The magnitude of average acceleration in half time period in a simple harmonic motion is
(A) 2 ω2A /π
(B) ω2A /2 π
(C) ω2A /√2 π
(D) Zero
Answer:
Option A - 2ω²A/π
Explanation:
The displacement of simple harmonic motion is usually given as;
x = Asinωt
Where;
A is amplitude
ω is angular frequency
Now, average acceleration in half time period is given as;
a_av = d²x/dt² = -ω²A sinωt
Thus;
a_av = ∫a(t)dt/(∫dt) with both numerator and denominator between the boundaries of T/2 and 0.
Full expression gives;
(2/T)(ω²A∫sin(ωt) dt between the boundaries of T/2 and 0.
Now, integrating gives;
(2/T)(ω²A × 1/ω)[-cos(ωt)] between the boundaries of T/2 and 0.
Plugging in the boundary conditions gives us;
(2/T)(ω²A × 1/ω)[-cos(ωT/2) + cos0]
Simplifying gives;
(2ωA/T)[-cos(ωT/2) + 1]
In simple harmonic motion, we know that ω = 2π/T
Thus we have;
(2ωA/T)[-cos(2π/2) + 1]
(2ωA/T)[-cos(π) + 1]
This gives;
(2ωA/T)[1 + 1]
= (4ωA/T)
Now, from earlier ω = 2π/T
Thus, T = 2π/ω
So, we have;
a_av = (4ωA/(2π/ω))
a_av = 2ω²A/π
7. Solve (3.96 x 10^2)/(1.6 x 10^-8). Be
sure your answer is in scientific notation.
Round to two decimal places.
(1 Point)
Enter your answer
Answer:
[tex]2.48*10^{10}[/tex]
Explanation:
Given the expression (3.96 x 10^2)/(1.6 x 10^-8), we are to express in scientific notation. Applying one of the laws of indices which says;
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
The expression becomes;
[tex]= \dfrac{3.96}{1.6}*\dfrac{10^2}{10^{-8}}\\ \\= \dfrac{3.96}{1.6}*10^{2-(-8)}\\\\= \dfrac{3.96}{1.6}*10^{2+8}\\\\= \dfrac{3.96}{1.6}*10^{10}\\\\= 2.475*10^{10}\\\\= 2.48*10^{10} (to \ 2dp)[/tex]
5. Carey and Heather wanted to know if the size of a coin will affect the number of drops of water it can hold. So they used a dropper to place water on a quarter, nickel, and penny. a. Question: b. Hypothesis + Prediction: c. Independent Variable (IV): d. Dependent Variable (DV): e. Controlling Variable (CV): f. Experiment:
Answer:
the correct answer is f EXPERIMENT
Explanation:
In this exercise on these young people we want to know to which part of the scientific method their statement corresponds.
In order to answer, we must describe the main parts of the scientific method.
* Question. It is a question that we unleash to answer
* Hypothesis. It is an assumption that we want to check
* Independent variable. It's the thing that researcher controls
* dependent variable . It is the magnitude is measured
* Experiment. It is the design of a methodology to test the hypothesis.
In this case, the young people describe a procedure to test a hypothesis, so this part corresponds to an EXPERIMENT
the correct answer is f
At a painfully loud concert, a 120-dB sound wave travels away from a loudspeaker at 343 m/s.
How much sound wave energy is contained in each 1.0-cm^3 volume of air in the region near this loudspeaker?
Answer:
2.9*10^-9 J
Explanation:
Given that sound level is B= 120dB
And B=10log(Io/I)
And I = (10^12)Io
So I = 1W/m²
So to find Energy
∆E= I∆V/v
Where ∆V= 1*10-6m³
v = 343
So ∆E=2.9*10^-9 J after substituting the values
Consider two positively charged particles, one of charge q0 (particle 0) fixed at the origin, and another of charge q1 (particle 1) fixed on the y-axis at (0,d1,0). What is the net force F⃗ on particle 0 due to particle 1? Express your answer (a vector) using any or all of k, q0, q1, d1, i^, j^, and k^.
