What makes science different from other fields of knowledge like art or philosophy?

Final answer:

The period of oscillation of a mass on a spring is the same on both Earth and the Moon, as it is independent of gravity.

Explanation:

The question asks where the period of oscillation of a mass on a spring is the greatest, either on Earth or on the Moon. The period of a spring-mass system, according to the formula T = 2π√(m/k), where T is the period, m is the mass, k is the spring constant, and π (pi) is approximately 3.14159, is independent of gravity. Hence, the gravitational differences between the Earth and the Moon do not affect the period directly. However, external forces like gravity can influence the amplitude of the oscillation, not the period itself. Therefore, the period of oscillation will be the same on both the Earth and the Moon, assuming no other factors are changed.

To increase the resistance of the copper wire by 18%, the temperature will be increase to 46.47 °C

α = R₂ – R₁ / R₁(T₂ – T₁)

0.0068 = 1.18R – R / R(T₂ – 20)

0.0068 = 0.18R / R(T₂ – 20)

0.0068 = 0.18 / (T₂ – 20)

Cross multiply

0.0068 (T₂ – 20) = 0.18

Divide both side by 0.0068

T₂ – 20 = 0.18 / 0.0068

T₂ – 20 = 26.47

Collect like terms

T₂ = 26.47 + 20

T₂ = 46.47 °C

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(a). The restoring force in the spring will be [tex]3F[/tex]  if it is stretched to a length of [tex]\boxed{13\,{\text{cm}}}[/tex] .

(b). The restoring force in the spring will be [tex]2F[/tex]  if it is compressed to a length of [tex]\boxed{8\,{\text{cm}}}[/tex] .

Further Explanation:

When we compress or stretch a spring from its natural length, there is a restoring force developed in the spring due to the compression and stretching of the spring.

The restoring force experienced by the spring due to stretching is expressed as:

[tex]F=k\cdot\Delta x[/tex]                                                           …… (1)

Here, [tex]F[/tex]  is the restoring force developed in the spring, [tex]k[/tex]  is the spring constant of the spring and [tex]\Delta x[/tex]  is the length through which the spring is stretched.

The spring experiences a restoring force of  [tex]F[/tex] when it is stretched to a length of [tex]11\,{\text{cm}}[/tex]  from its natural length [tex]10\,{\text{cm}}[/tex] .

[tex]\begin{aligned}\Delta x&={x_f} - {x_i}\\&=0.10 - 0.11\\&=0.01\,{\text{m}}\\\end{aligned}[/tex]

Substitute the values of force and change in length in equation (1).

[tex]\begin{aligned}F&=k\cdot0.01\hfill\\k&=\frac{F}{{0.01}}\hfill\\\end{aligned}[/tex]

Part (a):

When the spring experiences a restoring force of [tex]3F[/tex] , then the stretched length of the spring should be:

[tex]3F=k.\Delta x[/tex]

Substitute [tex]\frac{F}{{0.01}}[/tex]  for [tex]k[/tex]  in above expression.

[tex]\begin{aligned}3F&=\frac{F}{{0.01}}\cdot\Delta x' \\\Delta x'&=3\times0.01\,{\text{m}}\\&=3\,{\text{cm}}\\\end{aligned}[/tex]

So, the stretched length of the spring becomes:

[tex]\begin{aligned}L&={x_o}+\Delta x' \\&=10\,{\text{cm}}+3\,{\text{cm}}\\&=13\,{\text{cm}}\\\end{aligned}[/tex]

Thus, the restoring force in the spring will be [tex]3F[/tex]  if it is stretched to a length of [tex]\boxed{13\,{\text{cm}}}[/tex] .

Part (b):

The restoring force of magnitude [tex]2F[/tex]  is experienced by the spring on compression. The change in length due to compression will be:

[tex]2F=k\cdot\Delta x''[/tex]

Substitute [tex]\frac{F}{{0.01}}[/tex]  for  [tex]k[/tex] in above expression.

