Add the following vectors using head-to-tail method and verify your results using the component method.
1. Vector A has a magnitude of 4.0 cms at an angle of 30 degrees with the positive X-axis; vector B has a magnitude of 3.0 cms at 90 degrees with + X-axis; vector C has a magnitude of 5.0 cms at 120 degrees with + X-axis.
2. In addition to vectors A, B, and C in problem # 1, there is a vector D with a magnitude of 6.0 cms at an angle of 210 degrees with +X-axis.
Note: Use a graph paper to show your work for problem number 1 and 2 using the head-to-tail method.
Do the component method analysis of both of these problems using the component method of adding vectors. Show your work step by step by taking the x and y components of all the vectors; adding all the x and y components together and then finding the resultant vector magnitude and direction knowing x and y are perpendicular to each other.
Compare the results of the graphical analysis as well as the component method and find the percent error using the component method as standard result
Answers
Answer:
See attached image for the requested graphs.
Part 1 : Vector sum is about 9.4 cm long in the graph, from components: about 9.35 cm long. Percent difference = 0.5%
Part 2: Vector sum is about 7.6 cm long in the graph and from components: 7.57 cm long. Percent difference = 0.4%
Explanation:
Part 1.
The graphical addition of the three vectors A, B and C gives a vector sum of approximately 9.4 cm at an angle of about 84 degrees
The component form addition is
Ax + Bx + Cx = 3.5 + 0 + (-2.5) = 1
Ay + By + Cy = 2.0 + 3 + 4.3 = 9.3
Magnitude: [tex]\sqrt{1^2+9.3^2} \approx 9.35\,\,cm[/tex]
The percent difference is: (9.4-9.35) * 100 /9.35 = 0.5%
Part 2.
The graphical addition of the four vectors (A, B, C, and D) measures approximately 7.6 cm at an angle of about 124 degrees.
The component form addition is
Ax + Bx + Cx + Dx = 3.5 + 0 + (-2.5) + (-5.2) = -4.2
Ay + By + Cy + Dy = 2.0 + 3 + 4.3 + (-3) = 6.3
Magnitude = [tex]\sqrt{(-4.2)^2+6.3^2} \approx 7.57\,\,cm[/tex]
The percent difference is: (7.6-7.57) * 100 /7.57 = 0.4%
Related Questions
What tension must a 50.0 cm length of string support in order to whirl an attached 1,000.0 g stone in a circular path at 5.00 m/s?
Answers
Explanation:
Assuming the circular path is horizontal, the sum of forces in the centripetal direction is:
∑F = ma
T = mv²/r
T = (1.0000 kg) (5.00 m/s)² / (0.500 m)
T = 50.0 N
a wave is described by where x is in meters, y is in centimeters and t is in seconds. The angular frequency is
Answers
Complete Question
A wave is described by y(x,t) = 0.1 sin(3x + 10t), where x is in meters, y is in centimetres and t is in seconds. The angular wave frequency is
Answer:
The value is [tex]w = 10 \ rad /s[/tex]
Explanation:
From the question we are told that
The equation describing the wave is y(x,t) = 0.1 sin(3x + 10t)
Generally the sinusoidal equation representing the motion of a wave is mathematically represented as
[tex]y(x,t) = Asin(kx + wt )[/tex]
Where w is the angular frequency
Now comparing this equation with that given we see that
[tex]w = 10 \ rad /s[/tex]
11. A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side
Answers
Answer:
≈159.15
Explanation:
So displacment is the fastest, or shortest way to get somewhere
Youd take your circumference (500) and find the diameter from that using the 2 formulas
C=2πr
d=2r
your answer would be ≈159.15
If im incorrect please correct me! Im only just relearning this stuff (im a freshman)
A typical cell has a membrane potential of -70 , meaning that the potential inside the cell is 70 less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. Because a cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor. How much energy is stored in the electric field of a 50--diameter cell with a 7.0--thick cell wall whose dielectric constant is 9.0?
