Answer:
[tex]\mathbf{x = 3te ^{-2 \sqrt{2t}}}[/tex]
Explanation:
From the given information concerning the spring-mass system:
Let us apply Hooke law.
Then, we have:
mg = ks
8 = k4
k = 8/4
k = 2
Provided that the mass weighing 8 lbs is attached to a spring.
Then, we can divide it by gravity 32 ft/s².
∴
m = 8/32
m = 1/4 slugs
The medium that offers the damping force [tex]\beta = \sqrt{2}[/tex]
Now, let us set up a differential equation that explains the motion of the spring-mass system.
The general equation is:
[tex]mx '' + \beta x' + kx = 0[/tex]
where;
[tex]m = \dfrac{1}{4}[/tex]
k = 2, and
[tex]\beta = \sqrt{2}[/tex]
Then;
[tex]\dfrac{1}{4}x'' + \sqrt{2} x' + 2x = 0[/tex]
By solving the above equation, the auxiliary equation is:
[tex]m^2 + 4 \sqrt{2} m + 8n = 0[/tex]
Using quadratic formula:
[tex]\dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
[tex]m = \dfrac{-4 \sqrt{2} \pm \sqrt{(4 \sqrt{2})^2 -4(1)(8) }}{2}[/tex]
[tex]m = \dfrac{-4 \sqrt{2} \pm \sqrt{32 -32 }}{2}[/tex]
[tex]m = -2 \sqrt{2}[/tex]
Since this is a repeated root, the solution to their differential equation took the form.
[tex]x_c = c_1 e^{mt} + c_2 t e^{mt}[/tex]
[tex]x_c = c_1 e^{-2\sqrt{2} t} + c_2 t e^{-2\sqrt{2} t}[/tex]
From the initial condition.
At equilibrium position where the mass is being from:
x(0) = 0
Also, at the downward velocity of 3 ft/s
x'(0) = 3
Then, at the first initial condition:
[tex]x_c (0) = c_1 e^{-2\sqrt{2} *0} + c_2 (0) e^{-2\sqrt{2} *0}[/tex]
[tex]0= c_1 e^{0} + 0[/tex]
[tex]0= c_1[/tex]
At the second initial condition;
[tex]x' = -2 \sqrt{2} c_1 e^{-2 \sqrt{2} t } -2 \sqrt{2} c_2 t e^{-2 \sqrt{2} t } + c_2 e^{-2 \sqrt{2} t}[/tex]
where;
x'(0) = 3
[tex]x' (0) = -2 \sqrt{2} c_1 e^{-2 \sqrt{2}* 0 } -2 \sqrt{2} c_2 (0) e^{-2 \sqrt{2} *0 } + c_2 e^{-2 \sqrt{2} *0}[/tex]
[tex]3 = -2 \sqrt{2} * 0 *e^0 - 0 + c_2 e^0[/tex]
[tex]3 = 0 + c_2[/tex]
[tex]3 = c_2[/tex]
Replacing in the constraints, the equation of the motion is:
[tex]\mathbf{x = 3te ^{-2 \sqrt{2t}}}[/tex]
16. Explain the following observations:
i. Water wets glass surface but does not wet the waxed glass surface.
Answer:
because the cohesive forces within the drops are stronger than the adhesive forces between the drops and the wax. Water wets glass and spreads out on it because the adhesive forces between the liquid and the glass are stronger than the cohesive forces within the water.
Answer:
the adhesive forces between the drops are stronger than cohesive force between the liquid
Hydropower is alternative source of energy
Answer:
Hydropower is an alternate source!Its expensive and takes up large spaces and many natural resources Takes homes of natural species.Answer:
because Hydropower is fueled by water, so it's a clean fuel source, meaning it won't pollute the air like power plants that burn fossil fuels, such as coal or natural gas. Hydroelectric power is a domestic source of energy, allowing each state to produce their own energy without being reliant on international fuel sources.
Explanation:
please mark as brainlest
Fix this problem, please.
Answer:
The correct option is (a).
