(a) 4A
In a simple harmonic motion:
- The amplitude (A) is the maximum displacement of the system, measured with respect to the equilibrium position
- The period (T) is the time needed for one complete oscillation, so for instance is the time the system needs to go from position x=+A back to x=+A again
Therefore, we have that in one time period (1T) the distance covered is 4A. In fact, during one period (1T), the system:
- Goes from x=+A to x=0 (equilibrium position) --> distance covered: A
- Goes from x=0 to x=-A --> distance covered: A
- Goes from x=-A to x=0 (equilibrium position) --> distance covered: A
- Goes from x=0 to x=+A --> distance covered: A
So, in total, 4A.
(b) 20A
Since the system moves through a distance of 4A in a time interval of 1T, we can set a proportion to see what is the distance covered in the time 5.00 T:
[tex]1 T : 4 A = 5T : d[/tex]
Solving for d, we find
[tex]d=\frac{(4A)(5T)}{1 T}=20A[/tex]
So, the distance covered in the time 5.00 T is 20 A.
(c) 0.5 T
Since the system moves through a distance of 4A in a time interval of 1T, we can set a proportion to see the time t that the system needs to move through a total distance of 2A:
[tex]1 T : 4 A = t : 2A[/tex]
Solving for t, we find
[tex]t=\frac{(2A)(1T)}{4 A}=0.5 T[/tex]
So, the time needed for the system to move through a total distance of 2A is 0.5T (half period).
(d) 7/4 T
As before, since the system moves through a distance of 4A in a time interval of 1T, we can set a proportion to see the time t that the system needs to move through a total distance of 7A:
[tex]1 T : 4 A = t : 7A[/tex]
Solving for t, we find
[tex]t=\frac{(7A)(1T)}{4 A}=\frac{7}{4}T[/tex]
So, the time needed for the system to move through a total distance of 2A is 7/4 T
(e) 8/5 D
In a time of [tex]\frac{5}{2}T[/tex], the distance covered is 16D.
We also now that the distance covered in 1T is 4A.
So we can find the distance covered in a time of [tex]\frac{5}{2}T[/tex] in terms of A:
[tex]1T:4A = \frac{5}{2}T:d\\d=\frac{(4A)(\frac{5}{2}T)}{1T}=10A[/tex]
And we know that this distance must correspond to 16D, so we can find a relationship between A and D:
[tex]10A=16D\\A=\frac{16}{10}D=\frac{8}{5}D[/tex]
Electricity is distributed from electrical substations to neighborhoods at 15,000 V. This is a 60 Hz oscillating (AC) voltage. Neighborhood transformers, seen on utility poles, step this voltage down to the 120 V that is delivered to your house. a. How many turns does the primary coil on the transformer have if the secondary coil has 100 turns? b. No energy is lost in an ideal transformer, so the output power P out from the secondary coil equals the input power Pin to the primary coil. Suppose a neighborhood transformer delivers 250 A at 120 V. What is the current in the 15,000 V line from the substation?
a. 12,500 turns
The transformer equation states that
[tex]\frac{N_p}{V_p}=\frac{N_s}{V_s}[/tex]
where
Np is the number of turns in the primary coil
Ns is the number of turns in the secondary coil
Vp is the voltage in the primary coil
Vs is the voltage in the secondary coil
For the transformer in the problem,
Vp = 15,000 V
Vs = 120 V
Ns = 100
So we can find Np by rearranging the equation:
[tex]N_p = V_p \frac{N_s}{V_s}=(15,000 V)\frac{100}{120 V}=12,500[/tex]
b. 2 A
For an ideal transformer, the output power is equal to the input power:
[tex]P_i = P_o\\V_p I_p = V_s I_s[/tex]
where
[tex]V_p = 15,000 V[/tex] is the voltage in the primary coil
[tex]I_p[/tex] is the current in the primary coil
[tex]V_s = 120 V[/tex] is the voltage in the secondary coil
[tex]I_s = 250 A[/tex] is the current in the secondary coil
Solvign the formula for Ip, we find:
[tex]I_p = \frac{V_s I_s}{V_p}=\frac{(120 V)(250 A)}{15,000 V}=2 A[/tex]
The primary coil of the transformer has 12500 turns, and the current in the 15,000 V line from the electrical substation is 2 A.
Explanation:The number of turns in the primary coil of the transformer can be found using the transformer equation, which states that the ratio of the secondary voltage to the primary voltage equals the ratio of the number of loops in the secondary coil to the number of loops in the primary coil.
Therefore, if the secondary coil has 100 turns, and the voltages are 15000 V (primary) and 120 V (secondary), we can set up the equation (15000 V / 120 V) = (x turns / 100 turns), where x is the number of turns in the primary coil. Solving for x gives us x = 12500 turns.
The power input to the primary coil equals the power output from the secondary coil, since no energy is lost in an ideal transformer. Power (P) equals voltage (V) times current (I), so Pin = Pout, or (15,000 V * Iin) = (120 V * 250 A). Solving for Iin, the current in the 15,000 V line from the substation, gives us Iin = 2 A.
Learn more about Transformer here:https://brainly.com/question/11709244
#SPJ3
The space shuttle orbits 340km above the surface of the earth.What is the gravitational force on a 9.0kg sphere inside the space shuttle? The sphere floats around inside the space shuttle, apparently
The gravitational force on a 9.0kg sphere inside the space shuttle orbiting 340km above the Earth's surface cannot be precisely determined with the information provided. However, astronauts and objects appear weightless in orbit, not because there is no gravity, but because they are in a state of continuous free-fall towards Earth, experiencing what is known as microgravity.
