The light bends towards the normal line
If light enters any substance with a advanced refractive indicator similar as from air into glass it slows down.
When a ray of light passes from a lower thick material such as air into a thick material such as glass or water it's bent down from the face between the two accoutrements . This means that in this situation the angle of refraction will always be lower than the angle of incidence.
The angle of refraction is lower than the angle of incidence. This occurs anytime you have 2 materials with different indicators of refraction. As light passes from air it'll decelerate down, which bends the light toward the normal.
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calculate the wavelength, in meters, associated with a 1x10^2 g golf ball moving at 34 m/s (about 76 mph).
The the wavelength, in meters, associated with a 1x10^2 g golf ball moving at 34 m/s is 2.2 x 10⁻²⁵ nm.
Calculation:-
Using de Broglie Equation
= 6.626 x 10⁻³⁴j.s/0.1kg x 30ms⁻¹
= 2.2 x 10⁻³⁴m
= 2.2 x 10⁻³⁴m x 10⁹nm/1m
= 2.2 x 10⁻²⁵ nm
Wavelength is the distance between identical points in adjacent cycles of a waveform signal propagating in space or along a line. For wireless systems, this length is usually specified in meters centimeters, or millimeters.
Wavelength is the distance between two wave crests and the same for wave troughs. Frequency is the number of oscillations that pass through a particular point in one second, measured in cycles per second. Forms of electromagnetic radiation such as radio waves light waves and infrared radiation creates characteristic patterns as they travel through space.
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you decide to hike to a higher waterfall of 45 m. you watch as 600 kg of water go over the edge of the waterfall. we know that the water will come to a stop at the bottom, so where does this energy go?
From the law of conservation of energy, as the water falls down and touches the bottom, some of its potential energy gets converted into thermal energy.
What is the law of conservation of energy?According to this law, energy can be transformed from one to another and it can never be created or destroyed. For an isolated system, All forms of energy are considered, and the total energy remains constant.
In an isolated system, if there is a loss of energy in one region such as the cosmos, then there will be a gain of energy in another section of the system. There is no known case in the universe in which the principle of energy conservation is violated.
When the water falls and hits the surface, the potential energy of the water is converted into heat energy which leads to rising the temperature of the water.
The Potential energy of the water, P.E. = mgh
The heat energy of water Q = mC ΔT
The energy carried by the water depends upon the height from which it falls and the mass of the water.
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the velocity of a proton in an accelerator is known to an accuracy of 0.250% of the speed of light.
The smallest possible uncertainty in position of the proton is [tex]4.21 \times 10^{-14} \mathrm{~m}[/tex]
The velocity with the least degree of uncertainty using the Heisenberg principle.
[tex]\Delta x \Delta p \geq \frac{h}{4 \pi}[/tex]
Here, [tex]$\Delta x$[/tex] is uncertainty in position, [tex]$\Delta p$[/tex] is momentum uncertainty, and h is the plank constant.
Since the proton's velocity is 0.25% times the speed of light, the proton's speed equals.
The directional speed of an item in motion, as quantified by a specific unit of time and viewed from a certain point of reference, is what is referred to as velocity.
[tex]v & =(0.0025)\left(3.0 \times 10^8 \mathrm{~m} / \mathrm{s}\right) \\& =7.5 \times 10^5 \mathrm{~m} / \mathrm{s}[/tex]
By using the formula of uncertainty in position,
[tex]\Delta x=\frac{h}{4 \pi \Delta v m}[/tex]
Substitute the value in the above equation we get,
Universal plank constant value,
m= [tex]1.67 \times 10^{-27} \mathrm{~kg}[/tex]
[tex]\Delta v[/tex][tex]=7.5 \times 10^5 \mathrm{~m} / \mathrm{s}[/tex]
h=[tex]6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}[/tex]
Substitute we get,
[tex]$$\begin{aligned}\Delta x & =\frac{6.626 \times 10^{-34}}{4 \pi\left(7.5 \times 10^5\right)\left(1.67 \times 10^{-27}\right)} \\& =4.21 \times 10^{-14} \mathrm{~m}\end{aligned}$$[/tex]
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Note:- The correct question would be as bellow,
The velocity of a proton in an accelerator is known to an accuracy of 0.250 % of the speed of light. (This could be small compared with its velocity.) What is the smallest possible uncertainty in its position?
