The tug-of-war winner is the team who pulls the rope the hardest.
Reason being: The rope moves in the direction of greater force.
We are familiar with Newton's second law of motion, which describes circumstances in which all of the forces are not balanced. As a result, the acceleration is a function of our applied force. Inversely correlated with body mass is acceleration as well. The acceleration of the body produced is proportional to the net force we apply and in the direction of the force we apply, which is an alternative explanation for the second law. Consequently, the rope is pulled harder when playing tug of war. The acceleration of the rope increases as more force is applied. And the direction of the rope's movement is in the direction of a stronger force. Rope motion is in the direction of greater force.To know about Newton's second law of motion-
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A 45 lb (20 kg) child i having a temper tantrum in the middle of Wal-Mart. If the boy i itting on the floor and hi parent i pulling him up with a force of 150 N, what i the normal force on the boy?
The normal force on the boy would be 150 N.
What is force?
A force is indeed an influence that can alter an object's motion in physics. A force can cause an object to mass to change its velocity, or accelerate (for example, moving from a state of rest). An intuitive way to describe force is as a push or a pull. A force is a vector quantity because it has both magnitude and the direction. It is computed using the SI unit of newton (N). F is used to represent force (formerly P). The net force acting on an object is proportional to the frequency at which its momentum changes over time, according to Newton's second law in its original formulation. This law suggests that an object's acceleration is directly proportional to the total force acting on it if the object's mass remains constant.
The normal force on the boy is equal to his weight, or 45 lbs (20 kg). This is because the normal force is the force that the surface exerts on the object, in this case the boy, to prevent him from sinking or moving. The force of 150 N applied by the parent does not affect the normal force on the boy; it just provides the force to lift him up.
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a 950n basketball player jumps to block a jump shot. here is what you know: the average force applied to the floor: 1800n force is applied over a vertical distance of .5m (from the lowest point in the squat to the position at the instant of takeoff.
The instant take off speed is 2.96 m/s
What is force applied over distance?It is intimately correlated with both the amount of force applied to the item and its motion. The equation below may be used to compute work: Work is equal to force times distance. The Newton meter is the SI unit of work (N m). When an item is moved across a distance of 1 m with 1 N of force, one joule is equal to the amount of work that is accomplished.The forces and motion in a standing vertical leap are both vertical. F = FGRF - mg, where FGRF is the vertical ground reaction force applied to the jumper and mg is the jumper's body weight, results in a vertical force on the jumper.Given :
Weight of the Basket ball Player = 950 N.
Force Applied on the Floor = 1800 N
over Vertical distance = .5 m
resultant force f = 1800 N - 950 N = 850 N
work done = 850 * 0.5 m =425 J
kenetic energy = 1/2 mv^2= 425
mass = 950/ g = 96.9
v^2 = 425 * 2/ 96.9
v= [tex]\sqrt{8.78}[/tex] = 2.96 m/s
instant Take off is 2.96 m/s
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What are 3 facts about electromagnets?.
Magnetic objects are either drawn to or pushed away by magnetism. When two magnets with the same poles are positioned close to one another, they push apart and repel. When two dissimilar poles are positioned close to one another, they pull and attract to one another.
What three qualities do electromagnets possess?A soft iron core makes up an electromagnet. You may alter the magnetic field's strength. Simply cutting off the electricity will demagnetize an electromagnet. Reversing the polarity is possible.
A unique class of magnets called electromagnets has the following characteristics: By switching the direction of the current flow, the polarity of the magnets may be changed. They function as magnets when an electric current is passing through them; they are transient magnets that may be turned on and off.
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The mass of a carbon atom is 12. 00amu while the mass of a helium-4 atom is 4. 003amu. If three atoms of helium fuse to form carbon, how much mass is converted into energy?.
If three atoms of helium fuse to form carbon than 0.009 u of mass is converted into energy
Given: m(He) = 4.003 u
and m(C) = 12.000 u
Mass of 3 alpha particles =3×4.003 u
=12.009 u.
Mass of 1 carbon atom=12.000 u
Mass Defect =△m=12.009−12.000=0.009 u
Energy released =0.009×931.5=8.3835 MeV.