The sensation of weightlessness experienced by astronauts in the space shuttle is due to the phenomenon of microgravity. While it may seem that gravitational forces are absent in space, this is not the case. The space shuttle, and everything inside it, is in a constant state of free fall towards Earth. This happens because the shuttle is moving forward at a speed that matches the rate at which it falls towards the Earth, creating a steady orbit. According to Newton's law of universal gravitation, the force of gravity decreases with the square of the distance from the center of the Earth, but it is never zero. At the altitudes where the ISS and space shuttles orbit, gravity is only slightly weaker than on Earth's surface. Therefore, the 9.0kg sphere is subject to Earth's gravity, but it appears to float because it is in free-fall along with the shuttle.
what are the 8 steps of the scientific method, in order?
Identify a problem
Do background research
Form a hypothesis
Create and plan an experiment
Perform the experiment
Analyze the result
Create a conclusion
Communicate results
The major steps of a scientific method includes, observation, hypothesis, experiment, result and discussion and evaluation of the results and conclusion.
What is a scientific method?A scientific method includes several stages to find a solution for the scientific problem under study. The first step of the study includes an observation on the incident under study.
Based on the observations made make a scientific hypothesis which predict the solution of the problem. Later the hypothesis is tested with a well designed experiment.
So the next step is the planning of the experiment. Then perform the experiment and attain the results. Later the results are thoroughly evaluated and arrive at a conclusion.
The last step is to reveal and publish the results to communicate the important results and discussions.
To find more on scientific methods, refer here:
https://brainly.com/question/7508826
#SPJ2
Why is the efficiency of a machine always less than 100 percent? The work input is too small. It cannot have an IMA greater than 1. Some work input is lost to friction. The work output is too great.
Answer:
Some work input is lost to friction
Explanation:
The efficiency of a machine is defined as:
[tex]\eta = \frac{W_{out}}{W_{in}}[/tex] (1)
where
[tex]W_{out}[/tex] is the work output
[tex]W_{in}[/tex] is the work input
Due to the law of conservation of energy, the work output can never be larger than the work input (because energy cannot be created). Moreover, in real machines part of the work input is lost due to the presence of frictions: as a result, part of the energy in input is converted into thermal energy or other forms of energy, and so the work output is smaller than the work input, and so the ratio (1) becomes less than 1, and so the efficiency is less than 100%.
Answer:
Some work input is lost to friction
Calculate the energy of a photon having a wavelength in thefollowing ranges.(a) microwave, with λ = 50.00 cmeV(b) visible, with λ = 500 nmeV(c) x-ray, with λ = 0.50 nmeV
(a) [tex]2.5\cdot 10^{-6}eV[/tex]
The energy of a photon is given by:
[tex]E=\frac{hc}{\lambda}[/tex]
where
[tex]h=6.63\cdot 10^{-34}Js[/tex] is the Planck constant
[tex]c=3\cdot 10^8 m/s[/tex] is the speed of light
[tex]\lambda[/tex] is the wavelength
For the microwave photon,
[tex]\lambda=50.00 cm = 0.50 m[/tex]
So the energy is
[tex]E=\frac{(6.63\cdot 10^{-34}Js)(3\cdot 10^8 m/s)}{0.50 m}=4.0\cdot 10^{-25} J[/tex]
And converting into electronvolts,
[tex]E=\frac{4.0\cdot 10^{-25}J}{1.6\cdot 10^{-19} J/eV}=2.5\cdot 10^{-6}eV[/tex]
(b) [tex]2.5 eV[/tex]
For the energy of the photon, we can use the same formula:
[tex]E=\frac{hc}{\lambda}[/tex]
For the visible light photon,
[tex]\lambda=500 nm = 5 \cdot 10^{-7}m[/tex]
So the energy is
[tex]E=\frac{(6.63\cdot 10^{-34}Js)(3\cdot 10^8 m/s)}{5\cdot 10^{-7} m}=4.0\cdot 10^{-19} J[/tex]
And converting into electronvolts,
[tex]E=\frac{4.0\cdot 10^{-19}J}{1.6\cdot 10^{-19} J/eV}=2.5 eV[/tex]
(c) [tex]2500 eV[/tex]
For the energy of the photon, we can use the same formula:
[tex]E=\frac{hc}{\lambda}[/tex]
For the x-ray photon,
[tex]\lambda=0.5 nm = 5 \cdot 10^{-10}m[/tex]
So the energy is
[tex]E=\frac{(6.63\cdot 10^{-34}Js)(3\cdot 10^8 m/s)}{5\cdot 10^{-10} m}=4.0\cdot 10^{-16} J[/tex]
And converting into electronvolts,
[tex]E=\frac{4.0\cdot 10^{-16}J}{1.6\cdot 10^{-19} J/eV}=2500 eV[/tex]
A runaway railroad car, with mass 30x10^4 kg, coasts across a level track at 2.0 m/s when it collides with a spring loaded bumper at the end of the track. If the spring constant of the bumper is 2x10^6 N/m, what is the maximum compression of the spring during the collision? (Assume collision is elastic)
Answer:
0.775 m
Explanation:
As the car collides with the bumper, all the kinetic energy of the car (K) is converted into elastic potential energy of the bumper (U):
[tex]U=K\\frac{1}{2}kx^2 = \frac{1}{2}mv^2[/tex]
where we have
[tex]k=2\cdot 10^6 N/m[/tex] is the spring constant of the bumper
x is the maximum compression of the bumper
[tex]m=30\cdot 10^4 kg[/tex] is the mass of the car
[tex]v=2.0 m/s[/tex] is the speed of the car
Solving for x, we find the maximum compression of the spring:
[tex]x=\sqrt{\frac{mv^2}{k}}=\sqrt{\frac{(30\cdot 10^4 kg)(2.0 m/s)^2}{2\cdot 10^6 N/m}}=0.775 m[/tex]
Answer:
0.6 m
Explanation:
The law of conservation of energy states that:
[tex]\Delta E_m=0[/tex]
The mechanical energy ([tex]E_m[/tex]) is the sum of the kinetic energy and the potential energy:
[tex]\Delta K+\Delta U=0\\K_f-K_i+U_f-U_i=0\\\frac{mv_f^2}{2}-\frac{mv_i^2}{2}+\frac{kx_f^2}{2}-\frac{kx_i^2}{2}=0[/tex]
[tex]U_i[/tex] is zero since the spring is not initially compressed and [tex]K_f[/tex] is zero since all kinetic energy becomes potentital energy:
[tex]\frac{kx_f^2}{2}=\frac{mv_i^2}{2}[/tex]
Finally, we solve for x and replace the given values:
[tex]x_f^2=\frac{mv_i^2}{k}\\x_f=\sqrt{\frac{mv_i^2}{k}}\\x_f=\sqrt{\frac{(30*10^4kg)(2\frac{m}{s})^2}{2*10^6\frac{N}{m}}}\\x_f=0.6 m[/tex]
When the moon is between the earth and the sun what moon phase will this be
Answer: The new moon phase occurs when the Moon is directly between the Earth and Sun. A solar eclipse can only happen at new moon. A waxing crescent moon is when the Moon looks like crescent and the crescent increases ("waxes") in size from one day to the next. This phase is usually only seen in the west.
