A ray of light traveling in air strikes the surface of water at an angle of incidence of 35 degrees. Calculate the angle of refraction of the light in water. Index of refraction of water is 1.33, while that for air is 1.00.


Remember to identify all of your data, write the equation, and show your work.

Answer:

True

Explanation:

Answer: True

Explanation:

Climate is an average condition of weather for 30 years in a particular region. It can be measured on the basis of humidity, temperature, precipitation, wind speed and others.

The climates are generally define by the temperature and precipitation. The temperature may vary from cold to hot. The precipitation may also decide the climatic condition of a region such as the area which receives very low rainfall is expected to have dry and hot climatic condition.

In circuits, the average power is defined as the average of the instantaneous power  over one period. The instantaneous power can be found as:

[tex]p(t)=v(t)i(t)[/tex]

So the average power is:

[tex]P=\frac{1}{T}\intop_{0}^{T}p(t)dt[/tex]

But:

[tex]v(t)=v_{m}cos(\omega t) \\ \\ i(t)=i_{m}cos(\omega t)[/tex]

So:

[tex]P=\frac{1}{T}\intop_{0}^{T}v_{m}cos(\omega t)i_{m}cos(\omega t)dt \\ \\ P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}cos^{2}(\omega t)dt \\ \\ But: cos^{2}(\omega t)=\frac{1+cos(2\omega t)}{2}[/tex]

[tex]P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}(\frac{1+cos(2\omega t)}{2} )dt \\\\P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}[\frac{1}{2}+\frac{cos(2\omega t)}{2}]dt \\\\P=\frac{v_{m}i_{m}}{T}[\frac{1}{2}(t)\right|_0^T +\frac{sin(2\omega t)}{4\omega} \right|_0^T] \\ \\ P=\frac{v_{m}i_{m}}{2T}[(t)\right|_0^T +\frac{sin(2\omega t)}{2\omega} \right|_0^T] \\ \\ P=\frac{v_{m}i_{m}}{2}[/tex]

In terms of RMS values:

[tex]V_{RMS}=V=\frac{v_{m}}{\sqrt{2}} \\ \\ I_{RMS}=I=\frac{i_{m}}{\sqrt{2}} \\ \\ Then: \\ \\ P=VI[/tex]

Answer:

Explanation:

Assuming that h is much smaller than R, then we can say the acceleration of gravity is approximately constant.

Potential energy = Kinetic energy

mgh = 1/2 mv²

v = √(2gh)

v = √(2 (MG/R²) h)

v = √(2 MGh) / R

An expression for the object's speed as it hits the ground is:

v = √ [ ( 2GMh ) / ( R ( R + h ) ) ]

[tex]\texttt{ }[/tex]

Let's recall the Gravitational Force formula:

[tex]\boxed {F = G\ \frac{m_1 m_2}{R^2}}[/tex]

where:

F = Gravitational Force ( N )

G = Gravitational Constant ( = 6.67 × 10⁻¹¹ Nm²/kg² )

m = mass of object ( kg )

R = distance between object ( m )

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

Given:

mass of object = m

height position of object = h

mass of planet = M

radius of planet = R

initial speed of object = u = 0 m/s

Asked:

final speed of object = v = ?

Solution:

We will calculate the object's speed by using Conservation of Energy formula as follows:

[tex]Ep_1 + Ek_1 = Ep_2 + Ek_2[/tex]

[tex]-G \frac{Mm}{R + h} + \frac{1}{2}m u^2 = -G \frac{Mm}{R} + \frac{1}{2}m v^2[/tex]

[tex]-G \frac{Mm}{R + h} + \frac{1}{2}m (0)^2 = -G \frac{Mm}{R} + \frac{1}{2}m v^2[/tex]

[tex]-G \frac{Mm}{R + h} = -G \frac{Mm}{R} + \frac{1}{2}m v^2[/tex]

[tex]G \frac{Mm}{R} -G \frac{Mm}{R + h} = \frac{1}{2}m v^2[/tex]

[tex]G \frac{M}{R} -G \frac{M}{R + h} = \frac{1}{2} v^2[/tex]

