Answer:
a) T = 1.26 s , b) v_max = 0.14 m / s , a_max = 0.7 m / s²
c) x = 0.028 cos (5 t) , v = - 0.14 sin 5t, a = - 0.7 cos 5t
Explanation:
This is a simple harmonic motion exercise that is described by the equation
x = A cos (wt +Ф)
with
w = √ (k / m)
let's apply this expression to our case
a) Angular velocity is related to frequency
w = 2π f
frequency and period are related
f = 1 / T
we substitute
2π / T = √ (k / m)
T = 2π √(m / k)
let's calculate
T = 2π √(1/25)
T = 1.26 s
In the expression for the period, the amplitude does not appear, therefore there is no dependence, as long as Hooke's law is fulfilled, which is correct for small amplitudes.
b) in the initial equation we have the position as a function of time, let's use the definition of speed and acceleration
v = dx / dt
v = - A w sin (wt + Ф)
the speed is maximum when the sine is -1
v_max = A w
w = √ (k / m)
w = √ 25/1
w = 5 rad / s
the amplitude of the movement is equal to the maximum compression of the spring
A = 2.8 cm = 0.028 m
we substitute
v_max = 0.028 5
v_max = 0.14 m / s
acceleration
a = dv / dt
a = - A w² cos (wt + Ф)
the acceleration is maximum when the cosine is -1
a_max = A w²
let's calculate
a_max = 0.028 5²
a_max = 0.7 m / s²
c) let's start by finding the phase constant
v = -A w cos (wt + Ф)
at t = 0 they indicate that the system has v = 0
0 = -A w sin (0 + Ф)
Ф = sin⁻¹ 0
Ф = 0
we write the equation
x = 0.028 cos (5 t)
v = - A w sin (wt + Ф)
v = - 0.028 5 sin (5t + 0)
v = - 0.14 sin 5t
acceleration
a = - A w² cos (wt + Ф)
a = - 0.028 5 2 cos (5 t + 0)
a = - 0.7 cos 5t
calculate the force exerted by a mental ball having a mass of 70kg moving with speed of 20m/s>2
Answer:
F = 1400 N
Explanation:
It is given that,
Mass of the ball, m = 70 kg
It is moving with an acceleration of 20 m/s². We need to find the force exerted by the ball.
Force is given by the product of mass and acceleration. So,
F = ma
[tex]F=70\ kg\times \ 20m/s^2\\\\F=1400\ N[/tex]
So, the force of 1400 N is exerted by a metal ball.
How many minutes does it take for light to go from the sun to the planet Uranus, a distance of 2.88x109 km? (The
velocity of light is constant in free space and is 3.00x108 m/s)
Answer:
t = 160 minutes
Explanation:
Given that,
Distance of Uranus from Sun is [tex]2.88\times 10^9\ km[/tex]
We need to find the time taken by the light to go from sun to Uranus if the velocity of light is constant in free space and it is equal to c.
So,
[tex]t=\dfrac{d}{v}\\\\t=\dfrac{2.88\times 10^9\times 10^3\ m}{3\times 10^8}\\\\t=9600\ s[/tex]
Since, 1 minute = 60 seconds
t = 160 minutes
So, 160 minutes is taken by the light.
How do FITT principles help you on your sports related activity
Answer:
F.I.T.T. stands for frequency, intensity, time and type. These four key aspects of your workout program will help you achieve your athletic goal, whether it's to increase your endurance, strength or speed. Here is an in-depth look at what each means and how to modify it to make athletic gains on the field...
A 50.5-turn circular coil of radius 4.75 cm can be oriented in any direction in a uniform magnetic field having a magnitude of 0.455 T. If the coil carries a current of 22.5 mA, find the magnitude of the maximum possible torque exerted on the coil.