Answer: a new moon
Explanation:
when the moon is between the sun and the earth a new moon comes.
hope this helps btw this is correct
A puck moves 2.35 m/s in a -22° direction. A hockey stick pushes it for 0.215 s, changing its velocity to 6.42 m/s in a 50.0° direction. What was the direction of the acceleration?
The puck starts with velocity vector
[tex]\vec v_0=\left(2.35\dfrac{\rm m}{\rm s}\right)(\cos(-22^\circ)\,\vec\imath+\sin(-22^\circ)\,\vec\jmath)=(2.18\,\vec\imath-0.880\,\vec\jmath)\dfrac{\rm m}{\rm s}[/tex]
Its velocity at time [tex]t[/tex] is
[tex]\vec v=\vec v_0+\vec at[/tex]
Over the 0.215 s interval, the velocity changes to
[tex]\vec v=\left(6.42\dfrac{\rm m}{\rm s}\right)(\cos50.0^\circ\,\vec\imath+\sin50.0^\circ\,\vec\jmath)=(4.13\,\vec\imath+4.92\,\vec\jmath)\dfrac{\rm m}{\rm s}[/tex]
Then the acceleration must have been
[tex]\vec v=\vec v_0+(0.215\,\mathrm s)\vec a\implies\vec a=\dfrac{\vec v-\vec v_0}{0.215\,\rm s}=(9.06\,\vec\imath+27.0\,\vec\jmath)\dfrac{\rm m}{\mathrm s^2}[/tex]
which has a direction of about [tex]71.4^\circ[/tex].
The direction of the acceleration is determined by the direction of the change in velocity. This would be calculated by subtracting the initial velocity vector from the final velocity vector. However, the calculation would involve complex trigonometric functions.
Explanation:In order to find the direction of the acceleration, we need to calculate the direction of the change in velocity and that direction will be the direction of the acceleration.
To calculate the change in velocity, we subtract the initial velocity from the final velocity: (6.42 m/s, 50.0°) - (2.35 m/s, -22°). We then calculate the angle of this vector which represents the change in velocity, and hence the direction of acceleration.
However, this calculation is not straightforward because it involves vector operations and would require the use of trigonometric functions to solve. This is due to the fact that velocity is a vector, meaning it has both a magnitude and a direction. Consequently, this becomes a multi-step process involving trigonometry and physics.
Learn more about Direction of Acceleration here:https://brainly.com/question/33720661
#SPJ2
How many protons are in a single nucleus of 5626fe?
26 protons are in single nucleus of 5626fe
A long, slender structural steel [E = 29,000 ksi] HSS8 x 4 x 1/4 shape (see Appendix B for its cross-sectional properties) is used as a L = 43.50-ft-long column. The column is supported in the x direction at base A and pinned at ends A and C against translation in the y and z directions. Lateral support is provided to the column so that deflection in the x–z plane is restrained at mid-height B; however, the column is free to deflect in the x–y plane at B. Determine the maximum compressive load that the column can support if a factor of safety of 1.90 is required. In your analysis, consider the possibility that buckling could occur about either the strong axis (i.e., the z axis) or the weak axis (i.e., the y axis) of the steel column.
Answer:44(,5 v
Explanation:
Ggthnu
As more resistors are added in parallel across a constant voltage source, the power supplied by the source as more resistors are added in parallel across a constant voltage source, the power supplied by the source increases for a time and then starts to decrease. increases. decreases. does not change.
Answer:
increases
Explanation:
In a circuit, the power supplied by the source is given by:
[tex]P=VI[/tex] (1)
where V is the voltage of the source and I is the current in the circuit.
Using Ohm's law, we can rewrite the current as:
[tex]I=\frac{V}{R}[/tex]
where R is the equivalent resistance of the circuit. Substituting into (1), we can rewrite the power as
[tex]P= \frac{V^2}{R}[/tex] (2)
so we see that the power is inversely proportional to the resistance.
For resistors added in parallel, the equivalent resistance is given by the formula
[tex]\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}[/tex]
so we see that when adding new resistors in parallel, the term [tex]\frac{1}{R}[/tex] increases, so the equivalent resistance R will decreases. As a result, the power supplied by the source (given by eq.(2)) wil increase.
As more resistors are added in parallel across a constant voltage source the power will; increase
Formula for Poweer across a circuit with constant voltage is;
P = I²R
Where;
P is Power I is currentR is resistance Now, when resistors are connected in parallel, the total resistance is usually;1/R = 1/R1 + 1/R2 + 1/R3....
Where R is total resistance.
This means that the more resistors you add in parallel, the greater the value of R.
