what is the moment of inertia i of this assembly about the axis through which it is pivoted? express the moment of inertia in terms of mr , m1 , m2 , and x . keep in mind that the length of the rod is 2x , not x .

The correct answer is the movement of the ball because of conversation into kinetic energy.

Why here potential energy is changed to Kinetic energy?

The ball's stored potential energy becomes kinetic energy as it begins to move and rolls down the slope. The movement of the objects is caused by this kinetic energy.

Due to its height above the ground, the ball has gravitational potential energy when it is at the top of a hill.

Due to its velocity as it rolls down the hill, the potential energy is changed into kinetic energy.

Hence due to the ball's collision with the wall, it abruptly stops, converting its kinetic energy into internal energy.

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If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens because an outward force balances the pull of gravity on the water - True

What is centripetal force?

                                             F = mv^2/r

This experiment demonstrates Newton's first law of motion, which states that objects either remain still or move straight ahead. Inertia is the name for this quality. Force is required to cause an object to rotate in a circle.

The water inside the pail pulls on your arm as you swing it back and forth because it wants to keep moving in a straight line while you want it to go in a circle. The water pushes against the bottom of the bucket as you hold on to prevent it from flying away. The water pushes more forcefully against the bottom of the pail as you swing higher and higher. However, gravity tries to remove the water from the bucket when you turn it upside down. Ultimately, whichever force—gravity or centripetal—is stronger wins. The water will remain in the pail as long as you swing the bucket quickly enough for centripetal force—the force of the water pressing against the bottom of the bucket—to outweigh gravity.

Hence, the correct answer is True.

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The self-inductance of the RL circuit is 500 H.

We need to know about the time constant r-l circuit to solve this problem. The time constant of RL circuit depends on the resistance and inductance of its circuit. It can be written as

T = L / R

where T is the time constant, L is inductance and R is resistance.

From the question above, the given parameters are

T = 5 s

R = 100 Ω

By using the equation, we can calculate the self-inductance

T = L / R

L = T . R

L = 5 . 100

L = 500 H

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When the voltmeter pointer moves 2.1 centimeters on the scale, it rotates 20.06 degrees. The concept is the measure of an arc equals to the measure of the central angle.

The ratio of an arc length to the circumference equals to the ratio of a central angle to the total degrees of a circle.

[tex]\frac{x}{2 \pi r} = \frac{\alpha }{360}[/tex]

Where

Given the case a voltmeter pointer is 6 centimeters in length. When it moves 2.1 centimeters on the scale, what is the number of degrees through which it rotates?

Without the figure, we assume that the radius of the circle is 6 cm when the arc length is measured. So, we got:

The number of degrees through which it rotates is the central angle.

[tex]\frac{x}{2 \pi r} = \frac{\alpha }{360}[/tex]

[tex]\frac{2.1}{2 \times 3.14 \times 6} = \frac{\alpha }{360}[/tex]

[tex]\frac{2.1}{37.68} = \frac{\alpha }{360}[/tex]

[tex]\alpha = \frac{2.1 \times 360}{37.68}[/tex]

α = 20.06°

Hence, the number of degrees through which it rotates is 20.06 degrees.

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What is the magnitude of the acceleration of the space station as the astronaut is pushing off the wall?

Question Parameter(s):

The International Space Station has a mass of 1.8 × 105 kg. A 70.0-kg.

The station pushes off one wall of the station so she accelerates at 1.50 m/s2.

Generally, the equation for the  Force is mathematically given as

F = ma

Therefore

F = 70(1.50)

F= 105 N

In conclusion, the space station force

F = ma

105 = 1.8 * 10^5 a

a = 5.83 * 10^{-4} m/s^2

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.

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The general dependence of phase velocity on glass can be expressed as vₓ = v₀(1 + 2B/nλ²) and it is positive.

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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Annual saving energy produced *cost of oil/heating value is

$ 10020.46177.

Latitudes are lines that are horizontal and show how far a location is from the equator. In relation to the meridian in Greenwich, England, longitudes are vertical lines that show the east and west directions. Latitude and longitude are used in conjunction to locate points or places on the globe by cartographers, geographers, and others.

Puerto Rico's capital city's latitude and longitude are 18° 27' 58.7988" North and 66° 6' 20.5956" West.

