Correct question is;
A 4-foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to √2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 7 ft/s. (Use g = 32 ft/s²)
Answer:
x(t) = 7te^(-2t√2)
Explanation:
We are given;
Weight; W = 8 lbs
mass; m = W/g
g = 32 ft/s²
Thus;
m = 8/32
m = ¼ slugs
From Newton's second law we can write the equation as;
m(d²x/dt²) = -kx - β(dx/dt)
Rearranging this, we have;
(d²x/dt²) + (β/m)(dx/dt) + (k/m)x = 0
Where;
β is damping constant = √2
k is spring constant = W/s
Where s = 8ft - 4ft = 4ft
k = 8/4
k = 2
Thus,we now have;
(d²x/dt²) + (√2/(¼))(dx/dt) + (2/(¼))x = 0
>> (d²x/dt²) + (4√2)dx/dt + 8x = 0
The auxiliary equation of this is;
m² + (4√2)m + 8 = 0
Using quadratic formula, we have;
m1 = m2 = -2√2
The general solution will be gotten from;
x_t = c1•e^(mt) + c2•t•e^(mt)
Plugging in the relevant values gives;
x_t = c1•e^(mt) + c2•t•e^(mt)
At initial condition of t = 0, x_t = 0 and thus; c1 = 0
Also at initial condition of t = 0, x'(0) = 7 and thus;
Since c1 = 0, then c2 = 7
Thus,equation of motion is;
x(t) = 7te^(-2t√2)
WILL GIVE BRAINLIEST, ANSWER WITH ACTUAL ANSWER OR ELSE I WILL REPORT YOU!!!!!
Four students are assigned a project for which they must experimentally determine the coefficient of kinetic friction between a block of an unknown material and a table. Each student has their own idea of how to go about setting up the experiment. The group settles on two possible test to conduct: Student A's idea and Student B's idea. Student A believes the group can obtain the coefficient of kinetic friction by attaching a spring scale to the mass and pulling on the mass with the spring scale with a horizontally directed force. The reading on the spring scale at the moment the block begins to move is the coefficient of kinetic friction. Which of the following explains what is wrong with Student A's logic?
MC Options inserted in image below
Answer:
I know you said not to do this but I am doing a challenge and You asked this an hour ago. PLS DON'T REPORT ME.
Explanation: Sorry
You are testing a new car using crash test dummies. Consider two ways to slow the car from 90 km/h (56 mi/h) to a complete stop:
i) You let the car slam into a wall, bringing it to a sudden stop.
ii) You let the car plow into a giant tub of gelatin so that it comes to a gradual halt.
In which case is there a greater impulse of the net force on the car?
(Prove and select below.)
a) in case (i).
b) in case (ii).
c) The impulse is the same in both cases.
d) The impulse of the first case > the impulse of the second case.
e) The impulse of the first case < the impulse of the second case.
Answer:
c) The impulse is the same in both cases.
Explanation:
What drives the car is the amount of movement of the car during its journey. In this case, we can consider that in the car, presented in the question above, the movement is generated through speed and friction on the track, the impact that makes the car stop, is not part of the movement and therefore, not part of the impulse. In the two situations presented, the speed of the car is the same, the same car and the same track were also used, which shows us that the impulse, in both situations, is the same.
a highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of:
A car making this turn is pulled downward by its own weight, and pushed up by the road at an angle of 45°, so by Newton's second law,
• the net horizontal force on the car is
∑ F = N cos(45°) = m a = m v ² / R
• the net vertical force on the car is
∑ F = N sin(45°) - m g = 0
where
• N = magnitude of the normal force
• m = mass of the car
• a = v ² / R = centripetal acceleration of the car
• v = tangential speed of the car
• R = 100 m = radius of curvature
• g = 9.8 m/s² = acceleration due to gravity
From the net vertical force equation, we get
N = m g / sin(45°)
and substituting this into the net horizontal force equation and solving for v gives
(m g / sin(45°)) cos(45°) = m v ² / R
v = √(R g cos(45°) / sin(45°)) ≈ 31 m/s
We have that A highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of
V=32m/s
From the question we are told
a highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of:
Generally the equation for the Velocity is mathematically given as
[tex]V=\sqrt{rgtan\theta}[/tex]
Therefore
[tex]V=\sqrt{rgtan\theta}\\\\V=\sqrt{100*9.8*tan45}\\\\V=32m/s[/tex]
Therefore
A highway curve of radius 100 m, banked at an angle of 45 degrees, may be negotiated without friction at a speed of
V=32m/s
For more information on this visit
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Please solve this and please don’t put in a link.
