A free particle moving in one dimension has wave function
Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)]
where k and ω are positive real constants.
Part A
At t = 0 what are the two smallest positive values of x for which the probability function |Ψ(x,t)|2 is a maximum?
Express your answers in terms of the variable k and π. Enter your answers in ascending order separated by a comma.
Part B
At t = 2π/ω what are the two smallest positive values of x for which the probability function |Ψ(x,t)|2 is a maximum?
Express your answers in terms of the variable k and π. Enter your answers in ascending order separated by a comma.
Part C
Calculate vav as the distance the maxima have moved divided by the elapsed time.
Express your answer in terms of the variables ω and k
Answers
Part A:
The two smallest positive values of x for which the probability function |Ψ(x,t)|² is a maximum at t = 0 are x = π/k and x = 2π/k.
Part B:
The two smallest positive values of x for which the probability function |Ψ(x,t)|² is a maximum at t = 2π/ω are x = π/2k and x = 3π/2k.
Part C:
The average velocity, vav, can be calculated as the distance the maxima have moved divided by the elapsed time. Since the maxima occur at x = π/k and x = 2π/k, the distance traveled by the maxima is π/k - (2π/k) = -π/k. The elapsed time is t = 2π/ω - 0 = 2π/ω. Therefore, the average velocity can be calculated as:
vav = (distance traveled) / (elapsed time)
vav = (-π/k) / (2π/ω)
vav = -ω/(2k)
Part A:
To find the values of x for which the probability function |Ψ(x,t)|² is a maximum at t = 0, we need to maximize the expression |Ψ(x,0)|². The probability function is given by |Ψ(x,t)|² = |A[ei(kx) - ei(2kx)]|² = |A|² |ei(kx) - ei(2kx)|².
Using the identity |a - b|² = (a - b)(a* - b*), we can expand the probability function:
|Ψ(x,t)|² = |A|² [ei(kx) - ei(2kx)][ei(kx)* - ei(2kx)]
= |A|² [ei(kx)ei(kx) - ei(kx)ei(2kx)* - ei(2kx)ei(kx)* + ei(2kx)ei(2kx)]
= |A|² [1 - ei(kx)ei(2kx) - ei(2kx)ei(kx)* + 1]
= 2|A|² [1 - cos(kx)cos(2kx) + sin(kx)sin(2kx)].
To find the maximum values, we set the derivative of |Ψ(x,0)|² with respect to x equal to zero:
d/dx |Ψ(x,0)|² = 2|A|² [k sin(kx)cos(2kx) + 2k cos(kx)sin(2kx)] = 0.
Simplifying the equation gives:
k sin(kx)cos(2kx) + 2k cos(kx)sin(2kx) = 0.
Dividing both sides by kcos(kx)cos(2kx), we get:
tan(kx) = -2tan(2kx).
Using the trigonometric identity tan(2θ) = 2tan(θ)/(1 - tan²(θ)), we can rewrite the equation as:
tan(kx) = -4tan(kx)/(1 - tan²(kx)).
Simplifying further, we have:
tan(kx)[1 - 4/(1 - tan²(kx))] = 0.
Since tan(kx) ≠ 0, we have:
1 - 4/(1 - tan²(kx)) = 0.
Solving for tan²(kx), we get:
tan²(kx) = 4.
Taking the square root, we obtain:
tan(kx) = ±2.
From the properties of the tangent function, we know that the smallest positive values of kx for which tan(kx) = 2 are kx = π/4 and kx = 5π/4.
Therefore, the two smallest positive values of x for which |Ψ(x,t)|² is a maximum at t = 0 are x = π/k and x = 2π/k.
Part B:
To find the values of x for which the probability function |Ψ(x,t)|² is a maximum at t = 2π/ω, we follow a similar approach as in Part A.
The probability function at t = 2π/ω is given by:
|Ψ(x,t)|² = |A|² [ei(kx - 2ωt) - ei(2kx - 4ωt)][ei(kx - 2ωt)* - ei(2kx - 4ωt)*].