Local San Juan latitude divided by tilt angle equals 18.46 WBAN No. 11641 = for year = 5.5 provides information on solar radiation for flat plate collectors facing south with a fixed tilt.

KWh/m2/day = 5.5 KWh/m2/day (1 day =3600h)

Formula used-

Solar radiation at that place* Collector Area *Collector efficiency = Heat rate * Output

power*Capacity factor

1 KW= 3,412.14 BTU/h

Heat rate* output power* capacity factor = 10,811*400*10^3*0.53 BTU/h = 671699.2855

KW

Collector Area = 671699.2855*3600/5.5*0.17

= 25862218.48 m^2= 6390 acres

C.

Cost of oil = 290$ /10^3 kg

Energy produced= 400*10^3 KW = 1364856 *10^3 BTU/h

Heating value = 39,500 Btu/kg

Annual saving Energy produced *cost of oil/heating value

= $ 10020.46177

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The cylinder may move along its round path at the maximum speed vmax without falling off the turntable, which is 0.343 m/s. For a mass m body  at speed v in a circular of radius r, the centripetal force Fc is Fc| = m v 2/r.

The fastest a person can go is considered to be at maximum speed. Velocity is what is meant by the term "acceleration," and since velocity has both a greater acceleration, athletes' acceleration can fluctuate depending on whether they are accelerating in one direction or both.

Equation Speed = Wavelength x Frequency describes how wave speed relates to wave wavelength and wave frequency. Given the wavelength and frequency, this equation could be used to determine the wave speed.

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A parallel capacitor's geometrical characteristics determine its capacitance. the separation of the plates. The capacitance reduces as the distance between the plates grows.

Farad, denoted by the letter F, is the SI unit for electrical capacitance. In large part, the unit bears the name of English physicist Micheal Faraday. The capacity of a body or thing to hold an electrical charge is often referred to as farad. The SI base units used to describe it are s4A2m-2kg-1.

They are effective at lessening voltage pulsation. The capacitor is charged in a parallel circuit when a positive voltage is applied, and it discharges when a low voltage is applied. While most electronic circuits use DC, the electricity that comes out is AC.

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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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All the statements in the question about the rings of Neptune above are correct.

Neptune is the eighth planet in our Solar System. It has a planetary ring system that may consist of ice particles coated with silicates. The first was detected by a team led by Edward Guinan in 1968, with the following hypothesizes solved by Voyager 2's images in 1989.

There are three main rings in Neptune's planetary ring system:

The picture attached is a combined color and near-infrared image of Nepture created by NASA and ESA.

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Energy is transferred along the food chain from the producers to the decomposers.

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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Answer:

While measuring the length of a box he should use centimetres if he is using the metric system.

The conditions which would result in clockwise emf in loop are

a) The magnitude of B increases

c)The loop Rotates through 45 degrees about vertical axis

This all happens according to the right-hand thumb rule of electromagnetics. The EMF (Electro Motive Force) changes according to the movement of Loop as it is dependent on the motion which further connects to the right hand thumb rule as shown in the figure attached.

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Option 3. is the correct answer.

Mass of object 1 at one end = 20 kg

Mass of object 2 at the other end = 8 kg

The total length of a stick = 70 cm  

The mass of the stick is negligible

As we know that x =  m₁x₁+m₂x2/m₁ + m₂  

x = 20(0) + 8(70)/20 + 8  

As the first object is at the start so distance is equal to 0

x = 20 cm

Point B is the point from which the stick remains horizontal when suspended from the cord.  

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3.5 m / s  is their speed after the collision.

Mass of a car = 1000 kg,

Velocity car = 8 m/s,

Mass  lorry = 3000 kg,

Velocity lorry = 2 m/s.

u = initial velocity,

v = final velocity.

m₁ = 1000 kg, m₂ = 3000 kg, u₁ = 8 m/s, u₂ = 2 m/s

(1000)(8) + (3000)(2) = (1000 + 3000)·v

8000 + 6000 = 4000·v

4000·v = 14000

v = 3.5 m/s

velocity (often abbreviated as "s") is a scalar variable that describes how lots an item's vicinity modifications over time or how plenty it modifications in step with unit of time.

The average speed of an item in a period of time is the distance traveled with the aid of the object divided by way of the length of the length.