So, 0.009 u of mass is converted into 8.38 Mev energy.
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a flat, circular loop has 16 turns. the radius of the loop is 12.0 cm and the current through the wire is 0.53 a in clockwise direction. determine the magnitude and direction of the magnetic field at the center of the loop (in t).
The magnitude of the magnetic field is 3.8343168 × [tex]10^-^1[/tex] A-m²
and the direction is perpendicular to the field since the magnitude is not mentioned.
The given dimensions are ;
Number of turns or N = 16 turns
The radius of the loop = 12 cm = 0.12 m
And the current through the wire = 0.53 A
And the formula for magnetic field is ;
magnetic field = Ni A
= 16 × 0.53 × π× r²
= 16 × 0.53 × 3.14 × 0. 12 × 0. 12
We have taken the value of π = 22/7 as 3.14
= 0.38343168
= 3.8343168 × 10-1 A-m²
And the direction is perpendicular to the field.
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Why does an empty paper plate not heat up in the microwave electromagnetic?.
This is because the microwave oven heats the food by heating the water molecules that compose it.
This is achieved by increasing the vibration amplitude of the water molecules and their kinetic energy, therefore, increasing their temperature.
So, if the element that gets into the microwave oven does not contain water (as is the case of an empty paper plate), it will not heat up.
Therefore, this is all about the transfer of energy. This the principle on which microwave works. The transfer of heat energy from one object to the other increases the kinetic energy of the particle of the other object. But no object mean no heat energy transfer and the plate isn't heated.
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Light waves are electromagnetic waves that travel at 3. 00 108 m/s. The eye is most sensitive to light having a wavelength of 5. 50 10-7 m.
The frequency of light is calculated to be 5.45* 10¹⁴ Hz.
The relationship between frequency and wavelength of an electromagnetic wave is given by c = f λ
where, c is the speed of light (3* 10⁸ m/s)
f is the frequency
λ is the wavelength
In this problem, let us consider the wavelength of light as 5.5* 10⁻⁷ m
Substituting the values in the above equation, let us find out frequency.
f = c/λ = 3* 10⁸/5.5* 10⁻⁷ = 5.45 * 10¹⁴ Hz
Thus, the frequency of an electromagnetic wave is found to be 5.45* 10¹⁴ Hz.
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when first-mover advantage is crucial and a high degree of competitive intensity prevails, the approach is better for international expansion.
With the exception of Microsoft's Bing search engine, all of the following businesses were pioneers.
How Does First-Mover Advantage Work?Simply put, a first-mover advantage is a company's capacity to outperform its rivals as a result of being the first to market in a new product area. We believe it is important to distinguish between long-lasting first-mover advantages and those that are fleeting. Long-lasting first-mover advantages increase a firm's market share or profitability over time. Although no advantage lasts forever, businesses who are successful in establishing long-lasting first-mover advantages frequently dominate their product categories from a market's infancy to its mature stage for many years. Both the importance and endurance of early success are well demonstrated by Coca-Cola in soft drinks and Hoover in vacuum cleaners.The first mover advantage is used to describe the advantage of gained by a business when it first enters a market segment before every other business. This advantage allows the business more market share or monopoly in comparison to other businesses that enter the market later.From the above we liken this advantage to rock, scissors and papers where the first player to choose the right object such as rock Vs scissors wins.To know more about First-Mover Advantage
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1. Define a function, in which torque (Nm)
and angular velocity (rad/s)
are two inputs and power (W) is output. Then call this function and print the results. [power(W)=torque(Nm)*angular velocity
(rad/s)]
2. Define a [3*1]
array and take three user input number. Define an average function and a standard deviation function. Call these two functions and print the results. 3. Define a
[4*3]
array and take 12 user input number as 12 months temperature in Fahrenheit. Define a function take the array as the input and output a
[4*1]
array indicating average seasonal temperature in Celsius.
●The power of a rotating body can be expressed as
P = T ω
●Arrays are usually sets of numbers or objects, and they are typically organized in columns, rows, or a matrix.