Answer:
The maximum torque, τ = 3.67 × 10⁻³ Nm
Explanation:
The torque τ = NiABsinθ where N = number of turns of circular coil = 50.5, i = current in circular coil = 22.5 mA = 0.0225 A, A = area of circular coil = πr² where r = radius of circular coil = 4.75 cm = 0.0475 m, B = magnetic field strength = 0.455 T and θ = 90° for maximum torque.
So, τ = NiABsinθ
τ = Niπr²Bsinθ
τ = 50.5 × 0.0225 A × π × (0.0475 m)² × 0.455 T × sin90°
τ = 0.003665 Nm
τ = 3.665 × 10⁻³ Nm
τ ≅ 3.67 × 10⁻³ Nm
So the maximum torque, τ = 3.67 × 10⁻³ Nm
A storm is moving east towards your house at an average speed of 35 km / hr. If the storm is currently 80 km from your house, how much time do you expect it to arrive
Answer:
The expected time is 2.28 hours.
Explanation:
The speed of storm = 35 km/hr
The distance between the house and the storm = 80 km.
Now, we have to find the time taken by storm to arrive at the house. Here, we can determine the time by dividing the distance with speed.
The time, taken by storm = Distance/speed
The time, taken by storm = 80 / 35
The time, taken by storm = 2.28 hours.
solve for x, x=2.7(35)+1/2(-9.7)*35^2
The answer is:
-5846.75
Dennis throws a volleyball up in the air. It reaches its maximum height 1.1\, \text s1.1s1, point, 1, start text, s, end text later. We can ignore air resistance. What was the volleyball's velocity at the moment it was tossed into the air?
Answer:
If max height = 1.1 meters, then initial velocity is 3.28 m/s
If max height is 1.1 feet, then the initial velocity is 5.93 ft/s
Explanation:
Recall the formulas for vertical motion under the acceleration of gravity;
for the vertical velocity of the object we have
[tex]v=v_0-g \,t[/tex]
for the object's vertical displacement we have
[tex]y-y_0=v_0\,t - \frac{g}{2} \,t^2[/tex]
If the maximum height reached by the object is given in meters, we use the value for g in [tex]m/s^2[/tex] which is: [tex]9.8\,\,m/s^2[/tex]
If the maximum height of the object is given in feet, we use the value for g in [tex]ft/s^2[/tex] which is : [tex]32\,\,ft/s^2[/tex]
Now, when the ball reaches its maximum height, the ball's velocity is zero, so that allows us to solve for the time (t) the process of reaching the max height takes:
[tex]v=v_0-g \,t\\0=v_0-g \,t\\g\,\,t=v_0\\t=\frac{v_0}{g}[/tex]
and now we use this to express the maximum height in the second equation we typed:
[tex]y-y_0=v_0\,t - \frac{g}{2} \,t^2\\max\,height=v_0\,(\frac{v_0}{g}) - \frac{g}{2} \,(\frac{v_0}{g})^2\\max\,height= \frac{v_0^2}{2\,g}[/tex]
Then if the max height is 1.1 meters, we use the following formula to solve for [tex]v_0[/tex]:
[tex]1.1= \frac{v_0^2}{2\,9.8}\\(9.8)\,(1.1)=v_0^2\\v_0=10.78\\v_0=\sqrt{10.78} \\v_0=3.28\,\,m/s[/tex]
If the max height is 1.1 feet, we use the following formula to solve for [tex]v_0[/tex]:
[tex]1.1= \frac{v_0^2}{2\,32}\\(32)\,(1.1)=v_0^2\\v_0=35.2\\v_0=\sqrt{35.2} \\v_0=5.93\,\,ft/s[/tex]
Answer:
11
Explanation:
for khan academy, this is the answer
Which statement accurately describes electronic tools? Check all that apply
Answer:
Electronic tools provide more accurate data and this data is more efficient fast and easy to understand
Hope this helps you!!
If 5 complete oscillations of a sound wave pass through a point in 0.5 s and the speed of sound was recorded to be 10 m/s, then find the wavelength of the sound.
