[tex]\displaystyle W =\lim_{n\to\infty}{\sum_{i=0}^{n}{(678.16 - 36.26\;x_i)\cdot\dfrac{16}{n}}}[/tex].
ExplanationThe mass comes in three parts:
the mass of the rope,the mass of the water in the leaky bucket, andthe mass of the bucket.Both the mass of the rope [tex]m_\text{rope}[/tex] and the mass of the water in the bucket [tex]m_\text{water}[/tex] varies with the height [tex]x[/tex] of the bucket. Express the two masses as a function of [tex]x[/tex]:
[tex]m_\text{rope} = 0.7\;(16 - x)[/tex],The water in the bucket behaves like yet another rope of density [tex]48 \;\text{kg}/ 16 \;\text{m}= 3.0\;\text{kg}\cdot\text{m}^{-1}[/tex]. The mass of the water left in the bucket at height [tex]x[/tex] will be
[tex]m_\text{water} = 3.0\;(16 - x)[/tex].The mass of the bucket is [tex]10\;\text{kg}[/tex]. Combining the three:
[tex]m(x) = m_\text{rope}(x) + m_\text{water}(x) + m_\text{bucket} \\\phantom{m(x)} = 0.7\;(16-x) + 3.0\;(16 - x) + 10\\\phantom{m(x)} = 69.2 - 3.7\;x[/tex].Weight of the bucket at height [tex]x[/tex]:
[tex]F_\text{weight}(x) = m(x)\cdot g = 9.8\;(69.2 - 3.7\;x) = 678.16 - 36.26\;x[/tex].The bucket moves upward at a constant speed. As a result,
[tex]F(x) = W(x) = 678.16 - 36.26\;x[/tex].Express the work required as a definite integral:
[tex]\displaystyle W = \int_{0}^{16}{F(x) \cdot dx} = \int_{0}^{16}{(678.16 - 36.26\;x)\cdot dx}[/tex].Rewrite the definite integral as a Riemann Sum:
[tex]\displaystyle W = \int_{0}^{16}{(678.16 - 36.26\;x)\cdot dx} \\\phantom{W}= \lim_{n\to\infty}{\sum_{i=0}^{n}{(678.16 - 36.26\;x_i)\cdot\frac{16-0}{n}}}\\\phantom{W} = \lim_{n\to\infty}{\sum_{i=0}^{n}{(678.16 - 36.26\;x_i)\cdot\frac{16}{n}}}[/tex].The work done lifting a bucket of water draining at a constant rate can be calculated using the physics Work formula and approximating the varying force with a Riemann sum. The total work is the sum of the work done across several small intervals, calculated by multiplying the force required to lift the remaining water plus the bucket and the rope by the small altitude.
Explanation:The work done in lifting an object can be calculated using the formula Work = Force x Distance = (mass x gravity) x height. However, this situation is a bit more complex since the mass of both the bucket and the water it contains decrease continuously as the bucket is lifted.
We will approximate this varying force using a Riemann sum. We can imagine breaking up the 16 m into n small intervals. For each interval i from 0 to n-1, we calculate the force required to lift the remaining water plus the bucket and rope to a height xi*, and then multiply this by the small change in height Δx. This gives us the small amount of work done ΔW_i = (m(xi*)g)Δx, where m(xi*) is the mass of the system at height xi*.
The total work then is approximately the sum of all these small amounts of work, W ≈ Σ ΔW_i for i from 0 to n-1. The more intervals we use (the bigger n is), the better this approximation will be.
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What kind of waves do earthquakes produce
body and surface waves is the answer
A circuit has 3 resistors, all connected in parallel. Let R1 = 4.0 Ω, R2 = 3.0 Ω, and R3 = 6.0 Ω. What is the equivalent resistance of the circuit? Show all work and include units of measure.
