A mass M = 4 kg attached to a string of length L = 2.0 m swings in a horizontal circle with a speed V. The string maintains a constant angle \theta\:=\:θ = 35.4 degrees with the vertical line through the pivot point as it swings. What is the speed V required to make this motion possible?
Answers
Answer:
The velocity is [tex]v = 2.84 1 \ m/s[/tex]
Explanation:
The diagram showing this set up is shown on the first uploaded image (reference Physics website )
From the question we are told that
The mass is m = 4 kg
The length of the string is [tex]L = 2.0 \ m[/tex]
The constant angle is [tex]\theta = 35.4 ^o[/tex]
Generally the vertical forces acting on the mass to keep it at equilibrium vertically is mathematically represented as
[tex]Tcos (\theta ) - mg = 0[/tex]
=> [tex]mg = Tcos (\theta )[/tex]
Now let the force acting on mass horizontally be k so from SOHCAHTOA rule
[tex]sin (\theta ) = \frac{k }{T}[/tex]
=> [tex]k = T sin \theta[/tex]
Now this k is also equivalent to the centripetal force acting on the mass which is mathematically represented as
[tex]F_v = \frac{m v^2}{r}[/tex]
So
[tex]k = F_v[/tex]
Which
=> [tex]T sin \theta= \frac{ m v^2}{ r }[/tex]
So
[tex]\frac{Tsin (\theta )}{Tcos (\theta )} = \frac{mg}{ \frac{mv^2}{r} }[/tex]
=> [tex]Tan (\theta ) = \frac{v^2}{ r * g }[/tex]
=> [tex]v = \sqrt{r * g * tan (\theta )}[/tex]
Now the radius is evaluated using SOHCAHTOA rule as
[tex]sin (\theta) = \frac{ r}{L}[/tex]
=> [tex]r = L sin (\theta)[/tex]
substituting values
[tex]r = 2 sin ( 35.4 )[/tex]
[tex]r = 1.1586 \ m[/tex]
So
[tex]v = \sqrt{1.1586* 9.8 * tan (35.4 )}[/tex]
[tex]v = 2.84 1 \ m/s[/tex]
Related Questions
A crate is given a big push, and after it is released, it slides up an inclined plane which makes an angle 0.44 radians with the horizontal. The frictional coefficients between the crate and plane are (\muμs = 0.61, \muμk = 0.23 ). What is the magnitude of the acceleration (in meters/second2) of this crate as it slides up the incline?
Answers
Answer:
The acceleration is [tex]a = 6.2 m/s^2[/tex]
Explanation:
From the question we are told that
The angle which the inclined plane make with horizontal is [tex]\theta = 0.44 \ rad[/tex]
The frictional coefficients are [tex]\mu_{\mu s} = 0.61[/tex] and [tex]\mu_{\mu k} = 0.23[/tex]
The force acting on the crate is mathematically represented as
[tex]f = F_w + F_N[/tex]
Here f is the net force at which the crate is sliding down the plane which is mathematically represented as
[tex]f = ma[/tex]
[tex]F_w[/tex] is the force due to weight which is mathematically represented as
[tex]F_w = mg sin (\theta)[/tex]
and [tex]F_N[/tex] the force due to friction which is mathematically represented as
[tex]F_N = \mu_{\mu k } * mg cos(\theta )[/tex]
So
[tex]ma = mgsin(\theta ) + \mu_{\mu k} mg cos(\theta )[/tex]
[tex]a = gsin(\theta ) + \mu_{\mu k } * g cos(\theta)[/tex]
substituting values
[tex]a = 9.8 sin(0.44 ) + 0.23 * 9.8* cos(0.44)[/tex]
[tex]a = 6.2 m/s^2[/tex]
Find the rms (a) electric and (b)magnetic fields at a point 2.00 m from a lightbulb that radiates 90.0 W of light uniformly in all directions.