Answer:
λ = 2.5m
Explanation:
Given the following :
Speed of sound (v) = 10m/s
If 5 oscillations pass through a point in 0.5seconds;
Time taken (period) for 1 oscillation is :
Number of oscillations / total time taken
5 / 0.5 = 0.25 seconds
Wavelength, period and Velocity are related by the formula:
v = λ / T
λ = v * T
λ = 10 * 0.25
λ = 2.5 m
A car accelerate uniformly from rest at 5m/s2 . Determine it's speed after 10s
Answer:
50m/s.
Explanation:
Let's take acceleration as A and speed as S:
A = 5m/s²
S = A × 10s = 5 × 10 = 50m/s
The answer is 50m/s.
Answer:
50m/s
Explanation:
Given:
a=5m/s^2
t=10s
Required:
v=?
Formula:
a=v/t
Solution:
a=v/t
v=a*t
v=5m/s^2*10s
v=50m/s
Hope this helps ;)❤❤❤
what is the meaning of stroke
Answer:
Stroke has two emissions it could either be the meaning of lightly passing over something with the sense of touch for example stroking a dog/cat
And the medical term stroke where either a person has lost facial features of can't lift their arms up and keep them up or speak properly and their speech would be slurred
Hope this helps
If anything didn't meet your question please comment what you are looking for and I may change my answer thank you :)
Explanation:
FASTTT I BEG U An astronaut weighs 900 N on earth. On the moon he weighs 150 N. Calculate the moons’ gravitational strength. (Take g = 10 N/kg).
mass of an object is always constant
weight is a force, [tex]W=mg[/tex] where $g$ is acceleration due to gravity.
Weight on earth is , $900=m\cdot 10 \implies m=90$ kg
weight on moon is $150=90\times g_{\text{moon}} \implies g=\frac{5}{3}$
A baseball weights 1429 (0.142kg) were striked with force of 120N. Calculate its acceleration at
that time. Include the correct unit with your answer. Include one decimal place.
Answer:
a=845.07 m/s2
Explanation:
m=0.142kg
F=120N
a=?
F=m*a /:m
a=F/m
a=120N/0.142kg
a=845,07m/s2
Answer:
a = 845.07 m/s²
Explanation:
As we know ,
as per newton's 2nd law:-
F = ma
therefore
a = F/m
given:
a = ?
F = 120N
m = 0.142 kg
procedure:-
a = 120/0.142
therefore :
a = 845.07 m/s²
Systemic circulation requires help from which of the following bones, lungs, arteries and veins, or muscles
Answer:
Artery and viens
Explanation:
An electric field from a charge has a magnitude of 4.5 x 10^4 N/C at a certain
location that points outward. If another charge with a magnitude of -2.0 x 10^-6 C
is brought near it, what is the strength of the electrostatic force that acts on this
charge and how do the two charges behave?
0.09 N; repel each other
-0.09 N; attract each other
-2.3 N; repel each other
2.3 N; attract each other
Answer:
4.5 x 10^4 x -2 x 10^-6 = -0.09N
Explanation:
-0.09N
What is the value of work done on an object when a 0.1x102–newton force moves it 30 meters and the angle between the force and the displacement is 25°?
Answer: A. 2.7 x 10^2 joules
Explanation: I’m sorry for the guy above me!
Calculate the average kinetic energy of molecules of a gas at a temperature of 18 ° C
Answer:
6.0×10⁻²¹ J
Explanation:
KE = 3/2 kT,
where KE is average kinetic energy per molecule,
k is the Boltzmann constant,
and T is absolute temperature.
KE = 3/2 (1.38×10⁻²³ J/K) (18 + 273.15) K
KE = 6.0×10⁻²¹ J
Answer:
The answer is 6.0×10⁻²¹ J , because KE = 3/2 kT, where KE is average kinetic energy per molecule, k is the Boltzmann constant, and T is the absolute temperature.
