The maximum height of the baseball, time is the ball in the air and vertical velocity when it hits the ground are 215.25ft, 6.543s and -117.4ft/s respectively.
What is velocity, exactly?The displacement that an object or particle undergoes with respect to time is characterized vectorially as velocity. The metre per second (m/s) is the recognised unit of velocity magnitude (also known as speed). Alternately, the quantity of velocity can be represented in centimetres per second (cm/s).
a=g= -32ft/s^2
vi = 92ft/s
vf= 0ft/s
vf=vi+axt
0= 92-32xt
t=> 2.875s
di = 83ft
vi = 92ft/s
a=g= -32ft/s^2
t=> 2.875s
d= 83+ 92x 2.875 -0.5 x 32 x (2.875^2)
=> 215.25ft.
B) 0 = 215.25 + 0xt - 0.5 x 32 x t^2
t=> 3.668s.
total time => 2.875 + 3.668s. => 6.543s.
c) vf=vi + axt
vi = 0
vf= -32x3.668 => =-117.4ft/s (falling down)
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The lowest note on a tuba has a frequency of 9. 18 Hz. Find its wavelength in air. Use v = 343 m/s
The wavelength of tuba note which having frequency of 9. 18 Hz and velocity 343 m/s is 37.36 m
What is a wave length?A waveform signal's wavelengths, which is the distance between two identical locations (consecutive crests) in successive cycles, determines whether it is sent through space or via a wire. For wavelength, a Greek letter λ is frequently used. In wireless systems, this length is often specified in meters (m), centimetre (cm), or millimetre (mm) (mm).
Given data -
frequency (f) = 9. 18 Hz
velocity (v) = 343 m/s
By using the relation -
v = f × λ
Where 'λ' is wavelength
λ = v / f
λ = 343 / 9.18
λ = 37.36 m
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the force of gravity on the average person is about 700 n at the earth's surface. calculate the gravity on a person 10 times that distance from the center of the earth
At the surface of the Earth, the gravitational force acting on a typical individual is roughly 700N. Determine the gravitational pull on a person at a distance 10 times that.
Why does gravity exist?All things having mass, including our Earth, really bend and curve spacetime, which is what causes gravity to pull you toward the ground. What you experience as gravity is that curvature.
What three types of gravity are there?Gravity only comes in one variety. In nature, there is only one form of gravity. According to their masses and the separation across their centers, there is only one kind of gravitational pull which draws the two bodies together. The least powerful central force is gravity.
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ai dan is rowing along a river in canada. he can row at 3 m/s against the current and at 6 m/s with the current. find the speed of the current.
If Aidan moves at a speed of x and the current moves at y, then x+y=6 and x-y=3 results in y=1.5m/s (and x=4.5m/s).
What does Mbps mean?Megabits per second, or Mbps, is the unit of measurement for internet speeds. A megabit is one million bits, which are very small data units. Your internet activity should run more quickly the more Gbps (megabits) you have.
How do I determine my WiFi speed?The Begins with a series by Ookla app, which is compatible with both iPhone and Android, is a solid, comprehensive software. Their mobile app can track both speeds of download and upload and document your speed tests, much like their web-based counterpart.
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what could cause some inaccuracies if you rolled the ball down the ramp 5 separate times, starting at the same location without adjusting the ramp?
The ball will move at a faster speed the steeper the angle of a slope it is rolling down. The ball will travel farther and faster the more mass it has.
By mass, what do you mean?
It is the most fundamental characteristic of matter and one of the most essential variables in physics. Mass is a term used to describe how much matter is there in a body. The kilogramme is the SI mass unit (kg). A body's mass does not alter at any point in time.
What is the mass unit?
kilogramme (kg) Glossary: Units of mass (weight). The mass units used by the metric measurements of measuring are the gramme (g), kilogramme (kg), and tonne (t).
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discuss with your partner how you will test each claim and answer the questions below. claim a: more potential energy can be stored by moving against the magnetic force of a stronger magnet. which variable will you test and which variable(s) will you keep the same? claim b: more potential energy can be stored by moving against the magnetic force closer to a magnet. which variable will you test and which variable(s) will you keep the same? how will you measure the effect of each variable?
Thus, the claim is correct that there is more potential energy that can be stored by moving against the magnetic force of a stronger magnet.
What is called magnetic?Magnetism is the force exerted by magnets when they attract or repel each other. Magnetism is caused by the motion of electric charges. Every substance is made up of tiny units called atoms. Each atom has electrons, particles that carry electric charges.