Answer:
[tex]1.33\Omega[/tex]
Explanation:
The equivalent resistance of three resistors connected in parallel is given by:
[tex]\frac{1}{R_T} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}[/tex]
where in this problem we have
[tex]R_1 = 4.0\Omega[/tex]
[tex]R_2 = 3.0 \Omega[/tex]
[tex]R_3 = 6.0 \Omega[/tex]
Substituting into the equation, we find
[tex]\frac{1}{R_T} = \frac{1}{4.0\Omega}+\frac{1}{3.0\Omega}+\frac{1}{6.0\Omega}=0.75\Omega^{-1}[/tex]
And so, the equivalent resistance is
[tex]R_T=\frac{1}{0.75 \Omega^{-1}}=1.33\Omega[/tex]
A particle moves along the x axis. It is initially at the position 0.250 m, moving with velocity 0.050 m/s and acceleration -0.240 m/s2. Suppose it moves with constant acceleration for 3.70 s. (a) Find the position of the particle after this time. m (b) Find its velocity at the end of this time interval. m/s
(a) -1.208 m
The position of the particle at time t is given by
[tex]x(t) = x_0 + v_0 t + \frac{1}{2}at^2[/tex]
where:
[tex]x_0 = 0.250 m[/tex] is the initial position
[tex]v_0 = 0.050 m/s[/tex] is the initial velocity
[tex]a=-0.240 m/s^2[/tex] is the acceleration
Substituting into the equation t=3.70 s, we find the position after 3.70 seconds:
[tex]x(3.70 s) = 0.250 m + (0.050 m/s)(3.70 s) + \frac{1}{2}(-0.240 m/s^2)(3.70 s)^2=-1.208 m[/tex]
(b) -0.838 m/s
The velocity of the particle at time t is given by:
[tex]v(t) = v_0 + at[/tex]
where
[tex]v_0 = 0.050 m/s[/tex] is the initial velocity
[tex]a=-0.240 m/s^2[/tex] is the acceleration
Substituting t = 3.70 s, we find the velocity after 3.70 seconds:
[tex]v(3.70 s) = 0.050 m/s + (-0.240 m/s^2)(3.70 s)=-0.838 m/s[/tex]
Which process causes Earth’s surface to warm?
answer :the radiation of the Sun’s electromagnetic waves
The radiation of the sun's electromagnetic waves
Explanation;The energy that drives the climate system comes from the Sun. When the Sun's energy reaches the Earth it is partially absorbed in different parts of the climate system. The absorbed energy is converted back to heat, which causes the Earth to warm up and makes it habitable.Energy from the sun heats Earth's surface, warms the atmosphere, provides energy for photosynthesis, causes evaporation, drives the weather and water cycles, and powers the ocean currents.Answer:
the radiation
Explanation:
During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. A balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. Assume that the stretching of the hose obeys Hooke's law with a spring constant of 92.0 N/m. If the hose is stretched by 3.20 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length?
Answer:
294.4 N
Explanation:
Since the hose obeys Hooke's law, the force it exerts on the balloon in the pouch is given by:
[tex]F=kx[/tex]
where
k is the spring constant
x is the stretching
In this problem,
k = 92.0 N/m
x = 3.20 m
Therefore, the force exerted is
[tex]F=(92.0 N/m)(3.20 m)=294.4 N[/tex]
A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.50 × 10 4 1.50×104 rad/s to an angular speed of 3.35 × 10 4 3.35×104 rad/s. In the process, the bit turns through 2.02 × 10 4 2.02×104 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 6.90 × 10 4 6.90×104 rad/s, starting from rest?