Expanding and simplifying, we find:
|Ψ(x,t)|² = 2|A|² [1 - cos(kx - 2ωt)cos(2kx - 4ωt) + sin(kx - 2ωt)sin(2kx - 4ωt)].
Setting the derivative of |Ψ(x,t)|² with respect to x equal to zero, we obtain:
k sin(kx - 2ωt)cos(2kx - 4ωt) + 2k cos(kx - 2ωt)sin(2kx - 4ωt) = 0.
Dividing by kcos(kx - 2ωt)cos(2kx - 4ωt) and simplifying, we get:
tan(kx - 2ωt) = -2tan(2kx - 4ωt).
Using the tangent identity, we have:
tan(kx - 2ωt) = -4tan(kx - 2ωt)/(1 - tan²(kx - 2ωt)).
Simplifying further, we obtain:
tan(kx - 2ωt)[1 - 4/(1 - tan²(kx - 2ωt))] = 0.
Since tan(kx - 2ωt) ≠ 0, we have:
1 - 4/(1 - tan²(kx - 2ωt)) = 0.
Solving for tan²(kx - 2ωt), we get:
tan²(kx - 2ωt) = 4.
Taking the square root, we have:
tan(kx - 2ωt) = ±2.
From the properties of the tangent function, we know that the smallest positive values of kx - 2ωt for which tan(kx - 2ωt) = 2 are kx - 2ωt = π/4 and kx - 2ωt = 5π/4.
Adding 2ωt to both sides, we find:
kx = π/4 + 2ωt and kx = 5π/4 + 2ωt.
At t = 2π/ω, we substitute the given value and simplify:
kx = π/4 + 2(2π/ω) = π/4 + 4π/ω = (4π + 16π)/(4ω) = 20π/(4ω) = 5π/(ω).
Similarly,
kx = 5π/4 + 2(2π/ω) = 5π/4 + 4π/ω = (5π + 16π)/(4ω) = 21π/(4ω).
Therefore, the two smallest positive values of x for which |Ψ(x,t)|² is a maximum at t = 2π/ω are x = π/(2k) and x = 5π/(2k).
Part C:
The average velocity, vav, can be calculated as the distance the maxima have moved divided by the elapsed time.
From Part A, we found that the maxima move from x = π/k to x = 2π/k in the elapsed time t = 2π/ω.
Therefore, the distance traveled by the maxima is given by:
distance traveled = (2π/k) - (π/k) = π/k.
The elapsed time is t = 2π/ω.
Hence, the average velocity, vav, is given by:
vav = (distance traveled) / (elapsed time)
= (π/k) / (2π/ω)
= (π/k) * (ω/(2π))
= ω/(2k).
Therefore, the average velocity vav is equal to ω/(2k).
In conclusion, the two smallest positive values of x for which the probability function |Ψ(x,t)|² is a maximum at t = 0 are x = π/k and x = 2π/k. At t = 2π/ω, the two smallest positive values of x for which |Ψ(x,t)|² is a maximum are x = π/(2k) and x = 5π/(2k). The average velocity, vav, is equal to ω/(2k).
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Related Questions
Describe the relationship between the materials and amount of thermal energy transfer?
Answers
Answer:If you mean how much heat it can transfer as a thermal mass - in order to move heat from one place to another:
Typically the relationships are given by specific heat capacity (at different temperatures) and latent heats, plus the end-point temperatures to determine which of these conversion factors are relevant.
