Answer:
x = 4.85 cm
Explanation:
From work energy theorem when dealing with a spring in compression, we know that total work done is;
W_t = ½kx²
Where;
k is Force constant
x is max compression
Now, we know that this is also equal to the kinetic energy.
K.E = ½mv²
Thus;
½kx² = ½mv²
Making x the subject;
x = √(mv²/k)
We are given;
m = 5 kg
v = 2 m/s
k = 85 N/cm = 8500 N/m
Thus;
x = √(mv²/k)
x = √(5 × 2²/8500)
x = 0.0485 m
x = 4.85 cm
A spherical cell has a radius of 2.3 μm , and the phospholipid bilayer that constitutes its membrane has a thickness of 3.75 nm . At its normal resting state, the outer membrane is at a voltage of 0V, and the inner membrane is at a voltage of -70mV. The dielectric constant of the cell membrane is roughly 9.0. What is the capacitance of the cell? (Note: the surface area of a sphere is 4πr2)
Answer:
Explanation:
The cell is acting like a shell .
Capacity of a shell is given by the following expression.
C= 4πk ε₀ x ab / (b-a )
k is dielectric constant , b and a are outer and inner radius ε₀ is a constant .
Here a = 2.3 x 10⁻⁶ m
b = 2.3 x 10⁻⁶ + .00375 x 10⁻⁶
= 2.30375 x 10⁻⁶ m
b -a = 3.75 x 10⁻⁹ m .
k = 9
4π ε₀ = 1 / 9 x 10⁹ = .111 x 10⁻⁹
C= .111 x 10⁻⁹ x 9 x 2.3 x 10⁻⁶ x 2.30375 x 10⁻⁶ / 3.75 x 10⁻⁹
= 1.41 x 10⁻¹² F
= 1.41 pF .
explain what characterises a sound as noise or music
Explanation:
Noise is sound with a continuous structure. Music is composed of sounds with a fundamental frequency and overtones. Noise is composed of sounds with frequencies that range continuously in value from as low as you can hear to as high as you can hear — not necessarily at equal intensity, however.
An inquisitive physics student and mountian climber climbs a 43.6 m cliff that overhangs a calm pool of water. He throws two stones vertically downward, 1.35 s apart and observes that they cause a single splash. The first stone has an initial velocity of 1.8 m/s. How long after release of the first stone do the two stones hit the water
Answer:
Explanation:
What we are basically looking for here is how long it takes the first stone to hit the water. We have everything we need to figure that out. We will use the equation
Δx = . Filling in, we will solve for t, the time is takes the first stone to hit the water (which is the same for both since they both hit the water at the same time):
which is a quadratic that we will have to factor. Get it into standard form, setting it equal to 0:
and factor to get that
t = 3.2 s and t = -2.8 s
Since time can't ever be negative, it takes 3.2 s for the stones to hit the water.
What is the size of the force acting on a copper wire with a magnetic flux density of 3.6 x 10-2 T acting at
right angles to the wire of length 24 m and current of C:048 A? Give your answer to an appropriate
number of significant figures.
Answer:
F = 0.414 N
Explanation:
Given that,
Magnetic flux density,[tex]B=3.6\times 10^{-2}\ T[/tex]
The length of the wire, l = 24 m
Current, I = 0.48 A
We need to find the force acting on the wire. The formula for the force is given by:
[tex]F=ILB[/tex]
Put all the values,
[tex]F=0.48\times 24\times 3.6\times 10^{-2}\\\\F=0.414\ N[/tex]
So, the force acting on the copper wire is equal to 0.414 N.
The magnetic force of the copper wire is 41.472 N.
Magnetic force of the copper wire
The magnetic force of the copper wire is calculated by applying the following equation.
F = BIL x sinθ
Where;
θ is the inclination of the magnetic fieldI is the currentL is the length of the wireB is the magnetic field strength = flux densityF = (3.6 x 10⁻²) x (48) x 24 x sin(90)
F = 41.472 N
Thus, the magnetic force of the copper wire is 41.472 N.
