A group of students were investigating the force of gravity. They began by dropping a foam ball from a height of 3 meters into a bucket of sand. The ball hit the sand in 0. 306 seconds. They dropped additional balls of approximately the same diameter, but of different masses. Here is the data they collected. Based on this experiment and the collected data, what would their conclusion be?.

The distance travelled by the bowling ball is 18.6566 ft

Circumference = 2πr = 27

Weight of the ball = 14 lb

Radius of gyration = 3.28

Velocity = rω = 20 ft/s

Coefficient of friction = 0.20

Total force on y axis= 0, therefore N = W

= F = μN = μW

and, ∑M = Iα

Hence,

= Fr = Iα

Total force on x axis = 0,

= F = ma = μW

= a = μg

Combining all the equations,

= Fr = Iα

= μWr = mk²α

= α = (μgr) / k²

If initial velocity = 0 then, ω = αt

=  ω = αt = [ (μgr) / k² ] t

= t = (vk²) / (μgr²)

Now, v = u + αt

= v - u = (μg) + (vk²) / (μgr²)

= u = v [ 1 +(k²/r²) ]

Distance travelled by the ball = s =

= v² = u² - 2αs

= ( u² ) / [ 1 +(k²/r²) ] ² = u² - 2μgs

= s = (u²/2μg) [1 - (1/(1 + (k²/r²))²)]

= s = 18.6566 ft

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A transparent oil with refraction index 1.24 spills on the surface of water  Assuming the maximum occurs in the first order, Then the thickness of the oil slick 271 nm

Given refraction index is 1.24

The formula to apply for find the maximum for this thin film is

2nt = mλ

(2)(1.29)t = (1)(700 X 10-9)

t = 2.71 X 10-7 m   which is 271 nm.

Light travels more slowly at higher refractive indices, changing direction within a material with a correspondingly greater degree. This means that lenses made of materials with higher refractive indices can bend light more strongly and have lower profiles. A refractive index of 1.5 applies to glass. In other words, the speed of light in glass is not independent of the color of the light and is 1.5 times slower than in a vacuum.

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The overall magnification of the microscope is  - 588.23 .

Magnification is the process of increasing apparent size.

M = magnification

l = distance between the eyepiece and the objective lens

f₀ = focal length of the objective

f₁ = focal length of the eyepiece

l = 20 cm

f₀ = 0.500 cm

f₁ = 1.70 cm

M = - (l/f₀)(25/f₁)

M =  - (20/0.500)(25/1.70)

M = - (40)(14.70)

M = - 588.23

The overall magnification for the microscope is - 588.23.

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A reflection nebula is described by the explosion of hot large stars. Option B.

Reflection nebulae differ from emission nebulae in that they themselves do not emit radiation. This is a cloud of dust and gas that reflects light energy from a nearby star or group of stars. They usually tend to be blue due to the way light scatters.

This nebula is a reflection nebula that glows by reflecting the light of nearby stars. In contrast to emission nebulae, which emit a reddish glow from excited gas atoms, reflection nebulae are bluish because interstellar dust particles prefer to reflect blue starlight. A cloud of gas and dust that emits no light of its own and glows by reflecting light from nearby stars.

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The string will extend when the object is moved to the right, applying a restoring force to bring the weight back to its equilibrium position. The string will compress if the object is pushed to the left, and it will then exert a restoring force to bring the thing back to its starting position.

The displacement diminishes as the mass comes closer to the equilibrium position, and as a result, the restoring force and acceleration both decrease. There is no restoring force once the mass has reached equilibrium.

The linear density of the string and the tension in the string both affect how quickly a wave moves along a string. A string's linear density is its mass per unit length. In general, a wave's speed is determined by the square root of the medium's elastic property to inertial property ratio.

The speed would be higher in the low linear mass density of the string because the speed of a wave on a string is inversely proportional to the square root of the linear mass density.

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The gravitational force between two very large metal spheres in outer space if the mass of each sphere were halved is 14 N

F = G m1 m2 / r²

F = Gravitational force of attraction

G = Gravitational constant

m1, m2 = Masses of both spheres

r = Distance between the spheres

m1' = m1 / 2

m2' = m2 / 2

F' = G m1' m2' / r²

F' = G ( m1 / 2 ) ( m2 / 2 ) / r²

F' = G m1 m2 / 4 r²

F' = F / 4

F' = 56 / 4

F' = 14 N

Therefore, the force is 14 N

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The appropriate energy transformations are:
Kinetic energy changes into center of gravity from A to C.
Gravitational acceleration energy is converted into kinetic energy from C to E.