Answer:
[tex]F_{10} = - \frac{k_{q1}* qo }{d_{1} ^{2} } j[/tex]
Explanation:
The net force ( F ) on particle 0 due to particle 1 can be expressed as
[tex]F_{10} = \frac{K_{q1}*qo }{r_{10} ^{3} } r_{10}[/tex]
k = coulomb constant
[tex]r_{10}[/tex] = distance between charge o and charge 1
to get the vector form ( attached below ) we substitute [tex]d_{1}[/tex] for [tex]r_{10}[/tex] and [tex]- d_{1} j[/tex] for [tex]r_{10}[/tex]
The net force on [tex]q_{0}[/tex] by [tex]q_{1}[/tex] is , [tex]F=-K\frac{q_{0}*q_{1}}{r^{2} }j[/tex]
The force between two charges is given by Coulomb force law.
[tex]F=K\frac{q_{0}*q_{1}}{r^{2} }[/tex]
Where K is Coulomb constant, [tex]K=9*10^{9}Nm^{2}/C^{2}[/tex]
and r is the distance between both charges.
Here given that, [tex]q_{0}[/tex] is located as (0, 0, 0) and [tex]q_{1}[/tex] is located at [tex](0,d_{1}, 0)[/tex]
The force on [tex]q_{0}[/tex] by [tex]q_{1}[/tex] in the negative y - axis.
So that , Direction of force is, [tex]-j[/tex]
Hence, the net force on [tex]q_{0}[/tex] by [tex]q_{1}[/tex] is , [tex]F=-K\frac{q_{0}*q_{1}}{r^{2} }j[/tex]
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1. You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is negligible and that your car brakes with constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?
Answer:
-1.82m/s²
Explanation:
Given that the reaction time (t) is negligible and car brakes with constant acceleration.
Initial Velocity (u) = 20m/s
Distance(d) from Intersection when light turns red = 110m
Hence, the magnitude of braking acceleration that will bring the car to rest at exactly the intersection :
Using the motion equation:
v² = u² + 2as
Where v = final velocity at the intersection
u = initial velocity ; s = distance to intersection ; a = acceleration of the car
Exactly at the intersection ; v = 0
0 = 20² + 2×a×110
0 = 400 + 220a
-400= 220a
a = - 400 / 220
a = - 1.818
a = - 1.82 m/s²
- stands for negative acceleration (deceleration)
The deep scattering layer (DSL):_________
a) was discovered by Charles Darwin
b) is only seen at night
c) is a biological phenomenon that can be detected with sonar
d) is not a biological phenomenon
e) is a chemical boundary in the water
Answer:
C
Explanation:
Because its a region of high biological productivity with a lot of water organism allowing for high reflectivity of sonar pulse mimicking ocean bottom
How is it possible charge electrical devices when the power is out?
Answer:
generator
Explanation:
it can run an electric current to an outlet and let it charge
Which of the following quantities represent mass?
a. 12.0 lbs.
b. 0.34 g.
c. 120 kg.
d. 1600 kN.
e. 0.34 m.
f. 411 cm.
g. 899 MN.
Answer:
Explanation:
a ) 12.0 lbs - mass
b ) .34 g - mass
c ) 120 kg - mass
As lbs , g and kg are units of mass , these things represent mass . lbs is FPS unit of mass and kg is SI unit . g is CGS unit of force .
d ) 1600 kN It represents force because kN or kilonewton is unit of force .
e ) it represents , length or distance because m or metre is unit of length .
f ) 411 cm It represents length or distance because cm is smaller unit of length
g ) 899 MN or million newton . Like d ) It also represents force . Million newton is higher unit of force .
A cheetah is running at a speed of 19.5 m/s in a direction of 69° north of west. Find the cheetahs velocity component due north and due west.