KE = 3/2 (1.38×10⁻²³ J/K) (18 + 273.15) K
KE = 6.0×10⁻²¹ J
A body of mass 20 kh changes its velocity from 5m/s to 17 m/s in 3 seconds. find the force applied on this body .
please answer fast
Answer:
80 N.
Explanation:
The following data were obtained from the question:
Mass (m) = 20 Kg
Initial velocity (u) = 5 m/s
Final velocity (v) = 17 m/s
Time (t) = 3 secs
Force (F) =.?
Next, we shall determine the acceleration of the body.
Acceleration is simply defined as the rate of change of velocity with time. Mathematically, it is expressed as:
Acceleration = change of velocity /time
Acceleration (a) = (final velocity (v) – initial velocity (u)) / time (t)
a = (v – u) /t
With the above formula, we can obtain the acceleration of the body as follow:
Initial velocity (u) = 5 m/s
Final velocity (v) = 17 m/s
Time (t) = 3 secs
Acceleration (a) =?
a = (v – u) /t
a = (17 – 5) /3
a = 12/3
a = 4 m/s²
Finally, we shall determine the force applied to the body as follow:
Force (F) = mass (m) x acceleration (a)
F = ma
Mass (m) = 20 Kg
Acceleration (a) = 4 m/s²
Force (F) =.?
F = ma
F = 20 x 4
F = 80 M.
Therefore, the force applied on the body is 80 N.
Match words at the left to the correct blanks in the sentences on the right. Not all words will be used.1. The energy that drives the expansion of a star into a subgiant or red giant comes from HYDROGEN SHELL FUSION2. Stars with mass greater than about 8 solar masses are considered HIGH-MASS STARS3. The final stage of core fusion in a low-mass star is HELIUM FUSION4. Stars that are fusing hydrogen in their cores are MAIN-SEQUENCE STARS5. When it dies, a high-mass star explodes as a SUPERNOVA6. A star that is expanding (into a subgiant and then a giant) has a(n) INERT HELIUM CORE7. When it dies, a low-mass star expels a PLANETARY NEBULA8. Stars with masses less than about two solar masses are considered LOW-MASS STARS
Answer:
In what way is iron unique among the elements?
It has the lowest mass per nuclear particle.
Match words at the left to the correct blanks in the sentences on the right. Not all words will be used.
-The energy that drives the expansion of a star into a subgiant or red giant comes from HYDROGEN SHELL FUSION
-Stars with mass greater than about 8 solar masses are considered HIGH-MASS STARS
-The final stage of core fusion in a low-mass star is HELIUM FUSION
-Stars that are fusing hydrogen in their cores are MAIN-SEQUENCE STARS
-When it dies, a high-mass star explodes as a SUPERNOVA
-A star that is expanding (into a subgiant and then a giant) has a(n) INERT HELIUM CORE
-When it dies, a low-mass star expels a PLANETARY NEBULA
-Stars with masses less than about two solar masses are considered LOW-MASS STARS
which of the following best describes the kinetic theory model?
a. all particles in matter eventually stop moving
b. energy changes have no effect on the state of matter
c. when particles in matter gain or lose energy , they change state
d. no matter how much energy is present particles never move
Answer:
Answer c: "when particles in matter gain or lose energy , they change state"
Explanation:
As energy is provided to the molecules of the substance in question, they acquire more speed or vibration, increasing their separation in the substance, which can become then a liquid , or a gas. The reverse path also happens as the particles give away energy.
