The maximum height H to which she rises above the end of the track that is slanted upward by 48° above the horizontal at its end is 1.11 m
KE = 1 / 2 m v²
PE = m g h
According to law of conservation of energy,
KE ( Initial ) + PE ( Initial ) = KE ( Final ) + PE ( Final )
h ( Initial ) = 0
v ( Initial ) = 6.9 m / s
g = 9.8 m / s²
h = 0.4 m
1 / 2 m vi² + m g hi = 1 / 2 m v² + m g h
1 / 2 m vi² = 1 / 2 m v² + m g h
vi² = v² + 2 g h
6.9² = v² + ( 2 * 9.8 * 0.4 )
v² = 47.61 - 7.84
v² = 39.77 m / s
H = vi² sin²θ / 2 g
θ = 48°
H = 39.77 * sin²48° / ( 2 * 9.8 )
H = 21.78 / 19.6
H = 1.11 m
Therefore, the maximum height H to which she rises above the end of the track is 1.11 m
The given question is incomplete. The complete question is;
The drawing shows a skateboarder moving at 6.9 m/s along a horizontal section of a track that is slanted upward by 48° above the horizontal at its end, which is 0.40 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
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part k what is the magnitude of e at the point (0.50 m , 0.50 m , 0.50 m )? express your answer with the appropriate units.
The values constants magnitude are A=-6 MathrmV cdot m-2 A=6 Vm. B = 4 mathrm V cdot m 3, B = 4 mathrm V m 3, C = 2 V m 6, C = -2 V cdot m 6, l = 2 mathrm V m 6, m = 3 mathrm V m 3, and n = 6 mathrm V n = 6.
How would you define magnitude?Magnitude is simply "distance or quantity" in the context of physics. In terms of motion, it shows the absolute or relative size, direction, or movement of an object. It is used to describe something's size or scope. Magnitude in physics typically refers to a size or quantity.
What does force magnitude mean in physics?The amount that encapsulates the force's strength is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude can be thought of as simply the "value" or "amount" of any physical quantity.
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You can have refraction without dispersion, but you cannot have dispersion without refraction. Explain why
Answer:
Explanation:
Because dispersion is a property of refraction. A refractive medium is non-dispersive when waves of all frequencies pass at the same speed, otherwise there is a dispersion that is causing a distortion of waveforms.
the phase velocity of each wavelength of white light moving through ordinary glass is a function of the wavelength; that is, glass is a dispersive medium. what is the general dependence of vp on l in glass? is dvp>d l positive or negative?
The general dependence of phase velocity on glass can be expressed as vₓ = v₀(1 + 2B/nλ²) and it is positive.
What is phase velocity?The phase velocity of a wave is the speed at which the wave propagates through any medium. This is the speed at which the phase of any frequency component of the wave propagates. For such a component, arbitrary phases of the wave appear to travel with phase velocity.
For glass we know that, n = A + B/λ²
vₓ = v₀ - λ(dv₀/dλ)
Where, vₓ = velocity of light in glass
v₀ = phase velocity
λ = wavelength
vₓ = v₀ - λ(dv₀/dn × dn/dλ)
= v₀ - λ (-c/n²) dn/dλ
= v₀+v₀ (λ/n × dn/dλ)
Now,
dn/dλ = d(A + B/λ²)/dλ
= -2B/λ³ which is negative
vₓ = v₀ - v₀ (λ/n) (-2B/λ³)
vₓ = v₀(1 + 2B/nλ²)
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An ant travels 50.0 cm East, then turns 35 degrees North of East and moves for 40.0 cm. It then turns and moves another 30 cm North. What is the ant's total displacement (magnitude and direction)?
Please help :) I will also post questions similar to this so if you know how to solve them go ahead and look :)
The magnitude of ant's total displacement is 96.23 cm in a direction 41 degrees North of East.