Learn more about magnetic force here: https://brainly.com/question/13277365
Calculate the percent error of the distanc
A space shuttle was launched from the Earth to the
moon. The average, or accepted, value of the distance
of the Earth to the moon is 238,857 miles, but the
shuttle crew recorded that their trip took 226,316 miles
5.25%
07.15%
3.75%
4.45%
Answer:
5.25%
Explanation:
From the question given above, the following data were obtained:
Accepted value = 238857 miles
Measured value = 226316 miles
Percentage error =.?
Next, we shall determine the absolute error. This can be obtained as follow:
Accepted value = 238857 miles
Measured value = 226316 miles
Absolute Error =?
Absolute Error = |Measured – Accepted|
Absolute Error = |226316 – 238857|
Absolute Error = 12541
Finally, we shall determine the percentage error. This can be obtained as follow:
Accepted value = 238857 miles
Absolute Error = 12541
Percentage error =.?
Percentage error = absolute error / accepted value × 100
Percentage error
= 12541 / 238857 × 100
= 1254100 / 238857
= 5.25%
Therefore, the percentage error is 5.25%.
A 4 LBfweight is attached to a spring suspended from the ceiling. When the weight comes to rest at equilibrium, the spring has been stretched 3 inches. The damping constant for the system is 2 LBf−sec ft . If the weight is raised 9 inches above equilibrium and given an initial upward velocity of 2 ft/sec, determine the equation of motion of the weight and give its damping factor, quasiperiod and quasifrequency.
Answer:
attached below
Explanation:
The initial conditions :
x(0) = - 9 inches = -3/4 ft
x'(0) = - 2 ft/sec
spring stretched 3 inches = 1/4 ft
mass = w / g = 4 Ib / 32 ft/sec^2 = 1/8 slug
the spring constant ( k ) = w / l = 4 / ( 1/4 ) = 16 Ib/ft
applying the second law of motion
m d^2x/dt^2 + b dx/dt + kx
= 1/8 d^2x/dt^2 + 2 dx/dt + 16 x
= d^2x/dt^2 + 16 dx/dt + 128 x ------- ( 1 )
we will resolve the above equation to obtain the required equation of motion x( t )
Attached below is the remaining part of the solution
In a softball game a batter hits at the velocity of 28 and an angle shown 45 below . What is the maximum range of the ball
Answer:
80 m
Explanation:
Given :
Initial Velocity, U = 28 m/s
θ = 45°
The maximum range occurs at angle, θ = 45°
The maximum range, R is given by ;
R = U²sin2θ / g
g = acceleration due to gravity = 9.8 m/s²
Plugging in the values :
R = [28² * sin2(45)] / 9.8
R = [28² * sin90] / 9.8
R = 784 / 9.8
R = 80 m
Un móvil recorre una trayectoria en línea recta de 6000 metros y demora 30 minutos. ¿Cuál es su rapidez expresada en Km/h?
Answer:
La rapidez del móvil es 12 kilómetros por hora.
Explanation:
Asumamos que el móvil experimenta un movimiento rectilíneo uniforme, cuya ecuación cinemática es la siguiente:
[tex]v = \frac{x}{t}[/tex] (1)
Where:
[tex]x[/tex] - Distancia recorrida, en kilómetros.
[tex]t[/tex] - Tiempo, en horas.
[tex]v[/tex] - Rapidez, en kilómetros por hora.
Si tenemos que [tex]x = 6000\,m[/tex] y [tex]t = 30\,min[/tex], entonces la rapidez del móvil es:
[tex]v = \frac{6000\,m\times \frac{1}{1000}\,\frac{km}{m}}{30\,min \times \frac{1}{60}\,\frac{h}{min} }[/tex]
[tex]v = 12\,\frac{km}{h}[/tex]
La rapidez del móvil es 12 kilómetros por hora.
scientists are seen very busy in designing the solar power equipments, why?
Answer:
it is because solar energy is the perpetual source of energy and by using it non renewable sources of energy can be conserved for the future
If a planet has the same mass as the earth, but has twice the radius, how does the surface gravity, g, compare to g on the surface of the earth
Answer:
The surface gravity g of the planet is 1/4 of the surface gravity on earth.