Answer:
synthesis
Explanation:
It is a combination (synthesis) reaction.
A+B→AB
Answer:
i think it is a synthesis
Explanation:
synthesis reaction occurs when two substances combine and form a compound...
hope this helps!!
What is the medium of the wave shown in the photograph?
A. The water
B. Kinetic energy
C. The duck
D. Gravity
Answer:
A. The water
Explanation:
i got it right on A-P-E-X
Why is Rome warmer than New York in January
Answer:
The basic answer is sea flows. On the off chance that the air making a trip to New York moves via land, it will be cooler than the air and flows that reach, for instance, San Francisco. Along these lines, Rome is hotter than New York because of flows, topography and air development designs.
Explanation:
Brainliest?
[tex]\\ x^{2} \int\limits^a_b {x} \, dx \int\limits^a_b {x} \, dx \neq \pi \pi \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
Answer:
I think you have a problem trying to write the question down, can you re write it because it seems glitched.
Explanation:
The ear drum vibrates when struck by sound waves and directly sends a message to the brain that is then recognized as sound
True or False
Answer:
true
Explanation:
Guys please help. I need this question
When the car is moving the unbalanced force acting on the car is 150 N.
A) State the equation which relates unbalanced force, mass and acceleration?
Answer:
F = m a, a = 0.3 m / s²
this acceleration points in the direction of the unbalanced force
Explanation:
In this problem we must use Newton's second law. Let's fix a reference system with the x axis parallel to the surface and the y axis perpendicular
Y axis y
N-W = 0
N = W = mg
X axis
∑ F = m a
F = m a
we substitute
150 = m a
To find an acceleration value, the mass of the car must be known, if the mass is m = 500 kg
a = 150/500
a = 0.3 m / s²
this acceleration points in the direction of the unbalanced force
2. A kayaker is paddling south at 2.50 m/s, and encounters a weird current moving 1.15 m/s west.
What is the resultant velocity?
Answer:
v = 2.91 m/s
Explanation:
Given that,
A kayaker is paddling south at 2.50 m/s, and encounters a weird current moving 1.15 m/s west.
We need to find the resultant velocity. Both velocities are perpendicular to each other. So,
[tex]v=\sqrt{v_1^2+v_2^2} \\\\=\sqrt{2.5^2+1.5^2} \\\\=2.91\ m/s[/tex]
So, the magnitude of the resultant velocity is equal to 2.91 m/s.
True or False
Microscopic organisms grow on the rocks near a volcano if the rocks are cooled to 120 degrees Celsius or less.
Explanation:
it's true
Kiss me if I'm wrong. But dinosaurs still exist right?
Answer:
True
Definetely true
explain how renewable energy source help in the reducing the effects of global warming?
Answer:
Renewable energy minimizes carbon pollution and has a much lower impact on our environment. And it's having its moment in the sun. "Giving more New Yorkers access to renewable energy can allow them to reduce their own energy bills while reducing stress on the grid and demand for fossil fuel power.
a disk of a radius 50 cm rotates at a constant rate of 100 rpm. what distance in meters will a point on the outside rim travel during 30 seconds of rotation?
c
Which three continents contain coal fields that provide evidence for continental drift?
Africa, Antarctica, and North America
Eurasia, Africa, and South America
Antarctica, South America, and Africa
South America, North America, and Eurasia
Answer:
D
Explanation:
its D
HELP PLEASEEE it’s due soon
Answer:
254.982J
Explanation:
mass = 130kg
gravity = 9.807m/s^2
height = 0.200m
Answer:
potential energy = 254.8 jouleExplanation:
mass (m) = 130 kg
height (h) = 0.200 m
(g) = 9.8
potential energy = m×g×h
= 130×0.200×9.8
= 254.8 joule
a disk of a radius 50 cm rotates at a constant rate of 100 rpm. what distance in meters will a point on the outside rim travel during 30 seconds of rotation?