Answers
Answer:
energy is stored is 2.2 × 10⁻¹³ J
Explanation:
The capacitance of the cell is given with the expression
C = (KE₀A) / d
k is the dielectric constant, A is the area of the cell, d is the thickness of the cell.
Now given that; the diameter is 50,
Area A = 4πR²
A = 4π × ( 25 × 10⁻⁶ m)²
A = 7850×10⁻¹² m²
our capacitance C = (KE₀A) / d
C = [9 ( 8.85 × 10⁻¹² C²/N.m² × 7850×10⁻¹² m² )] / 7×10⁻⁹ m
C = 8.93 × 10⁻¹¹ F
Now Energy stored
E = 1/2 × CV²
E = 1/2 × (8.93 × 10⁻¹¹ F) × ( 70 × 10⁻³ V)²
E = 2.2 × 10⁻¹³ J
Therefore energy is stored is 2.2 × 10⁻¹³ J
The energy that should be stored in the electric field should be 2.2 × 10⁻¹³ J.
Calculation of the energy:Since
The capacitance of the cell should be
C = (KE₀A) / d
Here,
k is the dielectric constant,
A is the area of the cell,
d is the thickness of the cell.
Now the diameter is 50,
So,
Area A = 4πR²
A = 4π × ( 25 × 10⁻⁶ m)²
A = 7850×10⁻¹² m²
Now
our capacitance C = (KE₀A) / d
C = [9 ( 8.85 × 10⁻¹² C²/N.m² × 7850×10⁻¹² m² )] / 7×10⁻⁹ m
C = 8.93 × 10⁻¹¹ F
Now Energy stored should be
E = 1/2 × CV²
E = 1/2 × (8.93 × 10⁻¹¹ F) × ( 70 × 10⁻³ V)²
E = 2.2 × 10⁻¹³ J
Therefore energy is stored is 2.2 × 10⁻¹³ J.
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"Describe the distribution of electromagnetic radiation emitted from the sun (what wavelengths are emitted
Answers
Answer:
The Sun is known to emit almost all wavelengths of electromagnetic radiation but 99% of the radiation emitted by the sun lie in the ultraviolet, visible, and infrared regions.
Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm to 400 nm (750 THz). The wavelength is shorter than that of visible light but longer than X-rays. UV rays make up about 10% of the e-m waves from the sun. UV radiation is carcinogenic to the skin, and is absorbed by the melanin pigment in the skin.
Visible light is the only e-m wave that our eyes can pick up, i.e the only e-m wave we can see. The frequency of this spectrum corresponds to a band in the vicinity of 405–790 THz. It can further be separated into different colors. It makes up a large portion of the e-m waves coming from the sun.
Infrared wave is an e-m radiation whose wavelengths longer than those of visible light. It is is generally invisible to the human eye. The wavelength of an infrared wave extend from the red edge of the visible spectrum at 700 nanometers (frequency 430 THz), to 1 millimeter (300 GHz). Most of the thermal radiation emitted by objects near room temperature is infrared. Most of the heat from the sun reach us as infrared radiation. As with all e-m radiation, infrared radiation carries radiant energy and behaves both like a wave and like a photon.
3. Why does a cyclist bend cycle at the time of making circular
turn?
Answers
A cyclist must lean into a turn to prevent tipping over in the other direction.The frictional force provides the centripetal force necessary to turn the cyclist to the left.But the frictional force also produces a clockwise torque that will cause the rider and the bicycle to tip clockwise to the right.The force is provided by the friction of the tires.
Answer:
to become stable
Explanation:
when it bends it body, it moves closer to the center of gravity which makes the bicycle stable and hence the turn can be taken easily
Rigid-body mechanics is divided into two areas: ________deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity; whereas________ is concerned with the accelerated motion of bodies.