If time comes into it, you are looking at including shape and thermal conductivity at the minimum, so you really would need to be more specific
Explanation:
The position of a particle in millimeters is given by s=102−23t+t ^2 where t is in seconds. Plot the s-t and v-t relationships for the first 17 seconds. Determine the net displacement Δs during that interval and the total distance D traveled. By inspection of the s-t relationship, what conclusion can you reach regarding the acceleration? Answers: Δ5= mm D= mm
Answers
The given position equation of a particle is, s=102−23t+t2Here, t is in seconds.The first derivative of s is its velocity: v = ds/dt - 23 + 2tThe second derivative of s is the particle's acceleration:
The total distance traveled is the sum of all distance travelled in each interval of time: D = ∫|v|dt + ∫|v|dt + ... (From t 0 s to t = 17 s)From the graph of the velocity, the particle is moving to the left and toward the right side. The velocity-time graph is linear, which means that the acceleration is constant and uniform. Hence, the conclusion we can draw is that the particle is moving with uniform acceleration. a = dv/dt = 2The given equations are: s=102−23t+t2v
=−23+2ta
=2Plot of s-t and v-t graphs:
Net displacement (Δs) during the interval of 17 seconds can be calculated as:Δs = s(17) - s(0)Δs
= 102 - (2 × 3² / 2) - (23 × 3) + (17² / 2) - 102Δs
= -4 mmThe particle moves to the left side.
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what cells secrete myelin for neurons?
a. schwann cells
b. other neurons
c. osteocytes
d. leukocytes
Answers
Answer:
A. Schwann cells
Explanation:
suppose you were given a new unknown material and wanted to place it on the electrostatic series. describe tests you could do to accurately
Answers
electrostatic attempting to calculate the charges of two friction-charged items. Include an explanation of WHY electrons flow from one material to another.
Which substance produces static electricity the best?Wool, human hairs, dry skin, silk, rayon, tissue paper, plastic wrap, and polyester are examples of materials that tendency to gain or lose electrons; when you tested these materials, you should have discovered that they shifted the silver ball similarly to how the Expanded polystyrene plate did.
What is an example of electrostatic charge?On insulating or unground surfaces, an excess or deficit of electrons results in static electricity, often known as an electrostatic charge. Triboelectric charges—charges created by friction between the two surfaces, for example the movement of two surfaces—are what cause it to occur.
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how far must the microphone be moved to the right to find the first intensity minimum?
Answers
For your specific scenario, we need to consider the placement of the microphone relative to the two sound sources. Assuming the sources are equidistant from the microphone and are emitting identical frequencies, there will be a series of intensity maxima and minima as the microphone is moved horizontally.
To find the first intensity minimum, we need to locate the point where the path difference between the two sound waves is half of a wavelength. This can be calculated using the equation:
path difference = d * sin(theta)
Where d is the distance between the sound sources and theta is the angle between the two sources as seen from the microphone. Once we have the path difference, we can use the formula:
path difference = n * wavelength / 2
Where n is an odd integer (1, 3, 5, etc.) and wavelength is the distance between two consecutive peaks of the sound wave.
With these equations, we can determine the distance the microphone needs to be moved to the right to reach the first intensity minimum. This will vary depending on the specific values of d, theta, and wavelength, but can be calculated using the methods described above. Overall, finding the first intensity minimum requires an understanding of interference and some basic calculations using the path difference and wavelength formulas.
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A 2.0 kg disk is able to move on a straight, level track with negligible friction. With the disk initially at rest, a
horizontal force is applied to the disk. The force is measured as a function of the disk’s displacement, and the
data are shown in the graph. When the disk’s displacement is 2.0 m, the speed of the disk is most nearly
Answers
The graph has a force on the y-axis and displacement on the x-axis. Given that the disk is able to move on a straight, level track with negligible friction. the speed of the disk when the displacement is 2 m is most nearly 2 m/s.
With the disk initially at rest, a horizontal force is applied to the disk. The force is measured as a function of the disk’s displacement. Let the speed of the disk when the displacement is 2m be v.When the net force on an object is given as a function of position, it is usually easier to find the work done than to use Newton's second law directly, as the law involves finding acceleration, and it is often difficult to determine the acceleration as a function of position.Let's integrate the force to find the work done.