What is the total displacement of the ant?The total displacement of the is obtained by resolving the displacement of the ant into x and y components as shown below.
horizontal displacement (x) = d cosθ
vertical displacement (y) = d sinθ
where;
θ is the direction of the displacementd is the magnitude of the displacementFirst displacement at 50 cm East; (θ = 0⁰)
x = 50 cm x cos(0) = 50 cm
y = 50 cm x sin(0) = 0
second displacement at 40 cm at 35 degrees North of East;
(θ = 90⁰ - 35⁰ = 55⁰)
x = 40 cm x cos(55) = 22.94 cm
y = 40 cm x sin(55) = 32.77 cm
third displacement at 30 cm North; (θ = 90⁰)
x = 30 cm x cos(90) = 0
y = 30 cm x sin(90) = 30 cm
Net horizontal displacement;
∑x = 50 cm + 22.94 cm + 0 = 72.94 cm
Net vertical displacement;
∑y = 0cm + 32.77 cm + 30 cm = 62.77 cm
The total displacement is calculated as;
D = √[ (∑x)² + (∑y)² ]
D = √[ (72.94)² + (62.77)² ]
D = 96.23 cm
The direction of the total displacement;
θ = arc tan (Σy/Σx)
θ = arc tan (62.77/72.94)
θ = 40.7⁰ ≈ 41⁰
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name one advantage of the moment magnitude scale, and one disadvantage of the moment magnitude scale.
The main advantage why the moment magnitude scale is the most dependable approach to calculating the relative length of huge earthquakes
It is that its underlying calculation technique avoids the trouble of significance saturation because it's far based on measurements of an earthquake's overall power earthquake.
Mainly, for very big earthquakes, moment importance offers the most dependable estimate of earthquake length. the moment is a bodily quantity proportional to the slip at the fault expanded by using the place of the fault floor that slips; it is related to the full strength launched in the earthquake.
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which of the following would be the closest estimate to the number of times the sun has orbited the galactic center?
The closest estimate to the one times the sun has orbited the galactic center.
The Milky Way galaxy's rotational and barycenters are located at the Galactic Center . The Sagittarius A supermassive black hole, a compact radio source that is almost exactly at the galactic rotational center, is the object's central massive object. It has a mass of about 4 million solar masses. The Galactic Center is frequently referred to as a type of "cosmic homing signal" by astrologers. Far away on one of the spiraling arms of the galaxy, it is the hub around which our tiny solar system slowly revolves. It is enormous and unknowable. Whatever process produced the Milky Way is represented by the GC. The most difficult conditions for star formation can be found in the Galactic Center, which has more than 80% of the Milky Way Galaxy's dense molecular gas, high temperatures, significant turbulence, complex magnetic fields, and a powerful gravitational potential well.
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how do scientists predict the location of electrons in the modern model of the atom
Answer:
Scientists predict the location of electrons in the modern model of the atom by using the Heisenberg uncertainty principle.
Look at the diagram below. What is the total resistance of the resistors in this circuit?
The total resistance of the resistors in the circuit from the diagram is 20 Ω.
What is resistance?Resistance is a measure of the opposition to current flow in an electrical circuit.
To calculate the total resistance of the resistors in parallel, we use the formula below.
Note: Both resistors are connected in series.
Formula:
For series connection
R = R₁+R₂................ Equation 1Where:
R = Total resistance of the resistor in the circuit.From the diagram,
Given:
R₁ = 10 ΩR₂ = 10 ΩSubstitute these values into equation 1
R = 10+10R = 20 ΩHence, the total resistance is 20 Ω.
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Question 2
A car traveling at 114 km/h slows at a rate of 3 m/s² for 2.6 seconds. How far does the car move?
The car travels a distance of 72.202 m
What do you mean by deceleration?
Deceleration is a specific instance of acceleration that only applies to moving objects. Consequently, it is the rate of object slowing down.
It is a vector quantity is deceleration.The opposite of acceleration is deceleration.Its symbol is -a, where a stands for acceleration.Simply applying Galileo's equation, which accounts for both linear acceleration and deceleration equally if the deceleration is constant, the distance covered in deceleration is given by the formula:-
s = ut + ½at²
where
s represents the whole distance traveled during time t.
u is the object's speed when t is equal to 0.
a is the acceleration. If the object is speeding up, the value is positive; if it is slowing down, the value is negative.
Given in the question,
Velocity, u = 114 km/h
= 114 x 1000/ 60 x 60
= 31.67 m/s
Deceleration, -a = 3 m/s²
s = ut + ½at²
= 31.67 x 2.6 - 3 x 2.6 x 2.6/2
= 82.342 - 10.14
= 72.202 m
Hence, The car travels a distance of 72.202 m
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a movie stunt driver on a motorcycle drives off a 47.7-m tall cliff, in a horizontal direction. how fast is the motorcycle going at an instant that it leaves the cliff, if it lands on level ground below, 62.9 meters from the base of the cliff? answer to one decimal place.