Answer:
The cheetahs velocity component due north is 6.99 m/s
The cheetahs velocity component due west is 18.21 m/s
Explanation:
Given;
speed of the cheetah, v = 19.5 m/s
direction of the cheetah's speed, θ = 69°
Find the attached document for explanation
A car is on a cruise control driving in a circle. Which are constant and which are changing? Speed, Velocity. Is the car accelerating?
Answer:
Only the speed is constant.
The acceleration and velocity are changing.
Explanation:
The velocity of an object refers to its speed in a specific direction. Due to the fact that the car is driving in a circle, the direction of the car is changing. This makes the car not to have a constant velocity as this value changes each time the car makes a bend on the circular path. (which is pretty much all the time).
The acceleration is a direct derivative of the velocity of the car. As a result, if the velocity is changing, the acceleration is also changing.
Speed is a scalar quantity. This means it does not deal with the direction of the car. It only deals with how fast the car is moving. The car is on cruise control. this means that the speed of the car does not change.
what part of the stem cell provides instructions for building the heart
a. ribosomes
b. DNA
c. RER
d. lysosomes
A marathon runner runs at a steady 15 km/hr. When the runner is 7.5 km from the finish, a bird begins flying from the runner to the finish at 30 km/hr. When the bird reaches the finish line, it turns around and flies back to the runner, and then turns around again, repeating the back-andforth trips until the runner reaches the finish line. How many kilometers does the bird travel?
Answer:
The value is [tex]D = 15 \ km [/tex]
Explanation:
From the question we are told that
The speed of the marathon runner is [tex]v = 15 \ km /hr[/tex]
The distance from the distance from the finish is [tex]d = 7.5 \ km[/tex]
The speed of the bird is [tex]v_b = 30 \ km / hr[/tex]
Generally the time taken for the runner to reach the finish is mathematically represented as
[tex]t = \frac{d}{v}[/tex]
[tex]t = \frac{7.5}{15}[/tex]
[tex]t = \frac{1}{2}[/tex]
So the distance covered by the bird is
[tex]D = v_b * t[/tex]
[tex]D = 30 * \frac{1}{2}[/tex]
[tex]D = 15 \ km [/tex]
Question 2 (1 point)
The direction of the result of the cross product of two vectors is perpendicular to the
plane containing the two vectors, specified by the right hand rule.
True
ОО
False
The rifles in the figures are being fired horizontally (straight outward, off platforms). The bullets fired from the rifles are all identical, but the rifles propel the bullets are different speeds. The speed of each bullet and the height of each platform are given. All the bullets miss their targets and hit the ground. Rank the time it takes the bullets to hit the ground. Explain your reasoning.
Answer:
t = √ 2y₀ / g
if they are at the same height, all the bullets must carry the target, since when advancing the height decreases
Explanation:
In this exercise we see that the bullets are fired horizontally so the time it takes to reach the ground is
y = y₀ + [tex]v_{oy}[/tex] t - ½ g t²
as they are fired horizontally their vertical velocity is zero and the height upon reaching the ground is zero y = 0
0 = y₀ - ½ g t²
t = √ 2y₀ / g
from here we can see that the time it takes for the bullets to hit the floor depends only on the initial height
Therefore, all the bullets that come out of the same height reach the ground at the same time, but at a different distance, so if one misses the target, everything must fail since reaching the target is below the initial height.
The horizontal distance traveled by the bullets is
x = v₀ₓ t
v₀ₓ =v₀
x = v₀ √2y₀/g
For a more precise calculation we should know the height of the target and the bullets, but if they are at the same height, all the bullets must carry the target, since when advancing the height decreases
if 1 foot is 30.28 centimeters.how many cm is 130 feet
Answer:3,936.4
Explanation:
If 1 foot is 30.28 centimeters multiply 30.28 by 130
A moving roller coaster speeds up with constant acceleration for 2.3\,\text{s}2.3s2, point, 3, start text, s, end text until it reaches a velocity of 35\,\dfrac{\text{m}}{\text{s}}35 s m 35, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction. During this time, the roller coaster travels 41\,\text{m}41m41, start text, m, end text. We want to find the initial velocity of the roller coaster before it starts to accelerate. Which kinematic formula would be most useful to solve for the target unknown?