[tex]v^2 = 2GM ( \frac{1}{R} -\frac{1}{R + h} )[/tex]

[tex]v^2 = 2GM\frac{h}{R(R +h) }[/tex]

[tex]\boxed {v = \sqrt { \frac{ 2GMh } { R(R +h) } } }[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Gravitational Force

Answer:

Explanation:

time = 2s + 6s = 8s

distance = 150m

speed = ?

velocity = ?

speed = distance ÷ time

        v = d / t

        v = 150 / 8

        v = 18,75 m/s

i'm not sure about velocity only the total speed

Final answer:

To determine the car's velocity, we broke down the journey into an acceleration phase and a constant velocity phase, used the kinematic equations to relate velocity, time, and distance, and solved the resulting equation to find that the velocity is approximately 13.64 m/s.

Explanation:

To find out the velocity of the car, we need to consider two phases of its journey: the acceleration part and the constant velocity part. First, let's assume the initial velocity is zero since it's not provided, and the car accelerates for 6 seconds to reach a velocity of v m/s.

During the acceleration phase, we use the equation [tex]s_{1}[/tex] = ut + (1/2)[tex]at^2[/tex], with u being the initial velocity and a being the acceleration. Here, the initial velocity u is 0, so [tex]s_{1}[/tex]= (1/2)[tex]at^2[/tex]. We don't directly know a, but we know the car reached a velocity of v after 6 seconds. For the acceleration, we use v = u + at, which gives us a = v/6 since u is 0.

Now, substituting this in the first equation, we get [tex]s_{1}[/tex] = (1/2)(v/6)*[tex]6^2[/tex] = 18v/2, therefore s1 = 9v. During the constant velocity phase, [tex]s_{2}[/tex] is easier to find as [tex]s_{2}[/tex] = vt, with t being 2 seconds, so [tex]s_{2}[/tex]= 2v. The total distance covered by the car s = [tex]s_{1} + s_{2}[/tex] = 9v + 2v = 11v.

Using the total distance of 150 meters given in the problem, we can write 150 = 11v, and solving for v we get v = 150/11, yielding a velocity of approximately 13.64 m/s.

The loss of kinetic energy in a bouncing ball is due to the transformation of energy into other forms like heat and sound, and the inelastic nature of collisions, which prevent the ball from reaching its original dropped height.

The loss of kinetic energy during a collision when a ball bounces can be explained by several factors. When a ball is dropped from a certain height, it converts potential energy into kinetic energy. Upon hitting the floor, some kinetic energy is transformed into other forms of energy such as sound, heat, and internal energy due to the deformation of the ball. Therefore, not all the kinetic energy is available to convert back into potential energy, resulting in a lower rebound height. This conservation of energy principle dictates that the ball will only bounce up to a certain percentage of the original height, in this case, 80%. This energy transformation is due to the inelastic nature of real-world collisions.

Answer:

A. Brahe and Kepler

Explanation:

The Copernican model was a heliocentric model of the universe. Copernicus thought that the Sun is stationary, and the Earth and the other planets are orbiting around it. He also noted that the stars are further away from the Sun compared to the distance between the Earth and the Sun. Three very important hings in his theory are that he thought that the Earth rotates around its own axis, revolves around the Sun, and has annual tilting of its axis. At some things, Copernicus was right with his theory, at some he wasn't, but anyway he made one giant step forward in the understanding of the universe. His theory was supported by many, though mostly after his death, with one of the most noticeable supporters of him being Ticho Brache and Kepler who made model of his theory, as well as improving it.

Answer:

The correct answer will be option A- Brahe and Kepler.

Explanation:

Copernicus presented his heliocentric model of the solar system in 1543 which stated that the sun is present at the center with all planets revolving around it.

This model was supported by the works of Tycho Brahe who also said that sun is the center of the earth and Johannes Kepler who gave the laws related to the motion of the planetary objects with the sun at the center.

Thus,  option A- Brahe and Kepler is the correct answer.

Answer:Hydrogen and Helium.

Explanation:

Answer:

hydrogen compound ices.