Explanation:
Given that,
Radius of a horizontal circle, r = 80 cm = 0.8 m
Angular velocity, ω = 5 rev/minute = 0.523 rad/s
We need to find the magnitude of its centripetal acceleration. The formula that is used to find the centripetal acceleration is given by :
[tex]a=\omega^2 r\\\\a=(0.523)^2\times 0.8\\\\a=0.218\ m/s^2[/tex]
or
[tex]a=0.22\ m/s^2[/tex]
So, the magnitude of its acceleration is [tex]0.22\ m/s^2[/tex].
Suppose an astronaut floating in space throws a rock. What will happen to the rock?
Answer:
C
Explanation:
A spring with a spring constant of 50 N/m is stretched by an extension of 2 cm. Calculate the energy in its elastic energy potential store
hhhhuuuxuuuudddddddddddd
Hooke's law describes a certain light spring of unstretched length 32.1 cm. When one end is attached to the top of a doorframe and a 7.94 kg object is hung from the other end, the length of the spring is 42.4 cm. (a) Find its spring constant. .7554 Correct: Your answer is correct. kN/m (b) The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 178 N. Find the length of the spring in this situation. .7923 Incorrect: Your answer is incorrect.
Answer:
[tex]0.75623\ \text{kN/m}[/tex]
[tex]55.6\ \text{cm}[/tex]
Explanation:
m = Mass of object = 7.94 kg
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
x = Change in length of the spring = [tex](42.4-32.1)\ \text{cm}[/tex]
F = Force on the spring
Force of gravity on the object and the force on the spring will be equal
[tex]mg=kx\\\Rightarrow k=\dfrac{mg}{x}\\\Rightarrow k=\dfrac{7.94\times 9.81}{0.424-0.321}\\\Rightarrow k=756.23\ \text{N/m}[/tex]
The spring constant is [tex]756.23\ \text{N/m}=0.75623\ \text{kN/m}[/tex]
F = 178 N
Force on spring is given by
[tex]F=kx\\\Rightarrow x=\dfrac{F}{k}\\\Rightarrow x=\dfrac{178}{756.23}\\\Rightarrow x=0.235\ \text{m}=23.5\ \text{cm}[/tex]
The length of the spring will be [tex]32.1+23.5=55.6\ \text{cm}[/tex].
The highest surface temperature on any of the solar system’s planets is found on Venus. Partly because of its nearness to the sun and partly because of the extreme pressure of its atmosphere, the average daytime temperature on Venus is 453°C. What is this temperature in degrees Fahrenheit and in kelvins?
Answer:
Fahrenheit ⇒ 847.4 °FKelvin ⇒ 726.15KExplanation:
To convert Celsius to Fahrenheit, use the following formula;
= (°C * 9/5) + 32
= (453 * 9/5) + 32
= 847.4 °F
To convert Celsius to Kelvin, use the following;
= °C + 273.15
= 453 + 273.15
= 726.15K
A person pushes a 10 kg box from rest and accelerates it to a speed of 4 m/s with a constant force. If the box is pushed for a time of 2.5 s, what is the force exerted by the person?
The box is accelerated from rest to 4 m/s in a matter of 2.5 s, so its acceleration a is such that
4 m/s = a (2.5 s) → a = (4 m/s) / (2.5 s) = 1.6 m/s²
Then the force applied to the box has a magnitude F such that
F = (10 kg) (1.6 m/s²) = 16 N
2. What do pitch and loudness have in common?
Both are measured in decibels, or dB.
Both depend on a wave's frequency.
Both are subject to a person's interpretation.
Answer:
Both are subject to a persons interpretation
Explanation:
We hear people describe this when somebody is making an irresistible sound. usually people say the baby has a pitch scream.
You pull a 70-kg crate at an angle of 30° above the horizontal. If you pull with a force of 600N and the coefficient of kinetic friction is .4, how far will it move in 3 seconds?