Answers
Answer:
Statics and dynamics
Explanation:
Rigid-body mechanics is divided into two areas: statics deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity; whereas dynamic is concerned with the accelerated motion of bodies.
In rigid-body mechanics, there are two various branches: statics and dynamics. Statics studies the stability of bodies, i.e., those that are at rest or move at a constant speed, whereas dynamics studies the accelerated movement of bodies.
What is equilibrium?Even if neither a system's energy state nor its phase of motion tends to change over time, the system is said to be in equilibrium.
A simple mechanical body is considered to have been in equilibrium if it neither suffers accelerometers nor angular acceleration. Unless an external force disrupts this state, it will remain in equilibrium indefinitely.
When all forces acting on a single particle are added together and equal to zero, equilibrium results. In addition to the conditions outlined in the article above, a rigid body is said to be in equilibrium if the vector sum of any torques operating on it equals zero, maintaining the body's steady state of rotational motion.
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Convert an acceleration of 1km/h^2 into cm/8^2?
Answers
Answer:
1km/h^2 = 5/648 cm/s^2 [about 7.7 x 10^(-3) /s^2]
Explanation:
1km = 10^3 m = 10^5 cm
1h = 60x60 = 3600s
--> 1km/h^2 = 10^5 cm / (3600^2) s^2
<=> 1km/h^2 = 5/648 cm/s^2 [about 7.7 x 10^(-3) /s^2]
in a young's double-slit experiment the center of a bright fringe occurs wherever waves from the slits differ in the distance they travel by a multiple of
Answers
Answer:
Zero
Explanation:
Because using
Deta X= dsinစ x n(lambda)
But we know that for central maxima
n is zero
So after substituting
Deta x = 0
A cylindrical Benzene tank is 12ft high and 32in in diameter. How many kilograms of benzene can the tank store? help please make it good
Answers
Answer:
1670 kg
Explanation:
Convert the dimensions to cm.
12 ft × (12 in/ft) × (2.54 cm/in) = 365.76 cm
32 in × (2.54 cm/in) = 81.28 cm
Calculate the volume.
V = πr²h
V = π (81.28 cm / 2)² (365.76 cm)
V = 1,897,813.27 cm³
V = 1,897,813.27 mL
V = 1,897.81 L
Density of benzene is 0.88 kg/L.
m = (0.88 kg/L) (1,897.81 L)
m = 1670 kg
If white light illuminates a diffraction grating having 710 lines/mmlines/mm , over what range of angles does the visible mm
Answers
Complete Question
The human eye can readily detect wavelengths from about 400 nm to 700 nm. If white light illuminates a diffraction grating having 710 lines/mm, over what range of angles does the visible m = 1 spectrum extend
Answer:
The value [tex]\theta = 16.5 ^ o[/tex]
Explanation:
From the question we are told that
The diffraction grating haves [tex]a = 710 \ lines /mm[/tex]
Generally the separation of the slit is mathematically represented as
[tex]d = \frac{1}{710} \ mm =0.001408 \ mm = 1.408 *10^{-6} \ m[/tex]
Generally the condition for constructive interference is mathematically represented as
[tex]dsin(\theta ) = n \lambda[/tex]
So
[tex]\theta = sin ^{-1} [\frac{n * \lambda }{d} ][/tex]
=> [tex]\theta = sin^{-1}[\frac{1 * 400 *10^{-9}}{ 1.408*10^{-6}} ][/tex]
=> [tex]\theta = 16.5 ^ o[/tex]
A sinewave has a period (duration of one cycle) of 35 μs. What is its corresponding frequency (no of completed cycles in a second), in kHz, expressed to 3 significant figures?
If the frequency of this sinewave is now reduced by a factor of 2.5, using the value calculated above to 3 significant figures, what will be the new period?
Express your answer in μs, to 3 significant figures
Answers
Answer:
We know that the relation between period and frequency is:
T = period.
f = frequency.
T = 1/f.