Answers
Answer:
a) rms of electric field =
[tex]E_{rms}[/tex]= 25.97 V/m
b) rms of magnetic field
[tex]B_{rms}[/tex] = 8.655 × 10⁻⁸
[tex]B_{rms}[/tex] = 86.55nT
Explanation:
given
power p = 90.0W
distance d = 2.00m
Intensity = [tex]\frac{power}{area}[/tex]
I = [tex]\frac{p}{A}[/tex]
A = [tex]4\pi d^{2}[/tex]
I = [tex]\frac{p}{4\pi d^{2} }[/tex]
I = [tex]\frac{90}{4\pi(2^{2}) }[/tex]
I = 1.79 W/m²
a) [tex]I_{ave}[/tex] = ε₀ × [tex]E^{2} _{rms}[/tex] × c
where ε₀ is permittivity of free space = 8.85×10⁻¹², [tex]E^{2} _{rms}[/tex] is the root mean value and c is speed of light = 3×10⁸m/s
1.79 = 8.85×10⁻¹² × [tex]E^{2} _{rms}[/tex] × 3×10⁸
[tex]E^{2} _{rms}[/tex] = [tex]\frac{1.79}{8.85x10^{-12} x 3x10^{8} }[/tex]
[tex]E^{2} _{rms}[/tex]= 674.1996
[tex]E_{rms}[/tex]= 25.97 V/m
b)for rems magnetic field
[tex]E_{rms}[/tex]= c [tex]B_{rms}[/tex]
[tex]B_{rms}[/tex] = [tex]\frac{E_{rms} }{c}[/tex]
[tex]B_{rms}[/tex] = [tex]\frac{25.97 V/m}{3x10^{8} }[/tex]
[tex]B_{rms}[/tex] = 8.655 × 10⁻⁸
[tex]B_{rms}[/tex] = 86.55nT
A 3 kg rock is swung in a circular path and in a vertical plane on a 0.25 m length string. At the top of the path, the angular velocity is 11 rad/s. What is the tension in the string at that point
Answers
Answer:
The tension in the string at that point is 90.75 N
Explanation:
Given;
mass of the object, m = 3 kg
length of string, r = 0.25 m
the angular velocity, ω = 11 rad/s
The tension on string can be equated to the centrifugal force on the object;
T = mω²r
Where;
T is the tension in the string
m is mass of the object
ω is the angular velocity
r is the radius of the circular path
T = 3 x (11)² x 0.25
T = 90.75 N
Therefore, the tension in the string at that point is 90.75 N
a wire of a certain material has resistance r and diameter d a second wire of the same material and length is found to have resistance r/9 what is the diameter of the second wire g
Answers
Answer:
d₂ = 3dThe diameter of the second wire is 3 times that of the initial wire.Explanation:
Using the formula for calculating the resistivity of an object to find the diameter.
Resistivity P = RA/L
R is the resistance of the material
A is the cross sectional area
L is the length of the material
Since A = πd²/4
P = R( πd²/4)/L
P = Rπd²/4L ... 1
If the second wire of the same material and length is found to have resistance R/9, the resistivity of the second material will be;
P₂ = (R/9)A₂/L₂
P₂ = (R/9)(πd₂²/4)/L₂
P₂ = (Rπd₂²/36)/L₂
P₂ = (Rπd₂²)/36L₂
Since the length and resistivity are the same;
P = P₂ and L =L₂
Equating 1 and 2;
Rπd²/4L = (Rπd₂²)/36L₂
Rπd²/4L = (Rπd₂²)/36L
d² = d₂²/9
d₂² = 9d²
Taking the square root of both sides;
√d₂² = √9d²
d₂ = 3d
Therefore the diameter of the second wire is 3 times that of the initial wire
A flashlight is held at the edge of a swimming pool at a height h = 1.6 m such that its beam makes an angle of θ = 38 degrees with respect to the water's surface. The pool is d = 1.75 m deep and the index of refraction for air and water are n1 = 1 and n2 = 1.33, respectively.
Required:
What is the horizontal distance from the edge of the pool to the bottom of the pool where the light strikes? Write your answer in meters.
Answers
one of the answers that i found was 5.83 m i did some more research and it showed the same answer again. good luck with it. hope i was able to help you.
If an astronomer wants to find and identify as many stars as possible in a star cluster that has recently formed near the surface of a giant molecular cloud (such as the Trapezium cluster in the Orion Nebula), what instrument would be best for her to use
Answers
Answer:
Infrared telescope and camera
Explanation:
An infrared telescope uses infrared light to detect celestial bodies. The infrared radiation is one of the known forms of electromagnetic radiation. Infrared radiation is given off by a body possessing some form of heat. All bodies above the absolute zero temperature in the universe radiates some form of heat, which can then be detected by an infrared telescope, and infrared radiation can be used to study or look into a system that is void of detectable visible light.
Stars are celestial bodies that are constantly radiating heat. In order to see a clearer picture of the these bodies, Infrared images is better used, since they are able to penetrate the surrounding clouds of dust, and have located many more stellar components than any other types of telescope, especially in dusty regions of star clusters like the Trapezium cluster.
Earth moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is kilometers, and the eccentricity is . Find the minimum distance (perihelion) and the maximum distance (aphelion) of Earth from the sun.