Fast V=13.6 m/s is the motorcycle going at an instant that it leaves the cliff, if it lands on level ground below, 62.9 meters from the base of the cliff in projectile motion.
v=?
V1=0
a1=0
a2=-g
d1=47.7
d2=62
62=o*T-1/2gT²
T=3.5sec
47.7=vT
47.7=v*3.5
v=13.6 m/s
A projectile motion is a type of motion that an object or particle experiences when it is launched into a Gravity , such as from the surface of the Earth, and moves along a curved path only under the influence of gravity. The motion of an object being projected or thrown into the air is known as projectile motion, and it is only affected by the acceleration of gravity. Projectile and trajectory both refer to the same thing: an object. Any object that is launched into space and has only gravity acting on it is considered a projectile. Gravity is the main force at work when a projectile is launched. A projectile is an object that is launched or projected into the air and is only subject to the acceleration of gravity. Projectile and trajectory both refer to the same thing: an object.
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write short notes one effect of friction on efficiency of machine
Answer:
Friction reduces efficiency because when two surfaces slide past each other, friction resists their motion, and in real machines, some input work is always used to overcome friction.
Please give the brainliest.
A 15.5kg block is dragged horizontally at a constant force of 167 N at an angle of 27.8 above the horizontal. The block is displaced at 59m, and the coefficient of kinetic friction is 0.232. Acceleration is 9.8 m/s^2. Find the work done by 167 N. Answer in units of J.
The work done by the constant force of 167 N, given that the block is displaced at 59 m is 8715.97 J
How do I determine the work done?We know that work done is defined as:
Work done (Wd) = force (F) × distance (d)
Wd = fd
Since angle projection is involved, the work done is defined as:
Wd = FdCosθ
With the above formula, we can detertmine the work done as illustrated follow:
Force (F) = 167 NAngle (θ) = 27.8 degreesDistance (d) = 59 mWorkdone (Wd) =?Wd = FdCosθ
Wd = 167 × 59 × Cos 27.8
Wd = 9853 × 0.8846
Wd = 8715.97 J
Therefore, we can conclude from the calculation made above that the work done is 8715.97 J
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One of the tallest buildings in the world is the taipei 101 in taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15. 5°c. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that the taipei 101 is 0. 471 foot taller than its official height. What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel?.
Since a bar of length L₀ with a thermal expansion coefficient would experience a length fluctuation ΔL when the temperature changes ΔT, the equation of linear thermal expansion ΔL = ∝LΔT must be used.
The linear thermal expansion equation tells us that a ΔT = (ΔL/∝L₀) = 22.14° based on the following values: ΔL = 0.481 foot, L₀ = 1671 feet, and ∝ = 0.000013 per centigrade degree (this is simply the linear thermal expansion of steel that must be found in a table). As previously stated, these degrees are centigrades (Celsius or Kelvin, it makes no difference as this is merely a variation), and the foot units cancel on the equation, demonstrating that no additional conversion was required.
Our new temperature must be T = T₀ + ΔT = 35.14°C because our last reading on a chilly spring day was 13.0°C.
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at what velocity will the peak voltage of a generator be 450 v, if its 565-turn, 8.00-cm diameter coil rotates in a 0.250-t field?
The calculated velocity is 7295 rpm. Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path.
According to Faraday's law of induction, an induced electromotive force is produced when a magnet rotates inside a coil. Alternatively said, mechanical energy is changed into electrical energy. Electrical generators are built on the principles of this physical phenomenon. Let's calculate the coil cross section's area A.
A=π 4 d 2 \s= 5.0265 × 10 − 3 m2
Step 2
The following equation describes the greatest induced electromotive force (or peak voltage) in a coil:
ε p=N A B ω
Step 3
Let's use the equation above to calculate the angular velocity. Recall that 1 rpm is equal to 0.10472 radians per second, and 1 tesla is equal to 1 volt per second divided by 1 square meter.
= = p N A = 7295 r pm
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which of the statements below best describes longshore current? group of answer choices outgoing swash moves perpendicular to the beach. incoming backwash of water moves parallel to the beach. sand moves parallel to the beach. incoming swash of water moves parallel to the beach.
The statement which describes the longshore current is d.) incoming swash of water moves parallel to the beach.