Each minute, the disk completes 100 revolutions, so a point on the rim traverses a distance of 100 times the circumference of the disk and would have a linear speed of
100 rev/min
= (100 rev/min) × (2π × 50 cm/rev) × (1/100 m/cm) × (1/60 min/s)
= 5π/3 m/s ≈ 5.236 m/s
Then after 30 s of rotation, the point would have traveled a distance of
(5π/3 m/s) × (30 s) = 50π m ≈ 157.08 m
1. What is the heat energy when 114.32g of water ( c = 4.18 J/g °C) at 14.85°C is raised to
18.00°C?
true or false
The Total electric potential due to two or more charges is equal to the algebraic sum of the potentials due to the individual charges.
Answer:
i guess the answer is false
CiCi is hiking in the woods after a rainstorm when she sees a single large mass of rock and soil moving quickly downhill.
Which type of mass movement is this?
A. landslide
B. slump
C. creep
D. mudflow
Make a poem about waves with 12 Lines and 3 Stanzas.
In a ocean full of storms
A new wave was born
Deep into that darkness flooding
Suddenly, I heard some pummeling
By the grave I saw the winds
And the sun just shined
Answer:
a friendly face that comes with waves,
the waves of all the memorial days,
and with these days we smile with pride,
as for the waves we used to ride,
given up the day has passed,
how it went away like an hour glass,
as if we knew the world was right,
just like the waves, oh so bright,
the time has come the days have passed,
the waves ashore the waves alast,
as if the friendly face was right,
the waves that rode, oh goodnight.
a Ferris wheel with a diameter of 35 m starts from rest and achieves its maximum operational tangential speed of 2.3 m/s in a time of 15 s. what is the magnitude of the wheels angular acceleration?
b. what is the magnitude of the tangential acceleration after the maximum operational speed is reached?
(a) The magnitude of the wheels angular acceleration is 0.0088 rad/s².
(b) The magnitude of the tangential acceleration after the maximum operational speed is reached is 0.153 m/s².
Angular acceleration of the wheel
The angular acceleration of the wheel is calculated as follows;
α = ω/t
ω = v/r
α = v/(rt)
α = (2.3)/(17.5 x 15)
α = 0.0088 rad/s²
Tangential acceleration of the wheela = v/t
a = (2.3)/15
a = 0.153 m/s²
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Explain why it is not advisable to be in a garage when the car engine is being
heated.
Answer:
You can breathe in too much carbon monoxide, which will eliminate the flow of oxygen to your bloodstream and can kill you.
Explanation:
Please help me with this very easy question I just don’t get it.
Answer:
150m
Explanation:
The relation of speed/time and distance/time is a derivative/integral one, as in speed is the derivative of distance (the faster you go, the faster the distance changes, duh!).
So we need to compute the integral of speed over time from 0.0s to 5.0s.
The easiest way here is to compute the area under the line (it's going to be faster than computing the acceleration and using a formula of distance based on acceleration).
The area under the line is a trapezoid with "height" 5s, and the bases 10m/s and 50m/s. Using the trapezoid area formula of h*(a + b)/2
distance = 5s * (10m/s + 50m/s) / 2 = 5s * 60m/s / 2 = 5s * 30m/s = 150m
Alternatively, we can use the acceleration formula:
a = (50m/s - 10m/s)/5s = 40m/s / 5s = 8m/s^2
distance = v0 * t + a * t^2 / 2 = 10m/s * 5s + 8m/s^2 * (5s)^2 / 2 = 50m + 8m * 25 / 2 = 50m + 100m = 150m.
Tony ran 600 meters in 60 seconds. What was Tony's speed during the
race?