Time divided with the aid of distance are the rate-associated metrics.. The meter in keeping with second (m/s) is the SI unit of pace, while the kilometer consistent with hour (kph) is the most usually used unit of speed in each day existence.

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Answer:

Before the rubber ball moves, it's stationary. Therefore the energy is Potential. As it rolls, the energy is transferred equally between the ball itself and the ramp, making the energy transferred Kinetic Energy.

Explanation:

The energy stored in the field is 3.75*10-6J.

What is magnetic field?

The area in which magnetism acts, called the magnetic field, is where a magnetic substance or a moving electric charge is located. An illustration of the magnetic field that shows how a magnetic force is dispersed both within and outside of a magnetic substance.

What is inductor?

A wire coil called an inductor is used to store energy in the form of a magnetic field. Inductor energy storage capacity is increased by the coil's typical wrapping of an iron-containing core.

Energy density stored=B2/2?

                                       =5*5*10-6/4*?*10-7

                                        =125/4?

Total energy stored= Energy density stored*Volume

                                  =?r2*h (125/4?)

                                 =3.75*10-6J

Therefore, the energy stored in the field is 3.75*10-6J.

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Answer: 98 J

Explanation:

The starting GPE is 0 because the block is at h=0 (bottom of the incline).

The block moves 5.0 m up the incline, so you have to figure out its height (h) relative to the bottom of the incline, where h=0.

sin30 = h/5

solve for h:  h = sin30 x 5 = 2.5m  (height of the block, 5 m up the incline)

Now you can solve for GPE = mgh

GPE = (4 kg)(9.8 m/s2)(2.5 m) = 98J

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.

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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The inertia of the elephant Mel in terms of the inertia Mm of the monkey is 2Mm

the moment = 0

from monkey & giraffe

Mm*3d = Mg*d

Mg = 3*Mm

-------------------

for Me  & Mg

(Mg + Mm)*2d = Me*4d

(3Mm+Mm)*2d = Me*4d

4*Mm*2 = 4*Me

Me = 2Mm

Until some force changes the speed or direction of an object, it will continue to move in the same direction. This is known as inertia. The phrase is correctly understood as a shortened form of "the principle of inertia," which is a concept that Newton discussed in his first law of motion. Unless influenced by an unbalanced force, an object at rest stays at rest, and an object in motion stays in motion while maintaining a constant speed and a straight line. An object at rest has a tendency to stay at rest, and an object in motion has a tendency to continue moving in a straight line at a constant speed.

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Answer:

Scientists predict the location of electrons in the modern model of the atom by using the Heisenberg uncertainty principle.

It  will take the object a total time of 1.564 seconds to fall from a height of 12m.

Time is the apparent progression of events from past to future.

To calculate the time it takes the object to fall to the ground, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Solve for the value of t

Hence, it will take the object 1.564 seconds to fall to the ground.

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The magnitude of ant's total displacement is 96.23 cm in a direction 41 degrees North of East.

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;

First 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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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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If an astronaut is traveling in a spacecraft in outer space in a straight line at a constant speed of 0.500 c, she would feel heavier.

According to relativity, the faster one moves, the more mass they have. If one travels at speed of light, their mass becomes infinite and would have to slow down.

M = Mo / √ [ 1 - ( c² / v² ) ]

M = Mass of body at a given speed

Mo = Mass of body at rest

c = Speed of light

v = Speed of body

Here, v = 0.5 c

M = Mo / √ [ 1 - ( c² / ( 0.5 c )² ) ]

M = Mo / √ - 0.75 / 0.25

M = Mo / √ - 3

M > Mo

Therefore, f an astronaut is traveling in a spacecraft in outer space in a straight line at a constant speed of 0.500c, she would feel heavier.

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If two balls are projected with initial velocity v and 2v respectively, the ball that is projected with a velocity of 2v would reach the ground first.

The term projectile has to do with the kind of motion that uses a parabolic path. The parabolic path is a path that is curved. For instance, if you trough a ball from one point to the other, the ball does not follow a straight path, the path of the ball is curved.

The time that it takes for the ball to reach the ground from the point of projection is dependent on the initial velocity of the ball. Thus, if the ball has been projected with a higher initial velocity then the ball would reach the ground faster and vice versa.

Thus, given that the velocity 2v is twice the velocity v, the ball that is projected at this velocity would reach the ground first.

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