Answer:
The answer is C sometimes point in the same direction, and other times point in opposite to each other.
Explanation:
When you throw a ball straight up velocity direction head up to up side but the acceleration points opposite direction due to gravitation of earth. Gr aviation slows down the ball when it goes up, when it reaches the summit and starts to fall down both velocity and acceleration points the same way. The ball speeds up and drops down.
The velocity and acceleration of a ball thrown straight up sometimes point in the same direction and sometimes in opposite directions. On the way up, they are opposite, but when the ball peaks and begins falling, they align in the same direction (downward). Therefore, the correct answer is that they sometimes point in the same direction and other times in opposite directions.
Explanation:When you throw a ball straight up, it follows a parabolic trajectory due to the influence of gravity. Let's examine the ball's velocity and acceleration throughout its motion:
The ball's velocity is initially positive as it travels upwards after being thrown. When the ball reaches its highest point, its velocity becomes zero as it changes direction.From the moment the ball is released until it hits the ground, the acceleration due to gravity is a constant negative value, directed downward toward the center of the Earth.On the way up, the direction of the ball's velocity (upward) and the direction of acceleration (downward) are opposite. When the ball reaches its peak and starts to fall back down, the velocity (now downward) and the constant acceleration due to gravity (also downward) will be in the same direction.Therefore, during the motion of the ball, the acceleration does not always point in the same direction as the ball's motion. Instead, the direction of velocity and acceleration are opposite on the ascent and the same on the descent. Hence, our answer to the question is that the velocity and acceleration sometimes point in the same direction, and other times point in opposite to each other.
How well does the infographic ""Plastics in the Ocean"" present a solution to the problem it describes?
Explanation:
The infographic lacks a possible solution to the issue, but it does explain where plastics emerge from, how they get into the marine, what they will do to marine wildlife, and how they will be removed to eliminate ocean plastic waste.
According to estimates reported in 2015 in the journal Science, between 4.8 million and 12.7 million tons of plastic enter the ocean every year. As large, identifiable items or as micro plastics, plastic can enter the ocean-pieces of less than five millimeters in length.
How did the theory of plate tectonics come to be a theory?
Explanation:
Plate tectonics is the idea that the earth's outer solid crust (the lithosphere) is fragmented into a few dozen "plates" that pass relative to each other across the earth's surface, like ice slabs on a lake.
A scientist named Alfred Wegener in 1915 proposed that the continents rammed through ocean basin crust, which would clarify why the shapes of many coastlines (such as South America and Africa) seem to match together like a puzzle.
[Please help fast! Offering 100 points if it works!}
The diagram below shows four planets and their distances from the sun.
Light from the sun reaches Earth in 8.3 minutes. In how many minutes does light from the sun reach Mars?
12.62
13.34
15.85
16.60
Answer:
d=1.49×1011m
Explanation:
Velocity is defined as the rate of travel, and can be found using the distance formula.
velocity=distancetime
Rearranging this formula we can solve for distance given velocity and time of travel.
d=vt
We are given velocity and time, and so can solve for distance, but if we plug in the values given;
d=(3.00×108m/s)(8.3minutes)
We can see that the units do not match up. Since seconds are the SI unit for time, we will need to convert 8.3 minutes to seconds.
t=(8.3minutes)(60seconds/minute)=(498s)
Now our units work out and we can solve for distance.
= 15.85
(8.3 min)/(1 AU) = (T)/(1.52 AU)
(8.3 min)x(1.52 AU) = (T x 1 AU)
T = (8.3 min x 1.52 AU) / (1 AU)
T = 12.62 minutes
Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. (b) The skater with arms extended is approximated by a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.
Answer:
a) I = 0.363 kg*[tex]m^{2}[/tex]
b) [tex]I_{T}[/tex] = 0.82385 kg*[tex]m^{2}[/tex]
Explanation:
a) If we approximate the skater how a cylinder his moment of inertia is:
I = [tex]\frac{mr^{2} }{2}[/tex]
I = [tex]\frac{(60)(0.110)^{2} }{2}[/tex]
I = 0.363 kg*[tex]m^{2}[/tex]
b) If the skater has his arms extended then:
[tex]I_{T} = I_{B} + I_{A}[/tex]
where [tex]I_{B}[/tex]: Body’s moment of inertia
[tex]I_{A}[/tex]: Moment of inertia of the arms
[tex]I_{B}[/tex] = [tex]\frac{mr^{2} }{2}[/tex]
[tex]I_{B}[/tex] = [tex]\frac{(52.5)(0.110)^{2} }{2}[/tex] = 0.3176 kg*[tex]m^{2}[/tex]
[tex]I_{A}[/tex] = 2 * [tex]\frac{mL^{2} }{12}[/tex]
[tex]I_{A}[/tex] = 2 * [tex]\frac{(3.75)(0.9)^{2} }{12}[/tex] = 0.50625 kg*[tex]m^{2}[/tex]
[tex]I_{T}[/tex] = 0.3176 + 0.50625 = 0.82385 kg*[tex]m^{2}[/tex]
The moment of inertia for a skater can be calculated using the mass and radius in the formula for the moment of inertia of a cylinder. If the skater extends their arms, the moment of inertia increases, and this is calculated by adding the moment of inertia of the skater to the moments of inertia of the arms.
Explanation:The moment of inertia of a body is a measure of its resistance to rotational motion. It depends on the mass and how that mass is distributed relative to the axis of rotation. In the case of the skater (approximated as a cylinder), you calculate this using the formula for the moment of inertia of a cylinder, which is I=0.5MR², where M is the mass and R is the radius.
(a) For the skater without extended arms, substitute the given mass (60 kg) and radius (0.11 m) into the formula to get: I = 0.5 * 60 kg * (0.11 m)² = 0.363 kg-m².