Explanation:

Answer: [tex]2.13(10)^{-19} J[/tex]

Explanation:

The photoelectric effect consists of the emission of electrons (electric current) that occurs when light falls on a metal surface under certain conditions.  

If the light is a stream of photons and each of them has energy, this energy is able to pull an electron out of the crystalline lattice of the metal and communicate, in addition, a kinetic energy.  

This is what Einstein proposed:  

Light behaves like a stream of particles called photons with an energy  [tex]E[/tex]

[tex]E=h.f[/tex] (1)

Where:

[tex]h=6.63(10)^{-34}J.s[/tex] is the Planck constant  

[tex]f[/tex] is the frequency

Now, the frequency has an inverse relation with the wavelength [tex]\lambda[/tex]:  

[tex]f=\frac{c}{\lambda}[/tex] (2)  

Where [tex]c=3(10)^{8}m/s[/tex] is the speed of light in vacuum  and [tex]\lambda=400nm=400(10)^{-9}m[/tex] is the wavelength of the absorbed photons in the photoelectric effect.

Substituting (2) in (1):

[tex]E=\frac{h.c}{\lambda}[/tex] (3)

So, the energy [tex]E[/tex] of the incident photon must be equal to the sum of the Work function [tex]\Phi[/tex] of the metal and the maximum kinetic energy [tex]K_{max}[/tex] of the photoelectron:  

[tex]E=\Phi+K_{max}[/tex] (4)  

Rewriting to find [tex]K_{max}[/tex]:

[tex]K_{max}=E-\Phi[/tex] (5)

Where [tex]\Phi[/tex] is the minimum amount of energy required to induce the photoemission of electrons from the surface of a metal, and its value depends on the metal:

[tex]\Phi=h.f_{o}=\frac{h.c}{\lambda_{o}}[/tex] (6)

Being [tex]\lambda_{o}=700nm=700(10)^{-9}m[/tex] the threshold wavelength (the minimum wavelength needed to initiate the photoelectric effect)

Substituting (3) and (6) in (5):  

[tex]K_{max}=\frac{h.c}{\lambda}-\frac{h.c}{\lambda_{o}}[/tex]

[tex]K_{max}=h.c(\frac{1}{\lambda}-\frac{1}{\lambda_{o}})[/tex] (7)

Substituting the known values:

[tex]K_{max}=(6.63(10)^{-34}J.s)(3(10)^{8}m/s)(\frac{1}{400(10)^{-9}m}-\frac{1}{700(10)^{-9}m})[/tex]

[tex]K_{max}=2.13(10)^{-19} J[/tex] >>>>>This is the maximum kinetic energy that ejected electrons must have when violet light illuminates the material

As the photoelectric effect takes place, the maximum kinetic energy of ejected electrons is obtained to be [tex]2.13\times 10^{-19}\,J[/tex].

Einstein's photoelectric effect equation is given as;

[tex]KE_{max}=h\nu - \Phi[/tex]

But the work function can be written as;

[tex]\Phi = h \nu_0=\frac{hc}{\lambda _0}[/tex]

Therefore, the photoelectric equation can be rewritten as

[tex]KE_{max}=\frac{hc}{\lambda} - \frac{hc}{\lambda _0}= hc\,(\frac{1}{\lambda}+ \frac{1}{\lambda_0} )[/tex]

Now, substituting the known values, we get;

[tex]KE_{max}= (6.6\times 10^{-34}\,Js)\times (3\times 10^8\,m/s)\times(\frac{1}{400\times 10^{-9}\,m}- \frac{1}{700\times 10^{-9}\,m} )\\\\\implies KE_{max}=2.13\times 10^{-19}\,J[/tex]

Learn more about the photoelectric effect here:

https://brainly.com/question/25730863

Answer:

B

Explanation:

Friction acts in a direction opposite to the motion of an object

Friction force acts in a direction opposite to the intended motion of an object. It depends on the coefficient of friction between the surfaces and the normal force exerted in response to gravity.

In understanding the principles of Physics, the correct description of a friction force is that It acts in a direction opposite to the motion of an object. This phenomenon can be illustrated in several scenarios, such as a box sliding across a floor or objects moving on an inclined plane. In both cases, the friction force always opposes the motion of the object.