Who invented magnet?The ancient Greeks were the first known to have used this mineral, which they called a magnet because of its ability to attract other pieces of the same material and iron. The Englishman William Gilbert (1540-1603) was the first to investigate the phenomenon of magnetism systematically using scientific methods.
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a golf club exerts an average horizontal force of 1000 n on a 0.045-kg golf ball that is initially at rest on the tee. the club is in contact with the ball for 0.0018 s. what is the speed of the golf ball just as it leaves the tee?
The speed of the golf ball just as it leaves the tee is 40 m/s.
The force applied over a period of time is equal to the change in momentum of the ball. Thus, the initial momentum of the ball is 0 and the final momentum is equal to the force multiplied by the time.
Final Momentum = Force x Time
Final Momentum = 1000 N x 0.0018 s
Final Momentum = 1.8 kg m/s
What is momentum?
Momentum is the product of an object's mass and its velocity. It is a measure of an object's tendency to remain in motion, and is represented by the equation p = mv, where p is the momentum, m is the mass and v is the velocity.
Since momentum is equal to mass times velocity, we can calculate the velocity of the ball as it leaves the tee by dividing the final momentum (1.8 kg m/s) by the mass of the ball (0.045 kg):
Velocity = Final Momentum / Mass
Velocity = 1.8 kg m/s / 0.045 kg
Velocity = 40 m/s
Therefore, The speed of the golf ball just as it leaves the tee is 40 m/s.
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A mother has four times the mass of her young son. Both are running with the same kinetic energy. What is the ratio of their speeds?Kinetic energyThe kinetic energy K of a body with mass m and speed v isK=12 mv^2
The ratio of the mother's speed to the son's speed is equal to 0.5.
Kinetic energy is defined as K = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. Since both the mother and her son have the same kinetic energy, we can write:
1/2 * m_mother * v_mother^2 = 1/2 * m_son * v_son^2
Since the mother has four times the mass of her son, we can substitute:
m_mother = 4 * m_son
We can substitute this into the equation:
1/2 * 4 * m_son * v_mother^2 = 1/2 * m_son * v_son^2
We can then divide both sides by 1/2 * m_son to get:
4 * v_mother^2 = v_son^2
We can then take the square root of both sides:
v_mother * sqrt(4)= v_son
v_son=0.5
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Two parallel wires in free space are 10 cm apart and carry currents of 10 A each in the same direction. The force each wire exerts on the other per meter of length is
a) 2 * 10-4 N, repulsive
b) 2 * 10-7 N, attractive
c) 2 * 10-7 N, repulsive
d) 2 * 10-4 N, attractive
The current in both wires is in the same direction, and the force is attractive, so the answer is option B
The force each wire exerts on the other per meter of length is given by the equation:
[tex]F = (mu_0 * I1 * I2) / (2 * pi * d)[/tex]
where mu_0 is the permeability of free space (approximately[tex]4 * pi * 10^-7 T*m/A)[/tex], I1 and I2 are the current in each wire (10 A each), and d is the distance between the wires (10 cm or 0.1 m).
Plugging in these values, we get:
[tex]F = (4 * pi * 10^-7 * 10 * 10) / (2 * pi * 0.1)F = 2 * 10^-7 N[/tex]
Since the current in both wires is in the same direction, the force is attractive, so the answer is
b) [tex]2 * 10^-7 N[/tex], attractive
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the star vega has an average surface temperature of 10,000 k and has a luminosity 70 times greater than that of the sun. which type of star is vega
The absolute visual magnitudes of supergiants range from -3 to -8. Supergiant stars have a temperature range of from 3,450 K to 20,000 K. Supergiant stars can be 10 to 70 times more massive.
What is a magnitude example?
The magnitude of something refers to its magnitude. For instance, a car is travelling more quickly than a bike in terms of speed. The speed difference between the car and the bike in this case is greater. It reveals the absolute or relative size or direction that an object moves when in motion.
How do you define instrumental magnitude?
The visual size of a celestial body as measured by an instrument Magnitude (astronomy), a metric for determining brightness and brightness variations,
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A projectile is launched at an angle of 15 degrees above the horizontal and lands down range. For the same speed, what other projection angle would produce the same downrange distance
For the same speed, and for the maximum downrange distance the angle would be 45°. If the projectile is launched at an angle of 15° above the horizontal.
