Object A has mass m and is traveling forward with speed v. Which set of changes to object A will not affect its momentum?
mass reduced to 0.5m, speed increased to 2v

mass reduced to 0.25m, speed increased to 1.25v

mass increased to 2m, speed increased to 2v

the direction of velocity reversed, speed kept at v

If the potential energy of an object decreases by 10J in a frictionless system, the kinetic energy increases by the same amount, 10J, due to the Law of Conservation of Energy.

When the potential energy of an object decreases by 10J in a system with no friction, according to the Law of Conservation of Energy, there must be an equivalent increase in the object's kinetic energy. This is because the total mechanical energy (potential energy plus kinetic energy) of the system remains constant if no external work is done and no energy is lost to friction. Therefore, if the potential energy decreases by 10J, the kinetic energy will increase by 10J, assuming there is no energy lost to other forms like thermal energy or sound.

Final answer:

When potential energy decreases by 10J, the kinetic energy of the system increases by the same amount, following the Law of Conservation of Energy.

Explanation:

The potential energy of an object decreases by 10J, leading to a corresponding increase in kinetic energy by 10J. This change follows the Law of Conservation of Energy, where the loss of potential energy is accompanied by a gain in kinetic energy.

When there is no friction in the system, the energy transformation is purely between potential and kinetic energy, resulting in the described change. When potential energy decreases by 10J, the kinetic energy of the system increases by the same amount, following the Law of Conservation of Energy.

Organisms overproduce offspring, so only some survive and pass on their traits.

Natural selection is the fitting of a population to its environment.

Explanation:

Most organisms produce more than two or more offspring in their lifetime. Therefore the subsequent generations ideally have more individuals than the previous. However, naturally, the population size does not grow indefinitely. This is because some individuals do not survive to pass their genes to the next generation. Natural selection chooses the best fit individuals to habitat, and these live long enough to pass their traits to the next generation. Natural selection powers the evolution of a population even as environment changes  

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Answer:

The answer is C) Organisms overproduce offspring, so only some survive and pass on their traits

If you need any help on this question please ask me! :)

Answer:

one feels diffulcites to breath in a deep well while cleaning it because well has less amount of oxygen in it.

A fired paper piece can be thrown to check the amount of oxygen.

Answer:

Because usually oxygen is on the ground, and then if you dig a hole, all kinds of gases scramble to run in, then oxygen is naturally less, which is also because of the depth of the ground. The deeper the ground, the more gas will press on you. Simply put, the deeper the well, the greater the pressure. Most of the carbon dioxide you emit in that well is held down by other gases and cannot go out, so that there is less oxygen.

The efficiency of the machine is 0.53 (53%).

Explanation:

The efficiency of a machine is given by:

[tex]\eta = \frac{W_{out}}{W_{in}}[/tex]

where

[tex]W_{out}[/tex] is the output work

[tex]W_{in}[/tex] is the work in input

The output work is:

[tex]W_{out}=F_L d_L = (2000)(2)=4000 J[/tex]

where

[tex]F_L = 2000 N[/tex] is the load

[tex]d_L = 2 m[/tex] is the distance covered by the load

The input work is:

[tex]W_{in}=F_E d_E = (1250)(6)=7500 J[/tex]

where

[tex]F_E = 1250 N[/tex] is the effort force

[tex]d_E = 6 m[/tex] is the distance from the effort to the pivot

Solving for the efficiency,

[tex]\eta=\frac{4000}{7500}=0.53[/tex]

So, the efficiency of the machine is 0.53 (53%).

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From largest to shortest wavelength:

Radio waves, Microwaves, Infrared radiation, Red visible, Orange visible, Yellow visible, Green visible, Blue visible, Violet visible, Ultraviolet, X-rays, Gamma rays

Explanation:

Electromagnetic waves are oscillations of the electric and the magnetic field in a plane perpendicular to the direction of motion the wave.