Explanation:
Surface gravity is given by the following formula:
[tex]g=G\frac{m}{r^{2}}[/tex]
So the gravity of both the earth and the planet is written in terms of their own radius, so we get:
[tex]g_{E}=G\frac{m}{r_{E}^{2}}[/tex]
[tex]g_{P}=G\frac{m}{r_{P}^{2}}[/tex]
The problem tells us the radius of the planet is twice that of the radius on earth, so:
[tex]r_{P}=2r_{E}[/tex]
If we substituted that into the gravity of the planet equation we would end up with the following formula:
[tex]g_{P}=G\frac{m}{(2r_{E})^{2}}[/tex]
Which yields:
[tex]g_{P}=G\frac{m}{4r_{E}^{2}}[/tex]
So we can now compare the two gravities:
[tex]\frac{g_{P}}{g_{E}}=\frac{G\frac{m}{4r_{E}^{2}}}{G\frac{m}{r_{E}^{2}}}[/tex]
When simplifying the ratio we end up with:
[tex]\frac{g_{P}}{g_{E}}=\frac{1}{4}[/tex]
So the gravity acceleration on the surface of the planet is 1/4 of that on the surface of Earth.
What happens to the electric force between two particles if the distance
between them is doubled?
A. It decreases to half the original force.
B. It increases to twice the original force.
C. It increases to 4 times the original force.
D. It decreases to 1/4 of the original force.
Answer:
D.
Explanation:
Force and distance are inversely related, so a greater distance results in a weaker force.
what is gama rays an it's uses
Answer:
GAMMA RAYS:
A photon emitted spontaneously by a radioactive substance also : a photon of higher energy than that of an X-ray.
USES OF GAMMA RAYS:
Gamma rays are used in medicine (radiotherapy), industry (sterilization and disinfection), and the nuclear industry. Shielding against gamma rays is essential because they can cause diseases to skin or blood, eye disorders, and cancers.
one car accelerates at half the rate of another how much longer does it take the first car to travel a quarter mile
Answer:
t=1/4v1
Explanation:
Given data
Car one
Speed =v1
Time =t
Distance =1/4 mile
Given data
Car two
Speed =v1/2
Time =t
Distance =d
Speed =distance/time
v1=1/4/t
v1t=1/4
t=1/4*1/v1
t=1/4v1 seconds
Show that the path followed by a projected horizontally frop top of the tower with uniform speed is a parabola .
Answer:
Explained below.
Explanation:
Let the initial velocity from the top of the tower of height(h) be u'
Now, since it is projected horizontally, the horizontal distance covered will be due to having a uniform horizontal velocity (u) while it will possess a vertical distance in the downward direction due to constant acceleration due to gravity (g).
If the time it takes the ball to reach the ground is "t", then we can say the horizontal distance travelled by the ball is denoted as; x(t) = x, while the vertical distance is denoted by; y(t) = y
Now, since it's a projectile the intial velocity (u) will have vertical and horizontal components which are;
u_y and u_x respectively.
Applying kinematic equations, we have;
x = u_x•t + ½at²
Acceleration is zero in the horizontal x direction. Thus;
x = u_x•t
For the vertical y-direction;
y = u_y•t + ½at²
Here since direction is in that of gravity, then a = g.
Also, since the initial velocity has no downward component, then u_y = 0 m/s
Thus;
y = ½gt²
From x = u_x•t, we have;
t = x/u_x
Thus;
y = ½g(x/u_x)²
y = ½gx²/(u_x)²
Let g/(u_x)² be treated as a constant with the letter k.
Thus;
y = kx²
This is the form of a parabolic equation.
Thus, it has been proved that the projectile follows the path of a parabola.
Velocity is vector quantity because??
Velocity is vector quantity because it has both magnitude and direction.
Explanation:
velocity is a vector quantity because the person always returns to the original position,the motion would never result in a change in a position.
for the equation BaCI2 + Na2SO4 > BaSO4 + 2NaCI
A. reactants: 1 ;products: 1
B. reactants: 1 ;products: 2
C. reactants: 2 ;products: 1
D. reactants: 2 ;products: 2
Eli states that sodium phosphate is a mixture because it is composed of both sodium ions and phosphate ions.