Then, if the period is 35 μs = 35x10^-9 seconds.
The frequency will be:
f = (1/ 35x10^-9 s) = (1/35s)*10^9
now, 1Hz = 1/s
1KHz = 1/1000s = 10^-3 s
f = (10^9/35)*10^-3 KHz = 10^6/35 KHz = 28,571.429 KHz.
Now we must divide this by 2.5:
28,571.429 KHz/2.5 = 11,428.572 KHz
Now we can use the relation:
T = 1/f
T = 1/11,428.572 KHz = (1/11,428.572 Hz)*10^-3
T = 8.750x10^-8 seconds.
And we want this expressed in μs = 10`-9 seconds, we have:
T = 8.750x10^-8 s = (10/10)8.750x10^-8 s = 87.50x10`-9s = 87.50 μs
So as expected, if the frequency is reduced by a factor of 2.5, the period will increase by a factor of 2.5
As the initial period was 35 μs, and:
2.5*35 μs = 87.5 μs
A π_ ("pi-minus") particle, which has charge _e, is at location ‹ 4.00 10-9, -5.00 10-9, -2.00 10-9 › m. What is the electric field at location < -2.00 10-9, 4.00 10-9, 3.00 10-9 > m, due to the π_ particle?
Answers
Answer:
The electric field due to charge at distance r is [tex](-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]
Explanation:
Given that,
Initial position of particle [tex]r_{1}=4.00\times10^{-9}i-5.00\times10^{-9}j-2.00\times10^{-9}k\ m[/tex]
Final position of particle [tex]r_{2}=-2.00\times10^{-9}i+4.00\times10^{-9}j+ 3.00\times10^{-9}k\ m[/tex]
We need to calculate the magnitude of the position vector
Using formula of position vector
[tex]\vec{r}=\vec{r_{2}}-\vec{r_{1}}[/tex]
Put the value into the formula
[tex]\vec{r}=-2.00\times10^{-9}i+4.00\times10^{-9}j+ 3.00\times10^{-9}k-(4.00\times10^{-9}i-5.00\times10^{-9}j-2.00\times10^{-9}k)[/tex]
[tex]\vec{r}=-9\times10^{-9}i+9\times10^{-9}j+5\times10^{-9}k[/tex]
[tex]\vec{|r|}=\sqrt{(9^2+9^2+5^2)\times10^{-18}}[/tex]
[tex]\vec{|r|}=13.6\times10^{-9}\ m[/tex]
We need to calculate the unit vector along electric field direction
Using formula of unit vector
[tex]\hat{r}=\dfrac{\vec{r}}{|\vec{r}|}[/tex]
Put the value into the formula
[tex]\hat{r}=\dfrac{-9\times10^{-9}i+9\times10^{-9}j+5\times10^{-9}k}{13.6\times10^{-9}}[/tex]
[tex]\hat{r}=-0.66i+0.66j+0.36k[/tex]
We need to calculate the electric field due to charge at distance r
Using formula of electric field
[tex]E=\dfrac{kq}{r^2}\hat{r}[/tex]
Put the value into the formula
[tex]E=\dfrac{9\times10^{9}\times1.6\times10^{-19}}{(13.6\times10^{-9})^2}\times(-0.66i+0.66j+0.36k)[/tex]
[tex]E=7.78\times10^{6}\times(-0.66i+0.66j+0.36k)[/tex]
[tex]E=-0.8169\times10^{6}i+0.8169\times10^{6}j+2.800\times10^{6}k\ N/C[/tex]
[tex]E=(-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]
Hence, The electric field due to charge at distance r is [tex](-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]
True or False: The study of the motion of objects is a foundational part of Physics
Answers
Answer:
True
Explanation:
In the foundational topics of physics mechanics consists of motion, energy and forces, theses areas are core concerns in the study of physics hence they are the foundational topics and are often times treated first in all matters.
What is motion?