Electromagnetic waves are the only type of waves able to travel in a vacuum, and in a vacuum they always at the same speed, the speed of light,  equal to:

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

Electromagnetic waves are classified into 7 different types, according to their wavelength/frequency. From slongest to shortest wavelength, they are ranked as follows:

Radio waves

Microwaves

Infrared radiation

Visible light

Ultraviolet

X-rays

Gamma rays

Visible light is the only part of the spectrum that the human eye is able to see. Depending on the wavelength of the visible light, we perceive the radiation as a different color. In order from longest to shortest wavelength, colors are:

Red

Orange

Yellow

Green

Blue

Indigo

Violet

Therefore, the correct order from largest to shortest wavelength in the given list is:

Radio waves

Microwaves

Infrared radiation

Red visible

Orange visible

Yellow visible

Green visible

Blue visible

Violet visible

Ultraviolet

X-rays

Gamma rays

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Answer:

From largest to shortest wavelength:

Radio waves, Microwaves, Infrared radiation, Red visible, Orange visible, Yellow visible, Green visible, Blue visible, Violet visible, Ultraviolet, X-rays, Gamma rays

Explanation:

Electromagnetic waves are oscillations of the electric and the magnetic field in a plane perpendicular to the direction of motion the wave.

Electromagnetic waves are the only type of waves able to travel in a vacuum, and in a vacuum they always at the same speed, the speed of light,  equal to:

Electromagnetic waves are classified into 7 different types, according to their wavelength/frequency. From slongest to shortest wavelength, they are ranked as follows:

Radio waves

Microwaves

Infrared radiation

Visible light

Ultraviolet

X-rays

Gamma rays

Visible light is the only part of the spectrum that the human eye is able to see. Depending on the wavelength of the visible light, we perceive the radiation as a different color. In order from longest to shortest wavelength, colors are:

Red

Orange

Yellow

Green

Blue

Indigo

Violet

Therefore, the correct order from largest to shortest wavelength in the given list is:

Radio waves

Microwaves

Infrared radiation

Red visible

Orange visible

Yellow visible

Green visible

Blue visible

Violet visible

Ultraviolet

X-rays

Gamma rays

Explanation:

Answer:

-4714.28N

Explanation:

Given

This question is based on the concept of Impulse

Impulse is the force acting in a time interval(usually very short)

it is equal to force multiplied with time and also equal to change in momentum of body

⇒[tex]F\times t= mv-mu\\F \times0.35= 55\times (0-30)\\F\times 0.35= -1650\\F= -4714.28 N[/tex]

Therefore the seat belt exerts a force of -4718.28N on the person

The negative sign signifies that seat belt exerts force in opposite direction of Force

The average force exerted by the seatbelt on a 55 kg person in a car that decelerates from 30 m/s to a halt in 0.35s is 4714.05 N, acting in the direction opposite to the motion.

To calculate the average force that the seatbelt exerts on a person, we can use the formula derived from Newton's Second Law of Motion:

F = ma

However, since acceleration is not directly given, we can find it using the formula for acceleration (a) in terms of velocity change (∆v) and time (∆t):

a = ∆v / ∆t

In this case:

Now, we will calculate the acceleration experienced by the person:

a = -30 m/s / 0.35s = -85.71 m/s² (The negative sign indicates deceleration).

Using the calculated acceleration and the person's mass (55 kg), we can find the force:

F = 55 kg imes -85.71 m/s² = -4714.05 N

The negative sign indicates the direction of the force is opposite to the direction of motion. The average force exerted by the seatbelt on the person is therefore 4714.05 N.

1) His momentum before touching the ground is 442.5 kg m/s

2) The net force on the pole vaulter is 490 N

Explanation:

1)

The motion of the pole vaulter is a motion of free fall, so it is subjected only to the force of gravity. Therefore, he falls to the ground at constant acceleration ([tex]g=9.8 m/s^2[/tex], acceleration of gravity), so we can use the following suvat equation to find his final velocity:

[tex]v^2-u^2=2as[/tex]

where

v is the final velocity

u = 0 is the initial velocity

[tex]a=g[/tex] is the acceleration

s = 4 m is the distance covered during the fall

Solving for v,

[tex]v=\sqrt{u^2+2as}=\sqrt{0+2(9.8)(4)}=8.85 m/s[/tex]

And therefore, his final momentum before touching the ground is

[tex]p=mv[/tex]

where m = 50 kg is his mass. Substituting,

[tex]p=(50)(8.85)=442.5 kg m/s[/tex]

2)

As we said previously, the only force acting on the pole vaulter during his fall is the force of gravity, which is

[tex]F=mg[/tex]

where

m = 50 kg is the mass

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

Substituting, we find the force of gravity, and therefore the net force acting on the pole vaulter:

[tex]F=(50)(9.8)=490 N[/tex]

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Answer:

26i-28j

Explanation:

Mathematically, rate of change of something with respect to another is obtained through the operation called differentiation. Integration is the reverse process of differentiation.