What is a longshore current?
When the waves reach a beach, it liberates a large amount of energy that is usually generates a current and runs parallel to the shore. Such type of current is said to be longshore current.
Sea floor, shoreline features and depth of the water are the main factors on which the speed of the waves reaching the shore depends. The waves make their movement towards the beach where various segments of wave itself encounters before other and this results the segments to slow down. They do not reach the beach perfectly parallel to the shoreline. But when we talk about the longshore current, it moves parallel to the coastline or beach.
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What theory did Heisenberg propose?
Werner Heisenberg proposed the Unified Field Theory.
What is the Unified Field Theory?
A unified field theory (UFT) in physics is a sort of field theory that enables all of the concepts often associated with fundamental forces and elementary particles to be expressed in terms of two physical and virtual fields. Modern physics discoveries suggest that forces are instead characterised and disrupted by intermediary phenomena known as fields rather than being communicated directly between interacting objects. The fields are traditionally united into a single physical field as a duality. The term "unified field theory" was first used by Albert Einstein, who sought to combine electromagnetism and his general theory of relativity, and it has been an active area of study for more than a century.
Werner Heisenberg concentrated on Unified Field Theory in his final years of work. This "theory of everything" aims to explain the fundamental forces and elementary particles.
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Obtain an expression for fringe width with diagram.
Hope this above expression for fringe width helps you.
Answer:
Explanation:
To obtain an expression for fringe width, we need to consider the phenomenon of interference in wave patterns, such as in the case of Young's double-slit experiment. In this experiment, a coherent light source, such as a laser, is passed through two closely spaced slits, creating an interference pattern of light and dark fringes on a screen placed behind them.
The fringe width (w) can be determined using the following expression:
w = λ * D / d
Where:
- λ represents the wavelength of the light used,
- D is the distance between the double-slit and the screen,
- d is the separation between the two slits.
The diagram accompanying this explanation would illustrate a coherent light source passing through the double slits, with the resulting pattern of light and dark fringes observed on the screen placed behind them. The distance D between the double-slit and the screen, as well as the separation d between the slits, would be indicated in the diagram.
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which one of these represent total momentum of a system of two particles traveling one against the other?
The total momentum of a system is the vector sum of all the individual masses that comprise the system.
Moreover, To calculate the total momentum of two objects during a collision, add their individual momentums. You can calculate the momentum for each object using the formula p=mv, where p is the momentum, m is the mass, and v is the velocity. The law of conservation of momentum can be expressed as follows. For a collision between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.
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A 5000-kg freight car moving at 2 m/s collides with a 10,000-kg freight car at rest. They couple upon collision and move away at.
The correct answer of velocity is 0.66 m/s or 2 / 3m/s, at which the couple collide.
What is Collision concept?
A collision is a situation in which two or more objects.
Given data:
m1=5000kg
m2=10000kg
v1=2m/s
v2=0
An inelastic collision conserves momentum:
m1v1+m2v2 = (m1+m2) vboth
m1v1+m2v2 = (m1+m2) vboth
vboth =m1v2+m2v2m1+m2
vboth =(5000kg)(2m/s)+(10000kg)(0) / (5000kg+10000kg)
vboth= 10000 / 15000 = 2 / 3 m/s
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a .5 kg steel ball is suspended from teh ceiling by a 2.5 m long string. the ball is pulled to the side until it is 1 m above its lowest point and then released from rest. the tension in the string when the ball passes through its lowest position is
The tension in the string when the ball passes through its lowest position is 5N (rounded).
The pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements.
How to calculate the tension in the string when the ball passes through its lowest position?
Tension = m*g
T = 0.5 * 9.8
= 4.9N
Approximately the tension would be equal to 5N (rounded)
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A student needs to use the metric system while measuring the length of a box. Which units should he use?centimetersinchesfeetyards.
Answer:
While measuring the length of a box he should use centimetres if he is using the metric system.
What is the average speed in mph for a car that travels 400 miles in 5 hours and 20 minutes?.
For an automobile to cover 400 miles in 5 hours and 20 minutes, it must travel at an average speed of 75 mph.
What is the typical speed?Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time. Average speed refers to the average speed during the course of a journey.
What drives us to determine average speed?Average In order to comprehend the pace of a journey, speed is crucial. On a travel, the speed could occasionally change. Finding the average speed then becomes crucial to getting an idea of how quickly the route will be finished.