[tex]\begin{aligned}2F&=\frac{F}{{0.01}}\cdot\Delta x''\\\Delta x''&=2\times0.01\,{\text{m}}\\&=2\,{\text{cm}}\\\end{aligned}[/tex]

So, the compressed length of the spring becomes:

[tex]\begin{aligned}L'&={x_o}-\Delta x''\\&=10\,{\text{cm}}-{\text{2}}\,{\text{cm}}\\&=8\,{\text{cm}}\\\end{aligned}[/tex]

Thus, the restoring force in the spring will be [tex]2F[/tex]  if it is compressed to a length of [tex]\boxed{8\,{\text{cm}}}[/tex] .

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Work and energy

Keywords:

Spring, unstretched length, compressed, stretched, restoring force, 3F, 11 cm, F=kx, natural length of spring.

keep electrical hazards localized

Final answer:

The x-and y-components of the squirrel's average velocity for the given time interval are 1.4 m/s and -1.3 m/s, respectively. These are found by dividing the changes in position by the time interval.

Explanation:

The student is asking for the calculation of the components of the average velocity of a squirrel over a time interval. To find these components, we use the formula for average velocity, which is given by the change in position (Δx and Δy) divided by the change in time (Δt). The changes in the x- and y-coordinates are found by subtracting the initial coordinates from the final coordinates.

The change in the x-coordinate (Δx) is

5.3 m - 1.1 m = 4.2 m

The change in the y-coordinate (Δy) is

-0.5 m - 3.4 m = -3.9 m

The change in time (Δt) is

t2 - t1 = 3.0 s - 0 = 3.0 s

Thus, the x-component of the average velocity is

Δx/Δt = 4.2 m/3.0 s = 1.4 m/s

and the y-component of the average velocity is

Δy/Δt = -3.9 m/3.0 s = -1.3 m/s.

We must remember that the total net force equation at constant velocity is:

F – Ff = 0

of

F - µN = 0

Solution:

Ms = 1.99 × 1030 kg− mass of Sun;

Me = 5.98 × 1024kg− mass of Earth;

Mm = 7.35 × 1022kg − mass of Moon;

rSM = 1.50 × 1011m − distance to the Moon from the Sun;

rEM = 3.85 × 108m − distance to the Moon from the Earth;

The gravitational force that acts on the Moon by the Earth (Law of Gravity):

[tex]F_{e} = G \frac {M_{e} * M_{m} } {r^{2}_{EM}} = 6.67 x 10^{-11} N * (\frac {m} {kg})^{2}*\frac {5.98 * 10^{24} kg * 7.35 * 10^{22} kg} {(3.85 x 10^{8}m)^{2}} = 1.98 * 10^{20} N[/tex]

The gravitational force that acts on the Moon by the Sun (Law of Gravity):

[tex]F_{S} = G \frac {M_{s} * M_{m} } {r^{2}_{EM}} = 6.67 x 10^{-11} N * (\frac {m} {kg})^{2}*\frac {1.99 * 10^{30} kg * 7.35 * 10^{22} kg} {(1.50 x 10^{11}m)^{2}} = 4.34 * 10^{20} N[/tex]

Net gravitational force on the moon:

[tex]F = F_{e} + F_{s} [/tex]

Pythagorean theorem for a right triangle ABC:

[tex]F = \sqrt {F^{2}_{S} + F^{2}_{e}} = \sqrt {(1.98 * 10^{20}N)^{2} + (4.34 * 10^{20} N)^{2}} = 4.77 * 10^{20}N[/tex]

Answer: Answer: magnitude of the net gravitational force on the moon is 4.77 × [tex]10^{20} [/tex]N.

The net gravitational force on the moon due to the earth and sun can be calculated using Newton's Law of Universal Gravitation. We apply this law to both the earth-moon and sun-moon systems, and the net force is the vector sum of these two forces.

The net gravitational force exerted on the moon by the sun and the earth can be calculated using Newton's law of gravitation, which states that the force between two objects is proportional to the product of their masses divided by the square of the distance between them. We use this law twice: once for the earth-moon system and once for the sun-moon system.

For the Earth-Moon system: F_EM = (G * mass of earth * mass of moon) / (distance from earth to moon)². Given the values in the problem, this amounts to F_EM = (6.67 * 10⁻¹¹ N.m²/kg² * 5.98 * 10²⁴ kg * 7.35 * 10²² kg) / (3.85 * 10⁸ m)².

