The correct answer to Brewster’s angle is 48.8 degrees.
What is Brewsters's law?
The Brewster's angle is the angle of incidence at which polarised light travels perfectly through a clear dielectric surface without being refracted. The light that is reflected from the surface when unpolarized light is incident at this angle is therefore perfectly polarised.
This equation's name is Brewster's law, and the angle it specifies is Brewster's angle. For a glass medium in air, Brewster's angle for visible light is around 56° (n2 = 1.5), while it is roughly 53° for an air-water interface (n2 = 1.33)
Brewster's Angle is defined as the inverse tan of n 2 over n 1. The inverse tan of 1.52 divided by 1.33 is thus 48.8 degrees.
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A certain car is capable of accelerating at a rate of 0. 60 m/s2. How long does it take for this car to go from a speed of 55 mi/h to a speed of 60 mi/h?.
The time taken for a car that can accelerate at a rate of 0.6 m / s² to go from a speed of 55 mi/h to a speed of 60 mi/h is 3.68 s
a = ( v - u ) / t
a = Acceleration
v = Final velocity
u = Initial velocity
t = Time
a = 0.6 m / s²
v = 60 mi / h = 26.8 m / s
u = 55 mi / h = 24.59 m / s
t = ( v - u ) / a
t = ( 26.8 - 24.59 ) / 0.6
t = 3.68 s
Acceleration is the rate of change of velocity with respect to time. If the final speed is greater than the initial speed it is called as acceleration and if the final speed is lesser than the initial speed it is called as deceleration.
Therefore, the time taken for this car is 3.68 s
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Since the drag force is proportional to the square of speed, what can you do to improve your car’s gas mileage?.
Since the drag force is proportional to the square of speed, to improve your car’s gas mileage, you should drive in lower speed.
The drag force is a force experienced by an object when it is moving through a fluid. The fluid can be air, water, gas or liquid.
Some of the factors that affect the drag force are the speed of the object and its aerodynamic. The relation between drag force and velocity is given by:
F = 1/2 . CρAv²
Where:
C = drag coefficient
ρ = fluid density
A = area of the object that facing the fluid
v = velocity
Therefore, the drag force is directly proportional to the square of object's velocity, or
F ∝ v²
The power of car should overcome this drag force. The relation between power and force is given by:
P = F . v
Since F is proportional to v², then
P ∝ v³
Thus, we can conclude to use less power, which means to improve gas mileage, you should drive in lower speed.
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The students double the mass that hangs from the string. They also replace the original cart with a new cart that has double the mass. By doubling both masses, how will the tension in the string and the acceleration of the cart change?.
The difference between the string's tension and the cart's acceleration is that the tension doubles while the acceleration stays the same.
What does life's stress mean?In common language, tension is the physical and emotional stress that comes along with life's events. Positive or bad situations can cause this stress, which can be physical, psychological, or emotional.
What's an illustration of tension?Compression force's opposite is tension. All of the things in the scene that are in contact with one another apply forces to one another. The best demonstration of a tension force is when a rope is being pulled. The rope builds up a lot of tension when a pulling force is applied to it.
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The half-life of Ra-226 is 1600 yrs. If one had 0.25 g of a fossil at the beginning, how many grams would be left after 4800 yrs. has elapsed?
The amount of Ra-226 left after4800 yrs with a half-life of 1600 yrs is 0.03125 g.
What is half-life?Half-life is the time taken for half the sample of a radioactive substance to disintegerate.
To calculate the amount of Ra-226 left, we use the formula below.
Formula:
R' = R/[tex]2^{n/t}[/tex].............. Equation 1Where:
R' = Amount of Ra-226 leftR = Original amount of Ra-226n = Total time t = Half-lifeFrom the question,
Given:
R = 0.25 gt = 1600 yrsn = 4800 yrsSubstitute these values into equation 1
R' = 0.25/[tex]2^{4800/1600}[/tex]R' = 0.25/2³R' = 0.25/8R' = 0.03125 gHence, the amount of Ra-226 left after 400 yrs is 0.03125 g.
