Answer:
The required work done is [tex]6.5\times10^{9}\ J[/tex]
Explanation:
Given that,
Mass of each satellites = 940 kg
Altitude of A = 4500 km
Altitude of B = 11100 km
We need to calculate the potential energy
Using formula of potential
[tex]U_{A}=-\dfrac{Gm_{A}m_{E}}{r_{A}}[/tex]
Put the value into the formula
[tex]U_{A}=-\dfrac{6.67\times10^{-11}\times940\times5.98\times10^{24}}{6.38\times10^{6}+4.50\times10^{6}}[/tex]
[tex]U_{A}=-3.44\times10^{10}\ J[/tex]
We need to calculate the potential energy
Using formula of potential
[tex]U_{B}=-\dfrac{Gm_{B}m_{E}}{r_{A}}[/tex]
Put the value into the formula
[tex]U_{B}=-\dfrac{6.67\times10^{-11}\times940\times5.98\times10^{24}}{6.38\times10^{6}+11.10\times10^{6}}[/tex]
[tex]U_{B}=-2.14\times10^{10}\ J[/tex]
We need to calculate the value of [tex]k_{A}[/tex]
Using formula of [tex]k_{A}[/tex]
[tex]k_{A}=-\dfrac{1}{2}U_{A}[/tex]
Put the value into the formula
[tex]k_{A}=\dfrac{1}{2}\times3.44\times10^{10}[/tex]
[tex]k_{A}=1.72\times10^{10}\ J[/tex]
We need to calculate the value of [tex]k_{B}[/tex]
Using formula of [tex]k_{B}[/tex]
[tex]k_{B}=-\dfrac{1}{2}U_{B}[/tex]
Put the value into the formula
[tex]k_{B}=\dfrac{1}{2}\times2.14\times10^{10}[/tex]
[tex]k_{B}=1.07\times10^{10}\ J[/tex]
We need to calculate the work done
Using formula of work done
[tex]W=\Delta K+\Delta U[/tex]
[tex]W=(k_{B}-k_{A})+(U_{B}-U_{A})[/tex]
[tex]W=(-\dfrac{U_{B}}{2}+\dfrac{U_{A}}{2})+(U_{B}-U_{A})[/tex]
[tex]W=\dfrac{1}{2}(U_{B}-U_{A})[/tex]
Put the value into the formula
[tex]W=\dfrac{1}{2}\times(-2.14\times10^{10}+3.44\times10^{10})[/tex]
[tex]W=6.5\times10^{9}\ J[/tex]
Hence, The required work done is [tex]6.5\times10^{9}\ J[/tex]
A tiger leaps horizontally froma 7.5 m high rock with a speed of 3.0 m/s. How far from the base of the rock will she land?
Answer:
The tiger will land at 3.71 meters from the base of the rock
Explanation:
Horizontal Motion
When an object is thrown horizontally with a speed vo from a height h, the range or maximum horizontal distance traveled by the object can be calculated as follows:
[tex]\displaystyle d=v\cdot\sqrt{\frac {2h}{g}}[/tex]
The tiger leaps from a height of h=7.5 m with a speed of v=3 m/s. Substituting the values into the formula:
[tex]\displaystyle d=3\cdot\sqrt{\frac {2\cdot 7.5}{9.8}}=3.71\ m[/tex]
The tiger will land at 3.71 meters from the base of the rock
The mass of a fully loaded Boeing 747 is about 4,082,331.33 kg. If it is cruising eastward at a
velocity of 253 m/s, what is its momentum?
What is a characteristic common to sound waves and light waves
Answer:
Both light and sound can be described in terms of wave forms with physical characteristics like amplitude, wavelength, and timbre. Wavelength and frequency are inversely related so that longer waves have lower frequencies, and shorter waves have higher frequencies
The ability of both to cause interference is the resemblance between sound waves and light waves.
What are sound waves and light waves?While sound waves are mechanical, light waves are electromagnetic. Unlike sound waves, which are longitudinal, light waves are transverse. Light waves can go across a vacuum. Since sound waves need a physical medium to go through, they cannot move in a vacuum.