Thus, from the Power equation, when R increases, then P will also increase.Read more about Power - Resistance relationship at; https://brainly.com/question/1637533
Micah knows that a car had a change in velocity of 15 m/s. To determine acceleration, Micah also needs the_______________
of the total trip in seconds.
Answer:
Duration of the total trip
Explanation:
Acceleration is defined as the rate of change of velocity of an object:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
where
[tex]\Delta v[/tex] is the change in velocity
[tex]\Delta t[/tex] is the duration of the change in velocity
Acceleration is measured in meters per squared seconds, [tex]m/s^2[/tex]. Also, we should note that acceleration is a vector quantity, so in order to completely define acceleration we also need to specify the direction.
Answer: Time
Explanation: Took the test and got it right! :)
Steve is whirling a rubber cork, tied with a string to his finger, over his head as shown in the figure. The motion of the cork is similar to the motion of a planet in the solar system around the sun. Which force in the solar system is similar to the tension in the string?
The tension in the string corresponds to the gravitational attraction between the Sun and any planet.
Answer:
Gravitational Force.Explanation:
While Steve is whirling a rubber cork, it developes a situation which is similar to the Solar System. In the rubber cork movement, there's "circular" motion which is possible thanks to the string, that is, the string works as "attraction force", allowing the system to maintain its movement.
Now, in the Solar System, the graviational force is like the string, it's the physical magnitude that maintains planets on their movements, attached to the Sun someway.
Use the following half-life graph to answer the following question:
A graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. A curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.562.
The graph is attached.
When you are left with 6.25 mg of the radioactive isotope, how many half-lives have occurred from time equals zero? (5 points)
A. 1
B. 3
C. 6
D. 12
Answer:
B. 3
Explanation:
The half-life of a radioisotope is the time it needs for the mass of the radioisotope to halve with respect to its original value.
In this problem, the initial mass of the radioisotope at t=0 is
m0 = 50.0 mg
We see that after t = 1 min, the mass of the isotope is
m(1 min) = 25.0 mg
so, exactly half the initial mass: this means that 1 minute is exactly the half-life of this radioisotope.
So, the amount of mass left after each minute is the following:
m (1 min ) = 25.0 mg (1 half-life)
m (2 min) = 12.5 mg (2 half-lives)
m (3 min) = 6.25 mg (3 half-lives)
so, when we are left with 6.25 mg of isotope, 3 minutes have passed, which means that 3 half-lives have passed.
Low pH means that the hydrogen-ion concetration is ________.
in the middle
equal to the pH number
high
low
Final answer:
Low pH indicates a high hydrogen-ion concentration, showcasing that the environment is acidic.
Explanation:
Low pH means that the hydrogen-ion concentration is high. The pH scale is a logarithmic representation of hydrogen ion concentration, where a low pH number indicates a higher concentration of H+ ions, creating an acidic environment. In contrast, a high pH suggests a lower concentration of hydrogen ions and a basic or alkaline condition. For example, a pH of 3 is ten times more acidic than a pH of 4 due to the logarithmic scale of pH, where each whole number change represents a tenfold change in ion concentration.
The National Grid supplied a house with 18,000,000 J of energy in 1 hour. What was the average current supplied to the house during that hour?
I got 0.0126, but it feels wrong.
A 59kg physics student jumps, off the back of her laser sailboat (42 kg) after she jumps the laser is found to be traveling at 1.5 m/s. What is the speed of the physics student?
In order to be able to calculate an answer, we must assume that the boat, with her on it, was motionless in the water until she jumped off of it.
I'll make that assumption, and then I'll go ahead and answer the question that I just invented:
-- Before she jumped off of the boat, she had no momentum and the boat had no momentum.
-- The SUM of (her momentum) + (the boat's momentum) was zero.
-- Momentum is conserved, so the SUM of (her momentum) + (the boat's momentum) has to still be zero after she jumps off of the boat.
-- Momentum = (mass) · (speed in some direction)
The boat's momentum after the jump = (42kg) · (1.5 m/s) that way ==>
The boat's momentum after the jump = 63 kg-m/s that way ==>
Her momentum after the jump has to be 63 kg-m/s this way <==
Her momentum = 63 kg-m/s = (59 kg) · (her speed this way <== )
Divide each side by (59 kg):
Her speed this way <== = (63 kg-m/s <==) / (59 kg)
Her speed = (63/59) · (m/s this way <== )
Her speed = 1.07 m/s opposite to the direction the boat is moving.
= = = = = = = = = =
A casual but striking observation:
Our 'student' is carrying 17 kg more mass than the boat she sails !
The mind boggles at the implied zaftigkeit.
To find the speed of the physics student, we can use the principle of conservation of momentum. By setting up an equation using the initial and final velocities of both the student and the sailboat, we can solve for the final velocity of the student. The answer is approximately 0.038 m/s.
Explanation:To solve this problem, we can use the principle of conservation of momentum. The initial momentum of the system, which includes the student and the laser sailboat, is equal to the final momentum of the system. The momentum of an object is calculated by multiplying its mass by its velocity. We know the mass and velocity of the laser sailboat after the student jumps off, so we can use that information to find the speed of the physics student.
We can set up the equation as follows:
(mass of student)(initial velocity of student) + (mass of sailboat)(initial velocity of sailboat) = (mass of student)(final velocity of student) + (mass of sailboat)(final velocity of sailboat)
Plugging in the given values, we have:
(59 kg)(0 m/s) + (42 kg)(0 m/s) = (59 kg)(final velocity of student) + (42 kg)(1.5 m/s)
Simplifying the equation, we find that the final velocity of the student is approximately 0.038 m/s.
Learn more about Conservation of momentum here:https://brainly.com/question/33316833
#SPJ3
I will mark brainliest!
.............
...........
............