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When the current in the wire is decreasing the oppose magnitude of the magnetic flux in the loops is _____. Increasing support Induced currents in the loops and the forces exerted on them are directed so they _____ this change
When the current in the wire is decreasing the oppose magnitude of the magnetic flux in the loops is Decreasing. Increasing support Induced currents in the loops and the forces exerted on them are directed so they Oppose this change.
The above statement was proved in Ampere's Circuital Law. According to the law the Current induced is directly proportional to the magnetic flux in the loops. So increasing the current would definitely oppose the change of decreasing the current.
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you must show all your work. a boat leaves a dock at 2 : 00 pm and travels due south at a speed of 20 km/h. another boat has been heading due east at 15 km/h and reaches the same dock at 3 : 00 pm. at what time were the two boats closest together? (12 points)
The time at which the two boats get closest to each other is t=21.6 min
What is meant by time?Time and work are concerned with how long it takes a person or a group of people to finish a task and how effectively each of them completes it.
Given that,
A boat leaves a dock at 2 : 00 pm and travels due south at a speed of 20 km/h.
And another boat has been heading due east at 15 km/h and reaches the same dock at 3 : 00 pm.
At 2:00 pm,
t=0
At 3:00 pm,
t=1
Distance=Speed*Time
D=15(1)
D=15km
Now, if the speed is 20km/hr
D=20(t)
D=20t
C²=(15-15t)²+(20t)²
(C²)'=2(15-15t)(-15)+2(20t)(20)
(C²)'=-450+1250t
(C²)'=0
Then,
-450+1250t=0
t=9/25 hr
(C²)'=-450+1250t=0
(C²)"=1250>0
Therefore,
t=9/25 hr
t=21.6 min
The time at which the two boats get closest to each other is t=21.6 min
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can someone please help me in physics :( i need to scale this so i can draw it. i will be so thankful <33
Answer:
Explanation:
This sounds complicated but , Butternight, and maybe there is some difficulty in the ricochet. I think the question is asking if the bullet bounces off a rock and heads North East.... or NE, but you've got it as EN ? Then how far does it go. In my drawing, what is X, is the question.
We need to know how far the bullet travels East, and how far the bullet travels North.
Then we could put those two parts together and find the length of the red line in my drawing. The red line is also referred to as the Magnitude.
To find how far the bullet travels East, use sine and cosine. Do you know these? if not, start knowing :D
Sine(36) = 0.587785....
Cosine(36)=0.809016....
640 * Sine(36) => 640 * 0.587785 = 376.1825.... m North
640 *Cosine(36) => 640 * 0.809016 = 517.7708... m East
Then the total distance traveled by the bullet to the East is 850 + 517.7708 = 1367.7708... m East
we can find the magnitude by using this [tex]\sqrt{North^{2} + East^{2} }[/tex]
[tex]\sqrt{376.1825^{2} + 1367.7708^{2} }[/tex] = 1418.559.... m NE
I used my calculator to find that. :P
The Earth moves in a nearly perfect circle around the Sun. Assume the speed stays
constant. Is Earth accelerating?
Answer:
yes
Explanation:yes
Answer:
Yes
Explanation:
Earth is accelerated around the sun
what is the basic definition of a black hole? question 16 options: any compact mass that emits no light a dead star that has faded from view a dead galactic nucleus that can only be viewed in infrared any object from which the escape velocity exceeds the speed of light any object made from dark matter
The basic definition of a black hole is -
D) any object from which the escape velocity exceeds the speed of light.
What is a blackhole?
