The distance, x, covered by a particle in time, t, is given as x=a +bc+ct^2 +dt^3
.find the dimension of the constants a, b, c and d​

Answer:

Use Fc centripetal force as positive and W the weight as negative

N = m v^2 / R + m g

v^2 = (N - m g) R / m

v^2 = (995 - 57 * 9.8) 42.7 / 57 = 327 m^2/s^2

v = 18.1 m/s

Note: N - m g is the net force producing the centripetal force

Given data

*The weighing scale submerged in water is 3 N

*The weighing scale submerged out of water is 5 N

The buoyant force on the rock is calculated as

Thus, the buoyant force on the rock is 2 N

The weight of the pasta is 113.4g.

The weight of an object is defined as the force of gravity acting on it, and it can be calculated by multiplying the mass by the acceleration of gravity, w = mg.

The formula for calculating an object's mass based on its weight is Mass is equal to Weight divided by Gravity's Acceleration Convert the weight in pounds to the equivalent weight in Newtons. Mass is measured in Newtons in the formula for calculating mass based on weight.

Given,

The plastic container weighs 56.7 g

Total weight is 170.1 g

Solution:

The weight of the pasta = Total weight - Plastic container's weight

= 170.1 - 56.7

= 113.4g

Therefore,

The weight of the pasta is 113.4g.

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Answer:

Choice E.

Amplitude: \(20\; {\rm cm}\).

Frequency: \(2\; {\rm Hz}\).

Explanation:

The amplitude of a simple harmonic motion (SHM) is the maximum displacement from equilibrium.

In this question, the equilibrium is in the center of the two extremes. With one extreme at \(x = 10\; {\rm cm}\) and the other at \(x = 50\; {\rm cm}\), the center will be at \((1/2)\, (10 + 50)\; {\rm cm} = 30\; {\rm cm}\).

The maximum displacement will be \((50\; {\rm cm} - 30\; {\rm cm}) = 20\; {\rm cm}\) (or equivalently, \((30\; {\rm cm} - 10\; {\rm cm}) = 20\; {\rm cm}\).

Frequency measures the number of cycles completed in unit time (e.g., one second.) In one full cycle of an SHM, the oscillator will travel from one extreme to another and then back to the original extreme. In this question:

In other words, one full cycle of this SHM will take \(0.25\; {\rm s} + 0.25\; {\rm s} = 0.50\; {\rm s}\). The period of this SHM will be \(0.50\; {\rm s}\). Hence, the frequency of this SHM will be:

\(\begin{aligned} (\text{frequency}) &= \frac{1}{(\text{period})} \\ &= \frac{1}{0.50\; {\rm s}} \\ &= 2\; {\rm Hz}\end{aligned}\).

Answer:

Explanation:

"fuse wire" typically refers to a thin, single-use wire that is used to protect an electrical circuit from overloading or short circuiting. The wire is designed to melt and break the circuit if the current flowing through it exceeds a certain level, which helps to prevent damage to the electrical equipment or a potential fire hazard. Once the fuse wire has melted, it must be replaced with a new one.

an "MCB" (miniature circuit breaker) is a type of switch that automatically trips and breaks the circuit when there is an overcurrent or short circuit.

Unlike a fuse wire, an MCB can be reset after it has tripped, making it more convenient for protecting electrical circuits. MCBs are typically more expensive than fuse wires, but they offer greater protection and are often used in modern electrical systems.

Answer:

F_{total}= 8.25 \(\frac{G m^2}{L^2}\),      θ’= 194º

Explanation:

To solve this problem we must use the law of universal gravitation and vectorly add the forces

         F = \(G \frac{m_{1} m_{2} }{r^{2} }\)

Let us call the mass m with the subscript 1, the mass 3m with the subscript 3 and the mass 5m with the subscript 5, the total force on particle 1 is

          F_total = F₁₅ + F₁₃

The bold are vectors, in the attachment we can see a diagram of the angles and the forces, the distance between the masses is

           r = L

let's find the force between m1 and m5

           F₁₅ = G m₁ m₅ / r²

           F₁₅ = G m 5m / L²

           F₁₅ = G 5m² / L²

this force is on the line that joins the two masses, let's use trigonometry to decompose this force

           cos 30 = F₁₅ₓ / F₁₅

           sin 30 = \(\frac{Fx_{15y} }{F_{15} }\)

           F₁₅ₓ = F₁₅ cos 30

           \(F_{15y}\) = F₁₅ sin 30

equally with the force between mass 1 and mass 3

            F₁₃ = -G 3 m² / L²

            F₁₃ₓ = F₁₃ cos 30

            F_{13y} = F₁₃ sin 30

to find the total force we can add each component independently, see attached

X axis

           F_total x = -F₁₅ₓ + F₁₃ₓ

           F_total x = -G 5m2 / L² + G 3m² / L²

           F_total x = - G 2m² / L²

Y axis  

           F_total y = - F_{15y} - F_{13y}

           F_total y = - G 5m² / L² - G 3 m² / L²

           F_toal y = - G 8 m² / L²

We can give the result in two ways

1) F_total = - G m ^ 2 / L² (2 i ^ + 8 j ^)

2) in the form of module and angle.