We know that force is the rate of change of momentum.

that is,

F=[tex]\frac{dP}{dt}[/tex]

where,

P=momentum

t=time

dP=small change in momentum

dt=small change in time

dP=Fdt  (multiplying both sides with dt)

To get change of momentum within a particular time interval, we have to integrate the above expression giving the necessary limits according to the problem.

Here, we have to calculate the change in momentum between 1.0s and 2.0s. So, the limit of integration is 1.0 to 2.0.

Thus,

[tex]\int\limits^P_p {} \, dP[/tex]=[tex]\int\limits^2_1 {F} \, dt[/tex]

where,

p=momentum at t=1s

P=momentum at t=2s

substituting F in the above equation,

[tex]\int\limits^P_p {} \, dP[/tex]=[tex]\int\limits^2_1 {26i-12jt^{2}} \, dt[/tex]

[tex]\int\limits^P_p {} \, dP[/tex] = P-p = Change in momentum between 1.0s and 2.0s

[tex]\int\limits^2_1 {26i-12jt^{2}} \, dt[/tex] = [tex]\int\limits^2_1 {26i} \, dt - \int\limits^2_1 {12t^{2}j } \, dt[/tex] (Since we can integrate each term of an expression separately)

[tex]\int\limits^2_1 {26i} \, dt - \int\limits^2_1 {12t^{2}j } \, dt[/tex] = [tex]26i(2-1) - 12j(\frac{2^{3} -1^{3} }{3} )[/tex]

=26i-28j

therefore the change in momentum between 1.0s and 2.0s is 26i-28j.

Note: the answer we got is a vector. Because momentum is a vector and therefore change in momentum is also a vector

To find the change in momentum of a particle under the force F=26i-12t2j from 1.0s to 2.0s, we first integrate the force over the given time interval. The change in the particle's momentum is found to be 26i - 20/3j kg*m/s.

The question involves calculating the change in momentum of a particle when a force F=26i-12t2j is applied from 1.0s to 2.0s. To find the change in momentum, we first need to integrate the force over the given time interval, because the change in momentum (Δp) is equal to the integral of the force over time, according to the impulse-momentum theorem, Δp = ∫t1t2 F dt.

For the i-component, the force is constant (26i), so its contribution to the change in momentum from 1.0s to 2.0s is simply 26i N multiplied by the time interval, which is 26i N * (2.0s - 1.0s) = 26i kg*m/s. For the j-component, the force varies with time (-12t2j), so we need to integrate this force from 1.0s to 2.0s. The integral of -12t2 from 1 to 2 gives us -∫12 12t2 dt = -[4t3/3]12 = -8 + 4/3 = -24/3 + 4/3 = -20/3. Thus, the change in momentum in the j-direction is -20/3 j kg*m/s.

Combining the i and j components, the total change in the particle's momentum between 1.0s and 2.0s is 26i - 20/3j kg*m/s.

The heat transfer depends on the factors such as the amount of time of contact, the area of contact, and the specific heals of the substances.

The process of flow of energy from a body of higher temperature to a lower temperature is known as heat transfer.

The mathematical expressions governing the concept of heat transfer are given as follows-

Q = m × c × ΔT

here,

m is the mass of the body.

c is the specific heat.

ΔT is the change in temperature.

And,

Q = k × A×ΔT / L

here,

k is the thermal conductivity.

A is the area of contact and L is the length of the body.

So, clearly, heat transfer depends on the factors such as specific heat and the area of contact. Moreover, the time of contact is also a matter of discussion as the longer the contact time, the more amount of energy will get a transfer from one body to another.

Thus, we can conclude that the heat transfer depends on the factors such as the amount of time of contact, the area of contact, and the specific heals of the substances.

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1) The horizontal range of the laptop is 75.0 m

2) The initial vertical component of the velocity is 14.7 m/s

Explanation:

1)

The motion of the laptopin this problem is a projectile motion, so it follows a parabolic path which consists of two independent motions:  

- A uniform motion (constant velocity) along the horizontal direction  

- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction  

To find the horizontal range of the laptop, we just need to analyze its horizontal motion.