Answer:
c. when particles in matter gain or lose energy , they change state
we know that for example, if you add heat (energy) to ice it would melt (change state) or if you freeze water (change state) it would become ice.
d. Write the symbol for the nucleus that completes each nuclear equation. (1 point each)
Answer:
Ra, 88
Ru, 44
Cr, 24
Explanation:
i
the remaining mass number is 224(228 - 4), and it's atomic number is 88(90 - 2). The element is Radium, Ra
ii
the remaining mass number is 98(98 - 0), and it's atomic number is 44(45 - 1). The element is Ruthenium, Ru
iii
The remaining mass number is 52(52 - 0), and it's atomic number is 24(23 - -1). The element is Chromium, Cr
When the hydraulic conductivity Ks = 10 mm/hr; effective matrix potential Ns = 20 mm, and rainfall intensity I = 30 mm/hr , determine the amount of runoff generated when the runoff rate reaches 15 mm/hr?( 2.7 mm or 0.21 mm or 18 mm or 0.67 mm)
Answer:
[tex]t = 0.75 \ hr = 0.75 *60 = 45 \ minutes[/tex]
Explanation:
From the question we are told that
The hydraulic conductivity is [tex]Ks = 10\ mm/hr[/tex]
The effective matrix potential [tex]Ns = 20 \ mm[/tex]
The intensity of rainfall is [tex]I = 30 \ mm/hr[/tex]
The runoff rate [tex]R = 15 \ mm/hr[/tex]
Generally the run off rate is mathematically represented as
[tex]R = (I - Ks) t[/tex]
Here t is the amount of runoff generated
=> [tex]15 = (30 - 10) t[/tex]
=> [tex]t = 0.75 \ hr[/tex]
converting to minutes
[tex]t = 0.75 \ hr = 0.75 *60 = 45 \ minutes[/tex]
The model of the atom has changed as scientists have gathered new evidence. Four models of the atom are shown below, but one important model is missing. An image at left with overlapping red and blue balls in the center with a circular fuzzy green cloud outside them. An image at center left with a purple ball in the center surrounded by overlapping concentric black ovals, each with a small green ball on each of the 6 ovals. An image at center right with a large black cross in a purple circle with a black line around the purple, with 10 small green balls dispersed within the purple circle. An image at right with a purple center outlined in black with two concentric black circles around the center, the inner circle having 2 small green balls on it and the outer circle having 8 small green balls on it. Which atomic model is missing from this set? Bohr’s model Dalton’s model Rutherford’s model Thomson’s model
Answer:
Thomson’s model
Explanation:
Thompson regarded the atom largely as a sphere of positively charged matter in which negative charges were embedded.
This came to be known as the plum pudding model of the atom because it resembles a pudding studded with currants.
This was an early model of the atom and did not survive further experimental scrutiny of the structure of the atom.
Answer:
Thompsons model
Explanation:
i got it right on the quiz
Six members of a synchronized swim team wear earplugs to protect themselves against water pressure at depths, but they can still hear the music and perform the combinations in the water perfectly. One day, they were asked to leave the pool so the dive team could practice a few dives, and they tried to practice on a mat, but seemed to have a lot more difficulty. Why might this be
Answer:
The sound travels differently in different medium according the density of the medium.
Explanation:
The sound travels faster in dense medium and can be heard by the vibration of the bone present in the ear. The ear plugs reduce the sound intensity in both medium water and on land (air).
In air the sound is not heard properly due to the earplugs that stops the as the vibration are not able to produce as sound is not able to reach to middle ear, but Navy researchers have discovered that sound under water is heard by the bone present behind the ear, vibrations mastoid.
Find the odd one out a)Planets moving on it's axis,Strings of guitar (being played),Motion of a ferry wheel,The vehicles moving on a straight road. b)Motion of the moon around the earth,Motion of the earth around the sun,Motion of a merry-go-round,Heart-beat in a healthy person. c)Motion of a bullet fired from gun,Motion of a football player in the ground,Motion of a vehicle on a straight road,Motion of an apple falling from a tree
Answer:
a) Strings of guitar (being played)
b) Heart-beat in a healthy person
c) Motion of an apple falling from a tree
Explanation:
a) The motion of the string of a guitar being played is the only motion involving simple harmonic motion.
b) All the other motions are circular motion except the heart beat in a healthy person, which is periodic.
c) The motion of an apply falling from a tree is the only motion under the complete influence of gravity from the onset till the end.