For instance, if a box is being pushed to the right, the frictional force works to the left. If an object has a component of its weight pulling it down an incline, the frictional force acts upward on the incline, opposing the intended motion.

It's important to note that the force of friction depends on two factors: the coefficient of friction between the two surfaces and the normal force exerted by the surface supporting the object in response to gravity. Furthermore, friction runs parallel to the surface between objects and perpendicular to the normal force.

https://brainly.com/question/34015822

#SPJ3

Answer:

C) 6272 J

Explanation:

The work done by the student is equal to the increase in gravitational potential energy; therefore, it is given by

[tex]W=Fd[/tex]

where

F = 784 N is the force, which in this case is equal to the weight of the student

d = 8.0 m is the vertical distance covered

Substituting numbers into the formula, we find:

[tex]W=(784 N)(8.0 m)=6272 J[/tex]

At the beginning of the 20th century (especifically 1924) the French physicist Louis De Broglie proposed in its doctoral thesis the existence of matter waves, that is to say that all matter has a wave associated with it.

De Broglie, in addition, deduced an equation by which the electron had a wavelength that depended on its momentum (hence its velocity).

These postulations were tested with the double slit experiment (formerly applied to photons) applied to electrons, and the result was: electrons (as well as the other particles different from the photons) are able to behave as waves.

It is important to note, this experimente was done in 1927 by Clinton J. Davisson and Lester Halbert Germer and was called the electron diffraction experiment. It consisted of bombarding with an electron beam a sample (nickel) and observing the resulting interference pattern.

In this way they demonstrated what de Broglie deduced mathematically.

it can be 5 to 7. :)

Answer:

The law prohibits a person from barring access to an electric vehicle/"ev"-designated parking space.

Final answer:

The law prohibits a person from occupying an EV-designated parking space unless they are driving an electric vehicle. Improper usage of such spots results in fines, similar to other regulated parking spots. Laws exist to maintain public safety and order, including regulations on parking and driving practices.

Explanation:

The law generally prohibits a person from occupying or parking in an electric vehicle (EV)-designated parking space unless the vehicle is an electric vehicle. Misuse of such designated parking spots, similar to those reserved for handicapped persons or pregnant women, can result in fines or legal penalties.

This is akin to the example where parking in a handicapped spot resulted in a police officer issuing a ticket, implying that the action was prohibited and enforceable by law. Additionally, company policies, such as the one that was violated when a truck was parked front-end first in a fleet yard, can also dictate proper parking practices that must be adhered to avoid repercussions.

Related to similar legal boundaries, new legislation often aims to enhance public safety and order, as in the case with laws against texting while driving. Ignoring such laws not only endangers others but is also a subject to legal action. As society evolves, the creation of new laws and the modification of existing ones ensure that ethical and safety standards are maintained in all aspects of daily life, including the use of public spaces and adherence to road safety guidelines.

Answer:

The forces (magnitude) would be the same; the electron would have a larger acceleration, and they will travel in opposite directions

Explanation:

- The magnitude of the force exerted on a charged particle by an electric field is

[tex]F=qE[/tex]

where q is the magnitude of the charge and E is the electric field strength. Since the proton and the electron have same electric charge magnitude (e, elementary charge), they will experience the same force under the same electric field.

- The acceleration of a particle is given by

[tex]a=\frac{F}{m}[/tex]

where F is the force exerted on the particle and m is the mass. Here, we said that the electron and the proton experience the same force F, however the mass of the proton is much larger (approx. 1800 times larger) than the mass of the electron, so the electron will experience a larger acceleration (because acceleration is inversely proportional to the mass)

- The direction of travel corresponds to the direction of the force. Since the proton is positively charged, the force exerted on it has same direction as the electric field; while since the electron is negatively charged, the force exerted on it has opposite direction to the electric field. Therefore, the two particles will travel into opposite directions.

Answer:

4 times taller

Explanation:

The horizontal distance travelled by a projectile is

[tex]d=v_x t[/tex] (1)

where [tex]v_x[/tex] is the horizontal velocity (which is constant) and t is the total time of the fall.