Therefore, the work done by the net force as the disk moves from x1 to x2 is given by:
W = ∫F(x)dx (from x1 to x2)
The work-energy theorem states that the work done by all the forces acting on a particle equals the change in the particle's kinetic energy (the energy it has due to its motion)The change in kinetic energy of the particle is equal to the work done on the particle:
W = ΔKBy the work-energy theorem, W = ΔK = 1/2 mv² - 1/2 m (0)²= 1/2 mv²
When the displacement is 2.0 m, the work done, W is equal to the area under the curve between x = 0 and x = 2.0 m.Therefore, work done = area under the
curve = 0.5 (2 m) (4 N) = 4 J
From the work done above we can calculate the speed of the disk when the displacement is
2 m (v):W = ΔK1/2 mv² = Wv² = 2W/mv = √(2W/m)
When the disk’s displacement is 2.0 m, the speed of the disk, v is:
v = √(2W/m)Substituting W = 4J and m = 2.0kg we obtain:v = √(2 × 4J/2.0kg) = √4 = 2 m/s
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4. A pipe enters a water tank at a point 6.50 m below
the surface of the contained water. What is the
water pressure in this pipe?
Answers
Answer:
165 kPa
Explanation:
Absolute pressure is:
P = Patm + ρgh
where Patm is the atmospheric pressure,
ρ is the density,
g is acceleration due to gravity,
and h is the depth.
P = 101,300 Pa + (1000 kg/m³) (9.8 m/s²) (6.50 m)
P = 165,000 Pa
P = 165 kPa
Carbon emits photons at 745 nm when exposed to blackbody radiation. How much energy would be obtained if 44g of carbon were irradiated? assume each carbon atom emits one photon.
Answers
The energy would be obtained if 44 g of carbon were irradiated is 5.8863 x 10^5 J.
Assume each carbon atom emits one photon. For each photon.
E=hc/lambda
Where h = Plank's constant
C = speed of light
E = (6.625×10^-34)×(3×10^8)/(7.45×10^-7)
E = 2.66819x10^-19 J
So the total energy emitted is
E = E1xn
E = (2.66819x10^-19)×(6.022x10^23)/ 1 mol of carbon atom
E = 5.8863 x 10^5 J
What is black body radiation?Black body radiation is a type of radiation in which a body is in thermodynamic equilibrium, emitted by a black body. It has a specific, continuous spectrum of wavelength. Photons are energy stored in bundles.
In above question,
Wavlength (lambda)=745nm = 7.45x10^-7m.
Mass of carbon = 44 gram
Assume each carbon atom emits one photon. For each photon.
E=hc/lambda
Where h = Plank's constant
C = speed of light
E = (6.625×10^-34)×(3×10^8)/(7.45×10^-7)
E = 2.66819x10^-19 J
So the total energy emitted is
E = E1xn
E = (2.66819x10^-19)×(6.022x10^23)/ 1 mol of carbon atom
E = 5.8863 x 10^5 J
Therefore, The energy would be obtained if 44 g of carbon were irradiated is 5.8863 x 10^5 J.
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a kickball is struck with a 15.2 m/s velocity at a 63.0 angle. It lands on a rooftop 2.40 s later. How high is the roof
Answers
The height of the roof is approximately 2.876 meters.
Part the underlying speed into its components:
v₀x = v₀ * cos(θ)
v₀y = v₀ * sin(θ)
Given:
Using the provided values, we can determine v₀x and v₀y: v₀ = 15.2 m/s (initial velocity); = 63.0° (projection angle); t = 2.40 s (flight time).
Now, let's use the vertical displacement equation to determine the vertical displacement (y): v₀x = 15.2 * cos(63.0°), v₀y = 15.2 * sin(63.0°)
y = v₀y * t + (1/2) * (-9.8 m/s2) * t2 = v₀y * t - 4.9 * t2 Using the values we obtained as a starting point:
Δy = (15.2 * sin(63.0°)) * 2.40 - 4.9 * (2.40)²
=2.876 m
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Inquiry Skill
A student constructs a model of a natural resource using a can with a small hole
in the bottom. With the hole plugged, the can is filled with sand. When the plug is
removed, the sand drains out. What kind of resource does this model illustrate?
Answers
neglecting all other forces, if the pressure gradient force doubles in magnitude, then question 27 options: a. the winds moves in a circle with double the radius. b. the winds experience double the friction. c. the wind speed doubles in magnitude. d. the wind changes direction. e. none of the above
Answers
Neglecting all other forces, if the pressure gradient force doubles in magnitude, the wind speed doubles in magnitude as well. Therefore, the correct option is (c) the wind speed doubles in magnitude.