(b) For the skater with extended arms, first, calculate the skater's body moment of inertia as before, but now with 52.5 kg mass. Secondly, calculate the moment of inertia of each arm (approximated as a rod rotating about one end) with the formula I=1/3mL², where m is the mass of an arm and L is the length. Add those values to get the total moment of inertia.
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Which of the following increases atmospheric loss by thermal escape? A.increasing the mass of the gas particles B.increasing the temperature of the atmosphere C.increasing the escape velocity of the planet D.all of the above
Answer:
B. increasing the temperature of the atmosphere
Explanation:
Generally, atmospheric loss can be defined as the loss of the gases in the atmosphere to outer space. This process usually occur through either thermal escape or non-thermal escape. Atmospheric loss of gases to outer space by thermal escape occurs when the molecular velocity due to thermal energy is considerably high. One of the factors that can lead to increase in thermal energy and ultimately increase in atmospheric loss is increase in the temperature of the atmosphere. Therefore, the correct answer is option B.
A spherical object (with non-uniform density) of mass 16 kg and radius 0.22 m rolls along a horizontal surface at a constant linear speed without slipping. The moment of inertia of the object about a diameter is 0.59 M R2 . The object’s rotational kinetic energy about its own center is what fraction of the object’s total kinetic energy
Final answer:
The question pertains to the rotational kinetic energy of a rolling spherical object with non-uniform density and how it compares to the total kinetic energy using its moment of inertia.
Explanation:
The student is asking about the rotational kinetic energy of a spherical object with non-uniform density in comparison to its total kinetic energy. The given moment of inertia for the object is 0.59 M R2, where M is the mass, and R is the radius of the sphere. Using the formula for rotational kinetic energy, Krot = (1/2) I ω2, and the formula for translational kinetic energy, Ktrans = (1/2) m v2, we can find the energy components. However, because the spherical object rolls without slipping, there is a relationship between linear velocity (v) and angular velocity (ω) which is v = ωR. This allows us to compare the rotational kinetic energy to the total kinetic energy.
Electrolytes are considered ________ when placed in a solution and allow for adequate conduction of ________ charges.
Answer:
Electrolytes are considered ions when placed in a solution and allow for adequate conduction of particle charges.
Explanation:
Electrolytes are substances that, when are dissolved in solution, separates into electrical positive charges (cations) and electrical negative charges (anions) which are known as ions.
These ions have an adequate capacity to conduct particle charges and, therefore electricity.
Sodium, calcium, phosphate and potassium, are examples of electrolytes.
Hence, the correct answer is:
Electrolytes are considered ions when placed in a solution and allow for adequate conduction of particle charges.
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American eels (Anguilla rostrata) are freshwater fish with long, slender bodies that we can treat as a uniform cylinder 1.0 m long and 10 cm in diameter. An eel compensates for its small jaw and teeth by holding onto prey with its mouth and then rapidly spinning its body around its long axis to tear off a piece of esh. Eels have been recorded to spin at up to 14 rev/s when feeding in this way. Although this feeding method is energetically costly, it allows the eel to feed on larger prey than it otherwise could.An eel researcher uses the slow-motion feature on her phone's camera to shoot a video of an eel spinning at its maximum rate. The camera records at 120 frames per second. Through what angle does the eel rotate from one frame to the next?A. 1° B. 10° C. 22° D. 42°
Answer:
option D
Explanation:
given,
uniform length of cylinder = 1 m
diameter of the cylinder = 10 cm = 0.1 m
Eels have been recorded to spin = 14 rev/s
camera records at = 120 frames per second
time = [tex]\dfrac{1}{120}\ s/frame[/tex]
angle at which eel rotate = ?
ω = 14 rev/s
ω = 14 x 2 π rad/s
ω = 28 π rad/s
angle at which eel rotate
θ = ω t
θ = [tex]28\pi\times \dfrac{1}{120}[/tex]
θ = 0.733 rad
θ =[tex]0.733 \times \dfrac{180^0}{2\pi}[/tex]
θ =[tex]42^0[/tex]
Hence, the correct answer is option D
The angle of rotation is the angle at which the object is rotate about the fixed point.
The angle at which the eel rotates from one frame to next frame is 42 degree.
Given that, we can treat the eel as a uniform cylinder.
So, uniform length of cylinder = 1 [tex]\rm m[/tex] and diameter of the cylinder = 10 [tex]\rm cm[/tex] = 0.1 [tex]\rm m[/tex]. Eels have been recorded to spin at up to 14 rev/s when feeding in this way. The camera records at 120 frames per second.
Time taken by the camera to record one frame is [tex]t\;=\; \dfrac {1} {120} \;\rm s/\rm frame[/tex]
Revolution done by eel in radian per second is 14.
Angular Velocity is [tex]\omega\;=\; 14\;\times\;2\pi\;\times\;0.1\;\rm rad/s[/tex].
The angle of rotation can be calculated by the formula given below.
Angle of rotation [tex]\theta=\omega\;\times\;t[/tex].
Substituting the values in the above formula, the angle of rotation is,
[tex]\theta\;=\;14\;\times\;2\;\times\;3.14\;\times\;0.1\;\times\;\dfrac {1}{120}\;\rm rad[/tex]
[tex]\theta=0.0733\;\rm rad[/tex]
[tex]\theta=0.0733\;\times\;\dfrac {360^\circ}{2\pi}[/tex]
[tex]\theta=41.5^\circ[/tex] or [tex]42^\circ[/tex].
The angle at which the eel rotates from one frame to next frame is 42 degree.
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A segment of length 1 is drawn from the origin at an angle of 30∘30∘. What are the coordinates of segment’s other endpoint?