Answers
Complete question is;
Earth moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. Find the minimum distance (perihelion) and the maximum distance (aphelion) of Earth from the sun
Answer:
Minimum distance = 147,099,713.4 km
Maximum distance = 152,096,286.6 km
Explanation:
The formula for the eccentricity of an ellipse is given by;
e = c/a
where;
c is distance from the center of the ellipse to the focus of the ellipse.
a is distance from the center of ellipse to a vertex.
From the question, we are given;
a = 149,598,000
e = 0.0167
Thus;
0.0167 = c/149,598,000
c = 0.0167 × 149,598,000
c = 2,498,286.6
Now, formula for the minimum distance (perihelion) is;
Minimum distance = a - c
Minimum distance = 149598000 - 2498286.6
Thus;
Minimum distance = 147,099,713.4 km
Similarly, formula for the maximum distance (aphelion) is;
Max distance = a + c
Max distance = 149598000 + 2498286.6
Maximum distance = 152,096,286.6 km
Scattered light in the atmosphere is often partially polarized. The best way to determine whether or not light from a particular direction in the sky shows polarization is to
Answers
Answer:
Rotate a piece of polaroid film about an axis perpendicular to the ray while looking through it in that sky direction.
Explanation:
Polarization involves constraining a transverse wave e.g light waves to vibrate in one phase only. Since unpolarized light vibrates in all direction during propagation. Polarization can be achieved by a polaroid.
A polaroid is a material the make transverse waves to vibrate in one direction after passing through it. It has various applications in sun glasses, wind shield of a car etc.
If the slit of the polaroid is perpendicular to the polarized light from a particular direction in the sky, there would be no propagation of the light. But when it is parallel to the polarized light from the direction, the light would propagate through the polaroid.
Which of the following statements about Masters programs is not correct?
A. Most Masters athletes did not compete when they were in school.
B. The social life is as important as the athletics on most Masters
teams.
C. The level of competition is not very high in most Masters
programs.
D. Masters programs allow adults to work out and socialize with
people who share their love of a sport.
SUBMIT
Answers
The correct answer is C. The level of competition is not very high in most Masters programs.
Explanation:
In sports, the word "master" is used to define athletes older than 30 and that usually are professional or have trained for many years, although novates are also allowed. This means in most cases in Master programs and teams a high level of competition can be expected due to the experience and extensive training of Master athletes. Indeed, many records in the field of sport belong to Master athletes rather than younger athletes. According to this, the incorrect statement is "The level of competition is not very high in most Masters programs".
Which two types of electromagnetic waves have higher frequencies than the waves that make up ultraviolet light?
radio waves and infrared light
visible light and X-rays
microwaves and gamma rays
gamma rays and X-rays
Answers
The two types of electromagnetic waves that have higher frequencies than the waves that make up ultraviolet light are gamma rays and X-rays.
WHAT ARE ELECTROMAGNETIC WAVES?Electromagnetic waves are components of the electromagnetic spectrum, which is made up of the following:
Radio wavesInfraredUltravioletVisible lightX-raysGamma raysmicrowaveEach electromagnetic wave have a specific frequency and wavelength.
However, the two types of electromagnetic waves that have higher frequencies than the waves that make up ultraviolet light are gamma rays and X-rays.
Learn more about electromagnetic waves at: https://brainly.com/question/8553652
Answer:
gamma rays and X-rays
Explanation:
d on edge I got 100%
Which equations are used to calculate the velocity of a wave? velocity = distance × time velocity = wavelength × frequency velocity = distance/time velocity = wavelength/frequency velocity = distance/time velocity = wavelength × frequency velocity = distance × time velocity = wavelength/frequency
Answers
Answer:
velocity = distance/time
velocity = wavelength × frequency
Both of these are commonly known equations to calculate velocity with different variables.
A soap bubble is 115 nm thick and illuminated by white light incident perpendicular to its surface. What wavelength (in nm) and color of visible light is most constructively reflected, assuming the same index of refraction as water (nw = 1.33)?