If the initial velocity of the launched projectile = u
Horizontal component of the u, = ucosθ
Vertical component of the u, = usinθ
Horizontal downrange, R = ucosθ×T
T = usinθ/g
R = ucosθ × usinθ/g
R = u²sin(2θ)/(2g)
R = 0.25u²/g
For maximum value of the downrange sin(2θ) should be 1, or 2θ = 90°
θ = 45°
So the maximum downrange distance would be = u²sin(90)/(2g)
= u²/(2g)
= 0.5u²/g
It is double the distance of the projectile angle 15°.
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A boy of mass 60 kg grams up a set of stair of total in 3metre work done in joule(take g 10ms )
A boy of mass 60 kg grams up a set of stair of total in 3 metre work done in joule is 1800 J.
Option B is correct.
Evaluating the problem:Given: Mass of the boy, m = 60 kg
Total height of steps, h = 3 m
Acceleration due to gravity, g = 10 m/s²
➜ Work done = force × displacement
➜ Force = mass × acceleration
Acceleration due to gravity, g is 10 m/s².
∴ Force = mass × acceleration due to gravity
➜ Work done = mass × acceleration due to gravity × displacement
A/C to given problem, boy runs up a set of steps of total height 3 m hence displacement is 3m.
➜ Work done = 60 × 10 × 3
➜ Work done = 600 × 3
➜ Work done = 1800 Joule
What counts as completed work?A force's work is the sum of the object's applied force in the direction of the displacement and the object's displacement. The body moves with some acceleration when we push a block with some force, and the work is finished.
What does it mean to have completed work?An object should be transformed into energy in order to move. The use of force can be used to transfer energy. Work done refers to the amount of energy transferred by force to move an object.
How does one determine the amount of work completed?W=Fs is used to calculate the amount of work done on an object when it is moved x distances by a force F. We add a minus sign if the force is in the opposite direction of the object's movement.
Question incomplete:A boy of mass 60 kg grams up a set of stair of total in 3 metre work done in joule(take g 10ms ).
A. 1500 J
B. 1800 J
C. 2500 J
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if you push a boulder off a cliff and it falls 300 feet smashing a car below, what was the activation energy?
The stored potential energy is converted into activation energy of boulder when fall off from the 300 ft cliff.
How do mass and height affect potential energy?The force exerted on the two materials impacts the potential energy equation. The formula for gravitational force is P.E. = mgh, where g is the acceleration caused by gravity (9.8 m/s2 at the earth's surface) and h is the height in metres.
Potential stored in the car = mgh
= mass of boulderx 9.8 x 300ft
=> Kinetic activation of energy
What causes potential energy to rise with height?Since the greatest proportion of energy that can be transformed into other forms is called potential energy. In order to move the object at a higher altitude, more energy is needed. Therefore, potential energy grows along with height.
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an electrical grid system connects electricity producers with electricity consumers. the network allows electricity to flow where it is needed, when it is needed.what effect does energy efficiency have on the electrical grid?
The electrical grid is affected by energy efficiency. Generators don't need to produce as much electricity when individuals use electricity more effectively. There isn't an overload on the electrical grid.
Blackouts may occur if the electrical grid is overburdened because it may overheat and malfunction.
In geographically focused locations, energy efficiency is a particularly significant resource for reducing grid loads and system peak demands. Reducing peak demands helps the system and can reduce the need to generate or buy expensive electricity.
In geographically focused locations, energy efficiency is a particularly significant resource for reducing grid loads and system peak demands. Reducing peak demands helps the system and can reduce the need to generate or buy expensive electricity.
Distribution networks transport electricity from the transmission system to homes and businesses at lower voltages. National Grid, which manages the transmission system, is in charge of balancing it and ensuring that the supply and demand of power are met second by second.
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a box starts from rest and slides 40 m down a frictionless inclined plane. the total vertical displacement of the box is 20 m. how long does it take for the block to reach the end of the plane?
The block must travel 40 meters per second in order to reach the tip of the plane.
With one example, define distance in physics.The entire journey that an object has taken can be used to define distance. The entire distance travelled by a car, for instance, would be 13 km if it traveled 5 km east, 8 km north, and back again.
What is the distance known as?A scalar quantity known as distance measures how much land an object has traversed while moving. An object's total change in position is referred to as displacement, a vector variable that measures how far out of line an object is.