The total time of the fall can be found by analyzing the vertical motion of the projectile: the vertical position at time t is given by

[tex]y= h - \frac{1}{2}gt^2[/tex]

where h is the initial height, g = 9.8 m/s^2 is the acceleration due to gravity, t is the time.

The total time of the fall is the time t at which y=0 (the projectile reaches the ground), so

[tex]0=h-\frac{1}{2}gt^2\\t=\sqrt{\frac{2h}{g}}[/tex]

Substituting into (1),

[tex]d= v_x \sqrt{\frac{2h}{g}}[/tex]

This can be re-arranged as

[tex]d^2 = v_x ^2 \frac{h}{2g}\\h = \frac{2gd^2}{v_x^2}[/tex]

so we see that the initial height depends on the square of the horizontal distance travelled, d.

In this problem, one stands lands twice as far as the other stone does, so

d' = 2d

this means that the height of the taller builing is

[tex]h' = \frac{2g(2d)^2}{v_x^2}=4(\frac{2gd^2}{v_x^2})=4 h[/tex]

so the taller building is 4 times taller than the smaller one.

Answer:

142.2 m

Explanation:

The x-component of a certain vector can be found by using

[tex]v_x = v cos \theta[/tex]

where

v is the magnitude of the vector

[tex]\theta[/tex] is the angle between the direction of the vector and the positive x-direction

In this problem, we have

v = 253 m is the length (magnitude) of the vector

[tex]\theta=55.8^{\circ}[/tex] is the angle

Substituting into the formula, we find

[tex]v_x = (253 m) cos 55.8^{\circ}=142.2 m[/tex]

To find the X-component of a vector, use the formula Ax = A * cos(θ), where A is the magnitude and θ is the angle with the X-axis. For the given vector of 253 m at 55.8 degrees, calculate Ax = 253 * cos(55.8°).

The student is asking how to find the X-component of a vector with a given magnitude and direction. To find the X-component (Ax) of a vector, you can use the formula Ax = A * cos(θ), where A is the magnitude of the vector and θ is the angle it makes with the X-axis. In this case, the magnitude (A) is 253 m, and the angle (θ) is 55.8 degrees. Thus, applying the formula we get Ax = 253 m * cos(55.8°). You would need to use a calculator to find the cosine of 55.8 degrees and then multiply by 253 to find the X-component.

Answer:

42.6 N/m

Explanation:

The spring constant can be found by using Hooke's law:

F = kx

where

F is the force applied

k is the spring constant

x is the stretching/compression of the spring

In this problem, the mass applied is

m = 0.10 kg

so the force applied is the weight of the mass:

[tex]F=mg=(0.10 kg)(9.8 m/s^2)=0.98 N[/tex]

The stretching of the spring is

x = 2.3 cm = 0.023 m

So the spring constant is

[tex]k=\frac{F}{x}=\frac{0.98 N}{0.023 m}=42.6 N/m[/tex]

Answer: The value of spring constant is 42.6 N/m

Explanation:

Force is defined as the mass multiplied by the acceleration of the object.

[tex]F=m\times g[/tex]

where,

F = force exerted on the spring

m = mass = 0.10 kg

g = acceleration due to gravity = [tex]9.8m/s^2[/tex]

Putting values in above equation, we get:

[tex]F=0.10kg\times 9.8m/s^2\\\\F=0.98N[/tex]

To calculate the spring constant, we use the equation:

[tex]F=k\times x[/tex]

where,

F = force exerted on the spring = 0.98 N

k = spring constant = ?

x = length of the spring = 2.3 cm = 0.023 m   (Conversion factor:  1 m = 100 cm)

Putting values in equation 1, we get:

[tex]0.98N=k\times 0.023m\\\\k=\frac{0.98N}{0.023m}=42.6N/m[/tex]

Hence, the value of spring constant is 42.6 N/m

The size of a stable nucleus is limited due to the short range of the strong nuclear force. Heavy stable nuclei tend to have roughly the same number of protons as neutrons or fewer protons than neutrons.

