2. Three blocks, A,B and C of mass 2kg. 3kg. 5kg respectively kept side by side with one another are accelerated at 2m/s2 across a smooth horizontal surface by a force F evaluated the magnitude of F and what force the blocks exert on each other.​

Free Fall under gravity and time of meeting is used to find out the required answer.

∴ Let us assume, the upward direction to be positive and and downward direction to be negative.

Given, Velocity of P, = 40m/s

Distance travelled by P,

∴Using First Equation of motion for particle P,

v = u + at

⇒ 0 = 40 + (-10)t

⇒ t = 4s  ; which is the time taken by P to rise up

Now, Maximum Height(s) reached by particle P,

∴Using second equation of motion,

s = ut + 1/2at²

⇒ s = 40×4 + 1/2 × (-10) × 4²

⇒ s = 80m

a) Particle P is falling when Q is shot up after 4s from the initial time

∴ Using third equation of motion using Free Fall under Gravity,

V² = U² + 2aH₁

⇒ H₁ = 15² - 0/ 2(-10)

⇒ H₁ = 11.25m

Hence, Particle P and Q meet at a distance (H₂) from ground,

∴ Height, H₂ = s - H

⇒ H₂ = 80 - 11.25 = 68.75m

Hence, Particle P and Q meet at a distance of 68.75m from ground.

∴ Using First equation of motion for Particle P using the Time of Meeting,

v = u + at₁

⇒ 15 = 0 + (-10) t₁

⇒ t₁ = 1.5s  ; which is equal to the fall time of P and Rise time of Q

b) For particle Q

∴ Using second equation of motion,

H₂ = u₂t₁ + 1/2at₁

⇒ 11.25 = u₂ × 1.5 + 1/2 (-10) × 1.5

⇒ u₂ = 15 m/s

Hence, the Velocity with which Particle Q was shot is 15m/s in the upward direction.

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The rate energy is consumed this statement describes power.

Hence, Option C is correct answer.

Power is related to energy by that it is the rate at which energy is transferred.

It is a measure of the rate at which work is done.

According to the definition of power, Power is the amount of energy transferred or converted or consumed per unit time.

SI unit of power is watt.

By definition, 1 watt is equal to one joule of work done per second. So if P represents power in watts, E is the change in energy (number of joules) and t is the time taken in seconds then:

P=[tex]\frac{E}{t}[/tex]= [tex]\frac{1 Joule}{1 Second}[/tex]= 1 Watt.

Thus from the above conclusion we can say that, The rate energy is consumed describes power.

Hence, Option C is correct answer

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Answer:

C

Explanation:

Gravity is the main reason that make our planets to pull each other

The answers are :

(a) 23π/90 radians ≈ 0.803 radians

(b) 17/2π revolutions ≈ 2.706 revolutions

(c) 79.5/60 rad/s = 13.25 rad/s

*The important formulas to remember*

     [tex]\boxed {Radian = Degree \times \frac{\pi}{180^{o}}}[/tex]

    2. Radians to Revolutions

     [tex]\boxed {Revolution = \frac{Radian}{2\pi}}[/tex]

    3. rpm to rad/s

     [tex]\boxed {rad/s = \frac{rpm}{60}}[/tex]

Answer:

the light will reflect parallel to the principal axis

At point E

The energy of a roller coaster could either be potential energy, kinetic energy or a combination of both potential and kinetic energy.

Using analogies, the energy of the roller coaster at point E can be compared to a falling fruit from a tree which falls onto a pavement and is the rolling towards the floor. Point E can be compared to the midpoint of the fall of the fruit.

At point E

In conclusion, the energy of the rollercoaster at E is both Kinetic and potential energy,

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From the calculation, the force constant is 192 N. Also, friction would decrease the extension.

We know that the force constant can be obtained by the use of the relation;

F = Ke

F = applied force

K = force constant

e = extension

We know from Hooks law that the force applied is directly proportional to the extension.

We can write;

F = mgcosθ

F = 43 Kg * 9.8 m/s^2 * sin31°

F = 217 N

K = 217 N/1.13 m

K = 192 N/m

If there is friction between the incline and the crate, it will stretch less because some work will be lost due to friction causing only some fraction of the elastic potential energy to be converted to kinetic energy.

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The amount of time required for reflected sunlight to travel from the moon to the earth according to the given distance between then and the speed of light is; 1.28 seconds.

It follows from the task content that the time required for the reflected sunlight to reach the earth can be evaluated if the speed of light is known in which case, the speed of light, c = 3× 10⁸ m/s.