We know that:

- The laptop moves horizontally with a constant velocity of [tex]v_x = 25 m/s[/tex]

- The time of flight of the laptop is [tex]t=3.00 s[/tex]

So, the horizontal range of the laptop is given by

[tex]d=v_x t = (25)(3.00)=75.0 m[/tex]

2)

The total time of flight of a projectile is given by

[tex]t=\frac{2u_y}{g}[/tex]

where

[tex]u_y[/tex] is the initial vertical component of hte velocity

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

Here we know that the time of flight is

[tex]t=3.00 s[/tex]

Therefore, we can solve the formula for [tex]u_y[/tex], to find the initial vertical velocity:

[tex]u_y = \frac{tg}{2}=\frac{(3.00)(9.8)}{2}=14.7 m/s[/tex]

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c. Ben is correct. According to Newton's 2nd law of motion objects with more mass require more force to accelerate.

Explanation:

We can answer this question by using Newton's second law of motion, which states that the net force applied on an object is equal to the product between the mass of the object and its acceleration. Mathematically:

[tex]F=ma[/tex]

where

F is the net force

m is the mass of the object

a is its acceleration

From the equation, we notice that:

- The force is directly proportional to the mass of the object --> so if the mass increases, the force needed to accelerate the object will increase too

Therefore, the correct answer is

c. Ben is correct. According to Newton's 2nd law of motion objects with more mass require more force to accelerate.

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Answer:

2. 0.27 N/kg

3a. 210 N

3b. 23.3 N

Explanation:

The acceleration due to gravity is:

g = GM / r²

where G is the gravitational constant, M is the mass of the planet, and r is the distance from the planet's center.

2. At the surface of the Earth (r = R), the acceleration due to gravity is 9.8 N/kg.

9.8 = GM / R²

At r = 6R, the acceleration due to gravity is:

g = GM / (6R)²

g = (GM / R²) / 36

g = 9.8 / 36

g = 0.27 N/kg

3a. Weight is mass times acceleration due to gravity:

W = mg

W = (20 kg) (10.5 N/kg)

W = 210 N

3b. Find the new value of g:

g = GM / (3R)²

g = (GM / R²) / 9

g = 10.5 / 9

g = 1.17 N/kg

Now find the weight:

W = mg

W = (20 kg) (1.17 N/kg)

W = 23.3 N

Answer:

A) being influenced by equal amounts of gravity and air resistance.

Explanation:

B) slowing down because of an unbalanced force of air resistance.

False - if it was slowing down, then the velocity would go down.

D) on the ground and is not falling anymore.

False - This would be mistaken as the answer but it is not because if the person is not falling anymore the horizontal line should be at the x-axis, meaning that there is no more velocity.

C) accelerating because of an unbalanced force of gravity.

False - The line would otherwise be going up or down.

The shape of the graph of the magnitude of the acceleration versus time for a falling skydiver initially increases and then decreases towards zero as the skydiver reaches terminal velocity. The graph of the magnitude of the velocity versus time initially increases and then reaches a plateau at terminal velocity. The graph of the magnitude of the displacement versus time initially increases and then levels off as the skydiver experiences constant displacement.

In the case of a skydiver, the shape of the graph of the magnitude of the acceleration versus time will initially be positive and then decrease towards zero as the skydiver reaches terminal velocity. This is because the skydiver is initially accelerating due to the unbalanced force of gravity, but as they approach terminal velocity, the force of air resistance opposes the force of gravity and causes the acceleration to decrease.

Similarly, the shape of the graph of the magnitude of the velocity versus time for a falling skydiver will initially be positive and then reach a plateau at terminal velocity.

Lastly, the shape of the graph of the magnitude of the displacement versus time for a falling skydiver will initially be positive and then level off as the skydiver reaches terminal velocity and experiences constant displacement.

The mass of the cannonball is 75 kg

Explanation:

We can solve this problem by using the law of conservation of momentum: in fact, the total momentum of the ball-cannon system before and after the shot must be equal.