Both sound and light waves adhere to the rule of reflection, which states that the angle of incidence and angle of reflection are equal. Therefore, choice 2 is the right one. While light waves are transverse, sound waves are longitudinal.
In that, they both have an amplitude, a wavelength, a period, and a frequency, light, and sound waves are comparable to one another.
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sin20 + cos20 = 1
How?
If you have ever baked a cake or bread, you know that the ingredients that combine to make it taste different from the baked food. Why do you think that is?
Answer:
Well we all know that bread and cake taste different. We do this on purpose.
Explanation:
When we make cake we add plenty of sugar to make it the delectable dessert we all know and love while when making bread we focus more on the corn starch and yeast's.
To increase the current in a circuit, which can be increased?
voltage
resistance
interference
ohms
Answer:
voltage
Explanation:
the current in a circuit, the voltage can be increased.
What is ohm's law?According to Ohm's law, when all other physical parameters, including temperature, are held constant, the voltage across a conductor is directly proportional to the current flowing through it.
From ohm's law, we can state that voltage is directly proportional to current.
Looking at the following formula:
I = V/R
Where V is voltage,
I is current, and
R is resistance
In the above equation, Current and Voltage are in a direct relationship such that if I is increased, V is also increased, and vice versa.
Therefore, To increase the current, the voltage should be increased.
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a car travelling at 20m/s comes to a stop in 5 seconds. what distance is required for the car to come to a stop?
When we do dimensional analysis, we do something analogous to stoichiometry, but with multiplying instead of adding. Consider the diffusion constant that appears in Fick's first law:
J= -Ddn/dx
In this expression, J represents a flow of particles: number of particles per unit area per second, n represents a concentration of particles: number of particles per unit volume; and x represents a distance. We can assume that they have the following dimensionalities:
[J] = 1/L2T
[n] = 1/L3
[x] = L
Required:
From this, determine the dimensionality of D.
Answer:
The dimension is [tex]D = L ^{2} T^{-1}[/tex]
Explanation:
From the question we are told that
[tex]J = -D \frac{dn}{dx}[/tex]
Here [tex][J] = \frac{1}{L^2 T}[/tex]
[tex][n] =\frac{1}{L^3}[/tex]
[tex][x] = L[/tex]
So
[tex]\frac{1}{L^2 T} = -D \frac{d(\frac{1}{L^3})}{d[L]}[/tex]
Given that the dimension represent the unites of n and x then the differential will not effect on them
So
[tex]\frac{1}{L^2 T} = -D \frac{(\frac{1}{L^3})}{[L]}[/tex]
=> [tex]D = \frac{L^{-2} T^{-1} * L }{L^{-3}}[/tex]
=> [tex]D = L ^{2} T^{-1}[/tex]
Can someone please help ASAP :((
Answer:
Motion map #3
Explanation:
because with velocity negative the arrows have to be the same size in the reverse direction.
At a tractor pull, one machine has a pull that produces 27,000 joules of power in 3 seconds. How many watts of power did this tractor produce?
3
Answer:
28230 joules
Explanation:
becasue yes
Which term identifies the distance between any two adjacent crests on a
wave?
A. Compression
B. Frequency
C. Wavelength
D. Amplitude
Answer:
your answer is wavelength
Explanation:
the the highest service part of a weight is called the crest and the lowest part is the trough the vertical distance between the crest and the trough is the waist height the horizontal disc distance between two adjacent Crest or troughs is known as wavelengths
Which statement(s) is/are TRUE about photons?
SELECT ALL THAT APPLY
a Photons have greater mass than electrons.
b Photons are particles of light.
с
Photons carry a very specific quantum of
energy.
d Photons have zero mass.
Answer:
Not D, every substance in existence has mass and is made from it in any given form.
B and C
Explanation:
The statements which are true about photons are:
Choice B: Photons are particles of light.Choice C: Photons carry a very specific quantum of energy.Choice D: Photons have zero mass.Discussion:
The photon is a type of elementary particle. It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force.
Additionally, Photons are massless, so they always move at the speed of light in vacuum, 3 × 10⁸ m/s.