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what is the approximate numerical value of the slope of the lineweaver-burk plot of these kinetic data?
Using the theories of lineweaver-burk, we got that 0.05 as the approximate numerical value of the slope of the lineweaver-burk plot of these kinetic data.
The Lineweaver–Burk plot is correct when enzyme kinetics obey ideal second-order kinetics, however the non-linear regression is needed for systems that do not behave ideally. The double reciprocal plot distorts error structure of the data, and is therefore not most accurate tool for the determination of the enzyme kinetic parameters
Slope is equal to Km/Vmax
Km is half of Vmax
Vmax is 200 um/min, so Km is found at 100 um/min. At 100 um/min ,we know that the substrate concentration is 10 um. Thus, the Km is 10 um, which is equivalent to 10/200= 0.05
Hence, the approximate numerical value of the slope of the lineweaver-burk plot of these kinetic data is 0.05
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A 200 N object is resting on a surface with a maximum coefficient of static friction s = 0.15. A person pushes horizontally with a force of 20 N. Calculate how much force the push needs to be in order to get the object to start moving across the floor.
More than 30 N force needs to be in order to get the object to start moving across the floor.
F=μN
μ= 0.15
N= 200 N
F=200 N×0.15
F=30 N
In mechanics, a force is any action that seeks to preserve, modify, or deform a body's motion. Isaac Newton's three principles of motion, which are outlined in his Principia Mathematica, are frequently used to illustrate the idea of force (1687).
Newton's first law states that unless a force is applied to a body, it will stay in either its resting or uniformly moving condition along a straight path. According to the second law, when an external force applies on a body, the body accelerates (changes velocity) in the force's direction.
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When the temperature of a gas is increased from 27° the average speed of the molecules increases three-fold. Calculate the final temperature of the gas. (prove by calculation)
The final temperature of the gas is obtained as 2700 K or 2472° C.
What is the relationship between the speed of the gas and the temperature?We know that when the temperature of a gas is increased, the speed of the gas is also increased. Given that we have the initial temperature of the gas as 27° C or 300 K.
Given that;
[tex]V_{1}[/tex]/[tex]V_{2}[/tex] = √[tex]T_{1}[/tex]/[tex]T_{2}[/tex]
Where the [tex]V_{1}[/tex] and [tex]V_{2}[/tex] refers to the initial and the final velocities while the [tex]T_{1}[/tex] and the [tex]T_{2}[/tex] refer to the initial and the final temperatures.
[tex]V_{1}[/tex]/3 [tex]T_{1}[/tex] = √300/ [tex]T_{2}[/tex]
1/3 = √300/ [tex]T_{2}[/tex]
1/9 = 300/ [tex]T_{2}[/tex]
[tex]T_{2}[/tex] = 2700 K or 2472° C
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Research and draw a diagram showing a food chain with at least four levels of organisms, starting with plants or algae (producers). Show how each organism in your diagram gets energy, and use arrows and labels to indicate the relationship between each of the organisms. Research the average daily calories each organism on your food chain must consume in order to maintain proper body function. While this diagram is called a food chain, it should actually be called a food cycle because you’ll be including a decomposer to tie together the animal at the top of the food chain back to the producers. Along with the diagram, write a three-paragraph explanation of why energy transfer is not 100% efficient in a food chain. Explain where the lost energy goes, and include a paragraph at the end that explains the role of decomposers such as fungi and bacteria. How do they increase entropy to the maximum? Finally, explain how producers (the plants and algae) decrease entropy as the cycle starts over again. In your explanation, include definitions of the second law of thermodynamics and entropy.
Energy is transferred along the food chain from the producers to the decomposers.
What is the food chain?The term food chain has to do with the process by which energy is passed from one organism to another along the in the ecosystem. Let us recall that the ecosystem is a unit that is composed of living and non living parts and is able to sustain itself.
According to the principle of second law of thermodynamics, energy transfers is not 100% efficient. Thus as energy is transferred along the food chain, only 10% of the energy that was acquired from the pervious trophic level is passed on to the succeeding trophic level.
This is because of the fact that the remainder of the energy is utilized in the metabolic activities of organisms. We can rightly call the food chain a food cycle because as we can see from the image, energy is obtained from the sun and passed along the food chain and returned to the producers by the activities of the decomposers.