Before the shot, the total momentum is zero, since both objects are at rest:

[tex]p=0[/tex] (1)

After the shot, the total momentum is: given by:

[tex]p=mv+MV[/tex] (2)

where :

m kg is the mass of the cannonball

v = 100 m/s is the velocity of the ball

M = 2500 kg is the mass of the cannon

V = -3 m/s is the recoil velocity of the rifle  (in the opposite direction to the ball

Since the toal momentum is conserved, (1) = (2), therefore we can solve for m, the mass of the cannonball:

[tex]0=mv+MV\\m=-\frac{MV}{v}=-\frac{(2500)(-3)}{100}=75 kg[/tex]

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The acceleration of a 24.3 kg box being pushed with a force of 85.5 N is approximately 3.52 m/s². This is determined through the application of Newton's Second Law (F=ma) where acceleration (a) is obtained when the applied force (F) is divided by the mass (m).

The subject of the question is Physics, specifically the concept of Newton's Second Law. This law states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. It is represented by the formula F = ma, where F is the force, m is the mass, and a is the acceleration.

In this case, we have the force F = 85.5 N and the mass m = 24.3 kg. You're asked to find out the acceleration, denoted by 'a'. You can find the acceleration by rearranging the formula to a = F/m. Substituting the given values into the formula gives a = 85.5 N / 24.3kg, resulting in an acceleration of approximately 3.52 m/s².

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Answer:

neutron is a subatomic particle of about the same mass as a proton but without an electric charge, present in all atomic nuclei except those of ordinary hydrogen.

Answer:

According to Oxford dictionary neutron is a subatomic particle of about the same mass as a proton but without an electric charge, present in all atomic nuclei except those of ordinary hydrogen.

The electrical energy consumed by a toaster is 0.033 Kwh.

Explanation:

The power utilized by the toaster is 400 W.

[tex]\text { The power utilized by the toaster is } 400 \mathrm{W} \text { in kilo-watts is } \frac{400}{1000}=0.4 \mathrm{Kw}[/tex]

The toaster is operated for 5 Minutes.

[tex]\text { The toaster is operated for } 5 \text { Minutes in hours is } \frac{5}{60}=0.083 \text { hours. (One minute is } 60 \text { seconds) }[/tex]

We know that,

[tex]\text {power}=\frac{\text {energy}}{\text {time}}[/tex]

Substitute the values in the above formula to obtain electrical energy,

[tex]0.4=\frac{\text { energy }}{0.083}[/tex]

Electrical energy = 0.4 × 0.083

Electrical energy is 0.033 Kwh.

Answer:

The answer is 120,000 Joules

Explanation:

Final answer:

The statement is true, as pus is composed of dead neutrophils, dead tissue, bacteria, and living white blood cells. It reflects the immune system's response to infection, with pus indicating an accumulation of these elements at the site of infection.

Explanation:

The statement "Pus is a mixture of dead neutrophils, dead tissue, bacteria, and living white blood cells" is true. Pus is indeed an accumulation of these components. When neutrophils, which are a type of leukocyte, respond to an infection, they engulf pathogens in a process called phagocytosis. The dead neutrophils, along with any other cellular debris, dead pathogens, and living immune cells, such as macrophages still fighting the infection, aggregate to form pus at the infection site.

This purulent or suppurative discharge is a typical sign of the body's defensive responses engaging with the invading microorganisms. While small amounts of pus can indicate a healthy immune response, in history, there were attempts to produce pus artificially under the misguided notion that it could aid in healing. We now know that inducing pus does not promote recovery and that a natural immune response is best in fighting infections.

Everyone has a different reaction time because not everyone reacts the same to situations. Some people may be faster or slower than others. It could be a result of age, health,  and how they take care of themselves physically.

Gender, age, physical fitness, level of exhaustion, distraction, alcohol usage, personality type, the limb utilized for the test, biological rhythm, health, and whether the stimulus is auditory or visual have all been found to have an impact on reaction time. Social and cultural factors on reaction time are irrelevant.

A reaction is a deliberate, free response to an outside stimulus. The reaction time is the amount of time between the administration of an external stimulus and the appropriate motor response.

The period between the introduction of the stimulus and the emergence of the subject's proper voluntary response is referred to as the reaction time.

Typically, it is measured in milliseconds. It depicts the rate at which stimuli operate on a person's sensory system to produce neurophysiological, cognitive, and informational processes.

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Answer:

Mean: 114.8

Median: 112

Explanation:

The mean is the average of the numbers so you add them all together and divide by the number of terms. The median is the middle value when the terms are in order from least to greatest.