Power and Torque of Body in Angular Motion:
1.Power and Torque of Body in Angular Motion:
The power of a rotating body can be expressed as
P = T ω
Work is the result of a force acting over some distance. Work is quantified in joules (Nm) or foot-pounds.
Torque is a rotating force produced by a motor’s crankshaft. The more torque the motor produces, the greater is its ability to perform work. Since torque is a vector acting in a direction it is commonly quantified by the units Nm or pound-feet.
Power is how rapidly work is accomplished - work in a given amount of time. Power is quantified in watts (J/s) or horse power.
2.Arrays are usually sets of numbers or objects, and they are typically organized in columns, rows, or a matrix.
Arrays are frequently used to illustrate the principles of division and medication.
The SD measures spread around the average. It's a sort of average distance of values in the list from their overall average. Technically, it is the square root of the average squared difference between the numbers and their average.
Method 1: Averaging Standard Deviations for Equal Sample Sizes
Average standard deviation = √ (s12 + s22 + … + sk2) / k.
Average standard deviation = √ (122 + 112 + 82 + 82 + 62 + 142) / 6.
Average standard deviation = 10.21.
3.The formula to convert Celsius to Fahrenheit is :
feh = (9 * cel / 5 + 32)
C Code ==<<>>== #include //function named seasonal_average_celsius() //its return type is void //this function takes a 2-d array as parameter void seasonal_average_celsius(int temp[4][3]){ //Declaration of an integer variable.
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Which of the following is closest in size (radius) to a neutron star?A) the EarthB) a cityC) a football stadium D) a basketballE) the SunAnswer: B
B) A city is closest in size to a neutron star.
A typical neutron star has been found to be 1.4 times as heavy as Sun and has a radius of approximately 11 km.
Earth is not considered to be the closest since it has a radius of 6378 km which is much greater than the radius of a neutron star. Similarly, the Sun has a radius of 696,340 km therefore Sun is also not considered to be the closest.
The radius of a basketball is 4.7 inches which is equal to 0.00012 km so it is much less than the radius of a neutron star.
On the other hand, a city has a radius of approximately 10 to 30 km therefore it is considered to be the nearest in radius to a neutron star
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the fact that the astrolabe was developed in the Muslim empire implies that...
The Muslims empire was advanced in technology
The Muslim empire, from the s. VIII, gave a sumptuary use to the astrolabe, an instrument created by the Greeks in the 1st century BC, and this led to the development of astronomy.
What is the astrolabe?It is an ancient astronomical instrument used to determine the latitude, longitude, height or position of bodies in the sky, as well as to calculate the time.
It is not known exactly who invented it, but the construction of a spherical or armillary astrolabe is attributed to the Babylonians.
However, historical records refer to a first astrolabe used by the Greek astronomer Hipparchus of Nicea, while Ptolemy laid the foundations for the construction of the planispheric astrolabe.
Muslims furthered the technological development of the astrolabeThe Muslims put the astrolabe to religious use and spread its knowledge.
Ibn al-Saffar is credited with drafting a treatise in the fifth century that covered the construction and instructions for use of the astrolabe and became the most widely used treatise for centuries.
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50% part (b) to what maximum height, in meters, above the nozzle can this water rise? (the actual height will be significantly smaller due to air resistance.)
Our maximum height will be equal to V 2 squared divided by 2 G, or 1 63 m.
What is the maximum height to be calculated?Although diameters are not provided in this problem, we will put in several diameters that we can use as one. V one is equal to a two V two, which is 40 times 10 to the minus three.Therefore, our V1, or speed 1, is 40 times 10 to the negative three divided by pi over four times nine times 10 to the negative two squared. Thus, V1 is 6.28 m/s. In a similar vein, RV two is 56.5 m/s and we have a new diameter.A pressure drop is therefore equal to P one minus P two, or one half row V two squared minus V one squared, which is equal to 1581356 pascals. Our maximum height will be equal to V 2 squared divided by 2 G, or 1 63 m.To learn more about Maximum height refer to:
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an electric fan is turned off, and its angular velocity decreases uniformly from 600 rev/min to 200 rev/min in 4.00 s.