Points in space known that are so dense that they produce large gravity wells. Even light cannot escape a black hole's intense gravitational pull after a certain point. And in a theoretical process aptly known as spaghettification, anything that gets too close will be stretched and compressed.Stellar, intermediate, supermassive, and miniscule black holes are the four main categories. Stellar death is the process that creates black holes most often. Most dying stars will expand, lose mass, then cool to form white dwarfs as they approach the end of their lives. However, the biggest of these flaming bodies, those at least 10 to 20 times as massive as our sun, are doomed to become either super-dense neutron stars or so-called stellar-mass black holes.
Hence, option D is correct.
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Calculate the angle of incidence of a laer red light at which the reflected light i plane polaried. Let we are uing a material of crown gla in a medium of Helium
According to the Brewster's law The angle of incidence is θ=tan −1n.
What is Brewster's law?
Brewster's law is a relationship for light waves that states that if a light ray is allowed to fall on the surface of the a transparent medium in a way that refracted ray makes a 90° angle with the reflected ray, the maximum polarisation (vibration in one aircraft only) can be achieved. The law bears Sir David Brewster's name, a Scottish physicist who first suggested it in 1811. The illustration depicts a ray of regular (nonpolarized) light with a particular wavelength striking a transparent medium's reflecting surface (e.g., water or glass).
According to Brewster's law,
the angle of incidence at which the reflected light is totally polarized for reflection from air to glass is governed by the relation
n=tanθ
∴θ=tan −1n
Hence, the angle of incidence is θ=tan −1n.
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you decide that you want to be able to adjust the height of the views and the data visualizations about electric vehicle sales, charging stations, and battery range. which type of layout will enable you to do that?
The correct answer is vertical layout will enable to adjust height of the views and the data visualizations.
What is a vertical layout?
Use the Vertical Layout control to hold content vertically within it (stacked on-top of one another). Keep in mind that this control can be linked to a list, creating a recurring segment. The Horizontal Layout and Vertical Layout are two of the most often utilised controls when creating a user interface.
So according to given data that if we do require to change the height of views as well as Data Visualization, we require to implement Vertical Layout.
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when the person attempts to climb the ladder, how far up the ladder will the person reach before the ladder slips (kaboom)? the acceleration of gravity is 9.8 m/s
The maximum distance the person will reach before he slip is 1.82m. Not even close to the middle of the ladder.
What is distance?The extent of space between two things, points, lines, etc is called distance. The condition or fact that one is separated in space as if one were separated from another. Remoteness Linear expansion of space: Seven miles is too far to walk in one hour. Vastness; Area: A huge body of water surrounded the ship.The length along a line between two points on the line or line segment. Length is a measure of something like A segment of a room. Distance indicates how far objects are from each other. Two cities or two points. Neither length nor distance can be negative.To learn more about distance from the given link :
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a force of 20 n is directed at an angle of 609 above the x-avis. a second force of 20 n is directed at an angle of 60 below the x-axis. what is the vector sum of these toro forces?
20 N , in +x direction is the vector sum of these Toro forces.
What is force?The word "force" has a specific meaning in science. At this level, calling a force a push or a pull is entirely appropriate. A force is not something an object "has in it" or that it "contains." One thing experiences a force from another. There are both living things and non-living objects in the concept of a force.Force is used to describe a body's tendency to modify or change its state as a result of an external cause. When force is applied, the body can also alter its size, shape, and direction. kicking a ball, pushing and pulling on the door, or kneading dough are a few examples. The newton, abbreviated N, is the SI unit of force.To learn more about forces from the given link :
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you are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. if you instead tie a rope to the doorknob and then continue to pull in the same direction (i.e., perpendicular to the door) with the same force, how does the torque you exert on the door change?
The torque about the center of mass is the same as in a direction perpendicular to the door.
What is torque?The rotational equivalent of a force in physics and mechanics is called torque. Depending on the subject matter, it may also be referred to as the moment, moment of force, rotational force, or turning effect. torque symbolizes a force's ability to cause a change in the body's rotational motion around center of mass. The idea was developed as a result of Archimedes' studies on the application of levers. Similar to how a linear force pushes or pulls an object, torque is a twist about a particular axis. The ratio of the force's magnitude to the angle at which the force's line of action is perpendicular to the axis of rotation is known as the torque.