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bob and bill have the same weight and wear identical shoes. keeping both feet flat on the floor and the body straight, bob can lean over farther than bill can before falling. whose center of gravity is closer to the ground? account for your answer.
The taller individual must have reclined less than the smaller man because their shoes are the exact same size (leaning in terms of angle of body made with the ground). Bob's center of mass is consequently located closer to the ground.
what is centre of mass?
A position established in relation to an individual or group of items is the center of mass. It represents the system's average location as weighted by each component's mass. The center of mass for straightforward stiff objects with homogeneous density is found at the midpoint.
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The taller individual must have reclined less than the smaller man because their shoes are the exact same size (leaning in terms of angle of body made with the ground). Bob's center of mass is consequently located closer to the ground.
What is centre of mass?
In physics, the centre of mass of a distribution of mass in space (also known as the balancing point) is the unique location at which the weighted relative position of the dispersed mass accumulates to zero. This is the point at which a force can be applied to generate a linear acceleration without causing an angular acceleration. Calculations in mechanics are frequently simplified when expressed in terms of the centre of mass. It is a hypothetical point at which the entire mass of an item can be considered to be concentrated in order to visualise its motion. In other words, the centre of mass is the particle equivalent of a particular object for the purposes of applying Newton's equations of motion.
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Toy cars 1, 2, and 3 are launched horizontally with the trajectories shown below. Cars 1 and 2
are launched from a 15 m high cliff, while Car 3 is launched from a 30 m high cliff. We can
ignore air friction.
Initial launch speed of the cars are in order as Vcar 1 = Vcar 2< Vcar 3
Speed (often abbreviated as "s") is a scalar variable that describes how much an object's location changes over time or how much it changes per unit of time. The average speed of an item in a period of time is the distance traveled by the object divided by the duration of the period.
Time divided by distance are the speed-related metrics.. The meter per second (m/s) is the SI unit of speed, while the kilometer per hour (kph) is the most often used unit of speed in daily life.
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he wavelength of blue light is approximately 4.0 x 10 -7 meters. calculate the frequency of blue light in hertz. a. 2.5 x 10 7 b. 1.2 x 102 c. 3.3 x 10 -9 d. 7.5 x 1014 e. 1.2 x 10 1
The frequency of blue light in hertz is d.) 7.5 x 1014.
What is frequency of a light and how is it calculated?
The electromagnetic radiation differs from other radiations through frequency of that wave. Light is one of the forms of electromagnetic radiations. A hertz is said to be the number of oscillations in one second. For a wave, hertz is the number of wavelengths per second. All types of light travels at a same speed irrespective of their frequency.
The equation that relates frequency and wavelength is:
c= fλ
where, c= speed of light
λ = wavelength in meters
f= frequency in hertz
c= 3×10 8 m/s
λ = 4.0 x 10 -7 meters.
f=c/λ
⇒3×10 8 / 4.0 x 10 -7
⇒7.5 x 1014 Hz.
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1. For the series circuit in Fig. 21.51:
a. Find the value of XC for resonance.
b. Determine the total impedance of the circuit at resonance.
c. Find the magnitude of the current I.
d. Calculate the voltages VR, VL, and VC at resonance. How are VL and VC related? How does VR compare to the applied voltage E?
e. What is the quality factor of the circuit? Is it a high or low Q circuit?
f. What is the power dissipated by the circuit at resonance?
a) For resonance this circuit should be resistive hence Xc = 30 ohm.
b) Total impedance = |2+30i=30i| = 2ohm.
c) Current=50mV/2=25mA.
d) |VL|=|Vc|=30*25mA=0.75V=750mV since impedance same and they are in series VR= 50mV.
e) Q=wL/R=w*L/R=30/2=15 since wL = 30ohm it is a high Q circuit.
f) Power disspated=i^2R = (25*25*10^(-6).)*2 = 1.25mJ.
The higher the Q the lower the energy loss rate and the slower the vibration damping. A pendulum suspended from high-quality bearings and oscillating in the air has a high Q, while a pendulum immersed in oil has a low Q. High-Q resonators have lower damping, so they oscillate or oscillate longer.
A circuit's figure of merit Q is the electrical energy stored in the circuit divided by the energy consumed in one cycle. The Q of a circuit is an important quantity in certain applications, such as in electromagnetic waveguides and radio frequency cavities.
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