Answer:
0.32 s
Explanation:
Initial angular speed: [tex]\omega_i = 1.50 \cdot 10^4 rad/s[/tex]
Final angular speed: [tex]\omega_f = 3.35\cdot 10^4 rad/s[/tex]
Angular rotation: [tex]\theta=2.02\cdot 10^4 rad[/tex]
The angular acceleration of the drill can be found by using the equation:
[tex]\omega_f^2 - \omega_i^2 = 2 \alpha \theta[/tex]
Re-arranging it, we find [tex]\alpha[/tex], the angular acceleration:
[tex]\alpha = \frac{\omega_f^2 - \omega_i^2}{2\theta}=\frac{(3.35\cdot 10^4 rad/s)^2-(1.50\cdot 10^4 rad/s)^2}{2(2.02\cdot 10^4 rad)}=22,209 rad/s^2[/tex]
Now we want to know the time t the drill takes to accelerate from
[tex]\omega_i =0[/tex]
to
[tex]\omega_f = 6.90\cdot 10^4 rad/s[/tex]
This can be found by using the equation
[tex]\omega_f = \omega_i + \alpha t[/tex]
where [tex]\alpha[/tex] is the angular acceleration we found previously. Solving for t,
[tex]t=\frac{\omega_f - \omega_i}{\alpha}=\frac{22,209 rad/s^2}{6.90\cdot 10^4 rad/s}=0.32 s[/tex]
12. An electric motor is plugged into a standard wall socket and is run- ning at normal speed. Suddenly, some dirt prevents the shaft of the mo- tor from turning quite so rapidly. What happens to the back emf of the motor, and what happens to the current that the motor draws from the wall socket? (a) The back emf increases, and the current drawn from the socket decreases. (b) The back emf increases, and the current drawn from the socket increases. (c) The back emf decreases, and the current drawn from the socket decreases. (d) The back emf decreases, and the current drawn from the socket increases.
the answer would be B. the back emf increases, and the current drawn from the socket increases
more current is needed to make the motor move, like when you try to self crank a motor and the back wires are touching its harder to crank. and the emf increases since more current is being drawn in, strengthening the emf or increasing the emf
Using our understanding of orbits, which orbits (near or far) are moving more slowly?
near
far
The closer the planet is to the sun's gravitational pull, the planet will move faster because it takes less time to orbit the sun. The planets that are farther away have less gravitational pull, which means they will move slower and take more time to orbit the sun.
Using our understanding of orbits, objects in lower, near-in orbits move slower than objects in higher, far-out orbits.
Here's a set of examples:
International Space Station ...
Orbital height -- 254 miles
Speed in Orbit -- 76 mi/sec
Geostationary TV satellite ...
Orbital height -- 22,200 miles
Speed in orbit -- about 1.9 mi/sec
Moon ...
Orbital height -- 238,000 miles
Speed in orbit -- about 0.6 mi/sec
Which of the following statements are true for images formed by thin lenses?Check all that apply.A diverging lens always produces a virtual image of an object placed in front of it.A diverging lens always produces an upright image of an object placed in front of it.A converging lens always produces an inverted image of an object placed in front of it.A converging lens always produces an image that is larger than the object.A diverging lens always produces an image that is larger than the object.A converging lens always produces a real image of an object placed in front of it.
Answer:b
Explanation:
A diverging lens always produces a virtual and upright image of an object placed in front of it.
To determine the correct statement among all the options, we need to know about the properties of the image formed by converging and diverging lens.
What are the properties of images formed by converging lens?The properties of image formed by converging lens depends on the position of the object.The image for a far away object is real, inverted, diminished and is produced opposite side of the lens.As the object approaches the lens, the image remains real and inverted, but eventually becomes magnified.When the object passes the focal point of the lens, the image becomes virtual, erect, magnified and produced on the same side of the lens.What are the properties of image formed by diverging lens?The image formed by a diverging lens is always erect (upright), virtual and diminished.
Thus we can conclude the statements (a) and (b) are correct.
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If a car is moving to the left with constantvelocity, one can conclude thatthere mustbe no forces applied to the car.the netforce applied to the car is directed to the left.the netforce applied to the car is zero.there isexactly one force applied to the car.
Answer:
the net force applied to the car is zero.
Explanation:
According to Newton's second law, the acceleration of an object (a) is directly proportional to the net force applied (F):
[tex]a=\frac{F}{m}[/tex]
where m is the object's mass.
In this problem, the car is moving with constant velocity: this means that the acceleration is zero, a = 0. Therefore, according to the previous equation, the net force must also be zero: F = 0. So, the correct answer is
the net force applied to the car is zero.
Color depends on what characteristic of light?