The angular acceleration of fan whose angular velocity decreases uniformly from 600 rev/min to 200 rev/min in 4 sec is 100rev/min².
We know very well that angular acceleration is defined for the objects which are undergoing some rotation. It means if the body which holds angular velocity, it will also hold some amount of angular acceleration
We also know that angular acceleration is stated as rate of change of angular velocity.
Here we can see that angular angular velocity is dropping from 600 rev/min to 200 rev/min.
So, according to angular acceleration formula([tex]\alpha[/tex] )= Δω/Δt
whereas Δω=ω₂-ω₁
Now, here ω₂=200rev/min
and ω₁=600 rev/min
Therefore, angular acceleration equal to = (200-600)/4= -400/4= -100rev/min².
Here, Negative sign indicates that angular acceleration is decreasing with time.
Hence, angular acceleration is 100rev/min².
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(Complete question) is:
an electric fan is turned off, and its angular velocity decreases uniformly from 600 rev/min to 200 rev/min in 4.00 s. Find the angular acceleration of electric fan in 4.00 minutes.
Nearly the entire world uses the metric system for their measurements. The US is 1 of 3 countries that does not use metric. Would you support changing school curriculum to teach the metric system as the primary measurement system in the US? Why or why not?
The answer is yes, I would suggest using the same metric system because in whole world the metric system is same then it will be easy to solve the problems.
What is metric system?The progressions metric system, which had been implemented in France in the 1790s, was the measuring system that was replaced by the metric system. The International System of Units (SI), which was created in the middle of the 20th century with the help of an international standards body, was the historical culmination of the evolution of these systems. The term "metrication" refers to the adoption of the metric system.
The acknowledgement of various principles is the result of the historical development of metric systems. One base unit of measurement can be used to express each of nature's essential dimensions.
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derive an equation for specific gravity in terms of the dry sample weight and the apparently lighter submerged weight (which is the real weight minus the buoyant force). you will use no other quantities in the equation. calculate the specific gravity of each sample.
The Specific Gravity for sample 1 is 1.095g and for the Specific Gravity for sample 2 is 1.088g.
What is Specific Gravity?
The ratio of a substance's density (mass per unit volume) to the density of a specific reference material is known as its relative density or specific gravity. When determining a substance's specific gravity, liquids are typically compared to the densest form of water (at 4 °C or 39.2 °F); for hydrocarbons, the reference point is atmosphere at room temperature (20 °C or 68 °F). Scientific jargon favours the term "relative density," which is frequently abbreviated as "RD," while deprecating the term "specific gravity."
A substance is less dense than the reference if its relative density is less than 1, and it is denser than the reference if it is greater.
Specific Gravity = (Dry Sample Weight) / (Submerged Weight)
Sample 1:
Dry Sample Weight = 24.8 g
Submerged Weight = 22.7 g
Specific Gravity = 24.8 g / 22.7 g = 1.095
Sample 2:
Dry Sample Weight = 27.3 g
Submerged Weight = 25.1 g
Specific Gravity = 27.3 g / 25.1 g = 1.088
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truck covers 43.7 m in 6.8 s while smoothly slowing down to a final speed of 2.7 m/s. find its original speed. answer in units of m/s.
The original speed of the truck would 0.7 m/s covering 43.7m in 6.8s
What is velocity, for instance?Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. The scalar indicates that the velocity vector's absolute value magnitude will always equal the motion's speed.
Can velocity go backwards?The change in position (displacement) of an object over a period of time is referred to as its velocity. Speed can only be positive, whereas velocity can be either positive or negative because it combines both speed and direction.
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a point source of light illuminates an aperture 2.00 mm away. a 13.0 cmcm -wide bright patch of light appears on a screen 2.00 mm behind the aperture.
A point source of light illuminating an aperture is 2 mm away. A 13 cm wide bright patch of light appears on a screen 2 mm behind the aperture. The width of the aperture is 6.5 cm.