What is Kinetic energy?
Kinetic energy is a type of power that a moving object or particle possesses. An object gains kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. A moving object as well as particle has kinetic energy, which depends on both its mass and its rate of motion. Any combination of motions, including translation, rotation about in an axis, and vibration, may be the type of motion.

A body's translational kinetic energy, or 1/2mv2, is determined by multiplying its mass, m, by the square of it's own velocity, v.

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The distance in mm between these minima is 0.29 ×[tex]10^{-3}[/tex] m

For first minima, m=1, Then,

[tex]a\sin \theta_1 = \lambda_1 \Rightarrow \sin\theta_1 = \frac{\lambda_1}{a} \Rightarrow \theta_1 = \sin^{-1}\left(\frac{589.1\times10^{-9}}{2.4\times 10^{-6}}\right) = 14.2^{\circ}[/tex]

[tex]a\sin \theta_2 = \lambda_2 \Rightarrow \sin\theta_2 = \frac{\lambda_2}{a} \Rightarrow \theta_2 = \sin^{-1}\left(\frac{589.6\times10^{-9}}{2.4\times 10^{-6}}\right) = 14.22^{\circ}[/tex]

Hence the required angle is , (14.22 - 14.2) = 0.02o

The distance between these two minima,

[tex]\Delta y = y_2 -y_1 = \frac{D}{a}\left( \lambda_2-\lambda_1\right) = \frac{1.4}{2.4\times 10^{-6}}\left(0.5\times 10^{-9} \right ) = 0.29\times 10^{-3} \hspace{2mm} m[/tex]

This distance is best measured using a microscope.

The length of a particular path taken by an object between two points is its distance, such as the distance traveled through a maze. In some cases, such as when a ball is thrown straight up or the Earth completes an orbit, this can even be a closed distance along a closed curve that begins and ends at the same location. The mathematical term for this is the curve's arc length. It is also possible to signify the distance traveled: a "ahead" distance is positive and a "backward" distance is negative.

When building vehicles or mechanical gears, it can be helpful to take circular distance—the distance covered by a

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The velocity of the flare is -92 feet per second while it is going toward the earth, in accordance with the question.

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar number. In essence, the velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

We determine the speed at this time after first determining t.

131 = -3t^2 + 100t  + 3

-3t^2 + 100t - 128 = 0

-(3t - 4)(t - 32) = 0

t = 4/3, 32

At 32, the flare will be released.

s'(t) = -6t + 100

s'(32) = -6(32) +100 = -92

The velocity is 92 ft/sec down.

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The complete question is-

In a scene from the Martin Matt Damon shoots a flare straight up into the sky. The height( in feet) of the flare after t seconds is given by

s(t)= -3t squared + 100t + 3

What is the velocity of the flare when it is moving toward the ground and its position is equal to 131 feet?

The tension in the string when a 40 kg stone tied to a string is whirled horizontally at a speed of 2.2 m/s will be 488 N/m.

When two solid things come into touch with one another, tension is the force that is generated. A force of tension is the force generated by a rope, string, or chain.

When one mass is drawn vertically and another is being pulled horizontally, there is tension force acting on the string. In the absence of gravity, this gives the tension force pulling on a string.

We are aware that T = mg + ma is the formula used to compute the force of tension.

T = 40(10) + 40(2.2)

T = 488 N/m.

Given that tension is a form of force, it shares the same measurement and unit as force. The CGS unit for tension is dyne whereas the SI unit is newton (N).

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The centripetal acceleration of the stone is:

ac = v2 / r

Let us assume the radius of the string is 1m.

ac = (2.2 m/s)2 / 1

The tension in the string is:

T = m a = (40)*(2.2*2.2)

T = 40 * 2.2 * 2.2

T = 193.6 N

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The magnitude of velocity  will be  Δ=5.2 m/s.

What are vector quantities?

Any quantity which is defined by its magnitude and direction both are called as the vector quantities.