Which is the best analysis of Eli’s statement?
The question is incomplete, the complete question is;
Eli states that sodium phosphate is a mixture because it is composed of both sodium ions and phosphate ions. Which is the best analysis of Eli’s statement? It is correct because each ion is a pure substance, so sodium phosphate is made up of two pure substances. It is correct because the composition of sodium phosphate changes depending on the sample. It is incorrect because sodium phosphate is a compound that has a single composition. It is incorrect because the two types of ions in sodium phosphate cannot be seen.
Answer:
It is incorrect because sodium phosphate is a compound that has a single composition
Explanation:
A compound is a neutral substance made up of two or more atoms which are chemically combined together.
Ionic substances are made up of ions. These ions are not separate entities, they are part of the compound.
Hence, Eli's statement is incorrect because sodium phosphate is a compound that has a single composition.
What kind of waves are present during an earthquake?
Answer:
There are four main types of earthquake waves:
P-waves S-waves (which are body waves), Rayleigh waves Love waves (which are surface waves).HOPE IT HELPS!!
Unlike hard disks, which use magnetic charges to represent 1s and 0s, _____ use reflected light.
Answer:
Unlike hard disks, which use magnetic charges to represent 1s and 0s, Compact Disks, DVD's or Blue Rays use reflected light.
Explanation:
The way CD's work is that they are hit by a laser beam which is reflected on the surface of the disc. These disks have some valleys and mountains that reflect light differently so the CD player will interpret these differences in reflection as data which will then be turned into music, videos or computer files.
A plane is flying a circular path at a speed of 55.0 m/ s, with a radius of 18.3 m. The centripetal force needed to maintain this motion is 3000 N. What is the plane's mass?
The plane has a centripetal acceleration a of
a = v ²/r
where v is the plane's tangential speed and r is the radius of the circle. By Newton's second law,
F = mv ²/r
Solve for the mass m :
m = Fr/v ² = (3000 N) (18.3 m) / (55.0 m/s)² ≈ 18.1 kg
The picture below shows a person swinging a yo-yo in a circle. Which vector shows the velocity of the yo-yo at this moment?
A. B
B. A
C. C
D. D
What are the fundamental units involved in a unit of the given derived quantities
Density
Acceleration
Force
Pressure
Work
Answer:
Density → Mass and Length.
Acceleration → Length and Time.
Force → Mass, Length and Time.
Pressure → Mass, Length and Time.
Work → Mass, Length and Time.
a motorcyclist drives from A to B with a uniform speed of 30 km/h and returns back with a speed of 20km/h-¹ find the average speed ?
PLEASE DO IT AS FAST YOU CAN AND NO SCAM ANSWERS OR ELSE I WILL REPORT
Answer:
Average speed = 24 km/h
Explanation:
Let the distance be x.Given the following data;
Uniform speed A = 30 km/h
Uniform speed B = 20 km/h
To find the average speed;
Mathematically, the average speed of an object is given by the formula;
[tex] Average \; speed = \frac {total \; distance}{total \; time} [/tex] ..... equation 1
Total time = TA + TB
[tex] T_{A} = \frac {x}{30} [/tex]
[tex] T_{B} = \frac {x}{20} [/tex]
[tex] Total \; time = \frac {x}{30} + \frac {x}{20} [/tex]
[tex] Total \; time = \frac {5x}{60} [/tex]
Total distance = x + x
Total distance = 2x
Substituting the values into equation 1;
[tex] Average \; speed = \frac {2x}{\frac {5x}{60}} [/tex]
[tex] Average \; speed = \frac {2x*60}{5x} [/tex]
[tex] Average \; speed = \frac {120}{5} [/tex]
Average speed = 24 km/h
The standard metric unit of volume is the _____.
cubic centimeter
liter
milliliter
cubic meter
Answer:
. The SI unit of volume is the cubic meter (m3), which is a derived unit.