Answer:
Explanation:
Given
Length of segment is [tex]L=1 unit[/tex]
inclination of segment [tex]\theta =30^{\circ}[/tex]
To calculate the coordinates of segment we need to resolve its component in x and y co-ordinates
such that in triangle OPQ
[tex]\sin \theta =\frac{y}{L}[/tex]
[tex]y=L\sin 30[/tex]
[tex]y=1\times \frac{1}{2}=0.5 unit[/tex]
[tex]\cos \theta =\frac{x}{L}[/tex]
[tex]x=L\cos \theta [/tex]
[tex]x=1\times \cos 30[/tex]
[tex]x=1\times \frac{\sqrt{3}}{2}[/tex]
[tex]x=\frac{\sqrt{3}}{2} units[/tex]
What is the displacement current in the capacitor if the potential difference across the capacitor is increasing at 500
Answer:
I = 1.21x10^-5 A
Explanation:
You are missing the first part of the problem. This is an example, but it will give you the idea of how to solve yours with your data.
The first part is like this:
A 4.0 cm diameter parallel plate capacitor has a 0.44 m m gap. What is the displacement current in the capacitor if the potential difference across the capacitor is increasing at 500,000 V/s?
Now with this, we can solve the problem.
In order to do this, we need to use the following expression:
q = CV (1)
Where:
C: Capacitance of a parellel capacitor (in Faraday)
q: charge of plate or capacitor (In coulombs)
V: voltage in Volts.
However, we need is the current, and we have data of potential difference, so, all we have to do is divide the expression between time so:
q/t = CV/t
And the current is q/t, thus:
I = C * V/t (2)
And finally, Capacitance C with two plates of area A separated by a distance d is:
C = Eo*A/d (3)
Where:
Eo = constant equals to 8.85x10^-12 F/m.
A = Area of the plate, in this case, πr²
d = gap of the capacitor.
Let's calculate first the Capacitance using equation (3):
C = 8.85x10^-12 * π * (0.04/2)² / 0.00046 = 2.42x10^-11 F
Now, it's time to use equation (2) and solve for I:
I = 2.42x10^-11 * 500,000
I = 1.21x10^-5 A
Simone created a chart to summarize the energy transformations that take place when energy from the wind is used to generate electricity. Which best completes the chart?
a) nuclear energy transformed to electrical energy
b) chemical energy transformed to electrical energy
c) radiant energy transformed to mechanical energy
d) kinetic energy transformed to mechanical energy
Answer:
d) kinetic energy transformed to mechanical energy
Explanation:
Wind energy comes from its movement, so kinetic energy
Em = K = ½ m v²2
This energy spins the mill aspadle that this movement of the rotor within a magnetic field creates electricity in accordance with Faraday's law.
Consequently, from the above we should make a graph of the wind speed (kinetic energy) according to the electricity produced
The correct answer is d
kinetic energy transformed to mechanical energy this best completes the chart. Hence option D is correct.
What is Kinetic Energy ?Kinetic energy is the energy associated with a motion of a body. When a body is in motion having mass m then it has kinetic energy. Kinetic energy is denoted by K or T. it is expressed in joules. Kinetic energy is given by,
K = 1/2 mv²
Hence an object having zero mass or zero velocity have zero kinetic energy.
In line with Faraday's law, when the mill asp rotates under the influence of this energy, electricity is generated.
In light of the foregoing, we should create a graph showing the wind speed (kinetic energy) in relation to the power generated.
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A 92.0-kg skydiver falls straight downward with an open parachute through a vertical height of 325 m. The skydiver's velocity remains constant. What is the work done by the nonconservative force of air resistance, which is the only nonconservative force acting?
A) +2.93 times 10^5 J
B) 0J
C) Answer is not obtainable, because insufficient information about the skydiver's speed is given.
D) -2.93 times 10^5 J
The work done by air resistance on a skydiver with a constant velocity is -2.93 × 10⁵ J, as the air resistance force is equal but opposite to the gravitational force, and work is calculated as force times distance in the direction of the force.
Explanation:The work done by a nonconservative force such as air resistance can be calculated as the product of the force and the distance over which it acts, in the direction of the force. Since the skydiver is falling with a constant velocity, the force of air resistance must be equal and opposite to the gravitational force acting on the skydiver, resulting in no net force and therefore no acceleration. The work done by air resistance is thus equal to the gravitational force times the distance fallen, with a negative sign because the force of air resistance acts in the opposite direction to the displacement.
First, we need to calculate the gravitational force acting on the skydiver:
F_gravity = mass × acceleration due to gravity
F_gravity = 92.0 kg × 9.8 m/s²
F_gravity = 901.6 N
Now, we can calculate the work done by air resistance:
Work = force × distance × cos(ϸ)
Since the angle (ϸ) between the force of air resistance and the direction of displacement is 180 degrees (opposite directions), cos(ϸ) is -1. Therefore:
Work = -901.6 N × 325 m × -1
Work = -2.93 × 10⁵ J
The correct answer is D) -2.93 times 10⁵ J, which means the work done by air resistance is negative because it acts in the direction opposite to the displacement.
A hammer taps on the end of a 4.00 m long metal bar at room temperature. A microphone at the the other end of the bar picks up two pulses of sound, one that travels through the metal and one that travels through air. The pulse traveling through the metal arrives 9ms earlier because sounds travels faster through solids than air. What is the speed of the sound in the metal? Speed of sound through air is 343 m/s at room temperature. Give your answer in units of m/s but do not include units,
Final answer:
The speed of sound in the metal is 444.44 m/s.
Explanation:
To determine the speed of sound in the metal, we can use the information given and the speed of sound in air. The pulse traveling through the metal arrives 9ms earlier than the pulse traveling through air. From this, we can calculate the time difference it takes for the pulses to travel through the length of the metal bar. The speed of sound in air is given as 343 m/s. We can use the formula: speed = distance/time. Rearranging the formula, we have: time = distance/speed. As the distance is given as 4.00 m and the time difference is given as 9 ms (0.009 s), we can calculate the speed of sound in the metal by dividing the distance by the time difference: speed = 4.00 m / 0.009 s = 444.44 m/s.