The pressure gradient force is responsible for causing the wind to move from high pressure to low pressure areas. It is directly proportional to the magnitude of the pressure difference and inversely proportional to the distance between the two pressure points. If the pressure gradient force doubles, the wind speed will also double, as the wind will need to accelerate more to compensate for the stronger force acting upon it.
The other options are not affected by a doubling of the pressure gradient force. The wind moving in a circle with double the radius would be affected by changes in the Coriolis force, not the pressure gradient force. The wind experiencing double the friction would be affected by changes in frictional forces, not the pressure gradient force.
The wind changing direction would be affected by changes in the Coriolis force or by changes in the direction of the pressure gradient force, not the magnitude of the pressure gradient force alone.
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Kind of energy that an object has due to its motion.
Answers
Answer:
The energy an object has due to its motion is called kinetic energy
Explanation:
Factors Affecting Kinetic Energy: the kinetic energy of an object depends on both its speed and its mass.
Answer:
kinetic energy
Explanation:
In physics, the kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.
(d) 10 s
13. An object in motion has a displacement of +50 m. The average velocity is +25 m/s. Whats the time taken
Answers
The time taken to travel 50 m ina 25 m/s average velocity is 2 sec.
What is Velocity?The directional speed of an item in motion, as measured by a specific unit of time and viewed from a certain point of reference, is what is referred to as velocity.
An object's position changes if it moves in relation to a reference frame, such as when a passenger travels to the back of an airliner or a lecturer moves to the right in relation to a whiteboard. Displacement describes this shift in location.
When anything moves in connection to a reference frame, such when a passenger moves to the back of an airplane or a lecturer walks to the right in relation to a whiteboard, the location of the item changes. This locational change is described as displacement.
The displacement is = 50 m
The average velocity = 25 m /sec
The time taken is = displacement/ average Velocity = 50/25 = 2 sec.
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Which statement best describes what happens when forces
are balanced?
a The forces cause a change in motion.
b The forces cause a change in direction.
C The forces do not cause a change in stability.
d The forces do not cause a change in motion.
Answers
Answer: D
Explanation:
A rock is thrown straight up and reaches a height of 10m
How long was the rock in the air
What is the initial velocity of the rock
Answers
Answer:
1.41s,14.14m/s(approx.)
1 Explain what you understand about wave
Answers
Answer:
A wave transfer energy and information without transferring matter, the particles oscillates about a fixed point.
the current in a 50.0-mh inductor changes with time as i = 3.00t2 − 7.00t, where i is in amperes and t is in seconds.
Answers
The main answer to the given question is that the current in the 50.0-mH inductor is given by the equation i = 3.00t^2 - 7.00t, where i is in amperes and t is in seconds.
An explanation for this is that the current in an inductor is proportional to the rate of change of the magnetic field through the inductor. In this case, the magnetic field is changing with time as t increases. The equation given for the current is a polynomial function with a squared term and a linear term. This means that the rate of change of the magnetic field is increasing as time increases. At t=0, the current is -7.00A, and it increases with time. This can be seen by taking the derivative of the given equation, which gives the rate of change of the current with respect to time. Overall, the equation for the current in the inductor provides a mathematical description of the changing magnetic field and the resulting current in the circuit.
Your question is about finding the induced voltage across a 50.0-mH inductor when the current changes with time as i = 3.00t^2 - 7.00t, where i is in amperes and t is in seconds. To find the induced voltage (V) across the inductor, we will use the formula V = L * (di/dt), where L is the inductance and di/dt is the derivative of the current with respect to time.
Step 1: Identify the given values:
Inductance, L = 50.0 mH = 0.050 H
Current function, i(t) = 3.00t^2 - 7.00t
Step 2: Find the derivative of the current with respect to time:
di/dt = d(3.00t^2 - 7.00t) / dt = 6.00t - 7.00
Step 3: Use the formula V = L * (di/dt) to find the induced voltage:
V(t) = 0.050 * (6.00t - 7.00)
Step 4: Simplify the expression:
V(t) = 0.3t - 0.35So, the induced voltage across the 50.0-mH inductor is V(t) = 0.3t - 0.35 volts, where t is in seconds.