Answer:
Explanation:
Force of friction acting on the body = μ mg cosθ
= .4 x 70 x 9.8 x cos30
= 237.63 N
component of weight = mgsinθ
= 70 x 9.8 x sin30
= 343 N
Net upward force = 600 - mgsinθ - μ mg cosθ
= 600 - 343 - 237.63
= 105.37 N
acceleration in upward direction = 105.37 / 70
= 1.5 m /s²
s = ut + 1/2 a t²
= 0 + .5 x 1.5 x 3²
= 6.75 m .
The crate will move at a distance of 1.215 m in 3 seconds.
How do you calculate the distance of motion?Given that the mass m of the crate is 70 kg and the angle above the horizontal is 30°. External force F on the crate is 600 N and the coefficient of friction is 0.4.
The friction force applied to the crate is calculated as given below.
Friction force = [tex]\mu mgcos \theta[/tex]
Where [tex]\mu[/tex] is the friction constant, g is the gravitational acceleration and [tex]\theta[/tex] is the angle above the horizontal.
Friction Force = [tex]0.4\times 70\times 9.8\times cos30^\circ[/tex]
Friction force = 237.63 N.
There is a force applied on the crate due to its weight is calculated as given below.
Force (weight component) = [tex]mgsin\theta[/tex]
Force (weight component) = [tex]70\times 9.8\times sin 30^\circ[/tex]
Force (weight component) = 343 N.
The net force applied to the crate is given below.
Net force = External force - friction force - force (weight component)
Net force F' = [tex]600 - 237.63 - 343[/tex]
Net force F' = 19.37 N.
The acceleration of the crate can be calculated as given below.
[tex]a = \dfrac {F'}{m}[/tex]
[tex]a =\dfrac {19.37}{70}[/tex]
[tex]a = 0.27 \;\rm m/s^2[/tex]
Hence the distance traveled by the crate in 3 seconds is calculated by the formula given below.
[tex]s = ut + \dfrac {1}{2} at^2[/tex]
Where, s is the distance, u is the initial velocity, a is the acceleration and t is the time of motion of the crate.
[tex]s = 0\times 3 + \dfrac {1}{2} \times 0.27 \times 3^2[/tex]
[tex]s = 1.215[/tex]
Hence we can conclude that the crate will move a distance of 1.215 m in 3 seconds.
To know more about the force, follow the link given below.
https://brainly.com/question/26115859.
What is the launch speed of a projectile that rises vertically above the Earth to an altitude equal to 14 REarth before coming to rest momentarily
Answer:
v = 1.078 10⁴ m / s
Explanation:
To solve this exercise we can use conservation of mechanical energy
Starting point. Just clearing
Em₀ = K + U = ½ m v² - G m M / [tex]R_{e}[/tex]
Final point. At r = 14R_{e}
Em_{f} = U = -G m M / 14R_{e}
how energy is conserved
Em₀ = [tex]Em_{f}[/tex]
½ m v² - G m M /R_{e} = -G m M / 14R_{e}
½ v² = G M / R_{e} (-1/14 + 1)
v² = 2 G M / R_{e} 13/14
we calculate
v² = 2 6.67 10⁻¹¹ 5.98 10²⁴ / 6.37 10⁶ 13/14
v = √ (1,16 10⁸)
v = 1.078 10⁴ m / s
The launch speed of a projectile that rises above the earth will be
v = 1.078 10⁴ m / s
What is speed?
Speed is defned as the movement of any object with respect to the time the formula of speed is given as the ratio of the distance with time.
To solve this exercise we can use conservation of mechanical energy
Starting point. Just clearing
[tex]E_{mo} = K + U = \dfrac{1}{2}m v^2 - \dfrac{G m M} { r}[/tex]
Final point. At[tex]r = 14R_{e}[/tex]
[tex]Em_{f} = U = \dfrac{-G m M }{14R_{e}}[/tex]
how energy is conserved
[tex]E_{mo }= \dfrac{1}{2} m v^2 -\dfrac{-G m M }{R_{e}} = \dfrac{-G m M }{ 14R_{e}}[/tex]
[tex]\dfrac{1}{2} v^2 = \dfrac{G M }{ R_{e} (\dfrac{-1}{14} + 1)}[/tex]
[tex]v^2 = \dfrac{2 G M} { R_{e} \dfrac{13}{14}}[/tex]
we calculate
[tex]v^2 = \dfrac{2 6.67 \times10^{-11}\times 5.98 \times 10^{24}} { 6.37 \times 10^{6} \times \dfrac{13}{14}}[/tex]
[tex]v = \sqrt{ (1,16\times 10^8)}[/tex]
v = 1.078 10⁴ m / s
Hence the launch speed of a projectile that rises above the earth will be
v = 1.078 10⁴ m / s
To know more about speed follow
https://brainly.com/question/4931057
Given A = (0.210 + 0.41) (1.10 x 102). Show the result for A in correct number of
significant figures.