The formula for determining the width of the aperture is given by
D = f/N
where, D is diameter
f is focal length
N is f-number or wideness
DN = f
N = f/D
Given that, f = 13 cm = 130 mm
D = 2 mm
N = 130/2 = 65 mm = 6.5 cm
Thus, the width of the aperture is 6.5 cm.
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ib physics mcq a particle is oscillating with simple harmonic motion (shm) of amplitude xo and maximum kinetic energy ek. what is the potential
Maximum kinetic energy and maximum potential energy of a particle is oscillating with simple harmonic motion (SHM) of amplitude x₀ is = 1/2mω²x₀².
What is simple harmonic motion?A motion in which the restoring force is directly proportional to the body's displacement from its mean position is known as a simple harmonic motion, or SHM.
This restoring force always moves in the direction of the mean position. A particle moving in simple harmonic motion accelerates as a(t) = -ω²x (t). Here, ω denotes the particle's angular velocity.
Maximum kinetic energy of a particle is oscillating with simple harmonic motion (SHM) of amplitude x₀ is = 1/2mω²x₀².
Maximum potential energy of a particle is oscillating with simple harmonic motion (SHM) of amplitude x₀ is = 1/2mω²x₀².
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most waves approach the shore at an angle. however, they bend to be nearly parallel to the shore as they approach it because blank .
Most waves approach the shore at an angle. However, they bend to be nearly parallel to the shore as they approach it because when a wave reaches a beach or coastline, it releases a burst of energy that generates a current, which runs parallel to the shoreline.
Most waves approach shore at an angle. As each one arrives, it pushes water along the shore, creating what is known as a longshore current within the surf zone.Waves approach the coast at an angle because of the direction of prevailing wind.The part of the wave in shallow water slows down, while the part of the wave in deeper water moves at the same speed.Thus when wave reaches a beach or coastline, it releases a burst of energy that generates a current, which runs parallel to the shoreline.To know more about waves visit:
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two particles collide, one of them initially being at rest. is it possible for both particles to be at rest after the collision?
Both particles could be at rest after the impact. You cannot have both things at rest.
What causes collisions and why?Distracted driving is the most frequent reason for a vehicle accident. Speeding, disobeying traffic signs, unsafe maneuvers, and operating a vehicle while inebriated or under the influence of drugs are additional risk factors for car accidents.
Which collision kinds are there?Elastic, inelastic, and entirely inelastic collisions are the three main types that can occur. To reiterate, momentum is preserved in each of the three categories of collisions. What happens to the kinetic energy is what characterizes the impacts.
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111 -0.5 Drought resistance (change in biomass 1986–198 -1.0 After D. Tilman and ), A. Downing. 1994. Nature 367:363--365. -1.5 0 15 25 5 10 20 Plant species richness before drought Tilman and Downing studied the impact of plant species richness on drought resistance in prairie communities. What conclusion can you draw from their figure? Communities with more species before the drought lost less biomass during it Communities with fewer species before the drought lost less biomass during it Communities with intermediate species before the drought lost less biomass during it The number of species within the community did not affect biomass during drought
The conclusion drawn from Tilman and Downing studies on the impact of plant species richness on drought resistance is that Communities with more species before the drought lost less biomass during it
From the two graphs below from Tilman D and Downing JA (1994), it can be seen that communities having higher species richness (> 10 plant species richness ) has less deviation of biomass ratio compared to communities having low species richness (<5 plant species richness) before and after drought.
Communities having higher species richness before draught has higher draught resistance as well as higher biomass ratio. Plant species richness in 1989 shows that a higher species richness result in less higher biomass ratio.
Therefore, the conclusion drawn from their figure is " Communities with more species before the drought lost less biomass during it".
The given question is incomplete. The complete question is:
Tilman and Downing studied the impact of plant species richness on drought resistance in prairie communities. What conclusion can you draw from their figure shown in image attached below?
Communities with more species before the drought lost less biomass during it
Communities with fewer species before the drought lost less biomass during it
Communities with intermediate species before the drought lost less biomass during it
The number of species within the community did not affect biomass during drought
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shows two strong magnets on opposite sides of a small table. the long-range attractive force be- tween the magnets keeps the lower magnet in place.