Two point sources, vibrating in phase, produce an interferencepattern in a ripple tank. If the frequency is increased by 20%, thenumber of nodal lines:
A) is increased by 20%
B) is increased by 40%
C) remains the same
D) is decreased by 20%
E) is decreased by 40%
Answer:
option A
Explanation:
given,
frequency is increased by 20%
we know,
[tex]\dfrac{x_n}{L}d = (n-\dfrac{1}{2})\times \lambda[/tex]...........(1)
where
x_n is the perpendicular distance between the point the interference pattern is obtained,
L is the distance between the center of the two point sources
and λ is the wavelength of light.
If the frequency is increased by 20%, then the number of nodal lines is increased by 20%.
From equation (1),we observe that the frequency is directly proportional to the number of nodal lines.
Hence, the correct answer is option A
The force of friction on a sliding object is 10 N. The applied force needed to maintain a constant velocity is
A) more than 10 N.
B) less than 10 N.
C) 10 N
Answer:C. 10N
Explanation:
The applied force needed to maintain a constant velocity is 10N. This is because the moving force acting on the body will always be equal to the frictional force if the velocity of the body is constant.
But note that this is not the case if the body ia accelerating. If the body is accelerating then the frictional force will not be able to overcome the moving force acting on the body and such the moving force will be greater than the frictional force in that regards.
The applied force needed to maintain a constant velocity is 10 N.
The given parameters;
frictional force on the object, Fk = 10 NThe net horizontal force on the object is calculated by applying Newton's second law of motion as shown below;
∑F = ma
[tex]F- F_k = ma[/tex]
where;
F is the applied force on the objectm is the mass of the objecta is the acceleration of the objectAt constant velocity, the acceleration of the object is zero.
[tex]F-F_k = m(0)\\\\F-F_k = 0\\\\F= F_k\\\\F = 10 \ N[/tex]
Thus, the applied force needed to maintain a constant velocity is 10 N.
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In a Young’s double-slit experiment, a thin sheet of mica is placed over one of the two slits. As a result, the center of the fringe pattern (on the screen) shifts by an amount corresponding to 30 dark bands. The wavelength of the light in this experiment is 480 nm and the index of the mica is 1.60. The mica thickness is:
Answer:0.024 mm
Explanation:
Given
Fringe shifts by an amount to 30 dark bands i.e. [tex]m=30[/tex]
Wavelength [tex]\lambda =480 nm[/tex]
refractive index of mica [tex]n_2=1.6[/tex]
refractive index of air [tex]n_1=1[/tex]
Phase difference is given by
[tex]m=\frac{t\left [ n_2-n_1\right ]}{\lambda }[/tex]
[tex]30=\frac{t\left [ 1.6-1\right ]}{480\times 10^{-9}}[/tex]
[tex]t=\frac{30\times 480\times 10^{-9}}{1.6-1}[/tex]
[tex]t=0.024\ mm[/tex]
To determine the thickness of the mica in a Young's double-slit experiment, we can use the formula d = mλ / sinθ, where d is the thickness of the mica, λ is the wavelength of the light, θ is the angle of the shift in the fringe pattern, and m is the number of dark bands shifted. By substituting the given values into the formula and solving for d, we can calculate the thickness of the mica.
Explanation:In a Young’s double-slit experiment, the shift in the center of the fringe pattern on the screen is caused by the introduction of a thin sheet of mica over one of the slits. This shift corresponds to 30 dark bands. To determine the thickness of the mica, we can use the formula for double-slit interference:
d sinθ = mλ,
where d is the distance between the slits, θ is the angle of the shift in the fringe pattern, m is the number of dark bands shifted, and λ is the wavelength of the light. Rearranging the formula, we have:
d = mλ / sinθ.
Given that the wavelength of the light is 480 nm and the index of refraction for the mica is 1.60, we can calculate the thickness of the mica by substituting the values into the formula and solving for d.
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A student is asked to determine the work done on a block of wood when the block is pulled horizontally using an attached string. The student is supplied with a spring scale, a stopwatch, and a meterstick. Which of the following graphical analysis techniques will allow the student to determine the work done on the block by the string?
A. Graphing the force as a function of time and calculating the slope
B. Graphing the force as a function of time and calculating the area under the curve
C. Graphing the force as a function of distance and calculating the slope
D. Graphing the force as a function of distance and calculating the area under the curve
Answer:
D. Graphing the force as a function of distance and calculating the area under the curve.
Explanation:
Answer:
The correct option is (D). "Graphing the force as a function of distance and calculating the area under the curve"
Explanation:
1) As we know from the definition of Work done which is Work = Force × Displacement. Time doesn't have any use in the mentioned equation and thus the stop watch is of no use to us.
2) Using the meter stick, we can measure the distance for which the block is pulled horizontally i.e "Displacement"
3) Using the spring scale, we can calculate the "Force" applied on the block of wood to move it horizontally.
4) For example, lets say that for a constant force of 4 Newtons, the wooden block is pulled horizontally 4 meters. Plotting Force vs Displacement on a graph would yield a horizontal line as shown in the attachment. Area under the F vs D graph will give us the total work done.
A baseball player throws a baseball with a velocity of 13 m/s North it is caught by a second player seven seconds later how far is the second player from the first player
The second player is 91 meters far from the first player.
Why?
First, let be the +y the North, so, to solve the problem we can use the following formula:
[tex]y=yo+v_o*t+\frac{1}{2}*a*t[/tex]
Now, subsituting the given information, we have(assuming that the speed is constant):
\\\\y-yo=13\frac{m}{s}*7s+\frac{1}{2}*0*7s\\\\y-yo=91m\\\\distance=91m[/tex]
Hence, we have that the second player is 91m far from the first player.