Answer:
On the wavelength
Explanation:
Visible light is just a small portion of the electromagnetic spectrum, which classifies all the electromagnetic waves from shortest wavelength (gamma rays) to longest wavelength (radio waves).
Visible light refers to the part of the spectrum which has wavelength between 380 nm and 750 nm. These are the only electromagnetic wave that our eyes can see, and depending on their wavelength, they appear as a different color. In particular, each color corresponds to a different range of wavelengths:
Violet: 380-450 nm
Blue: 450-495 nm
Green: 495-570 nm
Yellow: 570-590 nm
Orange: 590-620 nm
Red: 620-750 nm
Color perception relies on the wavelength of light, as each wavelength corresponds to a particular color. A white object reflects all visible wavelengths, while a black object absorbs them all. The perceived color of an object depends on which wavelengths its atoms absorb and reflect.
Explanation:The color of an object or light depends greatly on the characteristic of light known as wavelength. Wavelength defines the energy of a photon in the visual spectrum, and each wavelength corresponds to a specific color.
Let's take a white object as an example: when it is illuminated by white light, which comprises all visible wavelengths, it appears white as well. This is because it reflects all visible wavelengths equally. On the contrary, a black object absorbs all light and doesn't reflect any, which is why it appears black to our eyes.
Also characteristic is how the atoms of a material interact with different light wavelengths. For instance, a simple red object like a tomato absorbs all wavelengths except red - the energy levels in its atoms correspond to all visible photons except red, which is reflected back to our eyes leading to its color perception.
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Which best describes what happens when light traveling through air enters water at an angle? It moves along straight lines in air and changes direction when it enters water. It moves in a curve in air and moves in straight lines when it enters water. It moves along straight lines in air and continues along the same lines when it enters water. It moves in a curve in air and continues moving in the same curve when it enters water.
Answer:
It moves along straight lines in air and changes direction when it enters water.
Explanation:
When light travels from one medium to another, it undergoes a phenomenon called refraction: the ray of light changes speed and also direction, but it continues to move in a straight line.
There is a relationship between the direction of the incident ray and the direction of the refracted ray: (Snell's Law)
[tex]n_1 sin \theta_1 = n_2 sin \theta_2[/tex]
where
n1 is the index of refraction of the first medium
[tex]\theta_1[/tex] is the angle that the incident ray forms with the normal to the surface
n2 is the index of refraction of the second medium
[tex]\theta_2[/tex] is the angle that the refracted ray forms with the normal to the surface
Answer:
A: It moves along straight lines in air and changes direction when it enters water.
Explanation:
Physics question, please help?
A cue ball with mass 170 g hits the stationary number 8 ball, which has mass 160 g. The cue ball and the 8 ball move with a speed of 0.2 m/s and 0.3 m/s respectively after the collision. What was the speed of the cue ball before the collision?
A) 0.2502 m/s
B) 0.4823 m/s
C) 0.5008 m/s
D) 0.5319 m/s
0.4823 m/s
The initial velocity u1 of the ball=0
From the law of conservation of linear momentum.
m1u1+m2u2=m1v1+m2v2
(160×0)+(170×u1)=(160×0.3)+(170×0.2)
u1=0.4823m/s
The speed of the cue ball before the collision is approximately 0.5319 m/s.
Explanation:Before the collision, we can use conservation of momentum to find the speed of the cue ball. In an isolated system, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the initial velocity of the cue ball as v1 and the initial velocity of the 8 ball as v2. The momentum before the collision is given by:
(mass of cue ball) x (velocity of cue ball) + (mass of 8 ball) x (velocity of 8 ball)
The total momentum after the collision is:
(mass of cue ball + mass of 8 ball) x (velocity of cue ball + velocity of 8 ball)
Using the given values, we know that the cue ball and 8 ball move with speeds of 0.2 m/s and 0.3 m/s, respectively, after the collision. Plugging these values into the equations, we can solve for v1 to find the speed of the cue ball before the collision.
The speed of the cue ball before the collision is approximately 0.5319 m/s.