Answer:

Mean of the sample set = 114.8  

Median of the sample set = 112

Explanation:

To calculate mean, add value of all samples and then divide with number of samples.

Mean of the sample set = (100+103+112+120+139)/5 = 114.8

To calculated median, arrange the values in ascending order then take the value which is at middle.

100, 103, 112, 120, 139

“112” is at the middle so,

Median of the sample set = 112  

Explanation:

Let east represent X axis and north represent Y axis.

We need to find what displacement would put the ball in the hole in one putt.

The first putt displaces the ball 6.50 m east

First displacement = 6.50 i m

The second putt displaces it 5.90 m south

Second displacement = -5.90 j m

Total displacement = 6.50 i - 5.90 j

[tex]\texttt{Magnitude = }\sqrt{6.50^2+(-5.90)^2}=8.78m\\\\\texttt{Direction = }tan^{-1}\left ( \frac{-5.9}{6.5}\right )=-42.23^0[/tex]

So displacement to hole from initial position is 8.78 m at direction 42.23° south of east.

Answer:

11.48 m

Explanation:

initial velocity (u) = 15 m/s

acceleration due to gravity (g) = 9.8 m/s

final velocity (v) = 0 ( the ball's speed reduces gradually when thrown until    

                                   becomes 0 at maximum height)

find the height reached.

          we cannot apply this formula directly because we do no know the time        

          (t), so we first need to find the time

       0 = 15 + (-9.8 x t)   (the negative sign is because the ball is decelerating

         upwards)

         15 = 9.8t

         t = 1.53 s

       height (s) = (15 x 1.53)  + (0.5 x (-9.8) x 1.53^{2})

       height = 22.95 - 11.47 = 11.48 m

Answer:#1 NEWTON’S THREE LAWS OF MOTION LAID THE FOUNDATION OF CLASSICAL MECHANICS    #2 HE WAS THE FIRST TO FORMULATE THE NOTION OF GRAVITY AS A UNIVERSAL FORCE

#3 NEWTON’S PRINCIPIA IS ONE OF THE MOST IMPORTANT WORKS IN THE HISTORY OF SCIENCE

#4 HE DISCOVERED THE GENERALISED BINOMIAL THEOREM IN 1665

#5 ISAAC NEWTON INVENTED CALCULUS

#6 HE INVENTED THE FIRST REFLECTING TELESCOPE

#7 HE DID GROUND BREAKING WORK IN OPTICS

#8 HE IDENTIFIED LIGHT AS THE SOURCE OF COLOUR SENSATION

#9 HE INFERRED CORRECTLY THE OBLATENESS OF EARTH’S SPHEROIDAL FIGURE

#10 SIR ISAAC NEWTON WAS THE SECOND SCIENTIST TO BE KNIGHTED

Answer:

Invented the reflecting telescope.

Proposed new theory of light and color.

Discovered calculus.

Developed three laws of motion.

Devised law of universal gravitation.

Advanced early modern chemistry.

Explanation:

Sir Isaac Newton had many great accomplishments. Here are some of his most notable achievements:

1. Newton's Three Laws of Motion: Newton formulated three fundamental laws that laid the foundation of classical mechanics. These laws describe how objects move and interact with each other. They are still widely used today to understand and predict the motion of objects.

2. Formulation of Gravity: Newton was the first to formulate the notion of gravity as a universal force. He explained that every object with mass attracts other objects towards it. His understanding of gravity helped explain why objects fall to the ground and why planets orbit the Sun.

3. Principia: Newton's book called "Mathematical Principles of Natural Philosophy" (commonly known as "Principia") is one of the most important works in the history of science. In this book, Newton presented his laws of motion and the law of universal gravitation. It revolutionized the field of physics and became the foundation for classical mechanics.

4. Generalized Binomial Theorem: In 1665, Newton discovered the generalized binomial theorem, which is a mathematical formula used to expand powers of binomials (expressions with two terms). This theorem is still studied and applied in various branches of mathematics.

5. Invention of Calculus: Newton independently developed calculus, a branch of mathematics that deals with rates of change and the accumulation of quantities. Calculus is widely used in many fields, including physics and engineering, and it provides a powerful tool for solving problems involving change and motion.