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scientists currently use planetary rovers to collect data on mars. what type of samples have they collected so far?
Answers
Scientists currently use planetary rovers to collect data on mars rovers collect infrared spectra, drill cores, photographs.
Designed to move across the solid surface of a planet or other planetary mass celestial bodies, a rover (or occasionally planetary rover) is a planetary surface exploration tool. Others have been created as partially or entirely autonomous robots. Some rovers have been created as ground vehicles to transfer members of a human spaceflight crew. When a lander-style spacecraft is used to land on a planet (other than Earth), rovers are often built to collect data about the topography and sample the crust, including dust, dirt, rocks, and even liquids. They are vital resources for space exploration. Due to the slow speed of radio communications, rovers that land on celestial worlds other than the Earth, like the Mars Exploration Rovers, cannot be remotely operated in real-time.
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A paper airplane is dropped from a balcony. what will friction from the air do to the paper airplane? speed up the airplane it will not change the airplane's speed. slow down the airplane
Answers
A paper airplane is dropped from a balcony, then the friction from the air slow down the airplane. As paper plane moves through the air, the air pushes against the airplane, hence slowing it down. This is called drag.
What is meant by drag?The force that slows the plane down as it pushes against the air it is moving through is called drag. It is a kind of friction and is also called as air resistance.
In fluid dynamics, drag is a force acting opposite to the relative motion of an object moving with respect to the surrounding fluid. Drag is non-existent, without motion.
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For the circuit shown in the figure, the current in the 8 resistor is 0.50 A, and all quantities are accurate to 2 significant figures. What is the current in the 2 resistor?
Answers
The current through the 2Ω resistor is 9.5A
The terminal voltage is 10.8 V
How to calculatea) The voltage V across 8 Ω resistor is V = I*R = 8*0.5 = 4V
the current through 16Ω resistor is then I = V/R = 4/16 = 0.25 A
the current through 20Ω resistor is then I = current through 8Ω resistor + current through 16Ω resistor = 0.75 A
voltage across 20Ω is V = I*R = 0.75*20 = 15 V
the source voltage is Vs = V8 + V20 = 4+15 = 19 V
therefore the current through 2Ω resistor is
I = V/R = 19/2 = 9.5 A
b) The terminal voltage is
Vterminal = VR = I*R = 0.450*24 = 10.8 V
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A 1.0 μF capacitor is charged for 20 s using a constant current of 10 μA.
What is the charge collected by the sphere each second?
Answers
Answer:
200 μC
Explanation:
The charge collected by the sphere each second is equal to the current multiplied by the time. In this case, the current is 10 μA and the time is 20 s, so the charge collected by the sphere each second is 10 μA * 20 s = 200 μC.
I hope this helps! Let me know if you have any other questions or need further assistance.
A person strikes a ball with a bat. The temperature of the ball increases by 0.06ᵒC. What accounts for the increase?
Answers
The increase in the average kinetic energy of the ball causes the increase in the temperature of the ball.
Kinetic energy of a particle is directly proportional to its temperature.
A ball initially at rest acquires kinetic energy when an external force is applied to it. As the person strikes the ball with a bat, the ball gains momentum which increases its kinetic energy of the ball.
Temperature on the other hand, is the measure of the average kinetic energy of a particle. Consequently, as the kinetic energy of the ball increases, the temperature of the ball increases as well.
Thus, we can conclude that the increase in the average kinetic energy of the ball causes the increase in the temperature of the ball.
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An arrow is shot an angle of 13 degrees to the horizontal with an initial speed of 100. Km/hr. Find the horizontal and vertical components of the velocity.
Answers
In this example, it’s important to know that sin represents the relationship between the opposite side (in this case y) and hypotenuse (100) and that cosine represents the adjacent side (in this case x) and hypotenuse.
For sin, the opposite divided by the hypotenuse equals the sin of the given angle. Similar for cos, but adjacent.