Kim is making a model of the energy pyramid for class. What level is represented at the bottom level of an energy pyramid?
A) biomass
B) producers
C) autotrophic level
D)primary consumers
Answer:
The correct answer is B. Producers
Please mark brainliest when possible! Thanks! Have a great day!!
Explanation:
A discrete, distinct pattern of specific wavelength against a background of continuous spectrum
answer:
absorption spectrum
An object is placed a great distance from a concave (converging) mirror. Where will light from the object be collected?
A) at the focal length of the mirror on the same side of the mirror as the object
B) at the focal length of the mirror on the opposite side of the mirror from the object
C) at the center of curvature of the mirror on the same side of the mirror as the object
D) at the center of curvature of the mirror on the opposite side of the mirror from the object
Answer: at the center of curvature of the mirror on the same side of the mirror as the object
A concave mirror has a reflective surface that is curved inwards. This type of mirrors reflects the light making it converge in a focal point, therefore they are used to focus the light.
This occurs because the light is reflected with different angles, since the normal to the surface varies from one point to another of the mirror.
Nevertheless, it is important to note the object must be within the radius of curvature of the mirror.
In addition, it is important to state clear the following:
-If the object is at a distance greater than the focal distance, a real and inverted image is formed that may be greater or less than the object.
-If the object is at a distance smaller than the focal distance, a virtual image is formed, right and larger than the object.
In this case the object is placed a great distance (it can be said at infinite) from the concave mirror, hence the image formed will be real, inverted and smaller than the object.
When we say real, it means the image is formed in the same side of the mirror as the object and the image can be seen on a screen.
Answer:
At the focal length of the mirror on the same side of the mirror as the object
Explanation: I had this question on USA test prep and I used the answer that the other guy said and it was incorrect. so the correct answer is
A)
at the focal length of the mirror on the same side of the mirror as the object
The Sun’s light only strikes one side of Earth at a time. The dark side of Earth stays warm because the Sun’s heat A) is stored in the ice caps. B) is trapped by the atmosphere. C) is blown there by the wind. D) is conducted through the Earth.
During the day, the atmosphere lets through solar radiation that heats the Earth's surface. Once the surface of the planet has warmed up, this heat is returned to space in the form of infrared radiation.
However, not all infrared radiation is returned to space, because the same atmosphere (specifically carbon dioxide and water vapor present in it) prevents the release of much of this thermal radiation, reflecting part of it and returning it to the surface; thus maintaining the heat and allowing life on our planet. This phenomenon is known as the greenhouse effect.
Thus, of the solar energy that reaches the Earth by radiation, only a small percentage is reflected back into space by the surface and the atmosphere.
In fact, if the atmosphere did not exist, all that heat would completely escape into space and the Earth would cool rapidly during the night.
Therefore, the correct option is B:
The dark side of Earth stays warm because the Sun’s heat is trapped by the atmosphere.You’re driving your car towards an intersection. A Porsche is stopped at the red light. You’re traveling at 36 km/h (10 m/s). As you are 15 m from the light, the light turns green, and the Porsche accelerates from rest at 3 m/s2. You continue at constant speed. a. How far from the stop line do you pass the Porsche? At what time, measured from when the light turned green, do you pass the Porsche? b. As the Porsche keeps accelerating, it eventually catches up to you again. How far from the stop line does it pass you? At what time, measured from when the light turned green, does it pass you? c. If a Boston police officer happens to get you and the Porsche on a radar gun at the instant the Porsche passes you, will either of you be pulled over for speeding? Assume the speed limit is 50 km/h.
To find the distances and times at which the two cars pass each other, we can use equations of motion. The car passes the Porsche at 20 meters and 2 seconds after the light turns green. The Porsche passes the car at 60 meters and 5 seconds after the light turns green.
Explanation:To solve this problem, we will use equations of motion to find the distances and times at which the two cars pass each other. Given that the Porsche starts from rest and accelerates at 3 m/s², we can use the equation x = xo + vot + ½at² to find the distance it travels before the other car reaches it. Similarly, for the other car which is traveling at a constant speed of 10 m/s, we can use the equation x = Ut. By solving these equations simultaneously, we can find the distances and times at which the two cars pass each other.
a. The distance at which you pass the Porsche can be found by setting the distances traveled by both cars equal to each other: 10t = 15 + 0.5(3)(t²). By solving this equation, we find that you pass the Porsche at a distance of 20 m from the stop line and at a time of 2 seconds after the light turns green.
b. To find the distance at which the Porsche passes you, we need to find the time at which the Porsche catches up to you. We can do this by setting the equation for the Porsche's distance equal to your distance: 15 + 0.5(3)(t²) = 10t. Solving this equation gives us a time of 5 seconds after the light turns green. Plugging this time into the equation for your distance, we find that the Porsche passes you at a distance of 60 meters from the stop line.
c. To determine if either of you will be pulled over for speeding, we need to compare your speeds to the speed limit of 50 km/h. Your speed is given as 36 km/h (10 m/s), which is less than the speed limit. The Porsche's speed can be found by taking the derivative of its distance equation with respect to time: v = at. Plugging in the time at which it passes you, we find that its speed is 30 m/s, which is also less than the speed limit. Therefore, neither of you will be pulled over for speeding.
Learn more about Motion here:https://brainly.com/question/35591666
#SPJ3
You pass the Porsche 16.65 meters beyond the stop line at 3.33 seconds, while the Porsche catches up 66.7 meters from the stop line at 6.67 seconds. Only the Porsche would be pulled over for speeding. The primary topic is the analysis of two moving vehicles using physics.
Part (a): When Do You Pass the Porsche?Your car's constant speed is [tex]36 km/h[/tex] or [tex]10 m/s[/tex] . The Porsche accelerates from rest at [tex]3 m/s^2[/tex].