Answers
Answer:
The wavelength is [tex]\lambda = 612nm[/tex] and the color is Orange
Explanation:
from the question we are told that
The thickness is [tex]D = 115 nm = 115 *10^{-9} \ m[/tex]
The refractive index of water is [tex]n_w = 1.33[/tex]
Generally the condition for constrictive interference is
[tex]2 * D = \frac{\lambda _n}{2}[/tex]
Where [tex]\lambda _n[/tex] is the wavelength of light in a particular medium
Now considering the medium of water(soap bubble )
The wavelength of light in this medium is mathematically represented as
[tex]\lambda = \frac{\lambda }{n }[/tex]
So
[tex]2 * D = \frac{\frac{\lambda }{n} }{2}[/tex]
[tex]2 * D = \frac{\lambda }{2 * n }[/tex]
=> [tex]\lambda = 4 *n * D[/tex]
substituting values
[tex]\lambda = 4 *1.33 * 115*10^{-9}[/tex]
[tex]\lambda = 6.118 *10^{-7} \ m[/tex]
[tex]\lambda = 612nm[/tex]
The color is orange because the wavelength range of yellow is
590–625 nm
The nonreflective coating on a camera lens with an index of refraction of 1.21 is designed to minimize the reflection of 570-nm light. If the lens glass has an index of refraction of 1.52, what is the minimum thickness of the coating that will accomplish this ta
Answers
Answer: 117.8 nm
Explanation:
Given,
Nonreflective coating refractive index : n = 1.21
Index of refraction: [tex]n_0[/tex] = 1.52
Wave length of light = λ = 570 nm = [tex]570\times10^{-9}\ m[/tex]
[tex]\text{ Thickness}=\dfrac{\lambda}{4n}[/tex]
[tex]=\dfrac{570\times10^{-9}\ m}{4\times1.21}\\\\\approx\dfrac{117.8\times 10^{-9}\ m}{1}\\\\=117.8\text{ nm}[/tex]
Hence, the minimum thickness of the coating that will accomplish= 117.8 nm
A solenoid 26.0 cm long and with a cross-sectional area of 0.580 cm^2 contains 490 turns of wire and carries a current of 90.0 A.
Calculate:
(a) the magnetic field in the solenoid;
(b) the energy density in the magnetic field if the solenoid is filled with air;
(c) the total energy contained in the coil’s magnetic field (assume the field is uniform);
(d) the inductance of the solenoid.
Answers
Answer:
A.21.3T
B.1.8x 10^6J/m^3
C.0.27x10^2J
D.6.6x10^-3H
Explanation:
Pls see attached file
Suppose a 185 kg motorcycle is heading toward a hill at a speed of 29 m/s. The two wheels weigh 12 kg each and are each annular rings with an inner radius of 0.280 m and an outer radius of 0.330 m.
Randomized Variables
m = 185 kg
v = 29 m/s
h = 32 m
A. How high can it coast up the hill. if you neglect friction in m?
B. How much energy is lost to friction if the motorcycle only gains an altitude of 33 m before coming to rest?
Answers
Answer:
a) Height reached before coming to rest is 42.86 m
b) Energy lost to friction is 17902.45 J
Explanation:
mass of the motorcycle = 185 kg
speed of the towards the hill = 29 m/s
The wheels weigh 12 kg each
Wheels are annular rings with an inner radius of 0.280 m and outer radius of 0.330 m
a) To go up the hill, the kinetic energy of motion of the motorcycle will be converted to the potential energy it will gain in going up a given height
the kinetic energy of the motorcycle is given as
[tex]KE[/tex] = [tex]\frac{1}{2}mv^{2}[/tex]
where m is the mass of the motorcycle
v is the velocity of the motorcycle
[tex]KE[/tex] = [tex]\frac{1}{2}*185*29^{2}[/tex] = 77792.5 J
This will be converted to potential energy
The potential energy up the hill will be
[tex]PE[/tex] = mgh
where m is the mass
g is acceleration due to gravity 9.81 m/s^2
h is the height reached before coming to rest
[tex]PE[/tex] = 185 x 9.81 x m = 1814.85h
equating the kinetic energy to the potential energy for energy conservation, we'll have
77792.5 = 1814.85h
height reached before coming to rest = 77792.5/1814.85 = 42.86 m
b) if an altitude of 33 m was reached before coming to rest, then the potential energy at this height is
[tex]PE[/tex] = mgh
[tex]PE[/tex] = 185 x 9.81 x 33 = 59890.05 J
The energy lost to friction will be the kinetic energy minus this potential energy.
energy lost = 77792.5 - 59890.05 = 17902.45 J
A) The motorcycle can coast up the hill by ; 42.86m
B) The amount of energy lost to friction : 17902.45 J
A) Determine how high the motorcycle can coast up the hill when friction is neglected
apply the formula for kinetic and potential energies
K.E = 1/2 mv² ---- ( 1 )
P.E = mgH ---- ( 2 )
As the motorcycle goes uphiLl the kinetic energy is converted to potential energy.