For the Sun-Moon system: F_SM = (G * mass of sun * mass of moon) / (distance from sun to moon)². Again, substituting the given values we have F_SM = (6.67 * 10⁻¹¹ N.m²/kg² * 1.99 * 10³⁰ kg * 7.35 * 10²² kg) / (1.5 * 10¹¹ m)².

The net gravitational force on the moon is given by the vector sum of these two forces, which form a right angle, due to the geometry of the situation. Hence, the net force is the hypotenuse of a right triangle with sides F_EM and F_SM, and can be calculated using Pythagoras' Theorem: Net Force = √(F_EM² + F_SM²).

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16.6 is the answer. Not 17.0 do not round.

In a ray diagram, the three rays usually originate from the same point on the object. Following predefined ray-tracing rules, these rays pass through or reflect off a lens or mirror, converging or diverging to form an image. The point where these rays intersect represents the location of the image.

In a ray diagram, the three rays typically start from the same point on the object. This point on the object is the source from which the rays emanate. As the rays travel towards the lens or mirror involved, they will follow particular paths based on a set of simple ray-tracing rules. For example, one ray might pass through the focal point on its way to the lens and exit the lens parallel to the optical axis. These rays will then converge or diverge to form an image, depending on the lens or mirror set-up.

It is important to note that although three rays are often drawn for clarity and verification, only two are necessary to locate a point in the image. The point at which these rays intersect on the other side of the lens or mirror is where the image of the point from which they originated is located. Following these ray-tracing rules correctly will provide an accurate representation of how light behaves in the given optical system, illustrating the fundamental principles of geometric optics.

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Answer:

B on EDGE2k21

Explanation:

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The average acceleration components of the jet plane for the given time interval are approximately 2.4, -1.9 m/s², calculated using the change in velocity components divided by the time interval.

To calculate the average acceleration of a jet plane flying at a constant altitude with given velocity components at two different times, we use the formula for average acceleration: a = (v_f - v_i) / Δt, where a is the average acceleration, v_f is the final velocity, v_i is the initial velocity, and Δt is the change in time.

Given the initial velocity components at t1=0 are v_x1 = 94 m/s and v_y1 = 110 m/s, and the final velocity components at t2=33.5 s are v_x2 = 175 m/s and v_y2 = 45 m/s, we can calculate the average acceleration components as follows:

Therefore, the average acceleration components for the time interval are approximately 2.4, -1.9 m/s².

A ball rolling down an incline has its maximum kinetic energy at the bottom of the incline because the potential energy is converted into kinetic energy as it descends down the slope.

In the context of Physics, a ball rolling down an incline has its maximum kinetic energy at the bottom of the slope. As the ball rolls downhill, potential energy (stored energy due to its position) is gradually converted into kinetic energy (the energy of motion). This is essentially the principle of conservation of energy. So, at the top of the incline, the ball's energy is primarily potential energy, but as it descends, it gains speed and thus kinetic energy. At the bottom of the slope, all the potential energy has been converted to kinetic energy, hence it is at its maximum. Friction and air resistance could decrease the kinetic energy slightly, but when neglecting these factors, the ball's kinetic energy is greatest at the lowest point.

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The ship that will speed up faster if they fire their rockets at the same time is; The one with the lower mass

We are told that;

There are two spaceships

Each spaceship has different masses

Each spaceship has rocket engines of identical force.

We know that formula for force is;

F = ma

Thus, if force is constant, the higher the mass, the lesser the acceleration and also the lesser the speed. Thus, the lower the mass the faster the speed.

This means the spaceship that will speed up faster will be the one with lesser mass.

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The mean and standard deviation are not appropriate for particle size distributions due to non-normal distributions, irregular particle shapes, discrete measurement methods, and differences in weighting methods that aren't captured by standard parametric statistics like mean and deviation.