We can use this to algebraically isolate the side we are looking for, and allow ourselves an easy calculator solution.
Both of my answers are rounded.
X-component = 97.437 m/s
Y-component = 22.495 m/s
I hope this helped, if you need any clarification, please comment.
What does the term "heat capacity" refer to? Question 2 options: The amount of heat energy needed to raise the temperature of a unit mass of a material one degree A ratio of the amount of heat a material will absorb to the amount of heat it immediately releases The amount of heat that must be applied to a solid to convert it to a liquid The amount of heat that a liquid can absorb until the particles speed up enough to become a gas
Answers
Answer:
Heat capacity is the ratio of the amount of heat energy transferred to an object to the resulting increase in its temperature. Molar heat capacity is a measure of the amount of heat necessary to raise the temperature of one mole of a pure substance by one degree K.
Explanation:
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A 50 kg ball traveling at 20 m/s would haveA50 kg ball traveling at 5 m/s would haveA 50 kg person falling at 10 m/s would havekinetic energy✓ kinetic energykinetic energythe same2 times more2 times less4 times more4 times lessDoneIntro5 of 9
Answers
We have the next formula to calculate the kinetic energy
\(KE=\frac{1}{2}mv^2\)where m is the mass and v is the velocity
For the kinetic energy of ball 50 kg traveling at 10 m/s
\(KE=\frac{1}{2}(50)(10)^2=2500\text{ joules}\)For the kinetic energy of ball 50 kg traveling at 20 m/s
\(KE=\frac{1}{2}(50)(20)^2=10000\text{ joules}\)A 50 kg ball traveling at 20 m/s would have 4 times kinetic energy.
For kinetic energy of the ball 50 kg at 5m/s
\(KE=\frac{1}{2}\mleft(50\mright)\mleft(5\mright)^2=625\text{ joules}\)A 50 kg ball traveling at 5 m/s would have 4 times less kinetic energy
For the person 50kg falling 10 m/s
\(KE=\frac{1}{2}\mleft(50\mright)\mleft(10\mright)^2=2500joules\)A 50 kg person falling at 10 m/s would have the same kineticenergy}.
The solution is
A 50 kg ball traveling at 20 m/s would have 4 times more kinetic energy.
A 50 kg ball traveling at 5 m/s would have 4 times less kinetic energy.
A 50 kg person falling at 10 m/s would have the same kinetic energy.
a straight wire of mass 9.7 g and length 5.0 cm is suspended from two identical springs that, in turn, form a closed circuit. the springs stretch a distance of 0.45 cm under the weight of the wire. the circuit has a total resistance of 14 . when a magnetic field directed out of the page (indicated by the dots in the figure) is turned on, the springs are observed to stretch an additional 0.30 cm. what is the strength of the magnetic field? (the upper portion of the circuit is fixed.)
Answers
The strength of the magnetic field is 1.28 T.
Step 1: Calculate the mass per unit length of the wire:
m/L = 9.7 g / 0.05 m = 194 g/m
Step 2: Calculate the tension in each spring before the magnetic field is turned on:
F = k * x
where k is the spring constant and x is the displacement from the equilibrium position.
F = 2 * k * 0.0045 m = 0.009 kN
Step 3: Calculate the current in the circuit before the magnetic field is turned on:
I = V / R
where V is the voltage across the circuit and R is the total resistance.
I = 0.009 kN / 14 Ω = 0.00064 A
Step 4: Calculate the magnetic force on the wire:
Fm = BIL
where B is the strength of the magnetic field, I is the current in the wire, and L is the length of the wire.
\(Fm = B * 0.00064 A * 0.05 m = 3.2 * 10^-5 B N\)
Step 5: Calculate the additional tension in each spring when the magnetic field is turned on:
\(F' = k * (0.0045 m + 0.0030 m) = 0.012 kN\)
Step 6: Equate the magnetic force with the increase in tension:
\(Fm = 2 * (F' - F)3.2 * 10^-5 B N = 2 * (0.012 kN - 0.009 kN)B = 1.28 T.\)
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Obtain an expression for fringe width with diagram.