Let's use the Pythagorean theorem

       \(F_{total}^{2} = F_{total x}^{2} + F_{total y}^2\)

       \(F_{total}\) = \(\frac{G m^{2} }{L^2} \sqrt{(2^2 + 8^2)}\)

       F_{total}= 8.25 \(\frac{G m^2}{L^2}\)

with trigonometry

        tan θ = \(\frac{F_{total y} }{F_{total x} }\)

        tan θ = 8/2

        θ = tan⁻¹ 4

        θ = 76º

if we measure this angle from the positive side of the x axis in a counterclockwise direction

       θ’= 270 -76

       θ’= 194º

Answer:

Less than the distance

Answer: A straight line on the coordinate plane where all points on the line have the same y-coordinate.

Explanation: The purpule iine is the horizontal line:

Answer:

Electromagnetic waves

As you pass over the top of the bump, the apparent weight of a 67 kg person in a car is therefore -17.80N.

Constant motion is a sort of motion that takes place when either the object's speed varies by the same amount every second or its distance travelled is the same every second. A car that goes continuously for 5 seconds in a straight line at 20 metres per second is said to be in motion. An object is considered to be moving at a constant speed when it covers the same distance in the same amount of time. When moving at a constant pace, an object covers a certain distance in a fixed amount of time. S = d t is a formula that can be used to express the speed.

The body is said to be moving at a uniform speed if it travels the same distance in the same amount of time. If the body goes in a straight line without changing its direction, the velocity is said to be constant. In all scenarios, there is no acceleration. Recall that the uniform velocity is a constant velocity as well.

-mg+N = -mass (v2/r) -(67(9.8) +N

= -(67(9.30/35) +N

=-17.80N

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ANSWER:

b. 10V

STEP-BY-STEP EXPLANATION:

The number of coils is the same when there are 3, we can see that in this case the voltage is 10 V.

Therefore, the correct answer is b. 10V

When Sally puts on wool socks and rubs her feet on a nylon carpet, static electricity builds up through a process involving the movement of electrons. The friction between the wool socks and the nylon carpet causes electrons from the wool socks to move to the carpet, resulting in Sally and her socks gaining a negative charge.

The correct answer would be the friction causes electrons from the wool socks to move to Sally, giving Sally a negative charge.

The friction between the wool socks and the nylon carpet causes electrons from the wool socks to move to the carpet, resulting in Sally and her socks gaining a negative charge. This is due to the phenomenon known as the triboelectric effect.

The triboelectric effect occurs when two materials come into contact and then separate. During the rubbing process, the atoms in the two materials interact, causing the transfer of electrons between them. In this case, the wool socks have a greater affinity for electrons compared to the nylon carpet. As a result, electrons from the socks are transferred to the carpet, leaving the socks with a positive charge and the carpet with a negative charge.

Sally, wearing the wool socks, experiences an accumulation of excess electrons on her feet, giving her a negative charge. This excess negative charge on her body can lead to static electricity-related phenomena, such as experiencing a shock when touching a metal object or seeing her hair stand on end when near certain surfaces.

It's important to note that the movement of electrons determines the charge distribution during the triboelectric effect. In this scenario, electrons move from the wool socks to the nylon carpet, resulting in Sally and her socks gaining a negative charge.

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Answer: The depth of the ocean is 650 feets at the bottom of the sunlight zone.

The distance travelled by echo sound is given by the formula -

Speed = 2×distance/time

So, calculating the speed of sound from the formula using distance and time

Speed = 2×25/(1/100)

Speed = 50×1000

Speed of sound = 5000 feet/second

Now, calculating the distance or depth of ocean at the bottom of the sunlight zone -

Distance = (speed×time)/2

Distance = (5000×26/100)/2

Distance = 1300/2

Distance = 650 feets

Hence, the depth of ocean is 650 feets.