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A microwave transmitter emits electromag-
netic waves of a single wavelength. The max-
imum electric field 0.963 km from the trans-
mitter is 8.04 V/m.
The speed of light is 2.99792 x 108 m/s
and the permeability of free space is 47 x
10-7 N/A².
a)Assuming that the transmitter is a point
source and neglecting waves reflected from
the Earth, calculate the maximum magnetic
field at this distance.
Answer in units of T.
b)Calculate the total power emitted by the
transmitter.
Answer in units of W.
determine the ratio of rotational kinetic energy to linear kinetic energy for a solid sphere of mass m and radius r that is rolling along a horizontal surface without slipping at a linear velocity v. group of answer choices 2/5 1/4 1/2 1/1
a solid sphere with mass m and radius, calculate the rotating angular momentum to linear angular momentum ratio. So, the aforementioned strategy is appropriate. = 2.4 J
What else could you use to describe determine?Determine has a number of popular synonyms, including resolve, decide, rule, and settle. All of these phrases refer to "coming to or causing to come to conclusions," but the word "determine" refers to settling on something's identity, style, scope, or direction. identified the issue's root source.
Calculation
Kinetic energy
According to the question,
Total Kinetic energy, KE' = 8.4 J
Mass, m = 3 kg
Center of mass's velocity, v = 2 m/s
Now,
KE(trans) = mv²
By substituting the values,
= × 3 × (2)²
= × 3 × 4
= 6 kgm³/s² or,
= 6 J
We know the relation,
→ KE(rot) = KE(total) - KE(trans)
By putting the values,
= 8.4 - 6
= 2.4 J
Thus the approach above is correct.
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A. Consider the time when the ball is at location 2. Which of the above vectors matches the direction of the velocity?B. Consider the time when the ball is at location 2. Which of the above vectors matches the direction of the acceleration?C. Consider the time when the ball is at location 6. Which of the above vectors matches the direction of the velocity?D. Consider the time when the ball is at location 6. Which of the above vectors matches the direction of the acceleration?E. Consider the time when the ball is at location 10. Which of the above vectors matches the direction of the velocity?F. Consider the time when the ball is at location 10. Which of the above vectors matches the direction of the acceleration?
A. Vector B matches the direction of velocity at location 2 (downward)
B. Vector A matches the direction of acceleration at location 2 (upward)
C. Vector B matches the direction of velocity at location 6 (downward)
D. Vector A matches the direction of acceleration at location 6 (upward)
E. Vector A matches the direction of velocity at location 10 (upward)
F. Vector C matches the direction of acceleration at location 10 (zero). At this location, the ball is in freefall, its acceleration is equal to gravity and its velocity is constant, so the acceleration is zero.
Why does the force of gravity change the speed of a satellite in an elliptical orbit?
a. The force of gravity is always perpendicular to the satellite motion.
b. Gravity slows the satellite as it moves away and speeds it up on its return.
c. Gravity speeds up the satellite as it moves away and slows it on its return.
d. The force of gravity is always tangent to the satellite motion.
The force of gravity change the speed of a satellite in an elliptical orbit by b. gravity slows the satellite as it moves away and speeds it up on its return so option b is the correct answer.
A satellite in an elliptical orbit, does the gravitational field affect its speed?Due to a component of the gravitational force acting in the satellite's motion's direction, the gravitational force affects the speed of a satellite in elliptical orbit.
Depending on how far from the Sun it is, a planet's orbital speed varies. A planet moves more quickly and is gravitationally more strongly pulled toward the Sun as it gets closer to the star. It moves more slowly in its orbit the further it is from the Sun because of the Sun's weaker gravitational pull.
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negative charges are accelerated by electric fields toward points (a) at lower electrical potential (b) at higher electrical potential (c) where the electric field is zero (d) where the electric field is weaker (e) where the electric field is stronger
Electric fields will push negative charges in the direction of places with higher electrical potential.
What does it mean to have an electric potential?Against an electric field, the amount of labor required to transport a unit charge from one location to another is known as electric potential. Although any location beyond the range of the applied electric charge can be used, Earth is typically selected as the reference point. power potential.
What are voltage and potential in an electric field?The external effort required to move a charge from one position to another in an electric field is known as an electric potential difference, or voltage. A test charge that has an electric potential differential of +1 will experience a shift in potential energy.
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the weight of an object on the moon is one-sixth of its weight on the earth. the ratio of the kinetic energy of a body on the earth moving with speed v to that of the same body moving with speed v on the moon is?