∴ K.E = P.E
1/2 * mv² = mgH
∴ H = ( 1/2 * mv² ) / mg ---- ( 3 )
where ; m = 185 kg , v = 29 m/s , g = 9.81
Insert values into equation ( 3 )
H ( height travelled by motorcycle neglecting friction ) = 42.86m
B) Determine how much energy is lost to friction if the motorcycle attains 33m before coming to rest
P.E = mgh = 185 * 9.81 * 33 = 59890.05 J
where : h = 33 m , g = 9.81
K.E = 1/2 * mv² = 77792.5 J ( question A )
∴ Energy lost ( ΔE ) = ( 77792.5 - 59890.05 ) = 17902.45 J
Hence we can conclude that The motorcycle can coast up the hill by ; 42.86m , The amount of energy lost to friction : 17902.45 J.
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Now, let's see what happens when the cannon is high above the ground. Click on the cannon, and drag it upward as far as it goes (15 m above the ground). Set the initial velocity to 14 m/s, and fire several pumpkins while varying the angle. For what angle is the range the greatest?
choices:
A. 45∘
B. 20∘
C. 30∘
D. 40∘
E. 50∘
Answers
Answer:
B. 20°Explanation:
Range in projectile is defined as the distance covered in the horizontal direction. It is expressed as R = U²sin2Ф/g
U is the initial velocity of the body (in m/s)
Ф is the angle of projection
g is the acceleration due to gravity.
Given U = 14m/s, g = 9.8m/s and range R = 15 m
we will substitute this value into the formula to get the projection angle Ф as shown;
15 = 15²sin2Ф/9.8
15*9.8 = 15²sin2Ф
147 = 225sin2Ф
sin2Ф = 147/225
sin2Ф = 0.6533
2Ф = sin⁻¹0.6533
2Ф = 40.79°
Ф = 40.79°/2
Ф = 20.39° ≈ 20°
Hence, the range is greatest at angle 20°
Estimate the peak electric field inside a 1.2-kW microwave oven under the simplifying approximation that the microwaves propagate as a plane wave through the oven's 700-cm2 cross-sectional area.
Answers
Answer:
The peak electric field is [tex]E_o = 3593.6 V/m[/tex]
Explanation:
From the question we are told that
The power is [tex]P = 1.2 \ kW = 1.2 *10^{3} \ W[/tex]
The cross-sectional area is [tex]A = 700 \ cm^2 = 700 *10^{-4} \ m^2[/tex]
Generally the average intensity of the microwave is mathematically represented as
[tex]I = \frac{c * \epsilon _o * E_o^2 }{2}[/tex]
Where [tex]c[/tex] is the speed of light with value [tex]c = 3.0 *10^{8} \ m/s[/tex]
and [tex]\epsilon_o[/tex] is the permitivity of free space with value [tex]\epsilon_o = 8.85*10^{-12} \ m^{-3} \cdot kg^{-1}\cdot s^4 \cdot A^2[/tex]
also [tex]E_o[/tex] is the peak electric field.
Now making [tex]E_o[/tex] the subject [tex]E_o = \sqrt{\frac{2 * I }{ c * \epsilon _o } }[/tex]
But this intensity of the microwave can also be represented mathematically as
[tex]I = \frac{ P }{A }[/tex]
substituting values
[tex]I = \frac{ 1.2 *10^{3} }{700 *10^{-4} }[/tex]]
[tex]I = 17142.85 \ W/m^2[/tex]
So
[tex]E_o = \sqrt{\frac{2 * 17142.85 }{ 3.0*10^{8}] * 8.85*10^{-12} } }[/tex]
[tex]E_o = 3593.6 V/m[/tex]
The peak electric field of the microwave is 3,593.1 V/m.
The given parameters;
power of the wave, P = 1.2 kW = 1,200 Warea of the plane, A = 700 cm²The intensity of the wave is calculated as follows;
[tex]I = \frac{P}{A} \\\\I = \frac{1,200}{700 \times 10^{-4}} \\\\I = 17,142.86 \ W/m^2[/tex]
The peak electric field is calculated as follows;
[tex]E_o = \sqrt{\frac{2I}{c \varepsilon _o} } \\\\E_o = \sqrt{\frac{2\times 17,142.86}{3\times 10^8 \times 8.85 \times 10^{-12}} } \\\\E_o = 3,593.1 \ V/m[/tex]
Thus, the peak electric field of the microwave is 3,593.1 V/m.
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An elastic circular bar is fixed at one end and attached to a rubber grommet at the other end. The grommet functions as a torsional spring with spring constant k. If a concentrated torque of magnitude Ta is applied in the center of the bar, what is the rotation at the end of the bar, φ(L)? Assume a constant shear modulus G and polar moment of inertia J.