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Answer:

We can start by using the formula:

distance = speed x time

where distance is twice the depth of the ocean at the bottom of the Sunlight Zone (since the pulse travels down to the seafloor and then back up), speed is the speed of sound in water, and time is the round-trip time of the pulse.

The speed of sound in water is approximately 1,500 meters per second (or 4,921 feet per second).

Converting the round-trip time to seconds, we have:

26 seconds - 1 second = 25 seconds

Substituting the values into the formula:

2 x depth = 4,921 feet/second x 25 seconds

2 x depth = 123,025 feet

depth = 61,512.5 feet

Therefore, the ocean at the bottom of the Sunlight Zone is about 61,512.5 feet deep.

The component of the cannonball's velocity parallel to the ground at the instant is 79.1 m/s.

What is a velocity?

Velocity is a vector quantity that describes the rate of change of an object's position in a given direction. It is equal to the displacement of an object divided by the time taken for the displacement to occur.

Vx = V * cos(theta)

where:

Vx = the component of the velocity parallel to the ground

V = the initial velocity of the cannonball, which is 96 m/s

theta = the angle that the cannon is tilted upward, which is 35 degrees

We can plug in the values and solve for Vx:

Vx = 96 m/s * cos(35 degrees)

Vx = 79.1 m/s (rounded to one decimal place)

Therefore, the component of the cannonball's velocity parallel to the ground at the instant it is fired is approximately 79.1 m/s.

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Answer:

A

Explanation:

electric force

The electrostatic force between the moon and the planet can be neglected. Hence, option (A) is correct.

The given problem is based on the comparison between the gravitational force and electrostatic force. Consider the two bodies as moon and a planet such that the force exerted between the moon and the planet is given as,

\(F_{g}=\dfrac{G\times M \times m}{r^{2}}\) ..................................................(1)

Here, G is the gravitational constant, M is the mass of moon, m is the mass of planet and r is the distance between the moon and the planet.

And the electrostatic force is the force between the two charged entities on moon and the planet. So, it is given as,

\(F_{e}=\dfrac{k \times Q \times q}{r^{2}}\) ....................................................(2)

Here, k is the Coulomb's constant, Q is the charge entity at moon and q is the charged entity on planet.

The forces obtained in equation (1) and (2) depends on the masses and charges, which clearly signifies that the masses have more numerical value than charges, hence the electrostatic force will leave much lesser influence than gravitational force. So, it can be neglected.

Thus, we conclude that the electrostatic force between the moon and the planet can be neglected. Hence, option (A) is correct.

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The period of the simple harmonic motion of the center of mass of the two spheres is approximately 0.770 seconds.

To find the period of the simple harmonic motion of the center of mass of the two spheres, we need to use the equation for the period of a mass-spring system:

T = 2π√(m/k)

where T is the period, m is the total mass of the system (two spheres), and k is the spring constant.

First, we need to find the total mass of the system:

m = 2m1 = 2(0.852 kg) = 1.704 kg

where m1 is the mass of one sphere.

Next, we need to find the spring constant:

k = 153 N/m

Now, we can calculate the period:

2π√(1.704 kg/153 N/m) ≈ 0.770 s

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Answer:

The boiling point of nitrogen on the absolute temperature scale is 77.15 K

Explanation:

Temperature in Kelvin(Absolute temperature) = Temperature in Celcius + 273.15.

Answer:

The answer of this question is windmill

Net force applied on the soccer ball was approximately 250 N (newtons) when it was kicked by the player.

We use Newton's second law of motion, which states that net force (F_net) applied to an object is equal to the product of its mass (m) and acceleration (a):

F_net = m * a

In this case, mass of the soccer ball is given as  0.5 kg and the acceleration is 500 (m)/(s²), so:

F_net = 0.5 kg * 500 (m)/(s²) = 250 N

Therefore,  net force applied on the soccer ball was approximately 250 N (newtons) when it was kicked by the player.

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Answer:

B. Photosynthesis occurs in all organisms

Hope this helps!! :)

Melvina's potential energy is 54,880 Joules.

To calculate Melvina's potential energy, we need to use the formula for gravitational potential energy:

Potential energy = mass × gravitational acceleration × height

Potential energy is a measure of the energy an object possesses due to its position relative to other objects. In this case, Melvina's potential energy is a result of her height above the ground. As she stands on the ledge of the burning building, her potential energy is stored and can be converted into other forms of energy if she were to jump or fall. The potential energy will decrease as she descends, and it will be converted into kinetic energy (energy of motion).