Simply put, it is alternating from points to points.
the areas of study that involves motion and force together is call dynamics.
while the area of study of motion without any applied force is call statics.
A hiker caught in a rainstorm absorbs 1.00 L of water in her clothing. If it is windy so that the water evaporates quickly at 20 ∘C, how much heat is required for this process?
Answers
Answer:
2260000 J
Explanation:
From the question,
Q = ml.................... Equation 1.
Where Q = Heat, m = mass of water, l = specific latent heat of vaporization.
But we can get the mass o water using the formula of density.
D = m/v........... Equation 2
Where D = density of water, v = volume of water.
make m the subject of the formula in equation 2
m = D×v............ Equation 3
Substitute equation 3 into equation 1
Q = D×v×l................. Equation 4
Given: v = 1.00 L = 0.001 m³.
Constant: l = 226000 J/kg, D = 1000 kg/m³
Substitute these values into equation 4
Q = 0.001(2260000)(1000)
Q = 2260000 J
How does the antenna work to detect the electromagnetic signal produced when radio stations broadcast
Answers
Answer:
The antenna which is a transmitting and receiving device emits energy from current as radio waves, it does this by attracting the radio waves which are a form of EMWs and converts it to small voltages which are amplified to the final voltage signal which hear
A bullet is fired horizontally with initial velocity of 800 m/s as a target located 200 mfrom the rifle.(a).How much time is required for the bullet to reach the target
Answers
Answer:
t = 0.25 seconds
Explanation:
Given that,
Initial speed of a bullet, v = 800 m/s
Distance from the target is 200 m
We need to find the time required for the bullet to reach the target. Time is simply calculated by the definition of velocity i.e.
[tex]t=\dfrac{d}{v}\\\\t=\dfrac{200\ m}{800\ m/s}\\\\t=0.25\ s[/tex]
So, it will take 0.25 seconds to reach the target.
Radio waves are readily diffracted around buildings, whereas light waves are negligibly diffracted around buildings. This is because radio waves
Answers
Answer:
Radio waves have longer wavelength
Explanation:
Radio wave is an electromagnetic frequency that has the ability to travel through long distance. They have frequencies shuttling been the range of 10^4 hz and a frequency of 10^12 hz
Light wave is also called visible light. This is because it is visible to the naked eye, despite it being in the electromagnetic spectrum. It's frequency is usually between 4*10^-7 hz and a frequency of 7*10^-7 hz.
As can be seen from both, the radio waves length are quite far stronger than that of the light waves.
A weight of 35.0 N is suspended from a spring that has a force constant of 220 N/m. The system is undamped and is subjected to a harmonic driving force of frequency 10.5 Hz, resulting in a forced-motion amplitude of 3.00 cm. Determine the maximum value of the driving force.
Answers
Answer:
The force is [tex]F = 423.04 \ N[/tex]
Explanation:
From the question we are told that
The weight is [tex]W = 35 .0 \ N[/tex]
The force constant is [tex]k = 220 \ N/m[/tex]
The frequency is [tex]f = 10.5 \ Hz[/tex]
The amplitude is [tex]A = 3.00 \ cm = 0.03 \ m[/tex]
Generally the maximum driving force is mathematically represented as
[tex]F = m * w^2 A[/tex]
Here m is the mass of the weight which is mathematically represented as
[tex]m = \frac{ W }{g}[/tex]
=> [tex]m = \frac{ 35 }{9.8 }[/tex]
=> [tex]m = 3.571 \ kg[/tex]
Also [tex]w[/tex] is the angular frequency of the weight which is mathematically represented as
[tex]w = 2 \pi * f[/tex]
[tex]w = 2* 3.142 * 10[/tex]
=> [tex]w = 62.84 \ rad/s[/tex]
So
[tex]F = 3.571 * 62.84^2 * 0.03[/tex]
[tex]F = 423.04 \ N[/tex]
A soccer ball and a volleyball moved on a plane surface very fast. If the two balls moved
at the same speed, which of the two balls is more difficult to stop?