Now the data given in the question will be given as:

V(a) = 3 m/s

θ =  north of east

V(b) = 6 m/s

θ =  south of east =  360-40=320 north of east

Now we will find the x and y component of V(a)

V(ax) = V(a) cosθ

V(ax) = 2.82m/s

V(ay) = V(a)Sinθ

V(ay) = 1.03 m/s

Now we will find the x and y component of V(b)

V(bx) = V(b) cosθ

V(bx) = 4.6 m/s

V(by) = V(b) sinθ

V(by) = -3.86 m/s

Now change in velocity will be

ΔV = V(b) - V(a)

ΔV = 1.78 i - 4.89 j

The magnitude of these vectors:

ΔV = 5.2 m/s.

Therefore the magnitude of the V will be 5.2 m/s.

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Yes, the outcomes are in perfect accordance with the basic lens equation.

1/f = 1/s1 + 1/s2. This is the equation for the Gaussian lens. The basic relationship between the size of both the optical system and the diffraction limit of the lens is given by this equation.

For a spherical mirror, the focal length, scale factor, and object distance are all related by the lens equation, often known as the lens formula. The formula is presented as follows: Lens Equation - 1/u + 1/v = 1/f, where v is the image's distance from the lens.

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According to general principles, the object distance shows that the light rays coming from the object are parallel to one another, giving rise to f=-4.221.

A small, often straight-moving light beam is called a ray. A ray is represented by the light beam of a laser or laser pointer. A ray of light travels in a straight line until it hits an object, like a mirror or perhaps the boundary between two materials, per the ray model of light.

Small light beams called rays travel in a straight line as electromagnetic waves. Light always moves in a straight line, despite the fact that reflection and refraction can alter the direction of its speed.

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An 8.0 lb blowing ball has a diameter of 8.5 inches. When lowered into water, this ball will sink.

The correct option is B.

The measure of how densely a material is packed together is called density.

It can be defined as the mass per unit volume.

Density Symbol: D or ρ

Density Formula: ρ = m/V, where ρ is the density, m is the mass of the object and V is the volume of the object.

Mass of the ball m=8lb

Radius of the ball r=8.5/2=4.25 inch=0.108m

Volume of the ball V=4/3[tex]\pi[/tex]r³=5.277 ×10⁻⁶m³

Density of the ball b = = 687.7 × 103 kg/m³

Density of water Pw 1 × 103 kg/m³

Since the density if the bowling ball is much larger than that of water, the ball will sink.

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The horizontal velocity component when the object is at its maximum height  Hmax = [tex]u^{2} sin^{2}[/tex]θ /2g

The vertical and horizontal components of motion are separated into two parts for solving velocity problems in physics. When solving problems involving a trajectory's angle, vertical velocity is used. When an object moves horizontally, its horizontal velocity becomes crucial. Any mathematical solution will consider the horizontal and vertical elements independently because they are not reliant on one another. Horizontal velocity, which can be expressed in terms of meters per second or miles per hour, is typically defined as horizontal displacement divided by time. The distance that an object has traveled since leaving a starting position is known as displacement.

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Consequently, the acceleration due to gravity of the pole voulter is 2000J.  any object at ground surface has a potential energy = zero newtons.

Gravitational potential energy is the energy that an object has due to its location within a gravitational field. The most usual use of gravitational potential energy is for a body at the surface of the Earth, where it is reasonable to assume that the gravitational pull is constant at about 9.8 m/s. 2.Any object at ground level has a potential energy of zero newtons becuase anything multiplied by zero is zero. An object with mass of 54 kg, 4 meters above the ground has a gravitatinal potential energy of 2116.8 Joules.

If an object is located at a height that is higher (or lower) than the zero height, it has gravitational potential energy. If an object is situated on an elastic media in a position besides the equilibrium position, it has elastic potential energy.

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Electromagnetic Force causes electric and magnetic effects such as the repulsion between like electrical charges or the interaction of bar magnets in a similar fashion of attraction & repulsion. It is long-ranged, but much weaker than the strong force. It can be attractive or repulsive and acts only between pieces of matter carrying electrical charge. Electricity, magnetism, and light are all produced by this force.

If the charge on q1 is doubled the force becomes 4 times its initial value.

Since, we know

F = (k×q1×q2)/r²

When the charges are doubled, we have :

F' = (k × 2q1 × 2q2)/r²

F' = 4 (k×q1×q2)/r²

Thus,

F' = 4F

Therefore, the force becomes 4 times its initial value.

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If a submarine's viewing port has a surface area of 0.0100 m2, the force exerted by the water on it at this depth will be 416,000 N in magnitude.