The correct statements concerning stable nuclei are:

The strong nuclear force is an attractive force between nucleons, but it has a short range. This means that for larger nuclei, the repulsive force between protons is stronger than the attractive force, so more neutrons are needed to overcome the repulsion and stabilize the nucleus.

Answer:

[tex]9.45\cdot 10^{15} m[/tex]

Explanation:

The speed of light in a vacuum is:

[tex]c=3.0\cdot 10^8 m/s[/tex]

The distance that light travels in a time t is given by

[tex]d=ct[/tex]

where t is the time.

One year corresponds to a time of

[tex]t=3.156\cdot 10^7 s[/tex]

So, the distance travelled by the light in one year is

[tex]d=(3.0 \cdot 10^8 m/s)(3.156\cdot 10^7 s)=9.45\cdot 10^{15} m[/tex]

Answer:F = qv * Bsin( θ)

F : Magnetic force

q : charge of the particle

v : velocity of the particle

B: magnetic field

θ: angle between v and B

Explanation:

Answer:

F = qv * Bsin( θ)

F : Magnetic force

q : charge of the particle

v : velocity of the particle

B: magnetic field

θ: angle between v and B

Explanation:

Answer:

By a magnetic field: no

By an electric field: yes

Explanation:

The force exerted by a magnetic field on an electron is

[tex]F=qvB sin \theta[/tex]

where

q is the electron charge

v is the speed of the electron

B is the strength of the magnetic field

[tex]\theta[/tex] is the angle between the direction of v and B

As we see from the formula, if the electron is at rest, then v = 0, and therefore the force is also zero: F = 0. Therefore, the magnetic field cannot set the electron into motion.

On the other hand, the force exerted on an electron by an electric field does not depend on the speed:

[tex]F=qE[/tex]

where E is the intensity of the electric field

Therefore, the electric force acts also when the electron is at rest, so it is able to set the electron into motion.

Final answer:

An electron at rest cannot be moved by a stationary magnetic field but can be set into motion by an electric field. The force exerted by electric fields acts on stationary charged particles, while magnetic fields only affect moving charges.

Explanation:

An electron at rest cannot be set into motion by a stationary magnetic field because a magnetic field only exerts a force on a moving charged particle. However, if an electron is at rest in an electric field, it will experience a force that can set it into motion. This is because electric fields exert forces on charged particles regardless of their state of motion. For instance, electrons starting from rest and accelerated through a potential difference will move in circular paths when entering a uniform magnetic field, due to the force that acts perpendicular to their velocity and the magnetic field

Moreover, the relationship between electric and magnetic fields demonstrates that a pure electric field in one reference frame can be perceived as a combination of electric and magnetic fields in another frame if the particle is moving. This interplay is fundamental to many devices that rely on electromagnetic forces to function.

Answer:

Explanation:ruhfu

Final answer:

When the bottom microscope slide is rotated to make the wedge angle smaller while illuminated with monochromatic light, the interference fringes observed due to thin film interference become more closely spaced due to the more uniform air layer thickness.

Explanation:

When considering two identical microscope slides in air illuminated with monochromatic light, if the bottom slide is rotated counterclockwise about the point of contact in the side view so that the wedge angle gets a bit smaller, the fringes observed would change. These fringes are a result of thin film interference, a phenomenon where light waves that reflect off the different layers of a thin film interfere with each other, creating a pattern of bright (constructive interference) and dark (destructive interference) bands.

As the wedge angle decreases, the thickness of the air layer between the two slides changes more uniformly across the length of the slides. This uniformity in thickness leads to a more regular pattern of interference fringes. The fringes would become more closely spaced as the wedge angle decreases because the path difference between the light reflecting off the top and bottom surfaces of the air wedge changes more gradually. If the slides eventually become parallel, the fringes would theoretically form an infinitely fine pattern, but practically, the fringes would disappear as the condition for constructive or destructive interference would no longer be met in a discernible pattern.

P=IV, where P is power, I is resistance, and V is voltage.  Plug in and solve:

P=400(20)

P=8000W

Hope this helps!!