Mass of the body is same on Earth and Moon. `K.E = 1/2 mv^2` . So, both scenarios are the same.
What does angular momentum mean exactly?Kinetic energy is the life force an item gains as a result of motion. To accelerate an object, a power must be supplied to it. To apply a force, we must put more effort. Energy is transferred to the object when the work is complete, which causes it to move at a new, constant pace.
A kinetic example is what?Every moving object or particle contains kinetic energy. A person walking, a baseball flying in the air, foods falling from a table, and charged particles in an electric potential were all utilized as examples of kinetic energy in action.
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when you used a stiffer or tighter elastic material, what effect did this have on the duration of the impulse? what effect did this have on the maximum size of the force? can you develop a general rule from these observations?
The use of a stiffer or tighter elastic material caused the duration of the impulse to be shorter, making the maximum force larger.
The general rule that can be formed would be that the shorter the time, the larger the force is to achieve the same impulse.
We can define it by impulse- momentum theorem.
Ft = mΔv( also, Ft = impulse)
F = mΔv/ t
Impulse is commensurable to the constant net force acting on an object and the time period that the net force acts.
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if a curve with a radius of 98 m is properly banked for a car traveling 68 km/h , what must be the coefficient of static friction for a car not to skid when traveling at 93 km/h ?
Thus, the coefficient of static friction for a car not to skid when travelling at 95 km/h is 0.32.
What is Centripetal force?
A centripetal force is a force that is delivered to a curved object and is directed toward the axis of rotation or the centre of curvature.
Centripetal force is measured in Newtons.
The centripetal force always acts in a direction that is opposite to the direction in which the object is travelling. Using Newton's second rule of motion, it is established that the centripetal force of an object moving in a circular path always acts in the direction of the circle's centre.
According to the Centripetal Force Formula, the centripetal force is calculated as the square of the radius and the product of the mass (in kg) and tangential velocity (in m/s) (in metres). According to this calculation, the tangential force will increase by twice as much as the centripetal force.
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calculate the de broglie wavelength of an electron accelerated from rest in an electric potential of 1.0 mv. how would the resolution of an electron microscope that uses this source differ from the em discussed in example 9.1?
The de Broglie wavelength of an electron accelerated from rest in an electric potential of 1.0 mV is 1.24 x 10⁻¹¹ m. This resolution is lower than the electron microscope discussed in example 9.1.
What is electron?Electron is a subatomic particle that carries a negative charge and is a fundamental building block of matter. Electrons are found in atoms and are responsible for chemical bonding and electrical conductivity. Electrons also interact with other particles to form a variety of forces, such as the electromagnetic force and the weak force.
Electrons are the particles responsible for the flow of electricity, and are a major factor in the structure of atoms, molecules, and solids. Electron’s mass is approximately equal to one-thousandth of the mass of a proton, and is the lightest of the known particles.
Momentum of accelerated electron is given by:
p = [tex]\sqrt{2mE}[/tex]
Here, E = 1.0 mv
m = 9.1 × 10⁻³¹ kg
p = [tex]\sqrt{2(9.1 \times 10^{-31})(1.0)}[/tex]
p = 1.3 × 10⁻¹⁵ kg·ms²
de-broglie's equation is
λ = h/p
where,
λ=Wavelength of moving particle.
P=Momentum of moving particle.
h=Planck's constant = 6.63 × 10⁻³ Js
λ = 6.63 × 10⁻³/1.3 × 10⁻¹⁵
λ = 1.24 x 10⁻¹¹ m
Thus, The de Broglie wavelength of an electron accelerated from rest in an electric potential of 1.0 mV is 1.24 x 10⁻¹¹ m.
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Give the key distinction in the eigenvalue spectrum of an operator defined over a finite domain (a confined system) compared to the spectrum of an operator defined over an infinite domain (an unconfined system)
The set of scalars that make up a finite-dimensional vector space's spectrum are those that cannot be inverted. The matrix's determinant is equal to the sum of its eigenvalues.
What do you name the spectrum?All of the electromagnetic energy present in the cosmos is collectively referred to as the electromagnetic spectrum, and EM spectrum. This kind of energy permeates the cosmos as magnetic and electric waves, enabling the exchange of energy & information.
What do you understand when you say "light spectrum"?When white light travels through a prism & separates into its individual colors, it creates a band of colors that may be seen on a screen. The colors of a spectrum are red, blue, green, yellow, orange, and indigo violet.