Pgauge is equal to F/A 412(1.01 x 105) = F/0.01 F = 416,000 N.

The two fluid pressures that are in play are the internal atmospheric air pressure and the external water pressure, which includes the atmosphere operating on it at the surface. The net force due to fluid pressure can be calculated by using the gauge pressure of the water since the atmospheric pressure acts both internally and is also included in the water pressure and the air pressures virtually cancel each other out.

A force is an influence that has the power to alter how an object moves. A force can cause an object with mass to accelerate and change its velocity (for example, moving from a state of rest). Force can also be conce.ptualized as a push or a pull. A force is a vector quantity since it has b0th magnitude and direction. It is calculated using newtons as the SI unit of mea.sure (N). F stands for force (formerly P).

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The frequency heard by the observer is 437.3 Hz.

What is doppler effect?

The Doppler effect or Doppler shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. Doppler shift is frequently demonstrated by the change in pitch that occurs as a car approaches and moves away from a viewer while sounding its horn.

It is estimated by the formula:

[tex]f_o = \frac{v +v_o}{v + v_s} f_s[/tex]

where,

[tex]f_o[/tex] = observer frequency of sound

[tex]v[/tex] = speed of sound waves

[tex]v_o\\[/tex] = observer velocity

[tex]v_s[/tex] = source velocity

[tex]f_s[/tex] = actual frequency of sound waves

Given,

[tex]f_s[/tex] = 405Hz

[tex]v_s[/tex] = 25.5 m/s

[tex]v[/tex] = 345 m/s

[tex]v_o\\[/tex] = 0 m/s

[tex]f_o = \frac{v +v_o}{v + v_s} f_s[/tex]

Observer to source = Positive

Source to observer = Negative

[tex]f_o = \frac{v}{v + v_s} f_s[/tex]

[tex]f_o = \frac{345}{345 - 25.5}[/tex]  × 405

[tex]f_o[/tex] = 437.3 Hz

The frequency heard by the observer is 437.3 Hz.

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7.87° is the first-order maximum for 550 nm.

Using diffraction equations,

d = 0.01/Number of lines, where 0.01 m = 1 cm and d = line spacing

Therefore,

d = 0.01/2070 = 4*10^-6 m

Similarly,

d x Sin X = m x Y;

When X = Angle

m = order = 1

Y = wavelength = 550 nm =550*10^-9 m

By substituting;

Sin X = mY / d = (1*550*10^-9)/(4*10^-6) = 0.1375

X = Sin⁻¹(0.1375) = 5.97°

As a result, the first-order maximum for 550 nm will be 7.87°.

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If two people start at the same place and walk around a circular lake in opposite directions with angular speed of 1.7 × 10−3 rad/s and 3.4 × 10−3 rad/s, they will meet after 20.5 minutes.

ω = θ / T

ω = Angular velocity

θ = Angular distance

T = Time period

ω1 = 1.7 * 10⁻³ rad / s

ω2 = 3.4 * 10⁻³ rad / s

θ = ω T

Let the angular distance covered by both person be θ1 and θ2. Since they start at same point, when they meet the sum of their total angular distances will be 360° which is 2π in radians.

θ1 + θ2 = 2 π

ω1 T + ω2 T = 2 π

T = 2 π / ( ω1 + ω2 )

T = ( 2 * 3.14 ) / ( ( 1.7 * 10⁻³ ) + ( 3.4 * 10⁻³ ) )

T = 1.2314 * 10³ s

T = 1231.4 s

T = 20.5 min

Therefore, they will meet after 20.5 minutes.

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Assume you have a sealed jug that only contains air. If you heat the air in the jug it will have a higher temperature.  Air Pressure properties of air will change.

What is  Pressure?

The force delivered perpendicularly to an object's surface per unit area across which that force is dispersed is known as pressure. In comparison to the surrounding pressure, gauge pressure is the pressure. Pressure is expressed using a variety of units.

The number of atoms of air in the sealed container cannot change. Assuming that the container does not expand when heated, the volume of the container cannot change when it is heated. If neither the mass nor the volume change as the can is heated, neither can the density change.

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Cataract is a condition in which there is a progressive thickening of the lens causing vision to become cloudy, opaque, and distorted.

The majority of cataracts occur when the tissue that makes up the eye's lens changes due to age or trauma.