Consequently, we have time taken, t evaluated as follows;

Time taken, t = distance/speed

t = 3.85 ×10⁵ × 10³/3× 10⁸

t = 3.85/3

t = 1.28 seconds.

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Answer:

One needs to know the initial speed of the bus to find distance traveled.

Answer:

average velocity = [tex]\bf 900 \space\ km/h[/tex]

Explanation:

We can find the average velocity using the following equation:

[tex]\boxed{average \space\ velocity = \frac{total \space\ distance \space\ travelled}{ \space\ time \space\ taken}}[/tex] .

In this case:

• total distance travelled = 450 km

• time taken = 30 min = 0.5 h

Substituting these values into the equation:

[tex]average \space\ velocity = \frac{450 \space\ km }{ 0.5 \space\ h}[/tex]

                          ⇒ [tex]\bf 900 \space\ km/h[/tex]

(a) The position of the coin placed next to the convex side of a thin spherical glass shell is 3.68 cm.

(b) The size of the image is 1.8.

The position of the coin placed next to the convex side of a thin spherical glass shell is calculated as follows;

1/d = 1/f - 1/d'

where;

Focal length = r/2 = 17 cm / 2 = 8.5 cm

1/d = 1/8.5 - (-1/6.5)

1/d = 1/8.5 + 1/6.5

1/d = 0.1176 + 0.1538

1/d = 0.2714

d = 1/0.2714

d = 3.68 cm

Magnification, M = d'/d

M = (6.5)/(3.68)

M = 1.8

Thus, the position of the coin placed next to the convex side of a thin spherical glass shell is 3.68 cm.

The size of the image is 1.8.

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He observes that "There are no miracles. There's no such thing as fate. Nothing's meant to be." this is a false statement.

The term miracle is known to be something that is said to be an extraordinary event and it is one that often manifest in a kind of a divine intervention in the lives and affairs of human such as healing miracles, miracle jobs, miraculous meeting, etc.

Note that bad things that happens to people often makes them not to believe in the extraordinary but it does exist.

Hence, He observes that "There are no miracles. There's no such thing as fate. Nothing's meant to be." this is a false statement.

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From the first circuit (see attached), it is correct to state that I₄ = 40mA. See the explanation below.

A path that is designed to transport electric current is that is referred to as a circuit.

I = 200mA

= 20mA + 140mA + I₄

I₄ = 200 - 160

I₄ = 40mA

From the above, we can rightly posit:

R₄ = 3/(40x 10⁻³)

= 75 Ω

Hence

V₆ =  V₄ - V₅

= 3v - 2v

= 1v

R₆ therefore, =

V₆/I₆

= 1/ (40 x 10 ⁻³)

= 14.28 Ω

I₃ = I₄ + I₆

= 40 + 140

= 180mA

R₃ = 9/(180 x 10⁻³)

= 50Ω

R₂ = 12/20 x (10⁻³)

= 60 Ω

Then,

Vbattery =

200 x 10⁻³ x90

= 18 volts

The above indices is used to complete the image. See Circuit Image II.

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Since T = 2πm/Be the period of revolution of the electron is independent of velocity and radius of path

For an electron moving in a uniform magnetic field, the force on the electron is given by

F = Bev where

Also, this magnetic force equals the centripetal force on the electron, F'

F' = mv²/r where

Since both forces are equal,

F = F'

Bev = mv²/r

Be = mv/r

We know that angular speed, ω = v/r. So,

Be = mω

Also, angular speed, ω = 2π/T where T = period of revolution of electron

So, Be = m2π/T

Making T subject of the formula, we have

T = 2πm/Be

so, since T = 2πm/Be the period of revolution of the electron is independent of velocity and radius of path

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Answer:

D. Waves combine and their amplitude increases

Explanation:

amplitude is the height of the wave in a graph

constructive interference happens when two waves are lined up perfectly

example when two speakers playing same music while facing each other, music will appear louder

Destructive interference happens when the peaks match the valleys and they cancel perfectly

like with noise cancelling headphones

during constructive interference, waves collide in phase

in phase means add together making the height of the wave in a graph bigger (amplitude increases)

Example: When we see two speakers right next to each other, we can experience constructive interference when the distance from each speaker to the observer is the same

two waves destructively interfere, they must have the same amplitude in opposite directions

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chegg

It is useful to use a model in order to demonstrate how an electric circuit works.

In science, a model is a graphical representation that my result useful to predict the behavior of the components of a given system that works together to produce a particular outcome.