Answer:
Δx=(v+v0/2)t
Explanation:
We can figure out which kinematic formula to use by choosing the formula that includes the known variables, plus the target unknown.
In this problem, the target unknown is the initial velocity v_0v
0
v, start subscript, 0, end subscript of the roller coaster.
During which step of the scientific method does a scientist make an educated
guess about the outcome of an experiment?
A. Collect data
B. Form a hypothesis
C. Analyze the results
O D. Design an experiment
SUBNA
Answer:B. Form a hypothesis
1. Classify What type of heat transfer occurs
when you roast a marshmallow by holding it
campfire?
over a co
Answer:
Convection
Explanation:
because it tis the transfer of energy through a fluid or gas
When you roast a marshmallow by holding it campfire, the heat transfer in the process of radiation.
What is thermal radiation ?Thermal radiation is a process in which energy, in the form of electromagnetic radiation, is emitted from a heated surface in all directions and moves at the speed of light directly to its site of absorption. Thermal radiation does not move through an intermediary medium.
From the longest infrared rays through the visible light spectrum to the shortest ultraviolet rays, thermal radiation spans the entire electromagnetic spectrum. The temperature of the emitting surface controls the distribution and intensity of radiant radiation within this range.
When you roast a marshmallow by holding it campfire, the heat transfer by the process of radiation through air.
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The observation of a "wet spot" on a hot highway in the summer is caused by:_________.
a. dispersion
b. diffraction
c. refraction
d. reflection.
Answer: Refraction
Explanation:
The observation of a wet spot on a hot highway in the summer season is caused by refraction. Therefore, option (C) is correct.
What is refraction?Refraction can be defined as the redirection of light as it passes from one medium to another medium. The redirection of light is caused by a change in the medium or by the wave's change in speed.
Refraction of light can be described as an observed phenomenon, but other waves such as sound waves and water waves also experience refraction.
Refraction of light obeys Snell's law that the ratio of the sines of the angle of incidence and refraction must be equal to the ratio of phase velocities in the two media to the refractive index of the two media.
When the sunlight makes a blacktop hot highway. The appearance of the wet spot is bright because of the refraction of light from the sky.
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An eagle is flying horizontally at a speed of 3.80 m/s when the fish in her talons wiggles loose and falls into the lake 3.90 m below. Calculate the velocity (in m/s) of the fish relative to the water when it hits the water. (Assume that the eagle is flying in the x-direction and that the y-direction is up.)
Answer:
the velocity of the fish relative to the water when it hits the water is 9.537m/s and 66.52⁰ below horizontal
Explanation:
initial veetical speed V₀y=0
Horizontal speed Vx = Vx₀= 3.80m/s
Vertical drop height= 3.90m
Let Vy = vertical speed when it got to the water downward.