Sometimes the north and south poles of atoms in a material will line up. What is the term for the region where this occurs?
Answer:
The term for the region where the north and south poles of atoms in a material line up is a "domain." In magnetic materials, the north and south poles of atoms are called "magnetic dipoles." When the magnetic dipoles in a material line up, they create a region of magnetic field called a "domain." This alignment of magnetic dipoles can produce strong magnetic properties in the material, which is why it is often used in applications such as magnets and motors.
a car is travelling with a uniform acceleration along a straight road it passes a point a with a velocity of 8 ms-1 and 5 seconds later it passes a point b with velocity 25 ms-1 find the velocity with which the car passes the mid-point of ab.
The speed of the car passing through midpoint AB is 18.5 m/s.
If an object (with an initial u) is moving at a straight-line speed with a constant acceleration a, its distance s from the starting point and final velocity v will change with time t.
You do not know the distances but as C is the mid-point of AB if you let AC be n, then AB = 2n. This use of n as the unknown allows you to form equations.
From A to B
u = 8, v = 25, s = AB = 2n
v² = u² + 2as
25² = 8² + 2a x 2n
625 = 64 + 4an
an = (625 – 64) ÷ 4 = 140.25
You are given information about speeds and distances. Time will not come into the question, so it is reasonable to try and make two equations with v² = u²+2as.
From A to C
u = 8, s = AC = n, v = ?
v² = u² + 2as
v² = 8² + 2an
v² = 82 + 2 (140.25)
v² = 64 + 280.5
v² = 344.5
v = √344.5
v = 18.5 m/s
The speed of the car at AB is 18.5 m/s
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the power plant comprises one-piston engine of 230 hp at sea level. calculate the maximum velocity of the airplane at sea lev
The maximum velocity of aircraft will be between 200- 300 ft.
What is velocity ?
Velocity is the rate at which something is travelling in a specific direction. An object's velocity can either be constant or variable. The object's speed, direction of travel, or both can be altered.
What is sea level ?
On Earth, sea level serves as the reference point for determining elevation and depth. Since the ocean is one continuous body of water, its surface tries to seek uniformity everywhere it is.
b= 35.8 ft
S= 174 ft2
W= 2950lb
fuel capacity= 65
cp₁₀= 0.025
e=0.8
p=0.8
powerplant= one piston engine of 230hp of sea-level
V= ?
Let us assume v= 200ft/s
G= W/ 1/2 lr v²s = 2950/ 1/2 *0.0002377 * (200)² *177
= 0.357
Aspect ratio b³/3 = (35.8)²/ 17 a
=7.37
=0.025+ (0.357)²/π (0.07) (7.37)²
=0.0319
L/D = 0.357/ 0.0319 = 11.2
T= W/ L/D = 2950/ 11.2 = 263lb
PR=TRV = 263lb* 200
= 52600lb/fts²
This engine has power of 230 hp
230*550lb
= 126500 lb/fts²
so it can flow more at velocity of sea level
Hence, the maximum velocity of aircraft will be between 200- 300 ft.
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consider two protons in the 39k nucleus located 1.9 fm apart. how strong does the nuclear force (in n) need to be to overcome the coulomb force?
The need to be to overcome the coulomb force is 79.63 N.
What is proton ?
A category of subatomic particle having a positive charge is the proton. The strong nuclear force holds the protons together in the atom's nucleus. A subatomic particle with no charge is called a neutron (they are neutral).
What is nuclear force ?
Strong attraction forces within an atom's nucleus hold the protons and neutrons together. These are referred to as nuclear forces.
Charge of proton q = 1.6 x 10 -19 C
Sepration r = 1.7 fm
= 1.7 x 10 -15 m
Required nuclear force F = Kqq / r 2
Where K = Coulomb's constant
= 8.99 x 10 9 Nm 2 /C 2
Subsitute the values we get F = 79.63 N
Therefore, need to be to overcome the coulomb force is 79.63 N.
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a car increases its speed, changing its kinetic energy from 60,000 j to 80,000 j. assuming no friction, how much work is done by the car’s engine to cause this change?
The work done by the car engine to cause the car to increase its speed, hence, changing its kinetic energy from 60,000 j to 80,000 is 20000 J
What is work done?Work done is the product of the force applied and the distance moved by the applied force in the direction of the applied force.