Answer:
69
Explanation:
Perform addition first as;
(0.210 + 0.41) = 0.62 -------{2 significant figures}
Perform product
(1.10 x 102) = 112 -------------- {3 significant figures}
The combined product
0.62 x 112 =69.44
= 69 ----------2 significant figures
Rule
The least number of significant figures in the numbers performing the operation determines the number of significant figures in the answer.
Suppose that you wanted to use either conservation of momentum or conservation of kinetic energy to predict the outcome when a large car collides with a smaller car in a demolition derby. Which of the two quantities would be more appropriate for your calculation? Explain please.
Answer:
Conservation of momentum
Explanation:
Out of the two options given, the more appropriate one is the law of conservation of momentum. This is particularly so because momentum deals with the velocity or speed of the car while considering its mass. So, if a large car is to collide with another car, small one, then the momentum is what is considered. Energy on the other hand is talking about the work that is done, while the momentum considers the mass of the car while it is moving and considering its speed also
A 10-foot ladder is leaning straight up against a wall when a person begins pulling the base of the ladder away from the wall at the rate of 1 foot per second. Calculate the true distance between the top of the ladder and the ground when the base of the ladder is 9 feet from the wall.
Answer:
[tex]y = 4.36[/tex]
Explanation:
Let the height of the ladder be L
[tex]L = 10[/tex]
Also:
Let [tex]x = distance\ from\ the\ base\ of\ the\ ladder[/tex]Let [tex]y = height\ of\ the\ base\ of\ the\ ladder[/tex]When the ladder leans against the wall, it forms a triangle and the length of the ladder forms the hypotenuse.
So, we have:
[tex]L^2 = x^2 + y^2[/tex] --- Pythagoras Theorem
When the base is 9ft from the wall, this means that:
[tex]x = 9[/tex]
Substitute 9 for x and 10 for L in [tex]L^2 = x^2 + y^2[/tex]
[tex]10^2 = 9^2 + y^2[/tex]
[tex]100 = 81 + y^2[/tex]
Make [tex]y^2[/tex] the subject
[tex]y^2 = 100 - 81[/tex]
[tex]y^2 = 19[/tex]
Make y the subject
[tex]y = \sqrt{19[/tex]
[tex]y = 4.36[/tex]
Hence, the true distance at that point is approximately 4.36ft
The true statement about the true distance between the top of the ladder and the ground when the base is 9 feets from the wall is - 9/√19
Let :
x = distance from base of ladder y = Length of ladderLadder forms a right angle triangle as it leans against the wall :
Hence, we have :
Opposite² + Adjacent² = hypotenus²x² + y² = 100Taking the implicit derivative of both sides:
2xdx/dt + 2ydy/dt = 0
xdx/dt + ydy/dt = 0
ydy/dt = - xdx/dt
dy/dt = (-xdx/dt) / y
When the ladder is 9 ft from the wall;
x = 981 + y² = 100
y² = 100 - 81 = 19
y = √19
Substituting into the equation :
dy/dt = -9(1)/√19
Hence, dy/dt = - 9/√19
Learn more : https://brainly.com/question/13511183
How do gamma rays use electromagnetic waves to function....PLS HELP
Answer:
Gamma-rays have the smallest wavelengths and the most energy of any other wave in the electromagnetic spectrum. These waves are generated by radioactive atoms and in nuclear explosions.
Explanation:
Gamma-rays can kill living cells, a fact which medicine uses to its advantage, using gamma-rays to kill cancerous cells.