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Whenever I visit one of the big membership-driven bulk wholesalers in town, without fail I end up using a junk cart with bum wheels that not only drag, but pull to the left. If a cart requires 20 lb of force forward to overcome the wheel’s drag, but there are also around 3 lb of force pulling it to the left, with what force and in what direction do I need to push in order to make the cart go forward?
Required:
Measure your angle from the forward direction and specify whether it’s to the left or right.
Answer: Force of magnitude 20.22lbf to the right at angle 8.5°
Explanation: The image named "Untitled" below shows the forces acting on the cart.
The second image, "Untitled2", demonstrate the vector diagram of the forces acting on the kart, in which:
f is force forward
f(left) is pull to the left
f(R) is the resulting force necessary for the kart to move
The drag force is not draw on the vector diagram because its value is already part of the force forward.
As we can see, the diagram forms a right triangle with f(R) as hypotenuse.
Using Pytagorean Theorem:
[tex][f(R)]^{2}=f^{2}+[f(left)]^{2}[/tex]
[tex][f(R)]^{2}=20^{2}+3^{2}[/tex]
[tex][f(R)]^{2}=409[/tex]
[tex]f(R)=\sqrt{409}[/tex]
f(R) = 20.22
Force forward equals 20.22lbf to the right.
The angle formed form the forward direction and the resulting force is
[tex]cos\theta=\frac{20}{20.22}[/tex]
cosθ = 0.989
θ = cos⁻¹(0.989)
θ = 8.5°
The forward force is to the right at angle 8.5° and magnitude 20.22lbf.
Two parallel plates having charges of equal magnitude but opposite sign are separated by 29.0 cm. Each plate has a surface charge density of 32.0 nC/m2. A proton is released from rest at the positive plate. (a) Determine the magnitude of the electric field between the plates from the charge density. kN/C (b) Determine the potential difference between the plates. V (c) Determine the kinetic energy of the proton when it reaches the negative plate. J (d) Determine the speed of the proton just before it strikes the negative plate. km/s (e) Determine the acceleration of the proton. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s2 towards the negative plate (f) Determine the force on the proton. N towards the negative plate (g) From the force, find the magnitude of the electric field. kN/C (h) How does your value of the electric field compare with that found in part (a)
Answer:
(a) E = 3.6 x 10³ N/C = 3.6 KN/C
(b) ΔV = 1044 Volts
(c) K.E = 1.67 x 10⁻¹⁶ J
(d) Vf = 4.47 x 10⁵ m/s
(e) a = 3.45 x 10¹¹ m/s²
(f) F = 5.76 x 10⁻¹⁶ N
(g) E = 3.6 x 10³ N/C = 3.6 KN/C
(h) Both values are same in part (h) and (a)
Explanation:
(a)
Electric field between oppositely charged plates is given as follows:
E = σ/ε₀
where,
E = Electric Field Intensity = ?
σ = surface charge density = 32 nC/m² = 3.2 x 10⁻⁸ C/m²
ε₀ = Permittivity of free space = 8.85 x 10⁻¹² C²/N.m²
Therefore,
E = (3.2 x 10⁻⁸ C/m²)/(8.85 x 10⁻¹² C²/N.m²)
E = 3.6 x 10³ N/C = 3.6 KN/C
(b)
E = ΔV/r
ΔV = Er
where,
r = distance between plates = 29 cm = 0.29 m
ΔV = Potential Difference = ?
ΔV = (3.6 x 10³)(0.29)
V = 1044 Volts
(c)
Kinetic Energy of Proton = Work done on Proton
K.E = F r
but, F = E q
K.E = E q r
where,
q = charge on proton = 1.6 x 10⁻¹⁹ C
Therefore,
K.E = (3600 N/C)(1.6 x 10⁻¹⁹ C)(0.29 m)
K.E = 1.67 x 10⁻¹⁶ J
(d)
K.E = (1/2)m(Vf² - Vi²)
where,
m = mass of proton = 1.67 x 10⁻²⁷ kg
Vf = Final Velocity = ?