For example, an electrical circuit can be modeled by taking into account resistance, voltage, and intensity as parameters of functioning.

The electrical circuits are graphically represented by modeling the movement or flow of negatively charged electrons (e-) from the negative pole to the positive pole of a closed electric circuit.

In conclusion, it is useful to use a model (ie., a scientific model) to demonstrate how an electric circuit works.

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As mass increases, the following which is found to be always true is a corresponding increase in the inertia and is therefore denoted as option C.

This is defined as the property of a body to resist changes in velocity or motion. Such feature is characterized by the body having the tendency to remain at rest or in uniform motion unless an external force acts on it.

When mass increase, inertia also increases due to the large amount of force which is needed to change the direction or motion of a body in this scenario. On the other hand, when mass decreases, there is a corresponding decrease in the inertia which is present in a given body over a period of time.

This is therefore the reason why mass of a body is directly proportional to its inertia and makes it the most appropriate choice.

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The gravitational acceleration on the board of the Deepsea Challenger when it is in the Mariana Trench, 11 km below the surface of the Pacific Ocean is very large due to the high pressure. That is option B

The gravitational acceleration is the acceleration of an object that is under free fall. The acceleration due to gravity is 9.81 m/s2. above the sea level.

One of the factors that affect gravitational acceleration is depth. This is because as the depth increases so will pressure increase.

Increase in pressure leads to increase in gravitational acceleration.

Therefore, the gravitational acceleration on the board of the Deepsea Challenger when it is in the Mariana Trench, 11 km below the surface of the Pacific Ocean is very large due to the high pressure.

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[tex]\huge\underline{\underline{\boxed{{ \mathbb{SOLUTION:}}}}}[/tex]

[tex]\leadsto[/tex] Total internal reflection occurs when a ray of light is traveling through a medium and, when that medium changes, it does not refract into the second medium but instead it reflects back into the first medium.

By Snell's law, we know that

[tex]\longrightarrow \sf{n_1 sin \emptyset_1 = n_2 sin \emptyset_2}[/tex]

If this happens, then [tex]\sf{n_2 \angle n_1}[/tex], and the ray does not lose intensity due to refraction.

[tex]\huge\underline{\underline{\boxed{\mathbb{ANSWER:}}}}[/tex]

[tex]\large \bm{ A.}[/tex] A ray of light has the same intensity both entering and exiting a fiber optic cable.

[tex]E = \int\limits^2_{-3} {} \, \frac{27dy}{( 4 - y)^2}[/tex] is the integrals for the magnitude of the electric field.

A characteristic of electricity exists at every location in space when charge of any kind is present. The value of E, often known as the electric field strength, electric field intensity, or just the electric field, expresses the strength and direction of the electric field.

The formula for the electric field due to a point charge is:

[tex]E = \frac{kq}{r^2}[/tex]

Here q is the charge, r is the distance from the charge, and k = 8.99 × [tex]10^9 Nm^2/ C^2[/tex]

Imagine an infinitely - tiny portion of this charge distribution that has a charge [tex]dq[/tex]. This charge produces an electric field dE with magnitude:

                           [tex]\int\limits^ {} \, dE = \int\limits^ {} \, \frac{k dq}{r^2}[/tex]

                               [tex]E = \int\limits^ {} \, \frac{k dq}{r^2}[/tex]

Here, λ = 3.0 nC/m dq

           = λ.dy dE = ∫k.dq

From y = -3 m to y = 2 m, there is a 3.0 nC/m uniform linear charge distributed along the y axis.

The integrals for the magnitude of the electric field at y = 4 m on the y axis:

[tex]E = k \lambda \int\limits^2_{-3} {} \, \frac{dy}{( 4 - y)^2}[/tex]

[tex]E = \int\limits^2_{-3} {} \, \frac{27dy}{( 4 - y)^2}[/tex]

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Aster's final position from her initial position is 63 m approximately. She will head north west direction to return to her initial position

Displacement is the distance travelled in a specific direction. It is a vector quantity.

Given that a person walks first 70 m in the direction 37° north of east, and then walks 82 m in the direction 20° south of east, and finally walks 28 m in the direction 30° west of north.

a) Let P be the Aster's final position from her initial position?

We can use bearing by using Cosine formula to solve this question.