Have a nice day!
The height of a cone is increasing at a rate of 10 cm/sec and its radius is decreasing so that its volume remains constant. How fast is the radius changing when the radius is 4 cm and the height is 10 cm?
Answer:
dr/dt = -2 cm/s.
Explanation:
The volume of a cone is given by:
[tex]V=\frac{1}{3} \pi r^{2}h[/tex] (1)
r is the radiush is the heightLet's take the derivative with respect to time in each side of (1).
[tex]\frac{dV}{dt}=\frac{1}{3} \pi \frac{d}{dt}(r^{2}h)=\frac{1}{3} \pi \left(2r\frac{dr}{dt}h+r^{2}\frac{dh}{dt} \right)[/tex] (2)
We know that:
dh/dt = 10 cm / s (rate increasing of height)dV/dt = 0 (constant volume means no variation with respect of time)r = 4 cm h = 10 cmWe can calculate how fast is the radius changing using the above information.
[tex]0=\frac{1}{3} \pi \left( 2\cdot 4\cdot \frac{dr}{dt} \cdot 10 + 4^{2}\cdot 10)\right[/tex]
Therefore dr/dt will be:
[tex]\frac{dr}{dt}=-\frac{160}{80}=-2 cm/s[/tex]
The minus signs means that r is decreasing.
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Using the information from Paul Hewitt's Conceptual Development Practice Page 25-1 and the image below, answer the following question.Image of a wave with two rulers, one vertical and one horizontal, measuring the wave is shown. The wave's first crest aligns from 0 to just less than 4 centimeters on the horizontal ruler and rises from the equilibrium located at 5 centimeters to just before 3 centimeters. The wave's first trough aligns continues to just less than 8 centimeters on the horizontal ruler and goes down from the equilibrium located at 5 centimeters to just before 7 centimeters.What was the measurement of the wavelength and amplitude respectively?
Answer:
A = 2 cm , λ = 8 cm
Explanation:
The amplitude of a wave is the maximum height it has, in this case the height is measured by the vertical ruler,
We are told the balance point is in the reading of 5 cm, that the maximum reading is 3 cm and the Minimum reading is 7 cm. Therefore, the distance from the ends of the ridge to the point of equilibrium is
d = 7-5 = 2 cm
d = 5-3 = 2 cm
A = 2 cm
The wavelength is the minimum horizontal distance for which the wave is repeated, that is measured by the horizontal ruler.
The initial reading for 4 cm and the final reading for 8 cm, this distance corresponds to a crest of the wave, the complete wave is formed by two crests whereby the wavelength is twice this value
Δx = 8-4 = 4 cm
λ = 2 Δx
λ = 8 cm
The amplitude of the wave is approximately [tex]2cm[/tex], measured from the equilibrium to the crest or trough. The wavelength of the wave is approximately [tex]8cm[/tex].
To determine the wavelength and amplitude of the given wave, we need to analyze the provided measurements.
Amplitude CalculationThe crest rises from the equilibrium position of [tex]5 cm `[/tex] to just before [tex]3 cm[/tex] , giving an amplitude measurement of approximately [tex]2 cm (5 cm - 3 cm)[/tex] .
Similarly, the trough falls from the equilibrium of [tex]5 cm[/tex] to just before [tex]7 cm[/tex], again giving a vertical displacement of approximately [tex]2 cm (7 cm - 5 cm)[/tex].
Wavelength CalculationThe horizontal distance from the start of the first crest to the start of the next crest should be measured. According to the provided data, the first crest aligns from [tex]0[/tex] to just under [tex]4 cm[/tex] , and the next crest starts just under [tex]8 cm[/tex].
The wavelength is the horizontal distance covering one complete cycle, measuring just less than [tex]8 cm[/tex]. Therefore, the wavelength is approximately [tex]8 cm[/tex] .
Hence,
Amplitude: [tex]2 cm[/tex]Wavelength: [tex]8 cm[/tex]The Royal Gorge bridge over the Arkansas River is 393 m above the river. A bungee jumper of mass 150 kg has an elastic cord of length 78 m attached to her feet. Assume the cord acts like a spring of force constant k. The jumper leaps, barely touches the water, and after numerous ups and downs comes to rest at a height h above the water. The acceleration of gravity is 9.81 m/s². Find h. Answer in units of m.
Answer:
188.7 m
Explanation:
height of bridge above water (h) = 393 m
mass of bungee jumper (m) = 150 kg
length of cord (L) = 78 m
acceleration due to gravity (g) = 9.8 m/s
initial energy = mgh = 150 x 9.8 x 393 = 577,710 J
since the jumper barely touches the water, the maximum extension of the cord (x) = 393 - 78 = 315 m
from the conservation of energy mgh = [tex](\frac{1}{2})kx^{2}[/tex]
therefore
577,710 = [tex](\frac{1}{2})kx315^{2}[/tex]
k = 11.64 N/m
from Hooke's law, force (f) = kx' ⇒ mg = kx'
where x' is the extension of the cord when it comes to rest
150 x 9.8 = 11.64 × x'
x' = 126.3 m
the final height at which the cord comes to a rest = height of the bridge - length of the cord - extension of the cord when it comes to rest
the final height at which the cord comes to a rest = 393 - 78 - 126.3 = 188.7 m
From the list below, identify the disease and its classification that is mismatched.
A) polio; meningitis
B) African sleeping sickness; encephalitis
C) La Crosse Virus infection; encephalitis
D) Naegleria fowleri infection; meningoencephalitis
E) Valley Fever; meningitis
Answer:E)Valley Fever;meningitis
Explanation:Valley fever is a a fungal lung infection while the meningitis is a viral or bacterial disease that affect the meninges.