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A ball has a mass of 50g and is revolving at the end of a string in a circle with a radius of 40cm. The Ball moves with a speed of 2.5m/s, or one revolution per second. What is the horizontal component of the tension needed to produce this acceleration (in N)?
0.781 N is the horizontal component of the tension needed to produce this acceleration.
F=ma
T=ma
m= mass=0.05
a= centripetal acceleration =15.6
T=ma
T=0.05×15.6
T=0.781 N
When pressures on opposing ends are tugging on a rope, thread, wire, or something similar, tension is a contact force communicated through it. For instance, the rope attaching a tire swing to a limb of a tree is under strain. Gravity pulls the rope downward, while the upward pull is caused by a branch that is resisting the rope's tug tension, which is just a pulling force. A slack rope has no tension when one pushes on it. As a result, in a free-body diagram, the force of tension must always be shown in the direction that the string is pulling the item.
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where was the sun located in the first maps of the milky way galaxy? where was the sun located in the first maps of the milky way galaxy? near the top of the nuclear bulge. at the center. near the edge of the disk. in the galactic halo.
star formation is the process by which dense regions within molecular clouds in Interstellar space.
As we know stars are born within the clouds of dust and scattered throughout most galaxies. A familiar example of such as a dust cloud is the orion nebula.
A molecular cloud, sometimes called a stellar nursery if star formation is occurring within is a type of Interstellar whose density and size permits the formation of molecule .
The most common in hydrogen.
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alice prevents on object from intersecting with another object. that is two objects cannot occupy the same space. true or false
All matter has volume but also impenetrability because it occupies space, and two objects cannot occupy a same space at the same time.
What matters is this?An object that occupies space and has inertia is said to be matter, which is composed of numerous types of particles. The different kinds of particles each get a unique mass and size, according to the fundamentals of current physics. The electron, proton, and neutron are three of the most prevalent instances of material particles.
What are matter's characteristics, exactly?Anything with mass and physical space is considered matter. Matter underlies everything that you can see and touch. The three primary types of matter are gases, liquids, and solids. It also possesses qualities that can be expressed through conductivity, magnetism, solubility, density, etc.
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Why do telescopes have to have a good motorized drive system to move them quickly and smoothly?.
Telescopes have to have a good motorized drive system to move them quickly and smoothly so that they can continue to point at the object being observed.
Astronomers use a telescope to observe distant things. Curved mirrors are used by the majority of telescopes, including all large telescopes, to collect and concentrate light from the night sky. The original telescopes employed lenses, which were curved pieces of clear glass, to focus light. The ability of an optical telescope to gather light is its most crucial ability. This capability is solely dependent on the telescope's aperture, or the diameter of the clear objective.
The telescope has a motorized drive mechanism that drives it smoothly from east to west at precisely the same rate that Earth is rotating from west to east in order to maintain the telescope's pointing at the object being seen because Earth is revolving.
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Hi! Can someone help me figure out the Fg(N) column? I don't know how to plug my information into the formula.
The gravitational force (Fg) for the first column is 1.96 x 10⁷ N.
The gravitational force (Fg) for the second column is 2.48 x 10⁷ N.
The gravitational force (Fg) for the third column is 3.24 x 10⁷ N.
The gravitational force (Fg) for the fourth column is 4.4 x 10⁷ N.
The gravitational force (Fg) for the fifth column is 6.36 x 10⁷ N.
The gravitational force (Fg) for the sixth column is 9.94 x 10⁷ N.
The gravitational force (Fg) for the seventh column is 1.77 x 10⁸ N.
What is Newton's law of universal gravitation?
Newton's law of universal gravitation states that every two objects in the universe attracts each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between the masses.