Calculate the time it takes for the Porsche to reach your speed:
Using the equation: [tex]v = u + at[/tex],
where[tex]v = 10 m/s[/tex],[tex]u = 0[/tex], and[tex]a = 3 m/s^2[/tex], we get [tex]t = v/a = 10/3 \approx 3.33 seconds[/tex].
Now, find the distance the Porsche covers in this time with the equation: [tex]s = ut + 0.5at^2[/tex], where[tex]u = 0[/tex], [tex]a = 3 m/s^2[/tex] and [tex]t = 3.33 seconds[/tex],
thus [tex]s = 0.5 \times 3 \times 3.332 \approx 16.65 meters[/tex].
Your car covers [tex]3.33 \times 10 = 33.3 meters[/tex] in this same time.
Hence, you pass the Porsche [tex]33.3 - 16.65 = 16.65 meters[/tex] beyond the stop line.
Part (b): When Does the Porsche Pass You Again?To find when the Porsche catches up, consider the distance equations for both vehicles:
Your distance: [tex]d_{you}(t) = 10t[/tex].
Porsche’s distance: dporsche(t) = 0.5 * 3 * t2.
Set the distances equal to solve for [tex]t: 10t = 1.5t2[/tex], leading to [tex]t = 0[/tex] or [tex]t = 10/1.5 = 6.67 seconds[/tex].
The Porsche catches up [tex]0.5 \times 3 \times 6.672 = 66.7[/tex]meters from the stop line.
Part (c): Speeding CheckDetermine both cars' speeds when the Porsche passes you again:
Your speed:[tex]10 m/s = 36 km/h[/tex], under the limit.
Porsche’s speed: [tex]v = u + at = 3 \times 6.67 = 20.01 m/s \approx 72 km/h[/tex], over the limit.
Thus, only the Porsche would be pulled over for speeding.
Consider a sample of water at 0 degrees C. If the temperature is slightly increased, the volume of the water
A) increases
B) decreases
C) remains the same
Answer:
B) decreases
Explanation:
The density of water is maximum at a temperature of [tex]4^{\circ} C[/tex]. This means that:
- For temperatures between 0 and 4 degrees C, as the temperature increases, the density increases
- For temperatures above 4 degrees C, as the temperature increases, the density decreases
The density is related to the volume by the formula:
[tex]d=\frac{m}{V}[/tex]
where m is the mass and V the volume. Therefore, density is inversely proportional to the volume. This means that, for a constant amount of mass:
- For temperatures between 0 and 4 degrees C, as the temperature increases, the volume decreases
- For temperatures above 4 degrees C, as the temperature increases, the volume increases
Therefore, for a sample of water at 0 degrees C, if the temperature is slightly increased, the volume of the water will decreases, because its density will increase.
Final answer:
If the temperature of water slightly increases from 0 degrees Celsius, the volume decreases because of the anomalous expansion of water until it approaches 4 degrees Celsius, where it begins to expand normally again.
Explanation:
When considering a sample of water at 0 degrees Celsius, if the temperature is slightly increased, the volume of water decreases. This is due to the anomalous expansion of water, which is a unique property where water expands as it cools down from 4 degrees Celsius to 0 degrees Celsius and reaches its maximum density at 4 degrees Celsius. As the temperature rises slightly above 0 degrees Celsius, water begins to contract until it approaches 4 degrees Celsius, where it will start expanding again. This is in contrast to most substances which expand when heated.
Describe the direction of the electric force between two opposite charges, between two like charges, and when a charge is in an electric field.
- Two opposite charges:
The electrostatic force between two opposite charges is attractive. This means that if we have a positive charge and a negative charge, the electrostatic force between them is attractive.
- Two like charges:
The electrostatic force between two like charges is repulsive. This means that if we have two positive charges, or two negative charges, the force exerted by one charge on the other one is repulsive.
- A charge in an electric field:
The direction of the electric force on a charge in an electric field depends on the sign of the charge. In fact, we have
[tex]F=qE[/tex]
where F is the electric force, q is the charge, and E the electric field. We have the two following situations:
- If the charge is positive, q > 0, then the electric force has the same direction as the electric field (so the charge will be accelerated in the same direction as the electric field)
- If the charge is negative, q < 0, then the electric force has opposite direction to the electric field (so the charge will be accelerated in the opposite direction to the electric field)
Like charges repel each other and unlike charges attract each other. The direction of the force when a charge is placed in an electric field depends on whether the charge is positive (same direction as the field) or negative (opposite direction as the field).
Explanation:The electric force that exists between two charges can be determined by their nature. If the charges are similar, that is, both are either positive or negative, then the direction of the electric force will be repulsive, and they push each other away. The electric field lines in this case would emanate away from the charges.
On the other hand, if the charges are dissimilar (that is, one positive and one negative), then the direction of the electric force is attractive—they pull towards each other. The electric field lines in this case would point from the positive charge towards the negative one.
When a charge is placed in an electric field, the direction of the force it experiences depends on its nature. If the charge is positive, it will experience a force in the direction of the field. If it's negative, the force will be in the opposite direction to the field.
Learn more about Electric Force here:https://brainly.com/question/21093704
#SPJ6
The wavelength of red helium-neon laser light in air is 632.8 nm.(a) What is its frequency? Hz(b) What is its wavelength in glass that has an index of refractionof 1.48? nm(c) What is its speed in the glass? Mm/s
The speed of a wave is given by:
[tex]v=f.\lambda[/tex] (1)
Where [tex]f[/tex] is the frequency and [tex]\lambda[/tex] the wavelength.
In the case of light, its speed is:
[tex]c=f.\lambda[/tex] (2)
On the other hand, the described situation is known as Refraction, a phenomenon in which the light changes its direction when passing through a medium with a refractive index different from the other medium.