A magnet is a substance that creates an unseen zone where other magnetic materials can experience a force (either attracted or repulsive).
What is a magnet, please?A magnet is any item that generates its own magnetic field and interacts with other magnetic fields. A magnet has two poles, the north pole as well as the south pole. The magnetic field of a magnet is depicted by field lines that start at its north pole but stop at its south pole.
What is in a magnet?Most permanent magnets have iron, chromium, perhaps cobalt as their principal metals. Cobalt, nickel, and aluminum are combined to form the alloy known as Alnico.
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As you approach a steady light source, the wavelength of the emitted light appears?.
As you approach a steady light source, the wavelength of the emitted light appears shorter.
The distance over which a periodic wave's shape repeats is known as its wavelength. It is a property of both traveling waves and standing waves, as well as other spatial wave patterns. It is the distance between two successive corresponding locations of the same phase on the wave, such as two neighboring crests, troughs, or zero crossings. The spatial frequency is the reciprocal of the wavelength. The Greek letter lambda () is frequently used to denote wavelength. The term wavelength is also sometimes used to describe modulated waves, their sinusoidal envelopes, or waves created by the interference of several sinusoids.
Wavelength and frequency are inversely related for a sinusoidal wave traveling at a constant speed.
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(b) how long after closing the switch will it take for the stored energy in the solenoid to reach one-half of its maximum value?
[tex]1.73×10^-5[/tex] s after closing the switch will the current through the inductor reach one-half of its maximum value.
What type of electric current is it?Electric current is a term used to describe how much electricity flows across a circuit and how it flows in an electronic circuit. Amperes are used to measure it (A). The more electricity flowing across the circuit, the higher the ampere value.
What is the current flow?While electrons move from negative to positive, current moves from positive to negative. The quantity of electrons that flow through a conductor's cross section in a second defines current. The unit of measurement for current is the ampere, abbreviated "amps." The letter "A" is used to represent amps.
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what is the wavelength of the light when it was emitted from the galaxy when the universe was only about 4 billion years old?
The exact wavelength of the light would depend on the type of light being emitted from the galaxy. However, it is likely that the light would have a wavelength in the range of ultraviolet (UV) to near-infrared (NIR).
What is wavelength?
A waveform signal that is propagated in space or along a wire has a wavelength, which is the separation between two identical points (adjacent crests) inside the adjacent cycles. This length is typically specified in wireless systems in metres (m), centimetres (cm), or millimetres (mm) (mm). The wavelength is more frequently specified throughout nanometers (nm), that are units of 10-9 m, as well as angstroms (), which are units of 10-10 m, for infrared (IR), visible light (UV), and gamma radiation ().
Frequency, which is defined as the quantity of wave cycles per second, and wavelength have an inverse relationship. The wavelength of a signal decreases with increasing frequency.
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what experimental problems would you encounter if you attempted to determine the concentration of the metal ions in solutions of each of the following reagents
We know that the following equation from Beer-Lambert Law:
A = ε.c.l
where,
A = absorbance of the radiant light
ε = molar absorptivity of the dissolved substance
c = concentration of the substance
I = path length in centimeters
Now, the values of ε's are given but we are not informed with the values of the absorbances which are required to calculate the concentrations (given path length 1 cm).
So, this is the experimental problem we might encounter.
In rest the substance does not absorb in the visible region. So the most frequently used spectrometer can not be used here. Rather we need to first determine in which region of electromagnetic spectrum this substance absorbs.
Therefore, this one has one different experimental problem than the previous one.
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what happens with the ratio of translation kinetic energy to rotational kinetic energy of the ball while the ball accelerating down the incline?
The ratio of translation kinetic energy to rotational kinetic energy of the ball while the ball accelerating down the incline is constant.