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An object is 16.0cm to the left of a lens. The lens forms an image 36.0cm to the right of the lens.Part AWhat is the focal length of the lens?Part BIs the lens converging or diverging?Part CIf the object is 8.00mm tall, how tall is the image?Part DIs it erect or inverted?
Final answer:
Using the thin-lens equation, the focal length of the lens is found to be -28.8 cm, indicating that the lens is a diverging lens. The magnification of the lens is -2.25, and because the initial height of the object is 8.00 mm, the image height is -18.0 mm, indicating that the image is inverted.
Explanation:
To find the focal length of the lens, we use the thin-lens equation:
1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. Given that do = -16.0 cm (negative because the object is to the left of the lens) and di = 36.0 cm (positive because the image is to the right of the lens), we can solve for f:
1/f = -1/16.0 cm + 1/36.0 cm
1/f = (-2.25 + 1)/36.0 cm
1/f = -1.25/36.0 cm
1/f = -0.0347 cm-1
Therefore, f = -28.8 cm.
The negative value of the focal length indicates that the lens is a diverging lens.
For Part C, the magnification (m) is given by the ratio of the image distance to the object distance: m = di/do = 36.0 cm / (-16.0 cm) = -2.25. Since the object height is 8.00 mm, the image height is magnified by 2.25 times, making the image height -18.0 mm (negative indicates an inverted image).
Finally, because the image height came out negative, we conclude the image is inverted.
Final answer:
The lens has a focal length of -28.8 cm, indicating it is a diverging lens. The image formed is erect and 18.00 mm tall, which is 2.25 times the height of the 8.00 mm object.
Explanation:
To find the focal length of the lens, we use the lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. Given that do = -16.0 cm (negative because the object is on the same side as the light is coming from) and di = 36.0 cm (positive because the image is formed on the opposite side of the light source), we can calculate the focal length as follows:
1/f = -1/16.0 cm + 1/36.0 cm = -0.0625 cm-1 + 0.0278 cm-1 = -0.0347 cm-1
Thus, f = -1/0.0347 cm-1 ≈ -28.8 cm.
Since the focal length is negative, the lens is a diverging lens.
For part C, the magnification m can be found using the equation m = -di/do. Substituting the given distances, m = -36.0 cm / (-16.0 cm) = 2.25. So, the image is 2.25 times the height of the object. If the object is 8.00 mm tall, the image will be 8.00 mm * 2.25 = 18.00 mm tall.
Since the magnification is positive, the image is erect.
I traveled 3.8 miles in 12 minutes. Calculate my average velocity in miles per hour. 2) A sprinter increased his/her speed from 18 mph to 28 mph over 3.5 seconds. Calculate his/her acceleration.
1) Average velocity: 19 mi/h
The average velocity is given by:
[tex]v=\frac{d}{t}[/tex]
where
d is the displacement
t is the time taken
In this problem,
d = 3.8 mi is the displacement
[tex]t=12 min \cdot \frac{1}{60 min/h}=0.2 h[/tex] is the time taken
Substituting,
[tex]v=\frac{3.8 mi}{0.2 h}=19 mi/h[/tex]
Note that this is actually the average speed, not the average velocity, since there is no information about the direction of the motion.
2) [tex]10,309 mi/h^2[/tex]
The acceleration is given by
[tex]a=\frac{v-u}{t}[/tex]
where we have
v = 28 mph is the final velocity
u = 18 mph is the initial velocity
t = 3.5 s is the time taken
Conerting the time from seconds to hours,
[tex]t=3.5 s \cdot \frac{1}{3600 s/h}=9.7\cdot 10^{-4} h[/tex]
So the acceleration is
[tex]a=\frac{28 mph-18 mph}{9.7\cdot 10^{-4} h}=10,309 mi/h^2[/tex]
A bike is pushed with a net force of 2.5 N, and it accelerates 0.5 m/s2. If you pushed the bike with twice that amount of net force, the acceleration would be __________.
0.25 m/s2 because net force and acceleration have an inverse relationship.
0.5 m/s2 because the net force and acceleration do not affect each other.
More than 0.5 m/s2, but less than 1 m/s2 because net force and acceleration do not have a proportional relationship.