In this context, the Refractive index [tex]n[/tex] is a number that describes how fast light propagates through a medium or material, and is defined as the relation between the speed of light in vacuum ([tex]c=3(10)^{8}m/s[/tex]) and the speed of light [tex]v[/tex] in the second medium:
[tex]n=\frac{c}{v}[/tex] (3)
In addition, as the light changes its direction, its wavelength changes as well:
[tex]n=\frac{\lambda_{air}}{\lambda_{glass}}[/tex] (4)
Knowing this, let's begin with the answers:
a) FrequencyFrom equation (2) we can find [tex]f[/tex]:
[tex]f=\frac{c}{\lambda}[/tex] (5)
Knowing that [tex]1nm=(10)^{-9}m[/tex]:
[tex]f=\frac{3(10)^{8}m/s}{632.8(10)^{-9}m}[/tex]
[tex]f=4.74(10)^{14}Hz}[/tex] (6) >>>Frequency of the helium-neon laser light
b) Wavelength in glassWe already know the wavelength of the light in air [tex]\lambda_{air}[/tex] and the index of refraction of the glass.
So, we only have to find the wavelength in glass [tex]\lambda_{glass}[/tex] from equation (4):
[tex]\lambda_{glass}=\frac{\lambda_{air}}{n}[/tex]
[tex]\lambda_{glass}=\frac{632.8(10)^{-9}m}{1.48}[/tex]
[tex]\lambda_{glass}=427(10)^{-9}m=427nm[/tex] (7) >>>Wavelength of the helium-neon laser light in glass
c) Speed in glassFrom equation (3) we can find the speed [tex]v[/tex]of this light in glass:
[tex]v=\frac{c}{n}[/tex]
[tex]v=\frac{3(10)^{8}m/s}{1.48}[/tex]
[tex]v=2.027(10)^{8}m/s[/tex] (8) >>>Speed of the helium-neon laser light in glass
The frequency of the red helium-neon laser light is approximately 4.74 x 10^14 Hz. When it travels in glass (with index of refraction 1.48), its wavelength shortens to 427.6 nm, and its speed reduces to about 203 Mm/s.
Explanation:The wavelength of the red helium-neon laser light in air is given as 632.8 nm.
(a) Frequency: To calculate the frequency of the light, we can use the formula: frequency = speed of light / wavelength. Given the speed of light (c) is approximately 3.00 x 10^8 m/s, we can convert the wavelength from nm to m (1 nm = 1 x 10^-9 m), giving us 632.8 x 10^-9 m. Therefore, frequency (f) = 3.00 x 10^8 m/s / 632.8 x 10^-9 m = 4.74 x 10^14 Hz.
(b) Wavelength in Glass: The wavelength of light is smaller in a medium as compared to vacuum. We use the formula: wavelength in medium = wavelength in vacuum / index of refraction. Substituting the values: wavelength in glass = 632.8 nm / 1.48 = 427.6 nm.
(c) Speed in Glass: The speed of light in a medium is also dependent on refractive index, calculated with the formula: speed in medium = speed in vacuum / index of refraction. Therefore, speed in glass = 3.00 x 10^8 m/s / 1.48 ≈ 2.03 x 10^8 m/s, which is 203 Mm/s when converted to Mm/s.
Learn more about Physics of Light here:https://brainly.com/question/9695421
#SPJ3
Help with vectors?
Find both the x and y components of the vector below.
Answer:
10 m and 17.3 m
Explanation:
We can notice that the vector B represents the hypothenuse of a right triangle, in which the x-component of the vector is the side opposite to the [tex]30^{\circ}[/tex] angle, while the y-component of the vector corresponds to the side adjacent to the [tex]30^{\circ}[/tex] angle. This means that we can find the two components of the vector by using the sine and cosine function as follows:
[tex]B_x = B sin 30^{\circ} = (20 m) sin 30^{\circ}=10 m[/tex]
[tex]B_y = B cos 30^{\circ} = (20 m) cos 30^{\circ}=17.3 m[/tex]
describe two different types of paths a raindrop falling in the mountains might take to reach the ocean
First surface runoff then ground water...
A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?
Answer:
-10.9 rad/s²
Explanation:
ω² = ω₀² + 2α(θ - θ₀)
Given:
ω = 13.5 rad/s
ω₀ = 22.0 rad/s
θ - θ₀ = 13.8 rad
(13.5)² = (22.0)² + 2α (13.8)
α = -10.9 rad/s²
Use the formula
[tex]{\omega_f}^2-{\omega_i}^2=2\alpha\Delta\theta[/tex]
[tex]\implies\left(13.5\dfrac{\rm rad}{\rm s}\right)^2-\left(22.0\dfrac{\rm rad}{\rm s}\right)^2=2\alpha(13.8\,\mathrm{rad})[/tex]
[tex]\implies\alpha=-10.9\dfrac{\rm rad}{\mathrm s^2}[/tex]
so the magnitude is 10.9 rad/s^2.