To calculate the power dissipated by a 400.0 ohm resistor with a 20.0 volt potential difference, use the formula [tex]P = V^{2}/R[/tex], yielding a result of 1.0 watt.

The magnitude of the power dissipated by a resistor can be calculated using the formula [tex]P = I^{2}R or P = V^{2}/R[/tex], where P is the power in watts, I is the current in amperes, V is the potential difference in volts, and R is the resistance in ohms.

Given a 400.0 ohm resistor with a potential difference of 20.0 volts, we can use the formula [tex]P = V^{2}/R[/tex] to find the power dissipated. Thus, P = (20.02)/400.0 = 400/400 = 1.0 watt.

Answer:

17 h

Explanation:

The command sent to the Voyager I is a radio wave signal, which travels at the speed of light:

[tex]c=3.0\cdot 10^8 m/s[/tex]

The distance between the Voyager I and the Earth is

[tex]d=1.8\cdot 10^{13} m[/tex]

So, the time taken for the signal to reach the probe is

[tex]t=\frac{d}{c}=\frac{1.8\cdot 10^{13} m}{3\cdot 10^8 m/s}=60,000 s[/tex]

Consindering that the number of seconds in 1 hour is

[tex]60\cdot 60 = 3600 s[/tex]

Then the time elapsed converted into seconds is

[tex]t=\frac{60000 s}{3600 s}=16.7 h \sim 17 h[/tex]

Final answer:

To determine the transmission time for a command sent to Voyager 1 when it entered interstellar space, we calculate the time for light to travel the distance of 1.8 x 10¹³ meters, which comes to approximately 16.67 hours.

Explanation:

The Voyager 1 spacecraft is known for being the farthest human-made object from Earth. When it entered interstellar space in August 2012, it was 1.8 x 10¹³ meters away from our planet. To calculate the time taken for a command to travel this distance, we use the speed of light, which is approximately 299,792,458 meters per second. The formula to calculate the time (t) taken for light to travel a certain distance (d) is t = d / c, where c represents the speed of light.

For Voyager 1:

Therefore, about 16.67 hours elapse between the time a command is sent from Earth and the time it is received by Voyager 1 when it entered interstellar space.

(a) -48.0 cm, diverging

We can use the lens equation:

[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]

where

f is the focal length

p = 16.0 cm is the object distance

q = -12.0 cm is the image distance (with a negative sign because the image is on the same side as the object, so it is virtual)

Solving for f, we find the focal length of the lens:

[tex]\frac{1}{f}=\frac{1}{16.0 cm}+\frac{1}{-12.0 cm}=-0.021 cm^{-1}[/tex]

[tex]f=\frac{1}{-0.021 cm^{-1}}=-48.0 cm[/tex]

The lens is diverging, since the focal length is negative.

(b) 6.38 mm, erect

We can use the magnification equation:

[tex]\frac{y'}{y}=-\frac{q}{p}[/tex]

where

y' is the size of the image

y = 8.50 mm is the size of the object

Substituting p and q that we used in the previous part of the problem, we find y':

[tex]y'=-y\frac{q}{p}=-(8.50 mm)\frac{-12.0 cm}{16.0 cm}=6.38 mm[/tex]

and the image is erect, since the sign is positive.

(c)

See attached picture.

The focal length of a provided lens is -9.6 cm, indicating a diverging lens. The image formed is inverted and has a height of 6.375 cm.

To help you with this question, we will take advantage of the lens formula, 1/f = 1/v - 1/u, where f is the focal length, v is the image distance and u is the object distance.

We can also utilize magnification formula for lenses, which is M = -v/u = h'/h, where h' is the height of the image and h is the height of the object.

(a) To ascertain the focal length of the lens, we plug given u and v into lens formula. The image is on the same side as the object, thus v is regarded as negative. By substituting the supplied figures, we get f = -9.6 cm. As the focal length is negative, the lens is a diverging lens.

(b) The magnification M can be calculated using the provided dimensions of the object and image. Given that object height (h) is 8.5mm and rearranging the magnification formula to solve for image height, h' equals -v * h / u, and what we get is -6.375cm. Therefore, the image is 6.375cm tall and it is inverted as its height is negative.