The radius of a cone is increasing at a rate of 333 centimeters per second and the height of the cone is decreasing at a rate of 444 centimeters per second. At a certain instant, the radius is 888 centimeters and the height is 101010 centimeters. What is the rate of change of the volume of the cone at that instant (in cubic centimeters per second)?
The rate of change of the volume of the cone at the specified instant is approximately [tex]\(6.03 \times 10^{9} \pi\)[/tex] cubic centimeters per second.
What is the rate of change of the volume of the cone at that instant?To find the rate of change of the volume of the cone, you can use the formula for the volume of a cone:
[tex]\[V = \frac{1}{3}\pi r^2 h\][/tex]
Where:
- V is the volume of the cone.
- r is the radius of the cone.
- h is the height of the cone.
You are given that the radius is increasing at a rate of 333 cm/s (dr/dt = 333 cm/s) and the height is decreasing at a rate of 444 cm/s (dh/dt = -444 cm/s). At a certain instant, the radius is 888 cm (r = 888 cm) and the height is 101010 cm (h = 101010 cm).
To find the rate of change of the volume (dV/dt) at that instant, you can use the product rule for differentiation:
[tex]\[ \frac{dV}{dt} = \frac{1}{3} \pi \left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right) \][/tex]
Now, plug in the values:
[tex]\[ \frac{dV}{dt} = \frac{1}{3} \pi \left(2(888 cm)(101010 cm)(333 cm/s) + (888 cm)^2(-444 cm/s)\right) \][/tex]
Calculate:
[tex]\[ \frac{dV}{dt} = \frac{1}{3} \pi \left(5910088880 cm^3/s + (-157593984 cm^3/s)\right) \][/tex]
Now, simplify:
[tex]\[ \frac{dV}{dt} = \frac{1}{3} \pi \cdot 5752494896 cm^3/s \][/tex]
[tex]\[ \frac{dV}{dt} \approx 6.03 \times 10^{9} \pi \; cm^3/s \][/tex]
So, the rate of change of the volume of the cone at that instant is approximately [tex]\(6.03 \times 10^{9} \pi\)[/tex] cubic centimeters per second.
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In one cycle a heat engine absorbs 450 J from a high-temperature reservoir and expels 290 J to a low-temperature reservoir. If the efficiency of this engine is 55% of the efficiency of a Carnot engine, what is the ratio of the low temperature to the high temperature in the Carnot engine?
The ratio of the low temperature to the high temperature in the Carnot engine, given that the real engine's efficiency is 55% of a Carnot engine's efficiency, is calculated to be 0.3535.
The question involves thermodynamics and specifically deals with the operation and efficiency of a Carnot engine.
The given heat engine absorbs 450 J of heat from the high-temperature reservoir and expels 290 J to the low-temperature reservoir. The efficiency (efficiency) of this engine is given as 55% of a Carnot engine's efficiency. Using the first law of thermodynamics, wecan calculate the work done (W) by the engine:
W = Qh - Qc = 450 J - 290 J = 160 J.
The efficiency of the engine is the ratio of the work done to the heat absorbed:
efficiency = W / Qh = 160 J / 450 J = 0.3556, or 35.56%.
Now, the efficiency of a Carnot engine is defined as:
efficiencyCarnot = 1 - (Tc / Th).
The problem states that the engine's efficiency is 55% of a Carnot engine's efficiency, which means:
0.3556 = 0.55 * efficiencyCarnot
From this equation, we can solve for efficiencyCarnot and then use it to calculate the ratio of the low temperature to the high temperature in the Carnot engine:
efficiencyCarnot = 0.3556 / 0.55
efficiencyCarnot = 0.6465, or 64.65%
Thus:
0.6465 = 1 - (Tc / Th)
Tc / Th = 1 - 0.6465 = 0.3535.
Therefore, the ratio of the low temperature to the high temperature in the Carnot engine is 0.3535.
The ratio of the low temperature to the high temperature in the Carnot engine is [tex]\( \frac{1}{3} \)[/tex].
The correct ratio of the low temperature to the high temperature in the Carnot engine is given by:
[tex]\[ \frac{T_{\text{low}}}{T_{\text{high}}} = 1 - \frac{W_{\text{actual}}}{Q_{\text{in}}} \cdot \frac{1}{\eta_{\text{Carnot}}} \][/tex]
where [tex]\( W_{\text{actual}} \)[/tex] is the work done by the actual engine, [tex]\( Q_{\text{in}} \)[/tex] is the heat absorbed from the high-temperature reservoir, and [tex]\( \eta_{\text{Carnot}} \)[/tex] is the efficiency of the Carnot engine.