1.0 m/s2 because net force and acceleration have a proportional relationship.
1.0m/s2 because net force and acceleration have a proprtional relationship
Study the scenario.
As a spacecraft moves beyond Pluto, its thrusters are turned on for a short time to boost its speed to approximately 32,500 mi/h. The thrusters are then turned off.
If no other forces ever act on the spacecraft what will it do?
it will continue moving in the same direction, but it will speed up because there are no forces to slow it down
it will continue moving at 32,500 mi/h the same direction because forces are not required for an object to continue its motion
it will stop immediately because a force is needed constantly for it to move at all
it will continue moving in the same direction, but it will gradually slow down because a force is needed to maintain its speed.
If no other forces act on the object, according to Newton’s first law, the spacecraft will continue moving at a constant velocity, assuming that a planet or something with large mass doesn’t cross its path. Forces are not required to continue the motion of an object on a frictionless plane at a constant rate.
If no other forces ever act on the spacecraft, it will continue moving at 32,500 mi/h in the same direction, because forces are not required for an object to continue its motion.
The spacecraft will eventually curve away from a straight line, and its speed will change, as it comes within the gravitational influence of one or more of the objects out there in the Kuiper Belt and the Oort Cloud.
What is the speed of sound in air at 42.0 ºC?
= 356.2 m/s
Explanation;The speed of the wave is dependent on temperature of the medium;
The equation to use will be;
Speed = 331 + 0.6 T ; where T is the temperature in degrees Celsius.
T = 42 °C
Therefore;
speed = 331 + 0.6 × 42
= 356.2 m/s
Who first proposed the existence of antimatter
The modern theory of antimatter began in 1928, with a paper by Paul Dirac.
The food we eat has ______________ potential energy because as our body digests it, it provides us with energy for basic metabolism.
A. gravitational
b. magnetic
c. chemical
Hi, the answer is C. (chemical potential energy)
A switch that connects a battery to a 10 µF capacitor is closed.Several seconds later you find that the capacitor plates are charged to 30 µC.What is the emf of the battery?
Answer:
3 V
Explanation:
The relationship between capacity (C), charge stored (Q) and potential difference across a capacitor (V) is
[tex]C=\frac{Q}{V}[/tex] (1)
The problem asks us to find the emf of the battery several seconds after the switch has been closed: this means that the capacitor had enough time to fully charge, so the potential difference across the capacitor (V) is equal to the emf of the battery.
Since we have:
[tex]C=10 \mu F=10\cdot 10^{-6} F[/tex]
[tex]Q=30 \mu C=30\cdot 10^{-6} C[/tex]
We can solve the equation for V, and we find
[tex]V=\frac{Q}{C}=\frac{30 \cdot 10^{-6}C}{10 \cdot 10^{-6} F}=3 V[/tex]
A switch that connects a battery to a 10 µF capacitor is closed for several seconds and the capacitor plates are charged to 30 µC then the voltage across the capacitor will be 3 V.
The emf of the battery will be equal to the voltage across the capacitor which is 3 V.
How do you calculate the emf of the battery?
The EMF or electromotive force can be defined as the energy supplied by a battery or a cell per coulomb (Q) of charge passing through it. The magnitude of emf is equal to V (potential difference) across the cell terminals when there is no current flowing through the circuit.
Hence the emf of the battery will be equal to the voltage across the capacitor.
The voltage across a capacitor can be calculated as given below.
[tex]V = \dfrac {Q}{C}[/tex]
Where Q is the amount of charge stored on each plate and C is the capacitance.
[tex]V = \dfrac { 30 }{10}[/tex]
[tex]V = 3\;\rm V[/tex]
Hence we can conclude that the emf of the battery is 3 V.
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Part A - Whale communication.
Blue whales apparently communicate with each other using sound of frequency 17.0Hz , which can be heard nearly 1000km away in the ocean. What is the wavelength of such a sound in seawater, where the speed of sound is 1521m/s ?
?1 =
m
Part B - Dolphin clicks.