Liter (L) is a special name for the cubic decimeter (dm3).
a vehicle starts from rest and has an acceleration of 2 metre per second square how long does it take to gain the speed of 20 metre per second
Answer:
x,y
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hofdhDJiyfuID pork chop it off the bus to school today I am not a mixture of my favorite thing in life that is the best of the day before
A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit, if the current exceeds a predetermined value. Suppose that the material to be used in a fuse melts when the current density rises to 540 A/cm2. What diameter of cylindrical wire should be used to make a fuse that will limit the current to 0.57 A
Answer:
0.0366 m
Explanation:
We are given;
Current density; J = 540 A/cm² = 540 × 10⁴ m
Current; I = 0.57 A
Now, formula for current density is;
J = I/A
Where A is area = πr²
Thus;
J = I/(πr²)
r = √(I/(Jπ))
r = √(0.57/(540π))
r = 0.0183 m
Diameter = 2 × radius
Diameter = 2 × 0.0183
Diameter = 0.0366 m
What is displacement?
An objects overall change in position
The total measure of how far one travels
a change in direction
Answer:
An object overall change in position
Explanation:
ans maybe corre6
A 90 kg astronaut Travis is stranded in space at a point 12 m from his spaceship. In order to get back to his ship, Travis throws a 0.50 kg piece of equipment so that it moves at a speed of 4 m/ s directly away from the spaceship towards the left . How long will it take him to reach the ship? *hint find his speed after the collision and consider it a constant speed all the way back to his spaceship*
Answer:
Explanation:
This is a recoil problem, which is just another application of the Law of Momentum Conservation. The equation for us is:
[tex][m_av_a+m_ev_e]_b=[m_av_a+m_ev_e]_a[/tex] which, in words, is
The momentum of the astronaut plus the momentum of the piece of equipment before the equipment is thrown has to be equal to the momentum of all that same stuff after the equipment is thrown. Filling in:
[tex][(90.0)(0)+(.50)(0)]_b=[(90.0)(v)+(.50)(-4.0)]_a[/tex]
Obviously, on the left side of the equation, nothing is moving so the whole left side equals 0. Doing the math on the right and paying specific attention to the sig fig's here (notice, I added a 0 after the 4 in the velocity value so our sig fig's are 2 instead of just 1. 1 is useless in most applications).
0 = 90.0v - 2.0 and
2.0 = 90.0v so
v = .022 m/s This is the rate at which he is moving TOWARDS the ship (negative was moving away from the ship, as indicated by the - in the problem). Now we can use the d = rt equation to find out how long this process will take him if he wants to reach his ship before he dies.
12 = .022t and
t = 550 seconds, which is the same thing as 9.2 minutes
A system consists of multiple objects connected by ropes. How many equations need to be written to solve this problem?
A) two for each object
B) one or two for each object
C) one for each object
D) two for the system
Answer:
the correct answer is B
Explanation:
To solve the system they must have the same amount of unknowns as equations,
a) If the system does not have friction, we must write the x-axis equation for each body, therefore we need to write N equations
b) if the system has friction, two equations are needed for each particle
therefore the correct answer is B
With what tension must a rope with length 3.00 mm and mass 0.105 kgkg be stretched for transverse waves of frequency 40.0 HzHz to have a wavelength of 0.790 mm
Answer:
the tension of the rope is 34.95 N
Explanation:
Given;
length of the rope, L = 3 m
mass of the rope, m = 0.105 kg
frequency of the wave, f = 40 Hz
wavelength of the wave, λ = 0.79 m
Let the tension of the rope = T
The speed of the wave is given as;
[tex]v = f\lambda = \sqrt{\frac{T}{\mu} } \\\\where;\\\\\mu \ is \ mass \ per \ unit \ length\\\\\mu = \frac{0.105}{3} = 0.035 \ kg/m\\\\v = f\lambda = 40 \times 0.79 = 31.6 \ m/s\\\\v = \sqrt{\frac{T}{\mu} } \\\\v^2 = \frac{T}{\mu} \\\\T = v^2 \mu\\\\T = (31.6^2)(0.035)\\\\T = 34.95 \ N[/tex]
Therefore, the tension of the rope is 34.95 N