Vi = Initial Velocity = 0 m/s
Therefore,
1.67 x 10⁻¹⁶ J = (1/2)(1.67 x 10⁻²⁷ kg)(Vf² - (0 m/s)²]
Vf² = (1.67 x 10⁻¹⁶ J)(2)/(1.67 x 10⁻²⁷ kg)
Vf = √(20 x 10¹⁰ m²/s²)
Vf = 4.47 x 10⁵ m/s
(e)
2as = Vf² - Vi²
2(a)(0.29 m) = (4.47 x 10⁵ m/s)² - (0 m/s)²
a = (20 x 10¹⁰ m²/s²)/0.58 m
a = 3.45 x 10¹¹ m/s²
(f)
F = ma
F = (1.67 x 10⁻²⁷ kg)(3.45 x 10¹¹ m/s²)
F = 5.76 x 10⁻¹⁶ N
(g)
E = F/q
E = (5.76 x 10⁻¹⁶ N)/(1.6 x 10⁻¹⁹ C)
E = 3.6 x 10³ N/C = 3.6 KN/C
(h)
Both values are same in part (h) and (a)
Look at the image if you need me to add the answers so you can see them better i will
Answer:
0.75 meters per second; north
Explanation:
speed (velocity)= distance/time
15 meters= distance
20 seconds= time
15/20= 0.75 meters per second; north
Hope this helps!
A book is sitting on a desk. What best describes the normal force acting on the book?
the upward force the desk pushes on the book
the upward force the book pulls on the Earth
the downward force the book pushes on the desk
the downward force the Earth pulls on the book
A book is sitting on a desk is due to the Gravitational force of Earth Gravity so D. the downward force the Earth pulls on the book.
What is the gravitational force of an object?The force of attraction between all masses that is objects in the universe, especially the attraction of the Earth's mass for bodies near its surface.
How gravity is formed?Einstein said that the shape of spacetime is responsible for the rise of force that we experience as gravity. A concentration of mass, such as the Earth or sun, bends space around it like a rock bends the flow of a river.
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In a game of tug of war, a rope is pulled by a force of 182 N to the right and by a force of 108 N to the left. Calculate the magnitude and direction of the net horizontal force on the rope.
Answer:
74 N to the right
Explanation:
the forces are going in opposite horizontal directions, meaning that they are directly opposing each other. this means that you can subtract the force applied in the direction that is greater from the direction that is less to get the net force for the greater direction
this means 182 N - 108 N = 74 N to the right
In a game of tug of war the magnitude and direction of the net horizontal force on the rope is 74 N.
What is force?A force in physics is an effect that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
In a game of tug of war, a rope is pulled by a force of 182 N to the right and by a force of 108 N to the left. The magnitude and direction of the net horizontal force on the rope is,
F = 182 - 108
F = 74 N
The magnitude and direction of the net horizontal force on the rope is 74 N.
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when three identical bulbs of 60W,200V rating are connected in series at a 200V supply the power drawn by them will be?
Answer:
P = 180 [w]
Explanation:
To solve this problem we must use ohm's law, which is defined by the following formula.
V = I*R & P = V*I
where:
V = voltage = 200[volts]
I = current [amp]
R = resistance [ohm]
P = power [watts]
Since the bulbs are connected in series, the powers should be summed
P = 60 + 60 + 60
P = 180 [watts]
Now we can calculate the current
I = 180/200
I = 0.9[amp]
Attached is an image where we see the three bulbs connected in series, in the circuit we see that the current is the same for all the elements connected to the circuit.
And the power is defined by P = V*I
we know that the voltage is equal to 200[V], therefore
P = 200*0.9
P = 180 [w]
A person walks 500m due north, turns and walks 300m due west, and finally walks 800m due south. Determine the persons resultant displacement from her starting point.
+500 because North is postiive direction
-300 because if you see it as a graph, left side is negative
-800 because South is downward
500-300-800 = -600
displacement is a vector, meaning it has both DIRECTION and magnitude
(literally the only physics problem i can easily solve lol)
Answer:
[tex]\mid D \mid = 424.26\ m[/tex]
Explanation:
Displacement
Suppose a moving object starts from point A and travels through a determined path to point B. The distance is the sum of all the partial distances traveled, and the displacement is the vector directed from A to B.