One type of sound that dolphins emit is a sharp click of wavelength 1.50cm in the ocean. What is the frequency of such clicks?
f =
kHz
Part C - Dog whistles.
One brand of dog whistles claims a frequency of 26.0kHz for its product. What is the wavelength of this sound?
? =
cm
Part D - Bats.
While bats emit a wide variety of sounds, one type emits pulses of sound having a frequency between 39.0kHz and 78.0kHz . What is the range of wavelengths of this sound?
?min,?max =
mm
Part E - Sonograms.
Ultrasound is used to view the interior of the body, much as x rays are utilized. For sharp imagery, the wavelength of the sound should be around one-fourth (or less) the size of the objects to be viewed. Approximately what frequency of sound is needed to produce a clear image of a tumor that is 1.00mm across if the speed of sound in the tissue is 1550m/s ?
f =
MHz
A) 89.5 m
The wavelength of a wave is given by:
[tex]\lambda=\frac{v}{f}[/tex]
where v is the wave speed and f the frequency. For the sound emitted by the whales,
[tex]f=17.0 Hz[/tex]
[tex]v=1521 m/s[/tex]
Therefore, the wavelength is
[tex]\lambda=\frac{1521 m/s}{17.0 Hz}=89.5 m[/tex]
B) 101.4 kHz
The speed of the sound emitted by the dolphins in the water is still
v = 1521 m/s
While the wavelength is
[tex]\lambda=1.50 cm=0.015 m[/tex]
So, re-arranging the previous equation we find the frequency:
[tex]f=\frac{v}{\lambda}=\frac{1521 m/s}{0.015 m}=101,400 Hz=101.4 kHz[/tex]
C) 1.31 cm
The frequency of the dog whistle is
f = 26.0 kHz = 26,000 Hz
While the speed of sound in air is
v = 340 m/s
Therefore, the wavelength is
[tex]\lambda=\frac{v}{f}=\frac{340 m/s}{26,000 Hz}=0.0131 m=1.31 cm[/tex]
D) 4.4 - 8.7 mm
The speed of the sound waves emitted by the bats in air is
v = 340 m/s
The minimum frequency is
f = 39.0 kHz = 39,000 Hz
So the corresponding wavelength is
[tex]\lambda=\frac{v}{f}=\frac{340 m/s}{39,000 Hz}=0.0087 m=8.7 mm[/tex]
The maximum frequency is
f = 78.0 kHz = 78,000 Hz
So the corresponding wavelength is
[tex]\lambda=\frac{v}{f}=\frac{340 m/s}{78,000 Hz}=0.0044 m=4.4 mm[/tex]
E) 6.2 MHz
The wavelength of the sound must be 1/4 the size of the tumor, so
[tex]\lambda=\frac{1}{4}(1.00 mm)=0.25 mm=2.5\cdot 10^{-4}m[/tex]
while the speed of sound across the tissue is
v = 1550 m/s
So the frequency must be
[tex]f=\frac{v}{\lambda}=\frac{1550 m/s}{2.5\cdot 10^{-4} m}=6.2\cdot 10^6 Hz=6.2 MHz[/tex]
Which disease is caused when the body tissues cannot get enough oxygen?
I believe it's hypoxia for your tissues and hypoxemia for your blood.
Answer:
Anemia
Explanation:
Edge 2021
Compared to a main-sequence star with a short lifetime, a main-sequence star with a long lifetime is __________.
The answer would be less luminous, cooler, smaller, and less massive.
A main-sequence star with a long lifetime is typically characterized by lower mass, cooler temperature and less luminosity, compared to a star with a short lifetime. They consume their nuclear fuel at a slower rate, allowing them to have a longer lifespan in the main-sequence phase, such as red dwarfs.
Explanation:Compared to a main-sequence star with a short lifetime, a main-sequence star with a long lifetime is typically less massive, cooler, and emits less light. The lifetime of a star is directly related to its mass. Stars with larger mass burn through their nuclear fuel at a quicker rate, leading to a shorter main-sequence lifetime. Conversely, stars with smaller mass, such as red dwarfs, consume their fuel more slowly and thus have longer main-sequence lifetimes.