The mean and standard deviation are not always appropriate for describing particle size distributions because particle sizes are often not normally distributed. In the case of particle size distribution, there can be significant skewness or a high level of kurtosis, leading to a distribution that significantly deviates from normality. Additionally, particles may be irregularly shaped, which affects how their size is represented and measured. When particle size is based on sieves, the analysis becomes discrete rather than continuous, which can limit the utility of standard deviation. Furthermore, different weighting methods, like number weighted distribution or intensity weighted distribution, significantly affect the representation of particle size, which the mean and standard deviation do not properly account for.

Moreover, in dynamic light scattering (DLS) methods, the assumption is made that particles are spherical and the distribution is monomodal, which might not hold true for all particle systems. Since the mass of a particle is proportional to the cube of its radius, if particles are crushed to become smaller, a sample with the same number of particles represents a significantly different mass, affecting the representativeness of mean and standard deviation.

Particle shape also influences the determination of size as particles often deviate from sphericity. The equivalent spherical diameter (ESD) used in dynamic measurements may vary, reflecting a limitation for standard mean and deviation metrics. Due to these complexities, particle size distributions are often better described using median particle sizes (such as D50) and span, a dimensionless number that provides insight into the width of size distribution.

Answer:

Explanation:

Torque is defined as the product of force and the perpendicular distance.

If we take a screw driver of small length then we need to apply a large force to open or tighten the screw.

If a screw driver of long arm, then we need to apply small force to open or tighten the screw.

The statement “When you jump start a vehicle, if the stalled vehicle started, then you remove the cables in the same order in which they were connected”, is false.

Go through these steps before you even connect the cables:

1.     Both batteries should have the same polarity and same voltage.

2.     Never let the vehicles touch each other and your cars should be near enough to connect the cables.

3.     Turn off the lights, accessories, and ignition switch in both cars. Put the vehicles in neutral mode and make sure the parking brake is set. Also wear safety glasses.

4.     Never smoke. An explosion is possible if sparks and ear a battery.

5.     Don’t try to it the battery if the weak battery is frozen because it can explode.

6.     Be sure to be able to identify the positive and negative terminals of both batteries. You need to have enough room to clamp to the cable terminals.

The temperature of the high-temperature reservoir of a Carnot engine releasing 80 MJ/hour to a 10°C reservoir and receiving energy at the rate of 40 kW is approximately 510.72 K. The power produced by this engine is approximately 17.78 kW.

The temperature of the high-temperature reservoir of the Carnot Engine can be determined using Carnot's theorem, which states that Qc/Qh=Tc/Th or its simplified version, efficiency (Eff) = 1 - (Tc/Th) for a Carnot engine. Given the energy released by the engine (Qc) as 80 MJ/hour or 22.22 kW, and the rate of energy addition (Qh) as 40 kW, we can determine the temperature of the high-temperature reservoir (Th) from the ratio of these values and the known temperature of the cold reservoir (Tc) of 10°C or 283.15 Kelvin (K).

To achieve this, we first determine the engine's efficiency. Given Qc and Qh, we have Eff = 1 - (Qc/Qh) = 1 - (22.22 kW / 40 kW) = 0.445 (or 44.5%). Applying this to the efficiency formula, 'Eff = 1 - (Tc/Th)', we can rearrange this to find 'Th = Tc / (1 - Eff) = 283.15 K / (1 - 0.445) = 510.72 K'. Hence, the temperature of the high-temperature reservoir is approximately 510.72 K.

The power produced is the difference between the energy added and the energy rejected, so Power = Qh - Qc = 40 kW - 22.22 kW = 17.78 kW.

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The power used to mow the lawn, with a force of 110 N applied to move the lawnmower at 0.80 m/s, is calculated using the formula P = F × v and results in 88 Watts.

To calculate the power used to mow the lawn, we use the formula for power, which is the rate of doing work. Power (P) is equal to the work done (W) divided by the time taken (t), or P = W/t. In this case, work done can also be described as the force applied (F) times the distance moved (d) in the direction of the force, but since the problem doesn't provide the distance and only provides the speed at which the lawnmower is moving, we can use another formula for power: P = F × v where v is velocity.

Given that the force (F) is 110 N and the velocity (v) is 0.80 m/s, we can find the power with P = 110 N × 0.80 m/s giving us:

P = 88 Watts.

This is the power used by the person to mow the lawn while applying a constant horizontal force to move the lawnmower at a constant speed.