A cat stalks an unsuspecting mouse. The movement of the cat is shown in the following graph of the horizontal position, x, against time, t. What is the average speed of the cat between t = 2s and t = 6s?
Answer:
0.25 m/s
Explanation:
Average velocity = change in displacement / change in time
v = (1.5 m − 2.5 m) / (6 s − 2 s)
v = -0.25 m/s
The average speed is 0.25 m/s.
Answer:
0.25 m/s
Explanation:
khan academy
a.
more iOCUS
8.
A force of 8N is applied to the body to cover 50 cm distance. How much work is done
by this fore?
400J
b. 40J
d. 40kg
a.
C.
Answer:
[tex] \boxed{\sf Work \ done = 4 \ J} [/tex]
Given:
Force = 8 N
Distance covered by the body = 50 cm = 0.5 m
Explanation:
Work Done = Force × Distance covered by the body
= 8 × 0.5
= 4 J
While driving on a highway, your HMMWV starts to pull to one side. You stop and check your tires – one tire is going flat. There is no spare, but the affected tire has a runflat device installed, and you are only 5 miles from the motor pool. What is your maximum allowable speed when driving with one flat tire?
Answer:
30 miles people hour (mph)
Explanation:
The maximum speed for one flat tyre is 30mph, for both tyres it is 20 mph and for two tyres on the same side it is 30mph. When a tyre is punctured driving at high speed should be avoided and not too long distance should be covered to avoid further accident and for the safety of other vehicles. Speed limit and distance for flat tires should be strictly followed.
A particle moves in a plane according to X=Rsinwt + wRt Y=Rcoswt+R where w and R constant this curved called cycloid path traced out by a point on rim of wheel that slipping with x-axis sketch the path calculate intantaneous velocity and acceleration when particle is its axis maximun and minimun value of Y
Answer:
maximum point y= 2R
vₓ = wR , v_{y} = 0, aₓ = 0, a{y} = - Rw²
minimum point y=R
vₓ = wR , v_{y} = - R w, aₓ = - R w², a_{y} = 0
Explanation:
The definition of velocity is
v = dr / dt
vₓ = dx / dt
[tex]v_{y}[/tex] = dy / dt
vₓ = Rw cos wt + wR
v_{y} = -Rw sin wt
acceleration is defined by
a = dv / dt
aₓ = -Rw² sin wt
a_{y} = - R w² cos wt
these are the general expressions for velocity and acceleration, to find the explicit values for the maximum and minimum y points, let's find these points and substitute
maximum point
y = R cos wt + R
the heat is maximum when the cosine is worth 1
y_max = 2R
at this point the speed is
vₓ = wR
v_{y} = 0
the acceleration is
aₓ = 0
a_{y} = - Rw²
minimum point
this occurs when the cosine is zero
y = R
speed is
vₓ = wR
v_{y} = - R w
acceleration is
aₓ = - R w²
a_{y} = 0
A 5000 pound car sitting in the last parking space in the block a scalar or vector quantity??
Answer:
scalar
Explanation:
pounds is a unit of mass, and mass is a scalar quantity.
if it was weight (in newtons) it would be a vector.
A 5000-pound car sitting in the last parking space in the block is a scalar quantity, not a vector quantity.
What are scaler quantity and vector quantity?The scaler quantity is only the quantity having some amount of magnitude but not direction and vector quantity is that which consists of both magnitude and the direction with them.
In 5000 pound car sitting in the last parking space in the block, it has a magnitude of 5000 pounds but does not have any direction to move and it comes under the scalar quantity.
Therefore, a car has scalar quantity not vector if, a 5000-pound car sitting in the last parking space in the block.
Learn more about scaler quantity and vector quantity, here:
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