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imagine a system composed of two different types of molecules, one much heavier than the other. at a particular temperature, how do their average kinetic energies compare? which, on average, is moving faster?
Temperature: Higher temperatures lead to more energy and, as a result, more molecular movement and diffusion.
Why do lighter particles go more quickly than heavier ones?
The particles gather kinetic energy and accelerate as the temperature rises. The actual average speed of the particles is influenced by both their mass and temperature; at a given temperature, larger particles travel more slowly than lighter ones.
In what system do molecules have the same mean kinetic energy?
There are no interactions between gas molecules (no attraction or repulsion). For all gases at a specific temperature, the average gas kinetic energy is the same.
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a motor drives a shaft of radius r/8 that is attached to the center of a wheel of radius r. the motor is turned off, and the force that the motor exerts on the shaft, fmotor, varies with time, as shown. there is also a constant friction force of 0.4n applied to the rim of the wheel in the opposite direction of the motion. during which time interval does the rotational kinetic energy increase and then decrease?
The time interval where the rotational kinetic energy increases is when fmotor is greater than 0.4n and decreases is when fmotor is less than 0.4n.
What is rotational kinetic energy?
Rotational kinetic energy is the kinetic energy associated with the rotation of an object. It is equal to the work done in rotating an object (a moment of force multiplied by the angular displacement) and is equal to one-half the moment of inertia of the object multiplied by the angular velocity squared.
The rotational kinetic energy of the wheel is given by the equation:
K.E. = 1/2 Iω2
where I is the moment of inertia and ω is the angular velocity.
The moment of inertia is given by I = mr2, where m is the mass of the wheel and r is the radius of the wheel.
The angular velocity is given by ω = v/r, where v is the linear velocity of the wheel.
The linear velocity of the wheel is given by v = 2πfr, where f is the frequency of rotation.
The frequency of rotation is given by f = (fmotor - 0.4n)/(2πr).
The rotational kinetic energy can therefore be written as:
K.E. = 1/2 m(2πfr)2r2
Time interval where the rotational kinetic energy increases:
The rotational kinetic energy increases when the linear velocity of the wheel (v) increases. This happens when the frequency of rotation (f) increases. This is when fmotor is greater than 0.4n.
Hence, the time interval where the rotational kinetic energy increases is when fmotor is greater than 0.4n.
Time interval where the rotational kinetic energy decreases:
The rotational kinetic energy decreases when the linear velocity of the wheel (v) decreases. This happens when the frequency of rotation (f) decreases. This is when fmotor is less than 0.4n.
hence, the time interval where the rotational kinetic energy decreases is when fmotor is less than 0.4n.
Therefore, The time interval where the rotational kinetic energy increases is when fmotor is greater than 0.4n and decreases is when fmotor is less than 0.4n.
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What were the main stages of the space race (USA/USSR)? I am looking for around 6-8 but i don’t want to miss anything out, so you can go over this. Also, please include anything extra you think is necessary.
The first collaborative Apollo-Soyuz mission is launched as US-USSR tensions ease on 15th July 1975. This is the final stage of the space race.
What is space race?The Soviet Union (USSR) and the United States competed in the Space Race during the 20th century (US). Both were vying for control of space flight technologies. When the Soviet Union responded to the US' disclosure of its intention to launch artificial satellites on August 2, 1955, the competition officially began.
German missile technology and scientists from their missile program were helpful to both sides. The Space Race resulted in ground-breaking attempts to launch artificial satellites, as well as lunar missions and human spaceflights to the Moon, Venus, and Mars.
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A ball of mass 500 g is dropped from rest from a height of 7 m. what is its speed as it reaches the ground? (g = 9.8 m/s2)
The speed of the ball when it reaches the ground is 11.71 m/s, when the mass of the ball is 500g and height is 7m.
What is mass?The best way to define mass is the quantity of matter that constitutes an object or body. Every object in our environment is made of mass. Even air has mass, as do a table, a chair, your bed, a football, a glass, and so on. Having said that, whether an object is light or heavy depends on its mass.