Mathematically;
Work done = force * distance
The unit for measurement of work done is Joules.
The work done by the car engine to cause the car to increase its speed, hence, changing its kinetic energy from 60,000 j to 80,000 is the difference between the initial kinetic energy of the car and the final kinetic energy of the car.
The work done by the car engine = final kinetic energy - initial kinetic energyThe work done by the car engine = 80000 J - 60000 J
The work done by the car engine = 20000 J
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a person is riding on a ferris wheel. when the wheel makes one complete turn, the net work on the person by the gravitational force . (a) is positive (b) is negative (c) is zero (d) depends on how fast the wheel moves (e) depends on the diameter of the wheel
A person is riding on a Ferris wheel. when the wheel makes one complete turn, the net work on the person by the gravitational force is Zero.
When a person rides on a ferris wheel, the gravitational force acting on them is constant. This force is directed downward, towards the center of the Earth. The person's displacement, or movement, is also constant, as they move in a circular path around the center of the ferris wheel. However, the displacement is perpendicular to the direction of the gravitational force.
Since the force and displacement are perpendicular, the work done by the gravitational force is zero. Work is defined as the product of force and displacement, and in this case, the dot product of the force and displacement vectors is zero because they are perpendicular.
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identify the stage in star life cycle in which hydrogen is the primary fuel for nuclear fusion?
The stage in star life cycle where hydrogen is the primary fuel for nuclear fusion is called the main sequence star.
The star life cycle comprises of different stages. All stars are formed from nebula, which is a huge cloud of gas. The different stages in a star's life are
1. Protostar - They are massive clumps of cloud and dust and are not hot enough to achieve fusion.
2. Main sequence star - This is where the fusion takes place. Hydrogen undergo nuclear fusion to become helium and emits a great amount of energy. As long as there is hydrogen for nuclear fusion, the star remains as main sequence.
3. Red giants- After the star run out of hydrogen, they becomes much larger than the size when they were Main sequence. These stars will be much cooler. Here fusion takes place between helium and carbon.
Even though all stars starts the same the end will be based on the mass of the star. Smaller stars form a white dwarf. Big stars can become super giants and explode as supernova. Massive stars becomes neutron stars or black holes.
Life cycle of star where Hydrogen fusion is the main source of energy is Main sequence star.
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the fastest rollercoaster in the world is the formula rossa in abu dhabi, united arab emirates. how many miles per hour does it travel?
The fastest rollercoaster in the world is the formula rossa in abu dhabi, united arab emirates, speed of this is 240 km/h (149.1 mph)
The rate at which an object's distance traveled changes is measured by its speed. In terms of measurement, speed is a scalar, meaning it has magnitude but no direction. Speed is the rate at which an object moves over a given distance. a thing that travels at a high rate of speed and covers a lot of distance quickly. A slow-moving object, on the other hand, travels a comparatively short distance in the same amount of time when moving at a low speed. An object with zero speed is completely immobile.
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(b) use a computer algebra system to graph the force field and circle on the same screen.
The questions is incomplete I answered in general way .
A Computer Algebra System for Graphs Almost all of your math classes require you to create graphs, and these graphs can help you understand more of what is happening.
Even though drawing curves on paper is a valuable ability, there are occasions when we are unsure of how a function should seem.
You'll discover that using a computer algebra system alters your perspective on mathematics completely. It significantly reduces the monotony of mathematics and gives you more time to reflect on your actions.
Any mathematical programme that can handle mathematical expressions in a way that is similar to the conventional manual calculations of algebra is referred to as a computer algebra system (CAS) or a symbolic algebra system (SAS).
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A body which moves from rest with a uniform acceleration travels 18m during the third second. What will be its velocity at the end of the eighth second?
what is the sequence of the anticodon, from the 3\' to 5\' end, of the trna in the a site?
The sequence of the anticodon, from the 3' to 5' end, of the trna in the a site is UGC.
'What is tRNA?'
A unique type of RNA molecule is called a transfer RNA (tRNA). Matching an mRNA codon to the amino acid it codes for is its responsibility. It functions as a sort of molecular "bridge" between the two, if you will.
An anticodon is a group of three nucleotides found in each tRNA. One or more distinct mRNA codons can bind to the anticodon of a particular tRNA. The amino acid encoded by the codons to which the tRNA binds is carried by the tRNA molecule as well.