Given that Melvina has a mass of 70 kg and the ledge is 80 m above the ground, we can substitute the values into the formula:

Potential energy = 70 kg × 9.8 m/s² × 80 m

Calculating this, we find:

Potential energy = 54,880 Joules

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The value of the inductance, in , microhenrys of Tarik's solenoid is approximately 1.6239 microhenrys.

To calculate the inductance of a solenoid, we can use the formula:

L = (μ₀ * N² * A) / l

where L is the inductance, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), N is the number of turns, A is the cross-sectional area of the solenoid, and l is the length of the solenoid.

In this case, we have:

N = 175 turns

Diameter = 8.05 mm = 0.00805 m (converted to meters)

Radius = Diameter / 2 = 0.00805 m / 2 = 0.004025 m

Length (l) = 2.37 cm = 0.0237 m (converted to meters)

First, let's find the cross-sectional area (A) using the formula for the area of a circle:

A = π * r² = π * (0.004025 m)² ≈ 5.08398 × 10⁻⁵ m²

Now we can plug in the values into the formula for inductance:

L = (4π × 10⁻⁷ T·m/A * (175)² * 5.08398 × 10⁻⁵ m²) / 0.0237 m

L ≈ (1.2566 × 10⁻⁶ * 30625 * 5.08398 × 10⁻⁵) / 0.0237

L ≈ (38.5086 × 10⁻⁶) / 0.0237

L ≈ 1.6239 × 10⁻⁶ H

Now, let's convert the inductance from henrys to microhenrys:

L ≈ 1.6239 × 10⁻⁶ H * 10⁶ μH/H ≈ 1.6239 μH

So the inductance of Tarik's solenoid is approximately 1.6239 microhenrys.

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The masses of the two objects MA and MB in the binary system are 4 Mo respectively.

The masses of binary systems can be calculated using Kepler's laws of planetary motion and observations of the system.

Let's denote the masses of the two objects as MA and MB, where MA is the mass of object A and MB is the mass of object B. We know that the total mass of the binary system is 8 Mo, so:

MA + MB = 8 Mo

We also know that the ratio of the distances between the two objects is 1/3. Let's denote the distance between the two objects as d, so we have:

d(A to B) / d(Binary System) = 1/3

We can simplify this equation by using the fact that the distances between the objects and the binary system add up to the total distance between the objects:

d(A to B) + d(B to binary system) = d(Binary system)

Since we know the ratio of the distances, we can substitute 1/3d for d(B to binary system):

d(A to B) + 1/3d = d(Binary system)

3d(A to B) + d = 3d(Binary system)

Substituting d(A to B) for d(Binary system) - d(B to binary system), we get:

3d(A to B) + d = 3(d(A to B) + d(B to binary system))

2d(A to B) = 2d(B to binary system)

d(A to B) / d(B to binary system) = 1

So the two objects are at the same distance from the binary system center of mass. This means that the masses of the two objects are equal:

MA = MB

Substituting this into the first equation, we get:

2MA = 8 Mo

MA = MB = 4 Mo

Therefore, the mass of each object is 4 Mo.

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Answer:

445 kPa

Explanation:

Use for conversion rates:

101.325 kPa = 760 mmHg = 14.7 psi

2637.5 mmHg × (101.325 kPa / 760 mmHg) = 351.6 kPa

13.6 psi × (101.325 kPa / 14.7 psi) = 93.7 kpa

The total pressure is:

351.6 kPa + 93.7 kPa = 445.3 kPa

Rounded to three significant figures, the pressure is 445 kPa.

As the book fell through the air and eventually hit the ground, the energies  of the system were converted from one form to another.

Option D is correct.

Energy is described as  the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.

The forms of energy includes:

Chemical energy.

Electrical Energy.

Mechanical Energy.

Thermal energy.

Nuclear energy.

Gravitational Energy.

In conclusion, When the book fell through the air and hit the ground, the potential energy it possessed due to its position above the ground was converted into kinetic energy as it accelerated towards the ground.

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Answer:

Decrease

Explanation:

Decrease

Vertical component = v sin (angle)

  sin 30 is less than sin 35

The required, it experiences a downward force due to gravity and a force due to air resistance.

Projectile motion is the movement of an entity projected into space. After the initial force that launches the object, it only experiences the force of gravity. The object is called a projectile, and its path is called its trajectory.

Here,

When throwing a ball vertically upward, there is a displacement of about 1.0 m from the initial position of the hand to the position where the ball leaves the hand. The mass of the ball is 0.80 kg and it reaches a maximum height of about 20 m above the initial position of the hand. While the ball is in the hand after it leaves, it experiences a downward force due to gravity and a force due to air resistance.

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