(c) The image is provided below.

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Answer:

No

Explanation:

The error in the sentence is that inertia is not a force.

In fact, inertia is just the tendency of an object to keep its state of rest/motion if the net force acting on it is zero. As stated in Newton's First Law, also called Law of Inertia:

"An object at rest will remain at rest and an object in motion will continue its motion with constant velocity if the net force acting on it is zero"

This law basically tells us that as long as there are no forces acting on an object, the object mantains its state of rest/motion. On the contrary, in order to change the state of motion of an object, we need a net force different from zero.

Answer:

Let's start by defining what is mass, gravity and weight:

The mass is the amount of matter that exists in a body, which only depends on the quantity and type of particles within it. This means mass is an intrinsic property of each body and remains the same regardless of where the body is located.

Gravity is an attraction force, which depends on the mass of the bodies and their distance.

Weight is the force that gravity exerts on matter and changes depending on where the body is located. Therefore, the weight of an object on Earth will not be the same as the weight of the same object on the Moon or on Mars.

Now, according to Newton's law of Gravitation, the force [tex]F[/tex] exerted between two bodies of masses [tex]m1[/tex] and [tex]m2[/tex]  and separated by a distance [tex]r[/tex]  is equal to the product of their masses and inversely proportional to the square of the distance:

[tex]F=G\frac{(m1)(m2)}{r^2}[/tex]    (1)

Where [tex]G[/tex]is the gravitational constant

In the case of our Earth, its mass  [tex]m1[/tex] and radius (distance [tex]r[/tex] from its center to its surface where an object is) are constant. So, we can write all these constant in one, in the following way:

[tex]g=G\frac{m1}{r^2}[/tex]   (2)

Where [tex]g[/tex]  is the gravity force on Earth and its value is [tex]9.8\frac{m}{{s}^2}[/tex]

.

Rewriting equation (1) with this consideration:

[tex]F=g.m_{2}[/tex]   (3)

Where [tex]F=W[/tex] is known as the weight:

[tex]W=g.m[/tex]    (4)

Here we can see the relationship among  mass [tex]m[/tex]  , weight [tex]W[/tex]  and gravity [tex]g[/tex]

Mass is a measure of the amount of matter in an object and is constant regardless of location. Weight, however, is a measure of the gravitational force acting on an object, varying with the force of gravity. Although often used interchangeably in everyday language, these concepts are distinct in physics.

Mass, weight, and gravity are closely related but distinct concepts in physics.

Mass is the quantity of matter in an object and does not change regardless of the object's location. It refers to how much 'stuff' an object is made of, measured typically in kilograms.

Weight, on the other hand, refers to the force that gravity exerts on an object. It is directly proportional to the object's mass and the acceleration due to gravity and is measured in newtons. Therefore, an object's weight can change depending on the gravitational force it experiences.

For example, an astronaut's mass remains the same whether she is on Earth or the moon. However, her weight changes, being only one-sixth on the moon of what it is on Earth because the moon's gravity is only one-sixth that of Earth's.

In conclusion, though often used interchangeably in everyday language, weight and mass are very different with weight being dependant on the force of gravity.

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1. Domain, kingdom, phylum, class, order, family, genus, species, and subspecies.

2. If a variety of the species with a certain gene is vulnerable to a specific disease, predator, or environmental development, other members of the species with variants of the gene may be better equipped to handle the problem, and the species won't die out, just a portion of the disadvantaged.

The taxonomic groups are ordered from largest to smallest as: domain, kingdom, phylum, class, order, family, genus, species, and subspecies. Genetic diversity promotes survival of a population by offering variability that could be beneficial in changing environments.

The taxonomic groups from largest to smallest are: domain, kingdom, phylum, class, order, family, genus, species, and subspecies. Genetic diversity significantly determines a population's chances of survival. A wide genetic diversity allows a population to be more resilient to changes in the environment as it reduces the chance of the entire population being wiped out by a single threat. For instance, in a disease outbreak, a genetically varied population is more likely to contain individuals with resistance, ensuring survival of the population.

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