A cell contains a wide variety of tRNAs, each of which has a unique anticodon and corresponding amino acid. In actuality, depending on the species, there are often 404040 to 606060 various varieties.
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for an electromagnetic wave in free space having an electric field of amplitude e and a magnetic field of amplitude b, the ratio of b/e is equal to
An electric field of amplitude e and a magnetic field of amplitude b, the ratio of b/e is equal to ratio of b/e is equal to 1/c.
Electromagnetic (EM) waves alter electric and magnetic fields, carrying energy and momentum into space. EM waves are solutions to Maxwell's equations, the fundamental equations of electrodynamics.
E(x,t) = Emaxcos(kx - ωt + φ), B(x,t) = Bmaxcos(kx - ωt + φ).
E is the electric field vector and B is the electromagnetic field vector. In electromagnetic waves, E and B are always perpendicular to each other and to the direction of propagation.
The speed of all electromagnetic waves in free space is the speed of light c = 3*108 m/s. An electromagnetic wave can have any wavelength λ or frequency f as long as λf = c.
Calulation:-
[tex]\frac{e}{h} = 120 \pi[/tex]
[tex]\frac{e m_{o} }{b} = 120\pi[/tex]
[tex]\frac{b}{e} = \frac{m_{o} }{120\pi }[/tex]
[tex]\frac{b}{e}[/tex] [tex]= {\frac{4\pi *10^{-7} }{120\pi } }[/tex]
[tex]\frac{b}{e}[/tex] [tex]= 3.33*10^{-9}[/tex]
[tex]\frac{b}{e}[/tex] [tex]= \frac{1}{3*10^{8} }[/tex]
[tex]\frac{b}{e}[/tex] [tex]= \frac{1}{c}[/tex]
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a 60 kg skier strats from the rest from top of a 50 m high slope. if work done by friction is -6 kj what is the speed of the skier on reaching the bottom of the slope
If the work done by friction is -6 kJ, the skier's speed when reaching the bottom of the slope is 28 m/s.
The work done by the friction force is a dissipation energy. Hence, according to the law of conservation of energy:
work done by friction = initial energy - final energy
Initial energy = potential energy = mgh
Final energy = kinetic energy = 1/2 . mv²
Where:
m = mass of skier = 60 kg
h = height = 50 m
v = speed
Hence,
mgh - 1/2 . mv² = 6000
60 x 9,8 x 50 - 1/2 x 60 x v² = 6000
1/2 x 60 x v² = 60 x 9,8 x 50 - 60 x 100
v² = 780
v = 28 m/s
Hence, the skier's speed when reaching the bottom of the slope is 28 m/s.
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if a 15-foot seesaw had a child weighing 100 pounds on the side where the seat was 10 feet away from the fulcrum, and the child on the opposite side weighed 200 pounds and was 5 feet away from the fulcrum, which formula would be correct to figure out if they were in static equilibrium?
The formula used to figure out if the two sides of the seesaw are in static equilibrium is force* perpendicular distance from the fulcrum.
The principle of moments is used to determine the seesaw's balancing point.
According to the principle of moments, the clockwise moment around a point equals the anti-clockwise moment.
The moment on one side of the seesaw = 100 pounds* 10 ft
⇒ 1000 pound-ft
The moment on the other side of the seesaw = 200 pounds* 5
⇒ 1000 pound-ft
Here, moment on one side of the seesaw = moment on the other side of the seesaw = 1000 pound-ft
So, according to the principle of moments, the seesaw is in static equilibrium.
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how may kilometers would you have to go above the surface of the earth for our weight to decrease to half of what it was at the surface
We have to go above 2651 kilometers of the earth for our weight to decrease to half of what it was at the surface
Geophysics applies the concepts of physics to the take a look at of the Earth. It deals with things like the motion of the Earth's crust and the temperatures of its interior.
Geology : is the medical take a look at of the earth- the material of which it is made, the methods that act on those materials, the products shaped, and the history of the planet and its existence paperwork due to the fact starting place. Geology now includes the take a look at of other planets as nicely.
We defile the earth via thinking about other people as our enemies, outsiders and foreigners; by dividing our earth into international locations and by developing enmity in opposition to any other institution of people.
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a disabled sailboat is drifting on a current that is moving at 15 kilometers per hour. fortunately, it's drifting toward a coast guard station 75 kilometers away, which picks up the distress call and sends a rescue craft directly toward the sailboat. the rescue craft can travel 53 kilometers per hour. how long will it be before the two vessels meet?