Answers
Answer:
soccer ball
Explanation:
Because it's round in shape and therefore cannot be stopped as both moves at same speed. There's no edges or corners to bounce up and slow the ball.
Answer:
They will both be since they are going the same speed
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Four students measured the same line with a ruler like the one shown below. The results were as follows: 5.52 cm, 6.63 cm, 5.5, and 5.93. Even though you cannot see the line they actually measured, which of the recorded measurements are possible valid measurements for this instrument, according to its precision? Select all that apply. 1. 5.52 2. 6.63 3. 5.5 4. 5.93
Answers
Answer:
1) 5.52 cm , C) 5.5 cm
Explanation:
When a measurement is carried out, in addition to the value of the magnitude, the error or uncertainty of the measurement must occur, in a direct measurement with an instrument the uncertainty is equal to the appreciation of the instrument.
Uniform see the errors by the number of significant figures days, in this cases they are two decimals for which the appreciation of the instrument ± - 0.01
now we can analyze the measurements made
1) 5.52 cm. Validate. It is a valid measurement is within the uncertainty range
2) 6.63 cm. It does not validate. It is out of the error range
3) 5.5 cm Valid. It is within the given error range,
4) 5.93 cm Not Valid. It is out of the error range.
Answer:
6.63 and 5.93
Explanation:
What accepted idea was replaced by copernicus's new approach to the solar system?
Answers
Answer:
The geocentric model of Ptolemy in which the sun and other planets were believed to move round the Earth.
Explanation:
The Copernicus heliocentric model of the solar system was put forward by Nicolaus Copernicus and was published in 1543. The model proposed by Copernicus puts the Sun near the center of the Universe, motionless, with Earth and the other planets orbiting around the sun in circular paths, modified by epicycles, and at uniform speed. This is contrary to Ptolemy's geocentric solar system that puts the Earth at the center of the solar system, in which the sun and other planets were believed to move round the Earth.
A) A spaceship passes you at a speed of 0.800c. You measure its length to be 31.2 m .How long would it be when at rest?
B) You travel to a star 145 light-years from Earth at a speed of 2.90
Answers
Answer:
a
[tex]l_o =52 \ m[/tex]
b
[tex]l = 37.13 \ LY[/tex]
Explanation:
From the question we are told that
The speed of the spaceship is [tex]v = 0.800c[/tex]
Here c is the speed of light with value [tex]c = 3.0*10^{8} \ m/s[/tex]
The length is [tex]l = 31.2 \ m[/tex]
The distance of the star for earth is [tex]d = 145 \ light \ years[/tex]
The speed is [tex]v_s = 2.90 *10^{8}[/tex]
Generally the from the length contraction equation we have that
[tex]l = l_o \sqrt{1 -[\frac{v}{c } ]}[/tex]
Now the when at rest the length is [tex]l_o[/tex]
So
[tex]l_o =\frac{l}{\sqrt{ 1 - \frac{v^2}{c^2 } } }[/tex]
[tex]l_o =\frac{ 31.2 }{ \sqrt{1 - \frac{(0.800c ) ^2}{c^2} } }[/tex]
[tex]l_o=52 \ m[/tex]
Considering b
Applying above equation
[tex]l =l_o \sqrt{1 - [\frac{v}{c } ]}[/tex]
Here [tex]l_o =145 \ LY(light \ years )[/tex]
So
[tex]l=145 * \sqrt{1 - \frac{v_s^2}{c^2 } }[/tex]
[tex]l =145 * \sqrt{ 1 - \frac{2.9 *10^{8}}{3.0*10^{8}} }[/tex]
[tex]l = 37.13 \ LY[/tex]
If a proton is traveling north directly above the wire, what is the direction of the magnetic force on the proton due to the wire?