Answers
Answer:
2.1 rad(anticlockwise).
Explanation:
So, we are given the following data or parameters or information in the question above:
=> "The torsional stiffness of the spring support is k = 50 N m/rad. "
=> "If a concentrated torque of mag- nitude Ta = 500 Nm is applied in the center of the bar"
=> "L = 300 mm Assume a shear modu- lus G = 10 kN/mm2 and polar monnent of inertia J = 2000 mln"
Hence;
G × J = 10 kN/mm2 × 2000 mln = 20 Nm^2.
Also, L/2 = 300 mm /2 = 0.15 m (converted to metre).
==> 0.15/20 (V - w) + θ = 0.
==> 0.15/20 (V - w ) = -θ.
Where V = k = 50 N m/rad
w = 183.3 θ.
Therefore, w + Vθ = 500 Nm.
==> 183.3 + 50 θ = 500 Nm.
= 6.3
Anticlockwise,
θ = 2.1 rad.
A capacitor that is initially uncharged is connected in series with a resistor and an emf source with E=110V and negligible internal resistance. Just after the circuit is completed, the current trhough the resistor is 6.5*10^-5A. the time constant for the circuit is 4.8s.
1) What is the resistance of the resistor?
2) What is the capacitance of the capacitor?
Answers
Answer:
1
[tex]R = 1.692*10^{6} \Omega[/tex]
2
[tex]C = 2.837 *10^{-6} \ F[/tex]
Explanation:
From the question we are told that
The voltage is [tex]E = 110 \ V[/tex]
The current is [tex]I = 6.5 *10^{-5} \ A[/tex]
The time constant is [tex]\tau = 4.8 \ s[/tex]
The resistance of resistor is mathematically evaluated as
[tex]R = \frac{E}{I}[/tex]
substituting values
[tex]R = \frac{ 110 }{ 6.5*10^{-5}}[/tex]
[tex]R = 1.692*10^{6} \Omega[/tex]
The capacitance of the capacitor is mathematically represented as
[tex]C = \frac{\tau}{R}[/tex]
substituting values
[tex]C = \frac{ 4.8}{ 1.692*10^{6}}[/tex]
[tex]C = 2.837 *10^{-6} \ F[/tex]
An electromagnetic standing wave in air of frequency 750 MHz is set up between two conducting planes 80.0 cm apart. At how many positions between the planes could a point charge be placed at rest so that it would remain at rest?
Answers
Answer:
The positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.
Explanation:
Given;
distance between the conducting planes, d = 80 cm
frequency of the electromagnetic wave, f = 750 MHz
speed of light, c = 3 x 10⁸ m/s²
Determine the wavelength
λ = C/f
where;
λ is the wavelength
C is the speed of light
f is the frequency
λ = C/f
λ = (3 x 10⁸) / (750 x 10⁶)
λ = 0.4 m = 40 cm
One complete cycle = one wavelength = 40 cm
half of the wavelength ( λ / 2) = 20 cm
one wavelength + half wavelength (3λ / 2) = 60 cm
The positions of the wave at zero amplitude (between 0 and 80 cm) = 20 cm, 40 cm, 60 cm
Thus, the positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.
The velocity of an object is given by the following function defined on a specified interval. Approximate the displacement of the object on this interval by sub-dividing the interval into the indicated number of sub-intervals. Use the left endpoint of each sub-interval to compute the height of the rectangles.
v= 4t + 5(m/s) for 3 < t < 7; n = 4
The approximate displacement of the object is______m.
Answers
Answer:
The approximate displacement of the object is 23 m.
Explanation:
Given that:
v = 4t + 5 (m/s) for 3< t< 7; n= 4
The approximate displacement of the object can be calculated as follows:
The velocities at the intervals of t are :
3
4
5
6
the velocity at the intervals of t = 7 will be left out due the fact that we are calculating the left endpoint Reimann sum
n = 4 since there are 4 values for t, Then there is no need to divide the velocity values
v(3) = 4(3)+5
v(3) = 12+5
v(3) = 17
v(4)= 4(4)+5
v(4) = 16 + 5
v(4) = 21
v(5)= 4(5)+5
v(5) = 20 + 5
v(5) = 25
v(6) = 4(6)+5
v(6) = 24 + 5
v(6) = 29
Using Left end point;
[tex]= \dfrac{1}{4}(17+21+25+29)[/tex]
= 23 m
Find the absolute value of the change of the gravitational potential energy (GPE) of the puck-Earth system from the moment the puck begins to move to the moment it hits the spring. Use 0.253 m for the displacement of the puck along the ramp and 9.80 m/s2 for the acceleration due to gravity. Assume that the mass of the puck is 0.180 kg. Express your answer using SI units to three significant figures.