The most fundamental characteristic of matter is its mass, which is also one of the fundamental quantities in this physics lesson. The term "mass" refers to a body's total amount of matter. The kilogramme, which is the SI unit of mass, is the kilogramme (kg).
the final velocity is the speed of the ball when it reaches the ground
i.e.
v²-u² =2as
v²-(0)² = 2(9.8)(7)
v²- 0 = 137.2
v = √137.2
v = 11.71
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newton's law of gravitation states that two bodies with mass m1 and m2 attract each other with a force where r is the distance between the bodies and G is the gravitation constant if one of the bodies is fixed
If any one of the entities is stationary, then the provided statement states that the necessary labour is W = Gm₁m₂(1/a-1/b)
How is gravity explained?The force of gravity, often known as gravitation, affects every material thing in the universe. The gravitational attraction tends to draw any different items or particles with nonzero mass toward one another. Through subatomic particles to galaxy clusters, gravity affects things of all sizes.
According to Newton's Law of Gravitation, two bodies with masses m1, m2 are attracted to one another by a force. [tex]F(r)=G \frac{m_1 m_2}{r^2}[/tex]
The bodies are separated from one another by r, and G is the gravitational constant. The needed work to move one of the bodies from r = to the a r = b is, if the other body bodies is fixed.
[tex]\begin{aligned}W & =\int_{r=a}^b F(r) d r \\& =\int_{r=a}^b\left(G \frac{m_1 m_2}{r^2}\right) d r \\& =G m_1 m_2 \int_{r=a}^b\left(\frac{1}{r^2}\right) d r \\& =G m_1 m_2\left[-\frac{1}{r}\right]_a^b \\& =G m_1 m_2\left[-\frac{1}{b}-\left(-\frac{1}{a}\right)\right] \\& =G m_1 m_2\left(\frac{1}{a}-\frac{1}{b}\right)\end{aligned}[/tex]
The needed work is thus W = [tex]G m_1 m_2\left(\frac{1}{a}-\frac{1}{b}\right)[/tex]
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The complete question is-
Newton's law of gravitation states that two bodies with mass m1 and m2 attract each other with a force [tex]F=G \frac{m_1 m_2}{r^2}[/tex] where r is the distance between the bodies and G is the gravitation constant if one of the bodies is fixed, find the work needed to move the other from r = a to r = b.
Suppose you have a tug of war with a friend who is the same size and weight as you are. You both pull as hard as you can, but neither of you seems to be winning. You move a little one way or the other, but mostly you are just at rest (although sweating some). Compare the magnitude of the force exerted by you on your friend, with the magnitude of the force exerted by your friend on you. Are they the same or different? If they are not the same, which is larger? Why or why not? b. Now you have a tug of war with your kid brother (who is much smaller and lighter than you). Again you both pull hard but end in a standoff with neither of you moving much. In this situation compare the magnitude of the force you exert on your brother with the magnitude of the force he exerts on you. Are they the same or different? If they are not the same, which is larger? Why or why not? c. The next tug of war is still with your kid brother but he is now standing on his skateboard. You can now make him roll across the floor (with a constant speed) when you pull hard. In this situation compare the magnitude of the force you exert on your brother with the magnitude of the force he exerts on you. Are they the same or different? If they are not the same, which is larger? Why or why not? 2.
The changes in magnitude are stated below.
What is magnitude?
The magnitude of a physical quantity is the numerical value of that quantity, without any regard to its direction. It is a scalar quantity. The magnitude of a vector can be obtained by the application of the Pythagorean theorem to its rectangular components. For example, the magnitude of a velocity vector can be found by taking the square root of the sum of the squares of its x, y, and z components.
a. In a tug of war with a friend who is the same size and weight as you, the magnitude of the force exerted by you on your friend is the same as the magnitude of the force exerted by your friend on you. This is due to the principle of action and reaction, also known as Newton's Third Law, which states that for every action, there is an equal and opposite reaction. In this case, the force you exert on your friend is equal in magnitude but opposite in direction to the force your friend exerts on you. This is why neither of you is able to move the other, as the forces are in balance.
b. In a tug of war with your kid brother, who is much smaller and lighter than you, the magnitude of the force you exert on your brother is likely to be larger than the magnitude of the force he exerts on you. This is because your brother's smaller size and weight means that he generates less force when pulling on the rope. However, the forces are still in balance, as per Newton's Third Law.
c. In a tug of war with your kid brother on his skateboard, the magnitude of the force you exert on your brother is the same as the magnitude of the force he exerts on you, as per Newton's Third Law. However, the force you exert on your brother causes him to move across the floor with a constant speed, while your brother's force on you does not cause you to move. This is because the skateboard provides a frictionless surface for your brother to move on and he accelerates.
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