The path of the person is shown in the image below. Note the 500 m due north and the 800 m due south produce a distance of 300 m due south. The displacement vector D is the resultant of the whole movement.
To find the magnitude of the displacement, we need to calculate the hypotenuse of a triangle of sides 300 m (already described) and 300 m, marked in red.
The magnitude of D is:
[tex]\mid D \mid = \sqrt{300^2+300^2}[/tex]
[tex]\mid D \mid = \sqrt{90000+90000}[/tex]
[tex]\mid D \mid = \sqrt{180000}[/tex]
[tex]\mid D \mid = 424.26\ m[/tex]
Based on Kepler's work, which best describes the orbit If a planet around the Sun?
a circle with the Sun at the very center
an ellipse with the Sun at the very center
a circle with the Sun at one edge
an ellipse with the Sun at one focus
Answer:
D. an ellipse with the Sun at one focus
Explanation:
Based on Kepler's work, the orbit of a planet around the Sun is an ellipse with the Sun at one focus.
What is Kepler's law of planetary motion?The sun is at one of the foci of the planets' elliptical orbits around the sun, according to Kepler's first law. Perihelion, the name for the point at which a planet is closest to the sun, and aphelion, the name for the point at which a planet is farthest from the sunThe radius vector extended from the sun to the planet sweeps out equal areas in equal amounts of time, according to Kepler's second law.The square of a planet's period of revolution around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis, states Kepler's law of periods.Hence according to Kepler's first law of planetary motion, the orbit of a planet around the Sun is an ellipse with the Sun at one focus.
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PLEASE HELP QUICKLY!
A volleyball player jumps to hit a ball horizontally at 7.0 m/s straight on. If the
height at which the ball was hit is 3.0 m tall, how far did the ball go horizontally
before it hit the ground?
5.5 m
3.6 m
O 4.3 m
4.2 m
Answer:
5.5 is the correct answer
please keeps as Brainly list
How much work is done when 25 N of force is used to push a crate 3.0 m
Answer:
The answer is 75 JExplanation:
The work done by an object can be found by using the formula
work done = force × distanceFrom the question
force = 25 N
distance = 3 m
We have
work done = 25 × 3
We have the final answer as
75 JHope this helps you
(Use 1.72×10-8 Ωm for the resistivity of copper.) Tries 0/20 For safety, the National Electrical Code limits the allowable amount of current which such a wire may carry. When used in indoor wiring, the limit is 15.0 A for rubber insulated wire of that size. How much power would be dissipated in the wire of the above problem when carrying the maximum allowable current? Tries 0/20 What would be the voltage between the ends of the wire in the above problem? Tries 0/20 What is the current density in the wire when it is carrying the maximum allowable current? (Current density is the current in the wire divided by the cross sectional area of the wire.) Tries 0/20 What is the drift velocity of the electrons when the wire is carrying the maximum allowable current? (The density of electrons in copper is 8.47×1028 m-3.)
Complete Question
A number 14 copper wire has a diameter of 1.628 mm. Calculate the resistance of a 37.0 m long piece of such wire.
(Use 1.72×10-8 ?m for the resistivity of copper.)
For safety, the National Electrical Code limits the allowable amount of current which such a wire may carry. When used in indoor wiring, the limit is 15.0 A for rubber insulated wire of that size. How much power would be dissipated in the wire of the above problem when carrying the maximum allowable current?
What would be the voltage between the ends of the wire in the above problem?
What is the current density in the wire when it is carrying the maximum allowable current? (Current density is the current in the wire divided by the cross sectional area of the wire.)
What is the drift velocity of the electrons when the wire is carrying the maximum allowable current?
(The density of electrons in copper is 8.47×1028 m-3.)