Answers
Answer:
Direction is downwards
Explanation:
This is by employing Flemings Right hand rule which says If you point your pointer finger in the direction the positive charge is moving, and then your middle finger in the direction of the magnetic field, your thumb points in the direction of the magnetic force pushing on the moving charge.
A sound source producing 1.00 kHz waves moves toward a stationary listener at one-half the speed of sound.
a) What frequency will the listener hear?
(b) Suppose instead that the source is stationary and the listener moves toward the source at one half the speed of sound. What frequency does the listener hear? How does your answer compare with that in par a? Did you expect to get the same answer in both cases? Explain on physical grounds why the two answers differ
Answers
Answer:
2000Hz and 1500Hz
Explanation:
Using
a) f = f0((c+vr)/(c+vs))
=>>> f0((c)/(c-0.5c))
=>>>1000/0.5 = 2000Hz
b) f = f0((c+vr)/(c+vs))
=>>>f0((c+0.5c)/(c))
=>>>>1000 x 1.5 = 1500Hz
Here we have a problem referring to the Doppler effect, the solutions are:
a) f = 2.0 kHzb) f = 1.5 kHzThe Doppler effect:
The Doppler effect is an effect that explains how the perception of waves changes as the source moves or as the listener moves.
The formula, for sound, is:
[tex]f = \frac{v + v_0}{v - v_1}*f_0[/tex]
where:
v = velocity of the wave = 340 mf = perceived frequencyf₀ = actual frequency = 1.00kHzv₀ = velocity of the observerv₁ = velocity of the source.a) First we have that the source moves towards a stationary listener, then we have:
[tex]f = \frac{v }{v - v/2}*1.0 kHz\\\\f = \frac{v }{v/2}*1.0 kHz = 2.0 kHz[/tex]
b) in this case, the listener moves towards the source, so we have:
[tex]f = \frac{v + v/2 }{v }*1.0 kHz\\\\f = \frac{ (3/2)*v }{v}*1.0 kHz = 1.5 kHz[/tex]
So in this case the perceived frequency is smaller than in the point a.
This is because the waves will move at a fixed rate in air, in one case, the successive waves are emitted from different points in space (each time closer to the listener) while in the other case the waves are emitted from a fixed point, and the listener moves towards them, thus feels that the waves move faster.
If you want to learn more about the Doppler effect, you can read:
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Circle the larger unit:
1.millimeter, centimeter
2. kilogram, megagram
3. microsecond, millisecond
4.dL, mL
5.mg, kg
6.Mm, mm
7.s, cs
8.m, Mm
9.μ s, Ks
Answers
2. Kilogram
3. Millisecond
4. DL
5. Kg
6. Mm
7. S
8. Mm
9. Us
In each case, the larger unit is the one that represents a greater quantity or magnitude compared to the other unit. For example, a centimeter is larger than a millimeter because one centimeter is equal to 10 millimeters. Similarly, a megagram is larger than a kilogram as one megagram is equivalent to 1,000 kilograms. The pattern continues for each pair, where the larger unit represents a higher order of magnitude or a greater number of the smaller units.
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A spinning top spinning at 16rad/s takes 88.9s to come to a complete stop. Find the angular acceleration of the top.
Answers
Answer:
The angular acceleration of the top is 0.18 rad/s²
Explanation:
Given;
angular velocity of the top, ω = 16 rad/s
time it takes to come to a complete stop, t = 88.9s
The angular acceleration of the top, is calculated as;
[tex]\alpha = \frac{\omega}{t}[/tex]
α is the angular acceleration
ω is angular acceleration
t is the time
[tex]\alpha = \frac{\omega}{t}\\\\\alpha = \frac{16}{88.9}\\\\\alpha =0.18 \ rad/s^2[/tex]
Therefore, the angular acceleration of the top is 0.18 rad/s²
What is the frequency (in Hz) at which he bounces, given that his mass plus the mass of his equipment is 84.0 kg?