Answers
Hope this above expression for fringe width helps you.
Answer:
Explanation:
To obtain an expression for fringe width, we need to consider the phenomenon of interference in wave patterns, such as in the case of Young's double-slit experiment. In this experiment, a coherent light source, such as a laser, is passed through two closely spaced slits, creating an interference pattern of light and dark fringes on a screen placed behind them.
The fringe width (w) can be determined using the following expression:
w = λ * D / d
Where:
- λ represents the wavelength of the light used,
- D is the distance between the double-slit and the screen,
- d is the separation between the two slits.
The diagram accompanying this explanation would illustrate a coherent light source passing through the double slits, with the resulting pattern of light and dark fringes observed on the screen placed behind them. The distance D between the double-slit and the screen, as well as the separation d between the slits, would be indicated in the diagram.
Hope it helps!! :))
Draw a diagram that represents how a mechanical wave interacts with a particular material.
Create a diagram and include reflection, absorption, and transmission.
Write a brief description (3+ sentences) of the interaction of the mechanical waves and the material. Include an explanation of how the amplitude and frequency of the wave are affected.
85 POINTS!!
Answers
When mechanical waves interact with material, it transfer its energy to the material.
What are mechanical waves?Mechanical waves are the type of waves that require a medium for transporting their energy from one region to another. Mechanical waves depend on particle interaction in order to transport their energy.
The amplitude and frequency of the wave are negatively affected due to the striking of mechanical waves with the material.
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Answer:
i have a screenshot just use mine https:/ss27
Explanation:
Fnet = 110 N
m = 1000 kg
275 N
395 N
Opposing force = 560 N
N= 275 N
f=560 N
N= 395 N
A=? Please need help to pass:(
Answers
Answer:
15 N. 5 N. 4.1 The Concepts of Force and Mass. Mass is a measure of the amount ... 275 N + 395 N – 560 N = +110 N ... If the mass of the car is 1850 kg then, by ... For two particles that have masses m1 and m2 and are ... N. Moreover, the water applies an opposing force R, whose magnitude is R = 40.0 × 103 N. The tanker ...
Explanation:
An apple weighing 100g, located at a height of 1.5m, falls from the tree. (Air resistance is not taken into account) Find:
a) Gravitational potential energy possessed by the apple.
b) What is the kinetic energy at the moment of collision of the apple
- We throw the apple from the tree, giving it an initial energy of 1.2 J
What is the initial speed of the apple? c) What is the speed with which the apple hits the ground?
Answers
a) Gravitational potential energy possessed by the apple is E = 1.47 J.
b) Kinetic energy at the moment of collision of the apple is E = 1.47 J.
The initial speed of the apple is 3.92 m/s.
c) The speed with which the apple hits the ground is 5.42 m/s.
a) Gravitational potential energy possessed by the apple:
Given that the apple weighs 100 g, located at a height of 1.5 m, the gravitational potential energy can be calculated as follows:
E = mgh = 0.1 kg × 9.8 m/s² × 1.5 m = 1.47 J
b) Kinetic energy at the moment of collision of the apple:
Kinetic energy can be calculated using the formula:
K.E. = 1/2 mv² where m is the mass of the apple and v is the velocity of the apple.
Initially, the apple is at rest. The potential energy of the apple transforms into kinetic energy as the apple falls.The potential energy calculated above is transformed into kinetic energy when the apple reaches the ground.
Therefore,
1.47 J = 1/2 × 0.1 kg × v²v² = 2 × 1.47 J/0.1 kgv² = 29.4v = √29.4v = 5.42 m/s
c) Speed with which the apple hits the ground:
The velocity of the apple can be calculated as follows:
v² = u² + 2gh
where u is the initial velocity of the apple and h is the height from which the apple falls.
u² = v² - 2gh = 5.42² - 2 × 9.8 × 1.5 = 15.37u = √15.37u = 3.92 m/s
Therefore, the initial speed of the apple is 3.92 m/s and the speed with which the apple hits the ground is 5.42 m/s.
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