Please help me please with both questions
Answer:
6 - iron
7 - by stringing many magnets together
Explanation:
6 - substances such as iron, cobalt, and nickel, most of the electrons spin in the same direction. This makes the atoms in these substances strongly magnetic—but they are not yet magnets. ... The piece of iron has become a magnet. Some substances can be magnetized by an electric current.
7 - it is that only
Squids and octopuses propel themselves by expelling water. They do this by keeping water in a cavity and then suddenly contracting the cavity to force out the water through an opening. A 6.50 kg squid (including the water in the cavity) at rest suddenly sees a dangerous predator. Part A If the squid has 1.55 kg of water in its cavity, at what speed must it expel this water to instantaneously achieve a speed of 2.40 m/s to escape the predator
Answer:
10.1 m/s
Explanation:
By Newton's third law, the force on the squid and that due to the water expelled form an action reaction pair.
And by the law of conservation of momentum,
initial momentum of squid + expelled water = final momentum of squid + expelled water.
Now, the initial momentum of the system is zero.
So, 0 = final momentum of squid + expelled water
0 = MV + mv where M = mass of squid = 6.50kg, V = velocity of squid = 2.40m/s, m =mass of water in cavity = 1.55 kg and v = velocity of water expelled
So, MV + mv = 0
MV = -mv
v = -MV/m
= -6.50 kg × 2.40 m/s ÷ 1.55 kg
= -15.6 kgm/s ÷ 1.55 kg
= -10.1 m/s
So, speed must it expel this water to instantaneously achieve a speed of 2.40 m/s to escape the predator is 10.1 m/s
A scientist notices that an oil slick floating on water when viewed from above has many different colors reflecting off the surface, making it look rainbow-like (an effect known as iridescence). She aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). The index of refraction of water is 1.33.
Part A: The index of refraction of the oil is 1.20. What is the minimum thickness of the oil slick at that spot? t= 313nm
Part B: Suppose the oil had an index of refraction of 1.50. What would the minimum thickness be now? t=125nm
Answer:
a) The minimum thickness of the oil slick at the spot is 313 nm
b) the minimum thickness be now will be 125 nm
Explanation:
Given the data in the question;
a) The index of refraction of the oil is 1.20. What is the minimum thickness of the oil slick at that spot?
t[tex]_{min[/tex] = λ/2n
given that; wavelength λ = 750 nm and index of refraction of the oil n = 1.20
we substitute
t[tex]_{min[/tex] = 750 / 2(1.20)
t[tex]_{min[/tex] = 750 / 2.4
t[tex]_{min[/tex] = 312.5 ≈ 313 nm
Therefore, The minimum thickness of the oil slick at the spot is 313 nm
b)
Suppose the oil had an index of refraction of 1.50. What would the minimum thickness be now?
minimum thickness of the oil slick at the spot will be;
t[tex]_{min[/tex] = λ/4n
given that; wavelength λ = 750 nm and index of refraction of the oil n = 1.50
we substitute
t[tex]_{min[/tex] = 750 / 4(1.50)
t[tex]_{min[/tex] = 750 / 6
t[tex]_{min[/tex] = 125 nm
Therefore, the minimum thickness be now will be 125 nm
How much gravitational force do two lead balls with a mass of 8 kilograms, the centers of mass of which are 17 cm apart, affect each other?
Answer:
1.48×10⁻⁷ Newtons
Explanation:
From the question,
According to newton's law of universal gravitation.
F = Gmm'/r²........................ Equation 1
F = gravitational force, G = gravitational constant, m = mass of the first ball, m' = mass of the second ball, r = distance between the balls.
Given: m = m' = 8 kg, r = 17 cm = 0.17 m,
Constant : G = 6.67×10⁻¹¹ Nm²/kg²
Substitute these values into equation 1
F = (6.67×10⁻¹¹×8×8)/(0.17²)
F = 1.48×10⁻⁷ N
Light rays enter a transparent material. Which description best describes what happens to the light rays
When light encounters transparent materials, almost all of it passes directly through them. Glass, for example, is transparent to all visible light. ... Most of the light is either reflected by the object or absorbed and converted to thermal energy. Materials such as wood, stone, and metals are opaque to visible light.