Hope this helps!
Brain-LIst?
Two masses sit at the top of two frictionless inclined planes that have different angles,__deleted9917f34947e1359b5705bbac0d9227f8ec5df862078213a2db19c72f00189109deleted__ 0N86-C1-52-40-A837-22820 50% Part (a) What can be said about the speeds of the two masses at the bottom of their respective paths
Answer:
v = [tex]\sqrt{2gh}[/tex]
the speed in the two planes will be the same since it does not depend on the angle of the same
Explanation:
In this exercise we are told that the two inclined planes have no friction force, so we can apply the conservation of energy for each one, we will assume that the initial height in the two planes is the same
starting point. Highest part of each plane
Em₀ = U = m g h
final point. Lowest part of each plane
[tex]Em_{f}[/tex] = K = ½ m v²
as there is no friction, the mechanical energy is preserved
Em₀ = Em_{f}
mg h = ½ m v²
v = [tex]\sqrt{2gh}[/tex]
As we can see, the speed in the two planes will be the same since it does not depend on the angle of the same
Fire trucks have the word FIRE written two ways, as seen here, on the front of the truck. Why is that?
Answer:
b.
Explanation:
A newly discovered particle, the SPARTYON, has a mass 455 times that of an electron. If a SPARTYON at rest absorbs an anti-SPARTYON, what is the frequency of each of the emitted photons (in 1020 Hz)? The mass of an electron is 9.11×10-31 kg.
Answer:
υ = 5.62 x 10¹⁴ Hz
Explanation:
The process of of formation of photons takes place due to interaction of a particle with its anti-particle is called Annihilation of Matter. Here SPARTYON absorbs anti-SPARYTON to form 2 photons. Applying conservation of energy to the to this scenario, we get:
2(Energy of Each Photon) = Rest Mass Energy of SPARTYON + Rest Mass Energy of anti-SPARTYON
[tex]2hv = m_{0}c^2 + m_{0}c^2\\\\2hv = 2m_{0}c^2\\\\hv = m_{0}c^2\\\\v = \frac{m_{0}c^2}{h}[/tex]
where,
υ = frequency of each photon = ?
m₀ = rest mass of SPARTYON = mass of anti-SPARTYON = 455*Mass of electron
m₀ = 455(9.1 x 10⁻³¹ kg) = 4.14 x 10⁻²⁸ kg
c = speed of light = 3 x 10⁸ m/s
h = Plank's Constant = 6.625 x 10⁻³⁴ J.s
Therefore, using these values in the equation, we get:
[tex]v = \frac{(4.14 x 10^{-28} kg)(3 x 10^8 m/s)^2}{6.625 x 10^{-34}J.s}\\\\[/tex]
υ = 5.62 x 10¹⁴ Hz
Describe any major landmarks (buildings, bridges, historical sites, etc.) that were destroyed during the valdivia earthquake.
Answer:
Homes, Workplaces, Statues, Meuseums
Explanation:
if you did look into it you would know after the earthquake there was a tsunami which flooded alot of places, this made many homeless, jobless, and many lossing vaklueable things
If the equal tensions T in the pulley cable are 300 N, express in vector notation the force R exerted on the pulley by the two tensions. Determine the magnitude of R.
Answer:
[tex]R=519.61N[/tex]
Explanation:
From the question we are told that
Tension T on a cable are T=300N
Generally the tensions on a pulley is
[tex]\sum f_x=T+T*cos(\theta)[/tex]
Therefore
[tex]\sum f_x=300+300*cos(60)[/tex]
[tex]\sum f_x=300 *1.5[/tex]
[tex]\sum f_x=450N[/tex]
Hence
[tex]T*sin(60) = 259.81N[/tex]
[tex]R= 450\=i +259.81\=i[/tex]
[tex]R=\sqrt{450^2+259.8^2}[/tex]
[tex]R=519.61N[/tex]
What is the velocity of the boat if the passenger shoots at an angle 60 with horizontal ? The mass of boat with the passenger is 100 kg ,mass of the bullet is 35g and its velocity is 400 m/s. <3
Answer:
400cos(60) = 200m/s
100(v) = 0.035(200)
v= 0.07m/s
If you drop a rock from 700 meters high, how long will it take the hit the ground? (Remember to make height negative when solving because it is falling)
Answer:
it would be 11.95 seconds
Explanation:
sorry for saying i did not know
9. Two moving objects will change their motion if which of the following is true? a.There is no friction on the objects. b. The objects collide with each other. c.One object is heavier than the other. d.The objects are moving in space.