Translation kinetic energy=1/2MV²
Rotational kinetic energy=1/2IW²=1/5MV²
translation kinetic energy/rotational kinetic energy=1/2MV²/1/5MV²=2.5 =Constant
We are aware that the kinetic energy (KE) in linear, or translational, motion is equal to 12 mv2. By swapping out mass m for the rotational equivalent of mass, rotational inertia I, and speed v for rotational speed, we can determine the rotational version of kinetic energy. The only distinction between rotational and translational kinetic energy is that the former moves in a straight line while the latter does not. A bike tire moving down a bike path is an illustration of both kinetic and translational kinetic energy. Through the use of a screw-and-nut assembly mounted on the motor shaft, rotation can be changed into linear speed. The two primary varieties of screw-and-nut systems are ball screw and lead screw. A ball screw works by the screw and nut rolling in contact with one another.
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The kinetic energy correction factor for laminar flow in a circular pipe is:
A 1.23
B 1.54
C 2
D None of these
For laminar flow in a circular pipe, the kinetic energy correction factor is 2
Kinetic energy correction factors for different cases are as follows:
1. For laminar flow in circular pipe =2
2. For laminar flow between parallel plates =1.543
3. For turbulent flow in circular pipe = 1.03-1.06
Laminar flow in fluid dynamics is characterized by fluid particles traveling in layers along clean routes, passing each other without much or any mixing between them. Adjacent layers glide past one another like playing cards when the fluid is moving at moderate speeds because it prefers to flow without lateral mixing. No fluid eddies, swirls, or cross-currents parallel to the flow direction exist. Laminar flow is characterized by relatively ordered fluid particle motion, with particles near a solid surface traveling in straight lines parallel to that surface. High momentum diffusion and low momentum convection are characteristics of laminar flow.
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A wheel accelerates with a constant angular acceleration of 4. 5 rad/s2 from an initial angular speed of 1. 0 rad/s. (a) through what angle does the wheel turn in the first 2. 0 s, and (b) what is its angular speed at that time?.
a. The angle does the wheel turn in the first 2.0 s is 1.7507 rev.
b. The angular speed at that time is 3.14 rad/s.
Angular accelerationin a circular motion, the angular change in an object moving in a circle in one unit of time. The size of this angle is the angle of travel in question in the problem. Circular motion consists of uniform circular motion and uniformly changing. In this problem using the concept of uniformly changing circular motion because the angular velocity changes, then:
a. The angle does the wheel turn in the first 2.0 s is:
Δθ = ω₀t + 1/2 αt²
= (1.0 rad/s) (2.0 s) + 1/2 (4.5 rad/s²) (2)²
= 11 rad= 1.7507 rev
b. The angular speed at that time is:
ω = 2π/T
= (2 x 3.14) / 2
= 3.14 rad/s
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find the direction of the velocity vector of each of the following points, as viewed by a person at rest on the ground: (i) the highest point on the hoop; (ii) the lowest point on the hoop, (iii) a point on the right side of the hoop, midway between the top and the bottom.
(i) The velocity vector at the highest point on the hoop is 3.12 î, θ = 0°.
(ii) The velocity on the lowest point on the hoop is 0.
(iii) The velocity vector midway on the right is 1.56 î - 1.56 j, θ = -45°
Given that, Mass of the hoop is 2.2 kg
Hoop diameter D = 1.2 m
Hoop rotational speed ω = 2.6 rad/s
The velocity vectors as viewed by someone at rest on the ground are:
The tangential velocity vector of the top of the hoop is tangential to the top, therefore, it is in the direction of the hoop.
The magnitude of the velocity | v tant | = ω × r
| v tant | = 2.6 × 0.6 = 1.56
As the direction is in the positive x- direction, | v tant | = 1.56 î
The velocity due to translation of the hoop is v htr = 1.56 î
The velocity at the top v t = v tant + v htr = 3.12 î
The magnitude of velocity is 3.12 m/s, the direction is forward θ = 0°
(ii) The direction of velocity at the bottom is v tan b = - v tan t
v b = - v tan t + v htr = -1.56 +1.56 = 0
Thus, the velocity vector at the lowest point is 0.
(iii) The velocity midway between the top and the bottom of the hoop is given as follows:
The tangential velocity v tan m = 1.56 j
Sum of the velocity v m = 1.56 î - 1.56 j
The direction of velocity is given as tan⁻¹(-1.56/1.56) = -45°
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