = mg ⇒ Where m is mass (15 kg) and g is gravity (9.8m/s²)
Since W is a type of force, we can replace this value in the previous general formula,
P = F/A = W/A = mg/A
AREA
Area A is defined by the following formula
A = π r²
Where
- π = 3.1416
- r = D/2
Now, we can replace A in the general formula as follows,
P = mg/A = mg / π (D/2)²
The pressure inside the cylinder is,
P = mg / π (D/2)²
P = (15 x 9.8) / 3.1416 (12)²
P = 147 / 452.39
P = 0.32494
P = 3249.4 Pa
The gas pressure inside the cylinder 3249.4 Pa.
B) What will the height of the piston be if the temperature is lowered to 18 ∘C?
T₁ = 588 K
T₂ = 18 ºC ⇒ 18 + 273 = 291 K
Now, volume can be calculated as follows,
V = π r² h = A h
Where
- π = 3.1416
- r = D/2 = 12
- h₁ = 0.9 m
- A = 452.39 cm² = 0.4524 m²
Replacing,
V₁ = A h₁
V₁ = 0.4524 m² x 0.9 m
V₁ = 0.4071 m³
Now, we have the initial volume V₁, and the inicial and final temperatures, T₁ and T₂. We will use this values and the Charles law to get the final volume, V₂.
V₁/T₁ = V₂/T₂
V₂ = T₂ (V₁/T₁)
V₂ = 291 (0.4071/588)
V₂ = 291 (0.4071/588)
V₂ =0.2014
Now that we have the final volume, we can use this value to get the final height.
V₂ = A h₂
h = V₂/A
h₂ = 0.2014 m³ / 0.4524 m²
h₂ = 0.4452 m
The height of the piston when the temperature is lowered to 18ºC is 0.4452 m.
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Final answer:
Starting with Part A, the gas pressure inside the cylinder is calculated using the piston's weight and area of the cylinder's cross-section, plus atmospheric pressure. For Part B, the height of the piston at 18 °C is found using the combined gas law, with the final volume corresponding to the new height under constant pressure.
Explanation:
To answer the student's questions regarding the cylinder and piston system, we must use the principles of gas laws and mechanics.
Part A: Gas Pressure Inside the Cylinder
The pressure exerted by the piston onto the gas can be calculated using the formula P = F/A, where F is the force and A is the area. The force due to the piston's weight (F) is the mass of the piston times the gravitational acceleration (F = m * g). The area (A) is the cross-sectional area of the cylinder, which is πr² for a circle. Adding the atmospheric pressure above the piston gives us the total pressure exerted on the gas inside the cylinder.
Part B: Height of the Piston at 18 °C
Assuming the process is isobaric (constant pressure), the change in height can be found using the combined gas law which relates pressure, volume, and temperature of a gas. In this case, P1V1/T1 = P2V2/T2, where V1 and V2 are the initial and final volumes, respectively, determined by the product of the cross-sectional area and the height of the piston, P is pressure, and T is temperature in Kelvin. We are looking for the final volume, and thus the final height of the piston when the temperature is lowered.