F = Gm₁m₂/r²
F = (Gm₁m₂) x 1/r²
where;
m₁ is the mass of the first objectm₂ is the mass of the second objectG is universal gravitation constantr is the distance between the two massesThe gravitational force (Fg) for the first column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = (6.626 x 10⁻¹¹ x 4 x 10⁹ x 6 x 10⁹) x 1/r²
Fg = 1.59 x 10⁹ x 0.0123
Fg = 1.96 x 10⁷ N
The gravitational force (Fg) for the second column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0156
Fg = 2.48 x 10⁷ N
The gravitational force (Fg) for the third column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0204
Fg = 3.24 x 10⁷ N
The gravitational force (Fg) for the fourth column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0277
Fg = 4.4 x 10⁷ N
The gravitational force (Fg) for the fifth column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0400
Fg = 6.36 x 10⁷ N
The gravitational force (Fg) for the sixth column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.0625
Fg = 9.94 x 10⁷ N
The gravitational force (Fg) for the seventh column is calculated as;
Fg = (Gm₁m₂) x 1/r²
Fg = 1.59 x 10⁹ x 0.1111
Fg = 1.77 x 10⁸ N
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Which periodic table groups do these elements belong in?
Answer:
Claim: Element J should be placed in group 2A (group 2), the Alkaline earth metals. Element Q should be placed on group 8A, Nobel Gases.
Evidence: Element J is Solid at room temperature, is a good conductor of electricity, and have reactions. All of which are properties of Alkaine earth metals. Nobel gases are extremely unreactive, rarely forming compounds and the elements in this group are also gases at room temperature.
Reasoning: Based off of the evidence provided, its safe to say that Element J would belong in group 2A because of its indistindistinct similarities to elemts within that group. Element J would go with the Nobel gases for the same reason
Explanation:
ᓚᘏᗢ meow
Who was awarded the highest-ever rank in the u. S. Armed forces? george patton douglas macarthur george washington dwight d. Eisenhower.
He attained the rank of military officer during the combat on the Western Front in World War I and was once more nominated for a Medal.
How do you define forces?The pushing or push on a phalanx item alters its speed. An unseen factor is an agent that possesses the power to change the resting or traveling position of a body. It has a direction as well as a quantity.
What kind of force is it?Contact forces and non-forces are two different kinds of forces. Nuclear force, gravitational force, frictional force, magnetic force, electrostatic force, spring force, and others are a few examples of forces.
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An in-line skater first accelerates from 0. 0 m/s to 5. 0 m/s in 4. 5 s, then continues at this constant speed for another 4. 5 s. What is the total distance traveled by the in-line skater?.
The total distance traveled by the in-line skater is 33.75 metres.
The total distance will be calculated by the sum of distance due to acceleration and distance due to constant speed. Converting the above mentioned formula in mathematical expression to be used:
d = (v+u/2)×t + v×t
Keep the values in formula to find the total distance.
d = (5+0/2)×4.5 + 5×4.5
Performing addition and multiplication on Right Hand Side of the equation
d = 2.5×4.5 + 22.5
Performing only multiplication on Right Hand Side of the equation
d = 11.25 + 22.5
Performing only addition on Right Hand Side of the equation
d = 33.75 metres
Thus, the skater traveled 33.75 metres.
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situation where middle polarizer is rotated. suppose the middle polarizer is rotated at 100 revolutions per minute. how many times per minute will you observe the light change from bright (max intensity) to dark (min intensity)? this effect, although not normally done with mechanical rotation, is the basis for making optical modulators that are used in high-speed digital communication systems. can you please explain? thanks
When middle polarizer is rotated rotated at 100 revolutions per minute we can take following steps into consideration-
Weight the 20gm of sugar and dissolve the whole of it in 60cc of distilled water and filter the solution by keeping the filter paper in a funnel in clean beaker. We can add distilled water to make the volume of solution equal to 100 cc. This 20% solution i.e. 0.20gm/cc.Now take 50 cc of 20% solution in measuring cylinder and add 50cc distilled water to form 10% solution. Pour it in beaker labeled as 10% solution.Now take 50cc of 10% solution and add 50cc of distilled water in it to form 5% solution.This effect although not normally done with mechanical rotation, is the basis for making optical modulators that are used in high-speed digital communication systems by inserting the thermometer in solution and note down the temperature.