Answer:
a
[tex]R =0.3057 \ \Omega [/tex]
b
[tex]P = 68.78 \ W [/tex]
c
[tex]V = 4.5855 \ V[/tex]
d
[tex]J = 7.205 *10^{6}\ A/m^2 [/tex]
e
[tex]v_d = 0.0005316 \ m/s[/tex]
Explanation:
From the question we are told that
The resistivity of copper is [tex]\rho = 1.72* 10^{-8} \ \Omega \cdot m[/tex]
The current limit is [tex]I = 15 \ A[/tex]
The diameter is [tex]d= 1.628 mm= 0.001628 \ m[/tex]
The length of the wire is [tex]l = 37.0 m[/tex]
The density of electron is [tex]n = 8.47*10^{28} m^{-3}[/tex]
Generally the radius is mathematically represented as
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{0.001628}{2}[/tex]
=> [tex]r =0.000814 \ m [/tex]
Generally the resistance is mathematically represented as
[tex]R = \frac{\rho * l }{A}[/tex]
Here A is the area which is mathematically represented as
[tex]A = 3.142 * (0.00081)^2[/tex]
=> [tex]A = 2.082 *10^{-6}\ m^2 [/tex]
=> [tex]R = \frac{1.72* 10^{-8} * 37.0 }{2.082 *10^{-6}}[/tex]
=> [tex]R =0.3057 \ \Omega [/tex]
Generally the power dissipated is mathematically represented as
[tex]P = I^2 R[/tex]
=> [tex]P = (15)^2 * 0.3057 [/tex]
=> [tex]P = 68.78 \ W [/tex]
Generally the voltage is mathematically represented as
[tex]V = I * R[/tex]
=> [tex]V = 15 * 0.3057[/tex]
=> [tex]V = 4.5855 \ V[/tex]
Generally the charge density is mathematically represented as
[tex]J = \frac{I}{A}[/tex]
=> [tex]J = \frac{15}{2.082 *10^{-6}}[/tex]
=> [tex]J = 7.205 *10^{6}\ A/m^2 [/tex]
Generally the drift velocity is mathematically represented as
[tex]v_d = \frac{I}{ n * A * e}[/tex]
Here e is the charge on an electron with value [tex]e = 1.60 *10^{-19} \ C[/tex]
So
[tex]v_d = \frac{15}{ 8.47*10^{28} * 2.082 *10^{-6} * 1.60 *10^{-19} }[/tex]
=> [tex]v_d = \frac{15}{ 8.47*10^{28} * 2.082 *10^{-6} * 1.60 *10^{-19} }[/tex]
=> [tex]v_d = 0.0005316 \ m/s[/tex]
Do electromagnetic waves occur in a continuous spectrum based on their wavelength?
Answer: Yes
Explanation: Because Electromagnetic waves form a continuous spectrum and all types of electromagnetic wave travel at the same velocity through a vacuum (space) or air. The waves that form the electromagnetic spectrum are grouped in terms of their wavelength and their frequency.
A motorcycle traveling south reaches a speed of 38.0 m/s. It then begins uniform negative acceleration and comes to rest after 7.359s. How far did the motorcycle travel in this time?
Answer: 30.641
Explanation: If you get the ave which is 38.0 then the vi which is 7.359
38.0-7.359=30.641/0.0 which is 30.641
Why are some substances dissolve both polar and nonpolar substances?
Answer:
Because water is polar and oil is nonpolar, their molecules are not attracted to each other. polar solvents dissolve polar solutes, and nonpolar solvents dissolve nonpolar solutes.
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use your brain :)
Substances that can dissolve both polar and nonpolar substances are called amphiphilic or amphipathic. This unique property arises due to their molecular structure, which contains both polar and nonpolar regions.
Amphiphilic molecules typically have a hydrophilic (water-attracting) or polar end and a hydrophobic (water-repelling) or nonpolar end. This dual nature allows them to interact with and dissolve in both polar and nonpolar solvents. Let's explore the reasons behind this ability:
Polar interactions: The hydrophilic end of the amphiphilic molecule can form hydrogen bonds and electrostatic interactions with polar solvents (like water) due to the presence of charged or partially charged atoms (such as oxygen or nitrogen). This makes them soluble in polar substances.
Nonpolar interactions: The hydrophobic end of the amphiphilic molecule is typically a long hydrocarbon chain or a nonpolar group. These nonpolar regions can interact with other nonpolar substances (like oils, fats, or hydrophobic portions of biomolecules) through van der Waals forces and London dispersion forces.