Answers
Answer:
0.16joules
Explanation:
Using the relation for The gravitational potential energy
E= Mgh
Where,
E= Potential energy
h = Vertical Height
M = mass
g = Gravitational Field Strength
To find the vertical component of angle of launch Where the angle is 22°
h= sin theta
So E = mghsintheta
= 0.18 x 0.98 x 0.253 sin22
=0.16joules
Explanation:
Which of the following options is correct and why?
Consider a spherical Gaussian surface of radius R centered at the origin. A charge Q is placed inside the sphere. To maximize the magnitude of the flux of the electric field through the Gaussian surface, the charge should be located
(a) at x = R/2, y = 0, z = 0.
(b) at the origin.
(c) at x = 0, y = 0, z = R/2.
(d) at x = 0, y = R/2, z = 0.
(e) The charge can be located anywhere since flux does not depend on the position of the charge as long as it is inside the sphere.
Answers
Answer:
Option (e) = The charge can be located anywhere since flux does not depend on the position of the charge as long as it is inside the sphere.
Explanation:
So, we are given the following set of infomation in the question given above;
=> "spherical Gaussian surface of radius R centered at the origin."
=> " A charge Q is placed inside the sphere."
So, the question is that if we are to maximize the magnitude of the flux of the electric field through the Gaussian surface, the charge should be located where?
The CORRECT option (e) that is " The charge can be located anywhere since flux does not depend on the position of the charge as long as it is inside the sphere." Is correct because of the reason given below;
REASON: because the charge is "covered" and the position is unknown, the flux will continue to be constant.
Also, the Equation that defines Gauss' law does not specify the position that the charge needs to be located, therefore it can be anywhere.
Exercise 1 - Questions 1. Hold the grating several inches from your face, at an angle. Look at the grating that you will be using. Record what details you see at the grating surface. 0 Words 2. Hold the diffraction grating up to your eye and look through it. Record what you see. Be specific. 0 Words 3. Before mounting the diffraction grating, look through the opening that you made for your grating. Record what you see across the back of your spectroscope.
Answers
Answer:
1) on the surface you can see the slits with equal spacing, on the one hand and on the other hand it is smooth.
2)If the angle is zero we see a bright light called undispersed light
For different angles we see the colors of the spectrum
3) must be able to see the well-collimated light emission source
Explanation:
1) A diffraction grating (diffraction grating) is a surface on which a series of indentations are drawn evenly spaced.
These crevices or lines are formed by copying a standard metal net when the plastic is melted and after hardening is carefully removed, or if the nets used are a copy of the master net.
The network can be of two types of transmission or reflection, in teaching work the most common is the transmission network, on the surface you can see the slits with equal spacing, on the one hand and on the other hand it is smooth.
The number of lines per linear mm determines which range of the spectrum a common value can be observed to observe the range of viable light is 600 and 1200 lines per mm.
2) when looking through the diffraction grating what we can observe depends on the relative angle between the eye and the normal to the network.
If the angle is zero we see a bright light called undispersed light
For different angles we see the colors of the spectrum, if it is an incandescent lamp we see a continuum with all the colors in the visible range and if it is a gas lamp we see the characteristic emission lines of the gas.
3) Before mounting the grid on the spectrometer, we must be able to see the well-collimated light emission source, this means that it is clearly observed.
The spectrometers have several screws to be able to see the lamp clearly, this is of fundamental importance in optical experiments.
In each of the following situations, a wave passes through an opening in an absorbing wall. Rank the situations in order from the one in which the wave is best described by the ray approximation to the one in which the wave coming through the opening spreads out most nearly equally in all directions in the hemisphere beyond the wall.
(a) The sound of a low whistle at 1 kHz passes through a doorway 1 m wide.
(b) Red light passes through the pupil of your eye.
(c) Blue light passes through the pupil of your eye.
(d) The wave broadcast by an AM radio station passes through a doorway 1 m wide. (e) An x-ray passes through the space between bones in your elbow joint.