Remove the caps of polarimeter glass tube and measure the length of tube.
Setting up of sodium source in front of slit will be placed at the principal focus of lens of polarimeter.
[tex]Rotation=\alpha =\frac{\beta }{y}[/tex]
β is the mean angle of rotation and y means length of polarimeter tube in decimeter.
[tex]y=\frac{len. of polarimeter}{10}[/tex]
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what is the magnitude of the acceleration of a skydiver who is currently falling at one-fifth his eventual terminal speed?
G = 9.81 m/s2 is the acceleration caused by gravity. The skydiver's acceleration, who is currently descending at a speed that is one-fifth of his ultimate terminal speed, is 3.5316.
What is an explain acceleration?Acceleration: the rate at which the speed and direction of a moving object vary over time. A object and item moving straight forward is propelled when it increases or depreciates.
Is zero acceleration possible?Acceleration is a component of velocity profile. As a result, velocity must remain constant if accelerations are zero. That constant, however, might be anything, such as 5 m/s. Additionally, zero acceleration is indicated if the speed is zero .
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summarize the energy transformations that occur when a tennis racket hits a tennis ball.
Answer:
See explanation...
Explanation:
the kinetic energy of the moving tennis racket is converted (not transformed) to the kinetic energy of the tennis ball.
Since not much description is given here, I didn't include the potential energy of the tennis ball. But in normal cases, the kinetic energy of the tennis ball would be converted to potential energy of the ball, and it falls back down after some time (because of gravity) and slows down due to friction on earth- kinetic energy is converted to heat energy because of friction.
other types of energy are not stated since they can be negligible.
A ball is dropped from rest from a height of 1.88 m. How long does it take to strike the ground? (use g = 10 m/s2)
A. 0.43 seconds
B. 0.38 seconds
C. 0.61 seconds
D. 0.19 seconds
It will take the ball 0.61 second of time to strike the ground. Option C is the right answer.
Motion Under GravityThe motion of an object under gravity is the object' s vertical motion under the influence of acceleration due to gravity.
Given that a ball is dropped from rest from a height of 1.88 m. Since the ball was dropped,
Initial velocity u = 0The height h = 1.88 mAcceleration due to gravity g = 10 m/s²Time t = ?How long it takes, that is, the time taken to strike the ground can be calculated by using the formula
h = ut + 1/2gt²
Substitute all the parameters into the formula
1.88 = 0 + 1/2 × 10 × t²
1.88 = 5t²
t² = 1.88/5
t² = 0.376
t = √0.376
t = 0.61 s
Therefore, the time taken for the ball to strike the ground is 0.61 s
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HELP HELP!!!!!!!!!!!!!!!!
Magnetic force is used in: A door catch or a latch on kitchen cabinet
and A directional compass.
Electric force is used in: Two shocks stacks together coming out of a clothes dryers and An air filter that traps dust and ion particle.
What is magnetic force?Electromagnetic force is a result of charge motion, which also produces magnetic force. We know that a moving charge creates a magnetic field around itself. In this situation, the magnetic force can be thought of as a force that results from magnetic fields interacting.
A door catch or a latch on kitchen cabinet and a directional compass are example of use of magnetic field.
Two shocks stacks together coming out of a clothes dryers and an air filter that traps dust and ion particle are example of use of etectric force.
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Next O Matter Around Us: Mastery Test
3
Select the correct answer from each drop-down menu.