g= 9.81m/s² = acceleration due to gravity
From kinematics equation of motion for vertical drop
Vy²= V₀y² +2 gh
Vy²= 0 + ( 2× 9.8 × 3.90)
Vy= √76.518
Vy=8.747457
Then we can calculate the velocity of the fish relative to the water when it hits the water using Resultant speed formula below
V= √Vy² + Vx²
V=√3.80² + 8.747457²
V=9.537m/s
The angle can also be calculated as
θ=tan⁻¹(Vy/Vx)
tan⁻¹( 8.747457/3.80)
=66.52⁰
the velocity of the fish relative to the water when it hits the water is 9.537m/s and 66.52⁰ below horizontal
Which of the following is one way creativity can help scientists? (20 points) +Brainiest
a
By ensuring they follow the scientific method
b
By increasing the amount of time it takes to complete scientific experiments
c
By making sure they only try things that have already been proven
d
By leading them to ask more questions about the natural world
The highest speed attained by a cyclist on level ground is 105 km/h. To attain this speed, the cyclist used a streamlined recumbent bike. Starting from rest, he gradually built up his speed by pedaling furiously over a distance of 3.2 km. If his acceleration was uniform over this distance, what was the acceleration and how long did the cyclist take to build up his final speed
Answer:
The acceleration is 0.133 m/s²
The time taken to build the final speed is 219.32 s
Explanation:
Given;
final speed of the cyclist, v = 105 km/h = 29.17 m/s²
distance traveled by the cyclist, d = 3.2 km = 3,200 m
initial speed, u = 0
Apply the following kinematic equation to determine the acceleration of the cyclist;
v² = u² + 2as
(29.17 )² = 0 + (2 x 3200)a
850.89 = 6400a
a = (850.89 ) / (6400)
a = 0.133 m/s²
The time taken to build up the final speed is given by;
v = u + at
29.17 = 0 + (0.133)t
t = 29.17 / 0.133
t = 219.32 s
launch a rocket ship weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 164 km/h ; at the end of the first 1.00 min , its speed is 1640 km/h . Part APart complete What is the average acceleration (in m/s2) of the rocket during the first 8.00 s? aav = 5.69 m/s2 Previous Answers Correct Part BPart complete What is the average acceleration (in m/s2) of the rocket between 8.00 s and the end of the first 1.00 min? aav = 7.88 m/s2 Previous Answers Correct Part CPart complete Assuming the acceleration is constant during each time interval (but not necessarily the same in both intervals), what distance does the rocket travel during the first 8.00 s? Express your answer with the appropriate units. x = 182 m Previous Answers Correct Part D Assuming the acceleration is constant during each time interval (but not necessarily the same in both intervals), what distance does the rocket travel during the interval from 8.00 s to 1.00 min? Express your answer with the appropriate units.
Answer:
A) a_av = 5.695 m/s²
B) a_av = 7.88 m/s
C) x_f = 182.24 m
D) x_f = 13029.12 m
Explanation:
A) Initial velocity at 0 seconds; v_i = 0 m/s
Final velocity at 8 seconds;v_f = 164 km/h = 45.56 m/s
So, formula for average acceleration is;
a_av = change in velocity/change in time.
Thus, for the first 8 seconds;
a_av = (45.56 - 0)/(8 - 0)
a_av = 45.56/8
a_av = 5.695 m/s²
B) From part A, we now want to find the average acceleration from 8 seconds to 1 minute (60 seconds)
After the 60 seconds, the speed is 1640 km/h = 455.56 m/s
Thus;
Average acceleration is;
a_av = (455.56 - 45.56)/(60 - 8)
a_av = 7.88 m/s
C) Now we are told the acceleration is constant and we want to find the distance the rocket travels during the first 8 seconds.
So, distance formula we will use is;
x_f = x_i + ½(v_i + v_f)t
So at this stage, v_i = 0 m/s and v_f = 45.56 m/s and x_i = 0 m
Thus;
x_f = 0 + ½(0 + 45.56)8
x_f = 182.24 m
D) Now we want to find the distance the rocket travels during the 8 seconds to 1 minute (60 seconds) interval.
From part B, v_i = 45.56 m/s and v_f = 455.56 m/s
Also, x_i = 0 while time interval(t) = 60 - 8 = 52 s
Thus;
x_f = 0 + ½(45.56 + 455.56)52
x_f = 13029.12 m
Calculate the magnitude and direction of the electric field (in N/C) 2.2 m from a long wire that is charged uniformly at λ = 3.6 ✕ 10−6 C/m. (Assume the wire goes through the origin and the point in question is located on the +z-axis. Express your answer in vector form.).
Answer:
29.5*10^3 k N/C
Explanation:
Using
E = λ/2πEor x k
So = 18*10^9 x 3.6 ✕ 10−6 / 2.2 x k
= 29.5*10^3 k N/C
Show that a tilted linearly polarized wave can be written as the sum of LCR and RCP.
Answer:
E_{z} = E_{z} (RCP) + E_{z} (LCP)
E_{z} = 2 E₀ cos (kz-wt) i^
Explanation:
An electromagnetic wave is said to be polarized if the electric field for a fixed point in space has a definite direction in time.