Answers
Answer:
A) geometric optics, B) geometric optics , c) geometric optics ,
e) geometric optics, f) geometric optics
Explanation:
For this exercise we must use the condition for interference and diffraction so that these phenomena are relevant the wavelength must be comparable to the gap spacing
λ> = a
Lam when the spacing is much greater than the wavelength, the description of geometric optics is more and more exact
let's analyze each situation
a) let's find the wavelength
v = λ f
λ= v / f
λ= 343/1000
λ = 0.343 m
0.343 << 1m
therefore the description of the geometric optics of
b) red light passes through the pupil of the eye
red light has a wavelength of 700 num or more, the lojo pupil has a maximum of 8 me
λ = 700 10⁻⁹ m = 7 10⁻⁷ m
a = 8 mm 10⁻³
longitudinal is much less therefore the geometric optics is correct
c) luz azul lam = 450 nm = 450 10⁻⁹ m = 4.5 10⁻⁷ m
again the wavelength is much less than the diameter of the pupil, for which the description with the optics is generally sufficient
d) a radio A transmits up to a maximum of f = 1400 Khz = 1,400 10⁶ Hz
let's find the wavelength
c = λf
λ = c / f
λ= 3 108 / 1,400 106
λ= 2.14 102 m
in this case the wavelength is greater than the width of the gate, so the description of diffraction should be used to explain the phenomenon
e) X-rays have wavelength lam = 10-10 m
the separation of the elbow bones is of the order of a few millimeters, for local the wavelength is much less than the separation, therefore with the relations of geometric optics it is sufficient
The length of a certain wire is doubled and at the same time its radius is also doubled. What is the new resistance of this wire
Answers
Answer:
R' = R/2
Therefore, the new resistance of the wire is twice the value of the initial resistance.
Explanation:
Consider a wire with:
Resistance = R
Length = L
Area = A = πr²
where, r = radius
ρ = resistivity
Then:
R = ρL/A
R = ρL/πr² --------------- equation 1
Now, the new wire has:
Resistance = R'
Resistivity = ρ
Length = L' = 2 L
Radius = r' = 2r
Area = πr'² = π(2r)² = 4πr²
Therefore,
R' = ρL'/πr'²
R' = ρ(2 L)/4πr²
R' = (1/2)(ρL/πr²)
using equation 1:
R' = R/2
Therefore, the new resistance of the wire is twice the value of the initial resistance.
what is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates
Answers
Answer:
m = 3,265 10⁻²⁰ E
Explanation:
For this exercise we can use Newton's second law applied to our system, which consists of a capacitor that creates the uniform electric field and the drop of oil with two extra electrons.
∑ F = 0
[tex]F_{e}[/tex] - W = 0
the electric force is
F_{e} = q E
as they indicate that the charge is two electrons
F_{e} = 2e E
The weight is given by the relationship
W = mg
we substitute in the first equation
2e E = m g
m = 2e E / g
let's put the value of the constants
m = (2 1.6 10⁻¹⁹ / 9.80) E
m = 3,265 10⁻²⁰ E
The value of the electric field if it is a theoretical problem must be given and if it is an experiment it can be calculated with measures of the spacing between plates and the applied voltage, so that the system is in equilibrium
a small bar magnet is suspended horizontally by a string. When placed in a uniform horizontal magnetic field, it will
Answers
Answer:
It will neither translate in the opposite direction nor .rotate so as to be at right angles, it will also neither rotate so as to be vertical direction
An FM radio station transmits a signal with a frequency of 89.1 MHz. Give the wavelength in meters. (use at least three significant digits)
Answers
Answer:
3m
Explanation:
89.1 MHz means
89.1×10^6 cycles/second.
Electromagnetic radiation (including radio waves) travel at
3.0×10^8meters/second
Wavelength = Speed/Frequency
The wavelength of a
89.1MHz radio signal is
3.0×10^8/89.1x10^6
= 0.03x10^2
= 3meters
Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitude for both masses during the collision are
Answers
Answer:
The quantities that always have equal magnitude for both masses during the collision are change in momentum of the colliding bodies and force exerted by each body
Explanation:
During collision of two bodies, the following quantities are affected;
Kinetic energy of the colliding bodies
change in momentum of the colliding bodies
Force exerted by each body
Two bodies that stick together after collision is inelastic collision.
For inelastic collision, the kinetic energy before collision is greater than kinetic energy after collision.
Change in momentum is zero, that is, momentum before collision is equal to momentum after collision.
According Newton's third law of motion, the force exerted by each body is equal but acts in opposite direction.
Therefore, the quantities that always have equal magnitude for both masses during the collision are change in momentum of the colliding bodies and force exerted by each body
The quantities that always have equal magnitude for both masses during the collision are change in momentum and force exerted by each body
Inelastic collision is a collision in which both bodies stick with each other after collision.
For inelastic collision, the momentum before collision is equal to momentum after collision.
Also, the force exerted by each body is equal but acts in opposite direction.
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