First, we calculate the actual efficiency of the given heat engine using the provided values:
[tex]\[ W_{\text{actual}} = Q_{\text{in}} - Q_{\text{out}} \][/tex]
[tex]\[ W_{\text{actual}} = 450 \, \text{J} - 290 \, \text{J} \][/tex]
[tex]\[ W_{\text{actual}} = 160 \, \text{J} \][/tex]
The actual efficiency [tex]\( \eta_{\text{actual}} \)[/tex] is then:
[tex]\[ \eta_{\text{actual}} = \frac{W_{\text{actual}}}{Q_{\text{in}}} \][/tex]
[tex]\[ \eta_{\text{actual}} = \frac{160 \, \text{J}}{450 \, \text{J}} \][/tex]
[tex]\[ \eta_{\text{actual}} = \frac{16}{45} \][/tex]
Given that the efficiency of the actual engine is 55% of the efficiency of a Carnot engine operating between the same two temperatures, we can write:
[tex]\[ \eta_{\text{actual}} = 0.55 \cdot \eta_{\text{Carnot}} \][/tex]
The efficiency of a Carnot engine is given by:
[tex]\[ \eta_{\text{Carnot}} = 1 - \frac{T_{\text{low}}}{T_{\text{high}}} \][/tex]
Combining the two equations, we get:
[tex]\[ \frac{16}{45} = 0.55 \left( 1 - \frac{T_{\text{low}}}{T_{\text{high}}} \right) \][/tex]
Solving for [tex]\( \frac{T_{\text{low}}}{T_{\text{high}}} \)[/tex]:
[tex]\[ \frac{16}{45} = 0.55 - 0.55 \cdot \frac{T_{\text{low}}}{T_{\text{high}}} \][/tex]
[tex]\[ 0.55 \cdot \frac{T_{\text{low}}}{T_{\text{high}}} = 0.55 - \frac{16}{45} \][/tex]
[tex]\[ \frac{T_{\text{low}}}{T_{\text{high}}} = \frac{0.55 - \frac{16}{45}}{0.55} \][/tex]
[tex]\[ \frac{T_{\text{low}}}{T_{\text{high}}} = \frac{0.55 \cdot \frac{45}{45} - \frac{16}{45}}{0.55} \][/tex]
[tex]\[ \frac{T_{\text{low}}}{T_{\text{high}}} = \frac{\frac{24.75}{45} - \frac{16}{45}}{0.55} \][/tex]
[tex]\[ \frac{T_{\text{low}}}{T_{\text{high}}} = \frac{\frac{8.75}{45}}{0.55} \][/tex]
[tex]\[ \frac{T_{\text{low}}}{T_{\text{high}}} = \frac{8.75}{45 \cdot 0.55} \][/tex]
[tex]\[ \frac{T_{\text{low}}}{T_{\text{high}}} = \frac{8.75}{24.75} \][/tex]
[tex]\[ \frac{T_{\text{low}}}{T_{\text{high}}} = \frac{1}{3} \][/tex]
PEG 400 is a liquid with a specific gravity of 1.13. What volume should be measured for the preparation?
Answer:
354 cm³
Explanation:
Step 1: calculate the density of PEG 400
[tex]Specific gravity({\gamma}) = \frac{density of liquid (\rho _{l})}{density of water (\rho_{w})}[/tex]
[tex]1.13=\frac{\rho _{l}}{1(\frac{g}{m^3})}[/tex]
[tex]{\rho _{l}[/tex] = 1.13X1 = 1.13 [tex]\frac{g}{cm^3}[/tex]
Step 2:
Molecular weight of PEG 400 = 400g/mol
Step 3: calculate the volume of PEG 400 to be measured
[tex]Volume _{PEG 400} =\frac{mass of _{PEG 400}}{density of _{PEG 400}}[/tex]
[tex]Volume _{PEG 400}=\frac{400}{1.13}(cm^3)[/tex]
= 353.98 cm³
≅354 cm³
353.4 cm³ volume should be measured for the preparation.
Given:
Specific gravity=1.13
To find:
Volume=?
Specific gravity is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material, often a liquid.
[tex]\text{Specific gravity}=\frac{\text{density of liquid}}{\text{density of water}}[/tex]On substituting the values, we will get:
[tex]\text{Density of liquid}=1.13*1=1.13 gcm^{-3}[/tex]
Molecular weight of PEG 400 =400g/mol
Now, we have the values of density and mass thus volume can be calculated easily:
The density of a substance is its mass per unit volume.
[tex]\text{Volume}=\frac{\text{mass}}{\text{density}}=\frac{400}{1.13} \\\\\text{Volume}=353.4 cm^{3}[/tex]
353.4 cm³ volume should be measured for the preparation.
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Assume that the equator of the Earth is 24,000 miles long (that’s its circumference). Now, pretend that you are standing somewhere on the equator, such as in the country of Ecuador. Now, if the Earth turns once, completely, in 24 hours, then, how fast would you be going (in miles per hour), even if you just stood still?
Answer:
1000 mph
Explanation:
P = Perimeter = 24000 mi
r = Radius of the equator
t = Time taken to complete one rotation = 24 h
Perimeter of a circle is given by
[tex]P=2\pi r\\\Rightarrow r=\dfrac{P}{2\pi}\\\Rightarrow r=\dfrac{24000}{2\pi}\ mi[/tex]
Angular speed is given by
[tex]\omega=\dfrac{2\pi}{t}\\\Rightarrow \omega=\dfrac{2\pi}{24}[/tex]
Velocity if given by
[tex]v=r\omega\\\Rightarrow v=\dfrac{24000}{2\pi}\times \dfrac{2\pi}{24}\\\Rightarrow v=1000\ mph[/tex]
The person would be going at a speed of 1000 mph
If two vehicles are traveling at a speed of 50 miles per hour and they collide with one another, the speed of the head-on impact is actually ___ miles per hour.
Answer:
[tex]v_{f}[/tex] = 0 miles/h
Explanation:
This exercise should be resolved with the moment. The system is formed by the two cars. Let's write the moment
Initial. Before the crash
p₀ = m v₁ - m v₂
The sign is because they go in the opposite direction
Final. After the crash
[tex]p_{f}[/tex] = (m + m) [tex]v_{f}[/tex]
The moment is preserved
p₀ = [tex]p_{f}[/tex]
m v₁- m v₂ = 2m [tex]v_{f}[/tex]
[tex]v_{f}[/tex] = m / 2m (v₁-v₂)
But the speed of the cars is the same v1 = v2 = 50 liters / h
[tex]v_{f}[/tex] = 0
so the two faces do not move after the crash
A spin bike has a flywheel in two parts—a 12.5 kg disk with radius 0.23 m, and a 7.0 kg ring with mass concentrated at the outer edge of the disk. A friction pad exerts a force of 9.7 N on the outside of the disk. A cyclist is pedaling, spinning the disk at a typical 180 rpm. If she stops pedaling, how long will it take for the flywheel to come to a stop?