P² = 70² + 82² - 2 × 70 × 82 cos 73

P² = 4900 + 6724 - 11480 cos 73

P² = 11624 - 3356.43

P² = 8267.57

P = √8267.57

P = 90.9 m

P = 90.9 - 28

P = 62.9 m

We can get the angle by using Sine rule

82/ sin Ф = 90.9 / sin 73

sin Ф = 0.8627

Ф = [tex]Sin^{-1}[/tex] (0.8627)

Ф = 59.6°

Ф = 60°

b)  She will head north west direction to return to her initial position

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(a) Converting 45.0° to radians is 0.785 radian.

(b) Converting 13.0 rad to revolutions is 2.1 rev.

(c) Converting 76.5 revolution per minute to rad/s is 8.02 rad/s.

To convert 45.0 degrees to radians, we use the following method;

180⁰ = π radians

45⁰ = ?

= (45 x π)/180

= 0.785 radian

2π radians = 1 rev

13 radians = ?

= (13)/(2π)

= 2.1 rev

= 76.6 rev/min x 2π rad/rev x 1 min/60 s

= 8.02 rad/s

Thus, converting 45.0° to radians is 0.785 radian.

Converting 13.0 rad to revolutions is 2.1 rev.

Converting 76.5 revolution per minute to rad/s is 8.02 rad/s.

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Answer:

by using a magnetic field

Use a magnet to attract the iron fillings from the sand!

Hope this helps!

Answer:

When an object is immersed in water. it is pulled downwards due to gravitational pull of earth. Water exerts upward force on the object. This makes object rise up. This upward force is called buoyancy or upthrust.

Answer:

The braking distance would be about nine times as long (assuming that acceleration during braking stays the same.)

Explanation:

Let [tex]u[/tex] denote the initial velocity of the vehicle ([tex]20\; \text{mph}[/tex] or [tex]60\; \text{mph}[/tex]) and let [tex]v[/tex] denote the velocity of the vehicle after braking ([tex]0\; \text{mph}[/tex]). Let [tex]x[/tex] denote the braking distance.

Assume that the acceleration during braking are both constantly [tex]a[/tex] in both scenarios. The SUVAT equations would apply. In particular:

[tex]\begin{aligned} x &= \frac{v^{2} - u^{2}}{2\, a}\end{aligned}[/tex].

Since [tex]v = 0[/tex] (the vehicle has completely stopped), the equation becomes [tex]x = (-u^{2}) / (2\, a)[/tex].

Assuming that [tex]a[/tex] (braking acceleration) stays the same, the braking distance [tex]x[/tex] would be proportional to [tex]u^{2}[/tex], the square of the initial velocity.

Hence, increasing the initial speed from [tex]20\; \text{mph}[/tex] to [tex]60\; \text{mph}[/tex] would increase the braking distance by a factor of [tex]3^{2} = 9[/tex].

Answer:

9 times

Explanation:

The constant angular acceleration (in rad/s²) of the centrifuge is 255.66 rad/s².

The constant angular acceleration of the centrifuge is calculated as follows;

ωf² = ωi² - 2αθ

where;

When the centrifuge is switched off, the final angular velocity = 0

Initial angular velocity: ωi = 3,750 rev/min x 2π rad/rev x 1 min/60 s = 392.7 rad/s

angular displacement: θ = 48 rev = 48 rev x 2π rad/rev = 301.6 rad

0 = ωi² - 2αθ

2αθ = ωi²

α = ωi²/2θ

α = (392.7²) / (2 x 301.6)

α = 255.66 rad/s²

Thus, the constant angular acceleration (in rad/s²) of the centrifuge is 255.66 rad/s².

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The volume of the tire at the given diameter and thickness of tube is determined as  1,128.2 cubic inch.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

The volume of the tire is the measure of the product of area and thickness of the tire.

The volume of the tire is calculated as follows;

Radius of the tire = 0.5 x 26" = 13"

Volume of the tire = Area x thickness

Volume of the tire = πr² x h

where;

Volume of the tire = π(13)² x (2.125)

Volume of the tire =  1,128.2 cubic inch

Thus, the volume of the tire at the given diameter and thickness of tube is determined as  1,128.2 cubic inch.

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The electric filed in V/m is 1.58 * 10^6 V/m

We know that the electric field is obtained as the ratio of the voltage to the distance that separates the plates.

Thus;

E = V/d

E = electric field

V = voltage

d = distance of separation

E = 24 * 10^3 V/1.52 * 10^-2 m

E = 1.58 * 10^6 V/m

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Answer:

B

Explanation:

friction opposes motion

Friction typically Slows down objects

While this is almost true for a wide range of low speeds, as speed increases and air friction is reckoned with, it has been found that friction depends not only on speed, but also on speed squared and sometimes on higher powers of friction. speed.

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