William finds a piece of pure iron in his garden. After a few days, the iron begins to rust. What are the two types of substances involved in the rusting
process of iron?
Iron is
atoms,
a compound
an element
a mixture
with one kind of atom that combines with oxygen from the air to form rust (iron oxide). Rust contains two types of
Reset
Subm
Next
Compounds, like water (H2O) and methane, are made of two or more atoms of various elements. Atoms are not scaled in drawings. Compound molecules contain atoms from two or more distinct elements.
As an illustration, the molecule of water (H2O) contains three atoms: two hydrogen (H) atoms and one oxygen (O) atom. Rust is created when oxygen from the air reactor with iron, which is BLANK with one type of atom (iron oxide). Oxidation reactions result in iron rusting. When something rusts, iron reacts with oxygen in the air and produces Fe2O3.xH2O, or hydrated iron (III) oxide.
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The energy flux from the sun has a peak value of around 1500 W/m2, and solar cells are around
15% efficient. Estimate the area needed to satisfy US energy needs using solar cells, using the
estimates that there are about 350 million people in the US and that we use an average of 90
kW/person. Also assume that there are about 6 hours of "peak" sunlight per day. Answer in square
kilometers (do not put units in your answer, however).
Answer:
Power required = 3.5E8 * 9.0E4 = 3.2E13 (watts)
Power supplied = 1.5E3 * .15 * 3600 * 6 (watts / m^2) * A
= 1.5E3* .15 * 3600 * 6 = 4.9E6 * A
A = 3.2 / 4.9 * E7 = 3.2 / 4.9 * 10 = 6.5 km*2 (1 km^2 = 10E6 m^2)
Note: 1 W = 1 J / sec 1 kw = 1000 W
The area needed to satisfy US energy needs using solar cells 6.5 km²
What is energy?Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.
Power required = 3.5E8 * 9.0E4 = 3.2E13 (watts)
Power supplied = 1.5E3 * .15 * 3600 * 6 (watts / m^2) * A
= 1.5E3* .15 * 3600 * 6 = 4.9E6 * A
A = 3.2 / 4.9 * E7 = 3.2 / 4.9 * 10
= 6.5 km*2
The area needed to satisfy US energy needs using solar cells 6.5 km².
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A 100gm GOLF BALL MOVING WITH A VELOCITY OF 20m/s COLLIDES WITH A 8kg STEEL BALL AT REST. IF THE COLLISION IS ELASTIC, COMPUTE THE VELOCITIES BOTH THE BALLS AFTER COLLISION
Answer:
Golf ball ([tex]0.1\; {\rm kg}[/tex]): approximately [tex](-19.506)\; {\rm m\cdot s^{-1}}[/tex] (backwards).
Steel ball ([tex]8\; {\rm kg}[/tex]): approximately [tex]0.49383\; {\rm m\cdot s^{-1}}[/tex] (forward.)
Explanation:
Apply unit conversion and ensure that the unit of all mass are in kilograms: [tex]100\; {\rm g} = 0.1\; {\rm kg}[/tex].
In an elastic collision, both momentum [tex]p = m\, v[/tex] and kinetic energy [tex]\text{KE} = (1/2)\, m\, v^{2}[/tex] are conserved. Momentum of the two balls before the collision are:
[tex]0.1\; {\rm kg} \times 20\; {\rm m\cdot s^{-1}} = 2\; {\rm kg \cdot m \cdot s^{-1}}[/tex] for the golf ball, and [tex]8\; {\rm kg} \times 0\; {\rm m\cdot s^{-1}} = 0\; {\rm kg \cdot m\cdot s^{-1}}[/tex] for the steel ball initially at rest.Hence, the total momentum of the two balls was [tex]2\; {\rm kg \cdot m\cdot s^{-1}}[/tex] before the collision and (by conservation) will still be [tex]2\; {\rm kg \cdot m\cdot s^{-1}}\![/tex] after the collision.