The risk of cataracts may be increased by some hereditary genetic abnormalities that can result in other health issues. Other eye diseases, previous eye surgery, or other disorders like diabetes might also lead to cataracts. Cataracts can also form as a result of prolonged steroid drug usage.

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When light travels from air into water, it slows down, causing it to change direction slightly.

What is  light travels?

Light moves in waves. It does not, however, require any substance or material to transport its energy forward, unlike sound waves or water waves. This implies that light may pass through a vacuum, or an area that is entirely devoid of air. (In contrast, sound must pass through a solid, liquid, or gas.)

Light slows down and somewhat changes direction as it passes through water from air. Refraction is the name for this shift in direction. Light "bends" more in the direction of the normal line when it enters a denser material (one with a higher refractive index).

Light bends in the direction of the normal as it passes through an interface into a material having a greater index of refraction. On the other hand, light bending over a higher n to lower n contact will deviate from the usual.

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When wind speeds up as it blows over the top of a hill, decreases atmospheric pressure there.

As the ratio of the force the atmosphere exerts per unit area, atmospheric pressure can be defined. Pascal can be used to both calculate and measure atmospheric pressure. 101325 pascals is what the normal atmospheric pressure is.

Your immediate environment is pressed against by the weighty air that surrounds you. It is known as air pressure or atmospheric pressure. It is the pressure from the air above a surface that pulls it toward Earth. Typically, a barometer is used to measure atmospheric pressure.

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assuming they were moving at the same speed and started riding at the same position and time, then no, her brother was not moving relative to ashley.

The speed of the projectile F= μο[tex]i^{2}[/tex]/2π  ㏑(1+ W/r)i^.

The projectile's path between y+dy should be considered. Equation is used to determine the magnetic force acting on the segment as well as the magnetic field of each semi-infinite wire (the top rail is known as wire 1 and the bottom rail as wire).

The field (in the region between the wires) set up by wire 1 is into the paper (the "k" direction), and that set up by wire 2 is also into the paper. The current. in rail. 1. is in the "+ i." direction, and. the current. in rail 2 is in the. " i" direction. The force element (a function of y) acting on the segment of the projectile (in which the current runs in the − j^ direction) is provided below. The coordinate. origin is  at the. bottom of the. projectile.

d F = d F1 +dF2 = idy(− j^)× B1 +dy(− j^ )× B2 =i[B 1 +B 2 ] i dy

F= μο[tex]i^{2}[/tex]/2π  ㏑(1+ W/r)i^.

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The fraction of atmospheric pressure at sea level is 0.047.

The stress present in the Earth's environment is known as atmospheric pressure, commonly referred to as barometer strain. One zero one,325 Pa, also known as 1013.25 millibars, 760 mm Hg, 29.9212 inches Hg, or 14.696 psi, is the measure of stress used to describe the same old environment.

The atmospheric sea level is known as

P sea level = P atm = 1.01325 × 10^5 N/m^2

Now pressure at the bottom of empire state will be

P1 = 1.01325 × 10^5 N/m^2

Pressure at the top of empire state will be:

P2 = P1 - rho × g × h

rho = density of air = 1.29 kg/m^3

g = 9.81 m/sec^2

Given:

h = height of empire state = 380 m

P2 = 1.01325 × 10^5 - 1.29 × 9.81 × 380

P2 = 96516.138 N/m^2

So,

Delta P = P1 - P2 = 1.01325 × 10^5 - 96516.138

Delta P = 4808.862 N/m^2

So fraction will be:

N = Delta P / P sea level

N = 4808.862/1.01325 × 10^5

N = 0.04745 = 4.745 × 10^-2

Hence in two significant figures

N = 4.7 × 10^-2 = 0.047

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Answer:

1040 Kilohertz = 1.04E6 /sec

Speed of electromagnetic waves = 3.00E8 m/s

3.00E8 / 1.04E6 = 288 m  (a λ/4 antenna still requires 72 m)

The recoil (springing or flying back of the gun when shots are fired) momentum of a gun is the same as the momentum of the bullet it fires.

option C is the correct answer.

The principle of conservation of linear momentum states that in an isolated system, the sum of the initial momentum of the system is equal to the sum of the final momentum of the system.

Mathematically, the principle of conservation of linear momentum is written as;

Pi = Pf

where;

m₁u₁ = m₂u₂

where;

Thus, based on the principle of conservation of linear momentum the final momentum of the gun will always be equal to the final momentum of the bullet.

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