Answer:
lol
Explanation:
lolllll i need points sorry
Which of the following is not a factor used to find climate?
pressure on a given day
wind and ocean currents
latitude and altitude
Answer:
pressure on a given day
Explanation:
because you can't find pressure in a day
It takes 10 lb of force to stretch a spring 2 in. What is the stiffness (spring constant) of the spring
Answer:
875.59 N/m
Explanation:
From the question given above, the following data were obtained:
Force (F) = 10 lb
Extention (e) = 2 in
Spring constant (K) =?
Next, we shall convert 10 lb to Newton (N). This can be obtained as follow:
1 lb = 4.448 N
Therefore,
10 lb = 10 lb × 4.448 N / 1 lb
10 lb = 44.48 N
Thus, 10 lb is equivalent to 44.48 N
Next, we shall convert 2 in to metre (m). This can be obtained as follow:
1 in = 0.0254 m
Therefore,
2 in = 2 in × 0.0254 m / 1 in
2 in = 0.0508 m
Thus, 2 in is equivalent to 0.0508 m.
Finally, we shall determine the spring constant i.e the stiffness of the spring as follow:
Force (F) = 44.48 N
Extention (e) = 0.0508 m.
Spring constant (K) =?
F = Ke
44.48 = K × 0.0508
Divide both side by 0.0508
K = 44.48 / 0.0508
K = 875.59 N/m
Therefore the spring constant i.e the stiffness of the spring is 875.59 N/m
What is the magnetic field strength at a point 2.5 mm radially from the center of the wire leading to the capacitor
Complete Question
A 8.0 A current is charging a 1.0 -cm-diameter parallel-plate capacitor. What is the magnetic field strength at a point 2.5 mm radially from the center of the wire leading to the capacitor?
Answer:
The magnetic field is [tex]B = 6.4*10^{-4} \ T[/tex]
Explanation:
From the question we are told that
The current is [tex]I = 8.0 \ A[/tex]
The diameter is [tex]d = \ cm = \frac{1}{100} = 0.01 m[/tex]
The position considered is [tex]d = 2.5 \ mm = 0.0025 \ m[/tex]
Generally the magnetic field is mathematically represented as
[tex]B = \frac{\mu_o * I }{ 2 \pi d}[/tex]
Here [tex]\mu_o[/tex] is permeability of free space with value
[tex]\mu_o = 4\pi * 10^{-7} \ N/A^2[/tex]
So
[tex]B = \frac{ 4\pi * 10^{-7} * 8 }{ 2 \pi * 0.0025 }[/tex]
=> [tex]B = \frac{ 2 * 10^{-7} * 8 }{ * 0.0025 }[/tex]
=> [tex]B = 6.4*10^{-4} \ T[/tex]
What type of energy transfer occurs
when two objects touch?
O conduction
O induction
O convection
Answer:
conduction
Explanation:
Which example is most likely made from both metals and gemstones?
Answer:
A Necklace is most likely made from both metals and gemstones
Explanation:
Brainliest?
A car is being driven down a level track with no net force on it. This motion is best described as
A)Linear motion
B)circular motion
C) periodic motion
D) projectile motion
A)Linear motion
If there is not net force on the car, then by the Newton Second Law, the acceleration is zero, and the only valid option for zero acceleration is A).
If you had to choose one device to use with the battery, what would it be? Do you think such a battery could be invented
someday? Explain
Answer:
I would choose refrigerator.
Explanation:
In my opinion, such a battery could be invented by changing the device as a low power mode. Plus, it is a must in order to decrease the CFC gas spreading through the atmosphere. That's all, thank you.