Answers
Complete question:
The length of nylon rope from which a mountain climber is suspended has an effective force constant of 1.40 ×10⁴ N/m.
What is the frequency (in Hz) at which he bounces, given that his mass plus the mass of his equipment is 84.0 kg?
Answer:
The frequency (in Hz) at which he bounce is 2.054 Hz
Explanation:
Given;
effective force constant, K = 1.40 ×10⁴ N/m.
The total mass = his mass plus the mass of his equipment, m = 84 kg
The frequency (in Hz) at which he bounce is given by;
[tex]f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}\\\\f = \frac{1}{2\pi} \sqrt{\frac{1.4*10^4}{84}}\\\\f = 2.054 \ Hz[/tex]
Therefore, the frequency (in Hz) at which he bounce is 2.054 Hz
If the brakes are applied and the speed of the car is reduced to 13 m/s in 17 s , determine the constant deceleration of the car.
Answers
Question: Initially, the car travels along a straight road with a speed of 35 m/s. If the brakes are applied and the speed of the car is reduced to 13 m/s in 17 s, determine the constant deceleration of the car.
Answer:
1.29 m/s²
Explanation:
From the question,
a = (v-u)/t............................ Equation 1
Where a = deceleration of the car, v = final velocity of the car, u = initial velocity of the car, t = time.
Given: v = 13 m/s, u = 35 m/s, t = 17 s.
a = (13-35)/17
a = -22/17
a = -1.29 m/s²
Hence the deceleration of the car is 1.29 m/s²
The tires of a car make 90 revolutions as the car reduces its speed uniformly from 88.0 km/hkm/h to 56.0 km/hkm/h. The tires have a diameter of 0.84 mm.
1. What was the angular acceleration of the tires?
2. If the car continues to decelerate at this rate, how much more time is required for it to stop?
3. If the car continues to decelerate at this rate, how far does it go? Find the total distance.
Answers
Answer:
1) α = 2.2 rad / s² , 2) t = 7.068 s , 3) in this interval s = 23.096 m
total distance s = 57.4 m
Explanation:
For this exercise we use the angular kinematic relations, before starting the problem we reduce all the magnitude to the SI system
v₀ = 88 km / h (1000 m / 1km) 1h / 3600s) = 24.44 m / s
v = 56.0 km / h = 15.55 m / s
θ = 90 rev (2pi rad / 1 rev) = 565,487 rad
d = 0.84 m
r = d / 2
r = 0.84 / 2
r = 0.42 m
1) ask for angular acceleration
w² = w₀² - 2 α Δθ
α = (w₀² -w²) / 2 Δθ
To find the angular velocities we use the acceleration between the linear and angular velocity
v = w r
w = v / r
w₀ = 24.44 / 0.42
w₀ = 58.20 rad / s
w = 15.55 / 0.42
w = 30.037 rad / s
we calculate
α = (58.20² - 30.037²) / (2 565.487)
α = 2.2 rad / s²
2) how much longer does it take to stop
w₂ = 15.55 rad / s
w = 0
w = w₂ - α t
t = (w₂ -0) / α
t = 15.55 / 2.2
t = 7.068 s
3) the distance that the car travels from the beginning of the movement, we can find it by looking for the number of revolutions until it stops and then using the relationship between the angular and linear variable
w² = w₀² - 2 α θ
at the end of the movement speed is zero
0 = w₀² - 2 α θ
θ = w₀² / 2 α
θ = 24.44² / (2 2.2)
θ = 135.80 rad
If the angles are measured in radians, we can apply the relation
θ = s / R
s = R ttea
s = 0.42 135
s = 57.4 m
this is the distance from when the movement starts
the distance for the final part of the movement is
w = 15.55 rad / s
θ = w² / 2 α
θ = 15.55 2 / (2 2.2)
θ = 54.99 rad
the distance in this interval is
s = 0.42 54.99
s = 23.096 m