Emulsification: The presence of both polar and nonpolar parts in an amphiphilic molecule allows it to act as an emulsifier. It can stabilize the interface between polar and nonpolar substances, preventing them from separating. For example, in the formation of an oil-in-water or water-in-oil emulsion, amphiphilic molecules form a barrier between the two immiscible substances, keeping them dispersed and forming a stable mixture.
Examples of amphiphilic molecules include surfactants (detergents), phospholipids (essential components of cell membranes), and lipoproteins (transporters of lipids in the bloodstream). These substances play vital roles in various biological processes and industrial applications due to their ability to interact with both polar and nonpolar substances.
Hence, Substances that can dissolve both polar and nonpolar substances are called amphiphilic or amphipathic. This unique property arises due to their molecular structure, which contains both polar and nonpolar regions.
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3. An 18.0 N force pulls a cart against a 15.0 N frictional force. The speed of the cart increases 1.0 m/s every 5.0 s. What is the cart's mass?
Answer:
The total force on the cart is:
F = F(applied) - F(friction) = (18 N) - (15 N) = 3.0 N
The acceleration of the cart is:
a = (change in velocity)/(time) = (1.0 m/s)/(5.0 s) = 0.20 m/s^2
Using F = ma, the mass of the cart is:
m = F/a = (3.0 N)/(0.20 m/s^2) = 15 kg
Seven little spheres of mercury, each with a diameter of 2 mm. When they coalesce to form a single sphere, how big will it be (i.e. what is its diameter)? How does its surface area compare with the total surface area of the previous Seven little spheres?
Answer:
The total surface area of the seven little spheres is 1.91 times the total surface area of the bigger sphere.
Explanation:
Volume of a Sphere
The volume of a sphere of radius r is given by:
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3[/tex]
The volume of each little sphere is:
[tex]\displaystyle V_l=\frac{4}{3}\cdot \pi\cdot 2^3[/tex]
[tex]V_l=33.51\ mm^3[/tex]
When the seven little spheres coalesce, they form a single bigger sphere of volume:
[tex]V_b=7*V_l=234.57\ mm^3[/tex]
Knowing the volume, we can find the radius rb by solving the formula for r:
[tex]\displaystyle V_b=\frac{4}{3}\cdot \pi\cdot r_b^3[/tex]
Multiplying by 3:
[tex]3V_b=4\cdot \pi\cdot r_b^3[/tex]
Dividing by 4π:
[tex]\displaystyle \frac{3V_b}{4\cdot \pi}= r_b^3[/tex]
Taking the cubic root:
[tex]\displaystyle r_b=\sqrt[3]{\frac{3V_b}{4\cdot \pi}}[/tex]
Substituting:
[tex]\displaystyle r_b=\sqrt[3]{\frac{3*234.57}{4\cdot \pi}}[/tex]
[tex]r_b=3.83\ mm[/tex]
The surface area of the seven little spheres is:
[tex]A_l=7*(4\pi r^2)=7*(4\pi 2^2)=351.86\ mm^2[/tex]
The surface area of the bigger sphere is:
[tex]A_b=4\pi r_b^2=4\pi (3.83)^2=184.33\ mm^2[/tex]
The ratio between them is:
[tex]\displaystyle \frac{351.86\ mm^2}{184.33\ mm^2}=1.91[/tex]
The total surface area of the seven little spheres is 1.91 times the total surface area of the bigger sphere.
Choose which best describes the following argument:
Two flowers of the same species were planted in adjacent plots. The first was fertilized with Miracle-Gro and it flourished. The second was not and it did not flourish, Therefore, Miracle-Gro stimulates plant growth.
a.
Inductive; weak
b.
deductive; sound
c.
Inductive; strong
d.
deductive; valid
Answer: The answer is a
Explanation:
How long does it take for a Ford Econoline van moving at 39.5 m/s to travel 600 m?
A.
0.0658 s
B.
15.2 s
C.
3.11 s
D.
23700 s
Answer: B. 15.2s
Explanation: 600/39.5 = about 15.2