It will take time 1 hour 6 min approx before the two vessels meet.
Relative speed is said to be the speed of a moving body in relation to another moving or stationary body. When there are two bodies moving in the same direction, the relative speed is the difference of their speeds with respect to the ground. But when two bodies are moving in the opposite direction, the relative speed is the addition of their speeds with respect to the ground.
Relative speed = 15 + 53 Km/h
= 68 Km/ h
Distance to be covered = 75 Km
So, the time when two vessels will meet = distance/ speed
= (75/ 68 ) × 60 =66.17 min.
= 1 hour 6 min approx.
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the captain of a plane wishes to proceed due west. the cruising speed of the plane is 246 m/s relative to the air. a weather report indicates that a 35.1-m/s wind is blowing from the south to the north. in what direction, measured with respect to due west, should the pilot head the plane?
The pilot of the plane should move 7.96° due west in order to proceed west direction.
According to the question the relative speed of plane with respect to air is 246 m/s. The speed of the wind is 35.1 m/s and the direction of the wind is from south to north. Now if we consider the velocity of plane with respect to ground as V m/s then in the west direction the components of this velocity will be
V cosθ = 246 m/s .....(1)
V sinθ = 35.1 m/s .....(2)
Dividing equation (2) by equation (1)
tanθ = 35.1/246
tanθ = 0.14
θ = tan⁻1(0.14)
θ = 7.96° which is the required value.
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the box is sitting on the floor of an elevator. the elevator is accelerating upward. the magnitude of the normal force on the box is
When an item is thrown vertically upwards, the acceleration because of gravity stays unchanged and acts in downward direction.
Since the axis became selected such that high quality is the upward direction, acceleration because of gravity is negative.N = mg if the elevator is at relaxation or shifting at consistent velocity. N = mg + ma if the elevator has an upward acceleration. N = mg - ma if the elevator has a downward acceleration.
This is an utility of Newton's 2d regulation to the forces felt in an elevator. If you're accelerating upward you experience heavier, and in case you are accelerating downward you experience lighter. If the elevator cable broke, you'll experience weightless considering the fact that each you and the elevator could be accelerating downward on the identical rate.
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a 1.5-v alkaline d battery can provide about 43100 j of electric energy. if a curreny of 0.5 a flows through two d batteries while theyre in a circuit of a flashlight, how long will the batteries be able to provide power to the flashlight
The batteries will be able to provide power to the flashlight for 15.96 hours with specified voltage, energy and current.
Given that,
Energy E = 43100 J
Voltage v = 1.5 V
Current i = 0.5 A
Let t be the time for which batteries provide power to the flashlight.
The relation between energy, time, voltage and current is Energy = v* i* t
where, v is voltage
i is current
t is time
By placing the values in the formula above,
43100 = 1.5* 0.5* t
t = 43100/(1.5* 0.5) = 57466.67 s = 957.78 minutes = 15.96 hours
Thus, the time upto which the batteries provide power to the flashlight is 15.96 hours.
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Which of the following statements about electromagnetic waves, sound waves and water waves is/are correct?
1. They exhibit reflection
2. They carry energy 3. They exert pressure 4. They can travel in vacuum
Select the correct answer using the code given below:1, 2, 32 & 41 & 31
All the mentioned statements are true about electromagnetic waves because they exhibit reflection, the carry energy, the exert pressure and they can travel in vacuum.
An Electromagnetic wave is a wave that has the electric field component and magnetic field component which are perpendicular to each other and also to the direction of the propagation of the wave.
An Electromagnetic wave does not need any medium to travel they can travel in vacuum.
For an example, light is also an Electromagnetic wave and it shows reflection so we can say that electromagnetic wave exhibit reflection.
We know that, light carries energy so we can stay that electromagnetic wave carries energy and they also exert pressure because we experience the pressure by the UV rays that fall on the surface of the earth.
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if sunlight were green instead of white, the most comfortable color to wear on a hot day would be
If the sunlight were some how green rather of white we have to wear green clothes.
Also on a veritably hot day green multicolored clothes will be most comfortable, while on a veritably cold day white clothes will absorb all the green color and will make you feel warmer.