Final answer:
To determine how long it takes for the flywheel to come to a stop, calculate the angular acceleration using the torque and moment of inertia. Then, use the angular acceleration to find the time.
Explanation:
To determine how long it takes for the flywheel to come to a stop, we need to calculate the angular acceleration first. To do this, we can use the formula:
α = τ / I
Where α is the angular acceleration, τ is the torque, and I is the moment of inertia. The torque can be calculated using the formula:
τ = rF
Where r is the radius of the flywheel and F is the force exerted on it. Once we have the angular acceleration, we can use it to find the time it takes for the flywheel to come to a stop using the formula:
t = ω / α
Where t is the time, ω is the initial angular velocity, and α is the angular acceleration.
A 1055-kg van, stopped at a traffic light, is hit directly in the rear by a 715-kg car traveling with a velocity of +2.25 m/s. Assume the transmission of the van is in neutral, the brakes are not being applied, and the collision is elastic. What is the final velocity of (a) the car (b)the van?
Answer:
1.81779 m/s in the same direction as the car
0.43220 m/s in the same direction
Explanation:
[tex]m_1[/tex] = Mass of van= 1055 kg
[tex]m_2[/tex] = Mass of car = 715 kg
[tex]u_1[/tex] = Initial Velocity of van = 0 m/s
[tex]u_2[/tex] = Initial Velocity of car = 2.25 m/s
[tex]v_1[/tex] = Final Velocity of van
[tex]v_2[/tex] = Final Velocity of car
As momentum and Energy is conserved
[tex]m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}[/tex]
[tex]{\tfrac {1}{2}}m_{1}u_{1}^{2}+{\tfrac {1}{2}}m_{2}u_{2}^{2}={\tfrac {1}{2}}m_{1}v_{1}^{2}+{\tfrac {1}{2}}m_{2}v_{2}^{2}[/tex]
From the two equations we get
[tex]v_{1}=\dfrac{m_1-m_2}{m_1+m_2}u_{1}+\dfrac{2m_2}{m_1+m_2}u_2\\\Rightarrow v_1=\dfrac{1055-715}{1055+715}\times 0+\dfrac{2\times 715}{1055+715}\times 2.25\\\Rightarrow v_1=1.81779\ m/s[/tex]
The final velocity of the van is 1.81779 m/s in the same direction as the car
[tex]v_{2}=\dfrac{2m_1}{m_1+m_2}u_{1}+\dfrac{m_2-m_1}{m_1+m_2}u_2\\\Rightarrow v_2=\dfrac{2\times 1055}{1055+715}\times 0+\dfrac{1055-715}{1055+715}\times 2.25\\\Rightarrow v_2=0.43220\ m/s[/tex]
The final velocity of the car is 0.43220 m/s in the same direction
Answer:
(a). The final velocity of the car is -0.432 m/s.
(b). The final velocity of the van is 1.82 m/s.
Explanation:
Given that,
Mass of van = 1055 kg
Mass of car = 715 kg
Initial velocity of car= 2.25 m/s
(a). We need to calculate the final velocity of the car
Using formula of velocity
[tex]v_{c}=\dfrac{m_{v}-m_{c}}{m_{v}+m_{c}}\times u_{c}[/tex]
Put the value into the formula
[tex]v_{c}=\dfrac{715-1055}{715+1055}\times2.25[/tex]
[tex]v_{c}=-0.432\ m/s[/tex]
(b). We need to calculate the final velocity of the van
Using formula of velocity
[tex]v_{v}=\dfrac{2m_{v}}{m_{v}+m_{c}}\times u_{c}[/tex]
Put the value into the formula
[tex]v_{v}=\dfrac{2\times715}{715+1055}\times2.25[/tex]
[tex]v_{v}=1.82\ m/s[/tex]
Hence, (a). The final velocity of the car is -0.432 m/s.
(b). The final velocity of the van is 1.82 m/s.
"In a Young’s double-slit experiment, the separation between slits is d and the screen is a distance D from the slits. D is much greater than d and λ is the wavelength of the light. The number of bright fringes per unit width on the screen is: "
A. Dd/λ
B. Dλ/d
C. D/dλ
D. λ/Dd
E. d/Dλ"
Answer:
The number of bright fringes per unit width on the screen is, [tex]x=\dfrac{\lambda D}{d}[/tex]
Explanation:
If d is the separation between slits, D is the distance between the slit and the screen and [tex]\lambda[/tex] is the wavelength of the light. Let x is the number of bright fringes per unit width on the screen is given by :
[tex]x=\dfrac{n\lambda D}{d}[/tex]
[tex]\lambda[/tex] is the wavelength
n is the order
If n = 1,
[tex]x=\dfrac{\lambda D}{d}[/tex]
So, the the number of bright fringes per unit width on the screen is [tex]\dfrac{\lambda D}{d}[/tex]. Hence, the correct option is (B).
Final answer:
The number of bright fringes per unit width in a Young's double-slit experiment is given by the reciprocal of the fringe spacing, which is d/(Dλ), corresponding to answer choice E.
Explanation:
In a Young's double-slit experiment, to find the number of bright fringes per unit width on the screen, we consider the separation between the slits (d), the distance from the slits to the screen (D), and the wavelength of light used (λ). The distance between adjacent bright fringes, or fringe spacing, is given by Δy = Dλ/d. From this relation, the number of bright fringes per unit width can be obtained by taking the reciprocal of the fringe spacing, which implies 1/Δy = d/(Dλ).
Therefore, the correct formula to calculate the number of bright fringes per unit width on the screen is the reciprocal of Δy, which is d/(Dλ), matching answer choice E.