Based on this definition we can define some types of polarization; Linear; right-hand, left-hand circular, and elliptical
Circular polarization is that for a fixed point in space, the electric field describes a circle in time, if this circle rotates clockwise it is called right circular polarization (RCP) and if it rotates counterclockwise it is called polarization left circular (LCP)
For wave moving in the z direction the electric fields must oscillate in the x or y direction
for right-hand circular polarization (RCP)
[tex]E_{z}[/tex] = E₀ cos (kz -wt) i^ + E₀ sin (kz -wt) j^
for left circular polarization (LCP)
E_{z} = E₀ cos (kz -wt) i ^ - E₀ sint (kz -wt) j ^
linear polarization can be obtained if we add these two polarizations
E_{z} = Ez (RCP) + Ez (LCP)
E_{z} = E₀(cos (kz -wt) i^ + sint (kz -wt) j^ + cos (kz -wt) i^ - snt (kz -wt)j^ )
E_{z} = 2 E₀ cos (kz-wt) i^
the latter is a linear polarization on the x axis
A 10 kg package is delivered to your house. Use one complete sentence to describe an example of how work is done on the package as it gets brought inside. Make sure to use proper spelling, grammar, and other language mechanics. In your explanation, make sure to use the terms related to the formula for work (W = Fd).
Answer:
Hey :)
Explanation:
Work is a net force applied through a distance in order to displace an object, commonly abbreviated as W. A net force is the sum of all forces acting on an object. Work is mass times acceleration and distance so to find out the work you simply calculate the acceleration of the box being brought in. Next find the distance it was carried to get in the house. Then find out the mas of the box and finally multiply those sums together to get the amount of work put in to bring the package inside.
hope this helps :) xo
Is rock a substance or homogeneous or heterogeneous
Answer:
substances is ur answer dear mate
comment in the comment section
Answer: A rock is a substance.
Explanation: Rock is a substance because a rock does no have genes like you and I. And most rocks are made of sediment. That have been compressed together overtime.
11. Angie runs around a circular track for 20mins. The track is 1km and she runs at a rate of
1km10min. What is her total displacement?
a. 2km counterclockwise
b. 0.1km
c. 2km clockwise
d. Okm
e. 2km
Answer:
0 km
Explanation:
Since she is running in a circle, her final position is where she started which is at 0 km.
0km is her total displacement. So, the correct option is (D).
What is Displacement?Displacement is described as a change in the position of an object which is a vector quantity and has a direction and a magnitude. It is represented as an arrow pointing from the starting position to the final position. For example- If an object moves from position A to position B, then the position of the object changes.
Displacement is defined as the shortest distance from the initial position to the final position of the object. For above given information, Angie is running in a circle, so her final position is where she started which is at 0 km.
Thus, 0km is her total displacement. So, the correct option is (D).
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A raft is made using a number of logs (TBD) with 25-cm diameter and 2-m-length. It is desired that a maximum 90 percent volume of each log will be submerged when carrying two boys with 400 N each. Determine the minimum number of logs that must be used. The specific gravity of the log is 0.75.
Answer:
6logs
Explanation:f
First finding the volume of the logs
V= π/4d²l
= 0.098m³
So number of logs will be
Weight of 2 boys + weight of log = buoyancy force.
So
2( 400)+ N ( Mlog x g) = density of water x volume displaced x g
2(400) = N x 0.098x 1000x 9.8 x 0.9- 0.75* 1000
N= 5.5 which is approx 6logs
The minimum number of logs that must be used is 6 logs.
Calculation of the number of logs:Here first determine the volume of the logs i.e.
V= π/4d²l
= 0.098m³
Now
number of logs will be
Weight of 2 boys + weight of log = buoyancy force.
2( 400)+ N ( Mlog x g) = density of water x volume displaced x g
2(400) = N x 0.098x 1000x 9.8 x 0.9- 0.75* 1000
N= 5.5
= 6logs
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