Kinetic energy of the two balls before the collision are:
[tex](1/2)\times 0.1\; {\rm kg} \times (20\; {\rm m\cdot s^{-1}})^{2} = 200\; {\rm kg \cdot m^{2} \cdot s^{-2}}[/tex] for the golf ball, and[tex](1/2) \times 8\; {\rm kg} \times (0\; {\rm m\cdot s^{-1}})^{2} = 0\; {\rm kg \cdot m\cdot s^{-1}}[/tex] for the steel ball initially at rest.Thus, the total kinetic energy of the two balls will be [tex]200\; {\rm kg \cdot m^{2} \cdot s^{-2}}[/tex] before and after the collision.
Let [tex]m_{a}[/tex] and [tex]v_{a}[/tex] denote the mass and velocity of the golf ball after collision; [tex]m_{a} = 0.1\; {\rm kg}[/tex].
Let [tex]m_{b}[/tex] and [tex]v_{b}[/tex] denote the mass and velocity of the steel ball after collision; [tex]m_{b} = 8\; {\rm kg}[/tex].
Total momentum after the collision shall be [tex]2\; {\rm kg \cdot m\cdot s^{-1}}\![/tex]. Thus:
[tex]m_{a}\, v_{a} + m_{b}\, v_{b} = 2\; {\rm kg \cdot m\cdot s^{-1}}[/tex].
Total kinetic energy after the collision shall be [tex]200\; {\rm kg \cdot m^{2} \cdot s^{-2}}[/tex]. Thus:
[tex]\displaystyle \frac{1}{2} \, m_{a}\, v_{a} + \frac{1}{2}m_{b}\, v_{b} = 200\; {\rm kg \cdot m^{2}\cdot s^{-2}}[/tex].
Assume that the unit of [tex]v_{a}[/tex] and [tex]v_{b}[/tex] are both "meters per second" ([tex]{\rm m\cdot s^{-1}}[/tex].) Combine and solve this system of two equations and two variables:
[tex]\left\lbrace\begin{aligned}&0.1\, v_{a} + 8\; v_{b} = 2 \\ &\frac{1}{2}\, {v_{a}}^{2} + 4\, {v_{b}}^{2} = 200\end{aligned}\right.[/tex].
Rewrite the first equation to obtain [tex]v_{a} = 20 - 80\, v_{b}[/tex]. Substitute this equation into the second one to eliminate [tex]v_{a}[/tex]:
[tex]\displaystyle \frac{1}{2}\, (20 - 80\, v_{b})^{2} + 4\, v_{b}^{2} = 200[/tex].
Solve this equation for [tex]v_{b}[/tex]:
[tex]324\, {v_{b}}^{2} - 160\, v_{b} = 0[/tex].
There are two solutions to this quadratic equation: [tex](40 / 81)[/tex] and [tex]0[/tex]. Note that the velocity of the steel ball must be non-zero right after the collision. Hence, [tex]v_{b} \ne 0[/tex]. Therefore, the only possible value for [tex]v_{b}[/tex] will be [tex](40 / 81)\![/tex], which is approximately [tex]0.49383\; {\rm m\cdot s^{-1}}[/tex].
Substitute [tex]v_{b} = (40 / 81)[/tex] back into the first equation of the system and solve for [tex]v_{a}[/tex]: [tex]v_{a} = 20 - 80\, v_{b} \approx (-19.506)\; {\rm m\cdot s^{-1}}[/tex]. Note that the velocity of the golf ball [tex]v_{a}\![/tex] is negative since the golf ball is travelling backwards, opposite to its initial direction of motion.
In other words, the velocity right after collision will be approximately [tex](-19.506)\; {\rm m\cdot s^{-1}}[/tex] (backwards) for the golf ball and approximately [tex]0.49383\; {\rm m\cdot s^{-1}}[/tex] (forwards) for the steel ball.