Consider an object with s=12cm that produces an image with s′=15cm. Note that whenever you are working with a physical object, the object distance will be positive (in multiple optics setups, you will encounter "objects" that are actually images, but that is not a possibility in this problem). A positive image distance means that the image is formed on the side of the lens from which the light emerges.Part AFind the focal length of the lens that produces the image described in the problem introduction using the thin lens equation.Express your answer in centimeters, as a fraction or to three significant figures.f = 6.67 cm SubmitMy AnswersGive UpCorrectPart BConsidering the sign of f, is the lens converging or diverging?Considering the sign of , is the lens converging or diverging?convergingdivergingSubmitMy AnswersGive UpCorrectPart CWhat is the magnification m of the lens?Express your answer as a fraction or to three significant figures.m = -1.25SubmitMy AnswersGive UpCorrectPart DThink about the sign of s′ and the sign of y′, which you can find from the magnification equation, knowing that a physical object is always considered upright. Which of the following describes the nature and orientation of the image?Think about the sign of and the sign of , which you can find from the magnification equation, knowing that a physical object is always considered upright. Which of the following describes the nature and orientation of the image?real and uprightreal and invertedvirtual and uprightvirtual and invertedSubmitMy AnswersGive UpCorrectNow consider a diverging lens with focal length f=−15cm, producing an upright image that is 5/9 as tall as the object.Part EIs the image real or virtual? Think about the magnification and how it relates to the sign of s′.Is the image real or virtual? Think about the magnification and how it relates to the sign of .realvirtualSubmitMy AnswersGive UpCorrectPart FWhat is the object distance? You will need to use the magnification equation to find a relationship between sand s′. Then substitute into the thin lens equation to solve for s.Express your answer in centimeters, as a fraction or to three significant figures.s = 12.0 cm SubmitMy AnswersGive UpCorrectPart GWhat is the image distance?Express your answer in centimeters, as a fraction or to three significant figures.s′ = 24 cm SubmitMy AnswersGive UpIncorrect; Try Again; 12 attempts remaining; no points deductedA lens placed at the origin with its axis pointing along the x axis produces a real inverted image at x=−24cmthat is twice as tall as the object.Part HWhat is the image distance?Express your answer in centimeters, as a fraction or to three significant figures.s′ = 24.0 cm
A. 6.67 cm
The focal length of the lens can be found by using the lens equation:
[tex]\frac{1}{f}=\frac{1}{s}+\frac{1}{s'}[/tex]
where we have
f = focal length
s = 12 cm is the distance of the object from the lens
s' = 15 cm is the distance of the image from the lens
Solving the equation for f, we find
[tex]\frac{1}{f}=\frac{1}{12 cm}+\frac{1}{15 cm}=0.15 cm^{-1}\\f=\frac{1}{0.15 cm^{-1}}=6.67 cm[/tex]
B. Converging
According to sign convention for lenses, we have:
- Converging (convex) lenses have focal length with positive sign
- Diverging (concave) lenses have focal length with negative sign
In this case, the focal length of the lens is positive, so the lens is a converging lens.
C. -1.25
The magnification of the lens is given by
[tex]M=-\frac{s'}{s}[/tex]
where
s' = 15 cm is the distance of the image from the lens
s = 12 cm is the distance of the object from the lens
Substituting into the equation, we find
[tex]M=-\frac{15 cm}{12 cm}=-1.25[/tex]
D. Real and inverted
The magnification equation can be also rewritten as
[tex]M=\frac{y'}{y}[/tex]
where
y' is the size of the image
y is the size of the object
Re-arranging it, we have
[tex]y'=My[/tex]
Since in this case M is negative, it means that y' has opposite sign compared to y: this means that the image is inverted.
Also, the sign of s' tells us if the image is real of virtual. In fact:
- s' is positive: image is real
- s' is negative: image is virtual
In this case, s' is positive, so the image is real.
E. Virtual
In this case, the magnification is 5/9, so we have
[tex]M=\frac{5}{9}=-\frac{s'}{s}[/tex]
which can be rewritten as
[tex]s'=-M s = -\frac{5}{9}s[/tex]
which means that s' has opposite sign than s: therefore, the image is virtual.
F. 12.0 cm
From the magnification equation, we can write
[tex]s'=-Ms[/tex]
and then we can substitute it into the lens equation:
[tex]\frac{1}{f}=\frac{1}{s}+\frac{1}{s'}\\\frac{1}{f}=\frac{1}{s}+\frac{1}{-Ms}[/tex]
and we can solve for s:
[tex]\frac{1}{f}=\frac{M-1}{Ms}\\f=\frac{Ms}{M-1}\\s=\frac{f(M-1)}{M}=\frac{(-15 cm)(\frac{5}{9}-1}{\frac{5}{9}}=12.0 cm[/tex]
G. -6.67 cm
Now the image distance can be directly found by using again the magnification equation:
[tex]s'=-Ms=-\frac{5}{9}(12.0 cm)=-6.67 cm[/tex]
And the sign of s' (negative) also tells us that the image is virtual.
H. -24.0 cm
In this case, the image is twice as tall as the object, so the magnification is
M = 2
and the distance of the image from the lens is
s' = -24 cm
The problem is asking us for the image distance: however, this is already given by the problem,
s' = -24 cm
so, this is the answer. And the fact that its sign is negative tells us that the image is virtual.
The correct answers to the questions are:
A. 6.67 cmB. ConvergingC. -1.25D. Real and invertedE. VirtualF. 12.0 cmG. -6.67 cmH. -24.0 cmCalculationsTo find the image distance for the question in question G is by the use of the magnification equation which is:
s1= -Ms
=> -5/9(12cm)
=> -6.67cm.
Because the value is negative, we know that the image is virtual.
Read more about lenses here:
https://brainly.com/question/9757866
A conductor carrying a conventional current in the positive-x direction is in a magnetic field whose vector points in the positive-y direction. A force on the conductor will be in the:
positive-z direction (out of the screen)
negative-z direction (into the screen)
negative-y direction
negative-x direction
Answer:
Positive Z direction (out of screen)
Explanation:
Magnetic force is given by [tex]F = il \wedge B[/tex]. A quick way to gauge the components is to put your left middle finger on the direction of the current, your index on the direction of the magnetic field, and the thumb gives you the answer you want.
Answer:
positive-z direction (out of the screen)
Explanation:
As we know that length vector of the current carrying conductor is always along the direction of conventional current
So here direction of length vector will be + X direction
magnetic field is along + Y direction
now we will have
[tex]\vec F = I(\vec L \times \vec B)[/tex]
now we will have
[tex]\vec F = ILB(\hat i \times \hat j)[/tex]
[tex]\vec F = ILB\hat k[/tex]
so magnetic force will be along +Z direction (out of the screen)