The color of the sun is white. The sun emits all colors of the rainbow more or less unevenly and in drugs, we call this combination" white". That's why we can see so numerous different colors in the natural world under the illumination of sun.
In conclusion, darker colors will warm up more snappily and absorb further heat in sun than lighter colors.
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you are flying on v306 from lake charles to daisetta. where is the vor changeover point? a. 50 nm west of lch. b. 30 nm west of lch. c. 50 nm east of das.
30 NM east of DAS the vor changeover point.
Aviation includes activities related to mechanical flight and the aircraft industry. Airplanes include fixed and rotary wing types, deformable wings, wingless lifting devices, and lighter-than-air vehicles such as hot air balloons and airships.
Aviation began in the 18th century with the development of the hot air balloon, a device capable of altering the atmosphere through lift. Some of the most important advances in aviation technology came with the controlled gliding of Otto his Lilienthal in 1896.
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FILL IN THE BLANK. if r is a real zero of even multiplicity of a function f, then the graph of f ____ the x-axis at r.
Answer: touches
Explanation:
what was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?
The power output of the speaker is 1922.2W.
What do power input and output mean?The quantity of energy put into a device is referred to as input, and the amount of energy that comes out is known to as output. The type of energy may be altered by a device, but not its quantity. For instance, a light bulb uses electrical energy as its energy input and produces light and heat as its output energy.
Briefing:
P= IA
Where,
I = Intensity
A = Area
P= I1A
P= I1(4πr2)
P= (31.62W/m2)(4π×(2.2m)2)
Therefore,
P= 1922.2W
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A bowling ball rolls without slipping up a ramp that slopes upward at an angle β to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.
Part A:
What is the acceleration of the center of mass of the ball?
Express your answer in terms of the variable β and appropriate constants.
Part B:
What minimum coefficient of static friction is needed to prevent slipping?
Express your answer in terms of the variable β and appropriate constants.
Friction is an opposing force that works on a body's surface and tries to stop it from moving. Newton (N) is its unit.
What is the friction force?
Friction is the force created when two surfaces of two things come into contact and slide against one another.
It is described mathematically as the product of the normal reaction and the coefficient of friction.
The equation becomes balanced once the provided force and acceleration in the various components have been resolved. elements moving in the x-direction
To find acceleration on an inclined plane
Ma(sin∅) - F = ma
mg(cos∅) = R
F = μR
To prevent slippage, the frictional force must be less than the maximum static friction force. We'll use constants to represent the ratio of the ramp's opposite and adjacent sides.
At this point, the frictional force equals ma. It was previously discovered that a=gsin
The frictional force is thus mgsin∅. The maximum static friction force, or normal force, is defined as kmgcos∅, where k is the minimal static friction coefficient.
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a 68-kg man standing on a scale in an elevator notes that as the elevator rises, the scale reads 827 n. what is the acceleration of the elevator?
N = mg while the elevator is stationary or travelling at a constant speed. If the elevator is moving upward, N = mg + ma. If the elevator has a downward acceleration, the scale reading can fall as low as 772.
How is an elevator's power determined?Calculating the elevator's effort over the 100 meters is simple: W equals mgh, which is (1000)(9.8)(100) = 9.8105 Joules.
As the elevator speeds up, what does the scale read?As a result of the scale reading the normal force, your weight is reported as being higher than it was at rest. The same two forces that propelled the elevator up are still at play. As opposed to when it was at rest, the scale will read the normal force.
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A massless rope connects a box on a horizontal surface and a hanging stone as shown below. The rope passes over a massless, frictionless pulley. The box is given a quick tap so that it slides to the right along the horizontal surface. The figure below shows the block after it has been pushed while it is still moving to the right. The mass of the hanging stone is larger than the mass of the box. There is friction between the box and the horizontal surface. Free-body diagrams that a student has drawn to scale for the box and for the hanging stone are shown.
Four students discussing these free-body diagrams make the following contentions: Ali:“I think there is a problem with the free-body diagram for the hanging stone. The two forces should have the same magnitude.” Brianna: “But the stone is moving upward – there should be a larger force in that direction.” Carlos:“No, the diagram for the hanging stone is okay, but there is a problem with the diagram for the box. The frictional force is in the wrong direction.” Dante:“No, all three of you are wrong. Both free-body diagrams are correct because both show the way the objects would be accelerating.” With which, if any, of these students do you agree?