For example, the Sun, a moderate mass star, is expected to remain in the main-sequence stage for about 10 billion (10¹0) years. This is much longer than a more massive star, like a blue giant, which might only last a few million years in the main sequence stage.
However, less massive stars, commonly known as red dwarfs, with masses less than half that of the Sun, can have main sequence lifetimes that stretch into the trillions of years, due to their efficient use of nuclear fuel.
Learn more about Main-Sequence Stars here:https://brainly.com/question/1966525
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In order to protect underground pipelines and storage tanks made of iron, the iron is made the cathode of a voltaic cell through a process called ___________________.sacrificial anodizationcathodic protectionrustinggalvanization
The answer would be that the process to protect the underground pipelines and storage tanks is cathodic protection.
About what is Rigel's surface temperature?
Answer:
it is bigger than, a higher temperature , and 11,000
Explanation:
Rigel is a star with a surface temperature of about 12,100 Kelvin, yielding a blue-white color due to its high surface temperature.
Explanation:The surface temperature of Rigel, a supergiant star, is approximately 12,100 Kelvin. This temperature contributes to Rigel's blue-white color, as higher surface temperatures in stars result in shorter wavelength light, which falls towards the blue end of the color spectrum.
Learn more about Rigel's surface temperature here:https://brainly.com/question/31797249
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The earth's crust is _____. thicker under the oceans than under the continents in motion because of convection currents in the mantle mostly made of iron and nickel made of one large piece called the crustal plate
In motion because of convection currents in the mantle.
How do we know galaxies are moving away from us
Answer:
Because their light is red-shifted
Explanation:
Doppler effect is a phenomenon that occurs when the source of a wave is moving relative to an observed. In particular, two situations are possible:
- The wave source is moving towards the observer --> in this case, the frequency of the waves appear to be higher than the original one; as a consequence, the wavelength of the waves appears to be shorter
- The wave source is moving away from the observer --> in this case, the frequency of the waves appear to be lower than the original one; as a consequence, the wavelength of the waves appears to be longer
This phenomenon occurs also for light waves. In particular, the light coming from distance galaxies undergoes Doppler effect as well, since those galaxies are moving relative to us. We have again two possible situations:
- The galaxy is moving towards the Earth --> in this case, the frequency of the light appear to be higher than the original one; as a consequence, the wavelength of the light emitted appears shorter (so, it shifts towards the blue color --> this is known as blue-shift)
- The galaxy is moving away from the Earth --> in this case, the frequency of the light emitted appears to be lower than the original one; as a consequence, the wavelength of the light appears to be longer (so, it shifts towards the red color --> this is known as red-shift)
Since the Universe is expanding, almost all galaxies are moving away from us: therefore, we notice a red-shift for the light coming from nearly all of them, and this is how we know they are moving away from us.
Pedro is planning to model how changes in weather affect evaporation from lakes. For his second experiment, he wants to test how winds affect the evaporation rate. He places one beaker with 300 mL of water in an area away from any fans, and he places another beaker with 300 mL of water near a small fan.
What is the dependent variable in Pedro's experiment?
A. Volume of water
B. Evaporation rate
C. Temperature
D. Movement of air
Most binary systems with an invisible companion contain a large, bright star and a small, dim star hidden by the light of its larger companion. However, in some binary systems, the unseen companion may be a black hole instead of a small star. One of the most likely black hole candidates in a binary system is an object called Cygnus X-1. If you were an astronomer trying to prove that Cygnus X-1 is a black hole, which of the following observations would provide evidence in support of your claim?CHECK ALL THAT APPLYA. Cygnus X-1 has a mass one-tenth that of the Sun.B. Cygnus X-1 produces a large amount of X-ray emissions.C. Cygnus X-1 produces no X-ray emissions.D. Cygnus X-1 has a diameter less than 300 kilometers.E. Cygnus X-1 has a mass of 10 solar masses.F. Cygnus X-1 has a diameter much greater than 300 kilometers.
Answer:
Brain signals are converted