6. Invention of the Reflecting Telescope: Newton constructed the first reflecting telescope, which used mirrors instead of lenses to gather and focus light. This invention greatly improved the quality and clarity of images observed through telescopes and had a significant impact on the field of astronomy.

7. Groundbreaking Work in Optics: Newton conducted groundbreaking experiments and made important discoveries in the field of optics. He demonstrated that white light is composed of different colors, which led to the understanding of the color spectrum. His work on optics laid the foundation for future developments in this field.

8. Identification of Light as the Source of Color Sensation: Newton proposed that light is the source of color sensation. He demonstrated that the colors we perceive are a result of how light interacts with objects and our eyes. This understanding of light and color perception has had lasting effects in fields like art and design.

9. Inference of Earth's Oblateness: Newton correctly inferred that the Earth is not a perfect sphere but rather oblate, meaning it is slightly flattened at the poles and bulges at the equator. His understanding of the Earth's shape was based on his knowledge of gravity and the forces acting on the planet.

10. Knighthood: Newton was knighted by Queen Anne in 1705, becoming the second scientist to receive this honor. His contributions to science and mathematics were recognized and celebrated during his lifetime.

A) The resultant force is 30.4 N at [tex]25.3^{\circ}[/tex]

B) The resultant force is 18.7 N at [tex]43.9^{\circ}[/tex]

Explanation:

A)

In order to find the resultant of the two forces, we must resolve each force along the x- and y- direction, and then add the components along each direction to find the components of the resultant.

The two forces are:

[tex]F_1 = 20 N[/tex] at [tex]0^{\circ}[/tex] above x-axis

[tex]F_2 = 15 N[/tex] at [tex]60^{\circ}[/tex] above y-axis

Resolving each force:

[tex]F_{1x}=F_1 cos \theta = (20)(cos 0)=20 N\\F_{1y}=F_1 sin \theta =(20)(sin 0)=0 N[/tex]

[tex]F_{2x}=F_2 cos \theta = (15)(cos 60)=7.5 N\\F_{2y}=F_2 sin \theta =(15)(sin 60)=13.0 N[/tex]

So, the components of the resultant are:

[tex]F_x = F_{1x}+F_{2x}=20+7.5 = 27.5 N\\F_y = F_{1y}+F_{2y}=0+13.0=13.0 N[/tex]

And the magnitude of the resultant is:

[tex]F=\sqrt{F_x^2+F_y^2}=\sqrt{27.5^2+13.0^2}=30.4 N[/tex]

And the direction is:

[tex]\theta=tan^{-1}(\frac{F_y}{F_x})=tan^{-1}(\frac{13.0}{27.5})=25.3^{\circ}[/tex]

B)

In this case, the 15 N is applied in the opposite direction to the 20 N force. Therefore we need to re-calculate its components, keeping in mind that the angle of the 15 N force this time is

[tex]\theta=180^{\circ}-60^{\circ}=120^{\circ}[/tex]

So we have:

[tex]F_{2x}=F_2 cos \theta = (15)(cos 120)=-7.5 N\\F_{2y}=F_2 sin \theta =(15)(sin 120)=13.0 N[/tex]

So, the components of the resultant this time are:

[tex]F_x = F_{1x}+F_{2x}=20-7.5 = 12.5 N\\F_y = F_{1y}+F_{2y}=0+13.0=13.0 N[/tex]

And the magnitude is:

[tex]F=\sqrt{F_x^2+F_y^2}=\sqrt{13.5^2+13.0^2}=18.7 N[/tex]

And the direction is:

[tex]\theta=tan^{-1}(\frac{F_y}{F_x})=tan^{-1}(\frac{13.0}{13.5})=43.9^{\circ}[/tex]

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The man lands 12.1 m far from the base of the cliff, so he will survive

Explanation:

The motion of the person is a projectile motion, which consists of two independent motions:  

- A uniform motion (constant velocity) along the horizontal direction  

- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction  

We start by considering the vertical motion, to find the time of flight of the person, with the following suvat equation:

[tex]s=ut+\frac{1}{2}gt^2[/tex]

where :

s = 50 m is the vertical displacement of the man (the height of the cliff)

t is the time of flight

u = 0 is the initial vertical velocity

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

Solving for t,  we find

[tex]t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(50)}{9.8}}=3.19 s[/tex]

Now we know that the man moves horizontally, with a constant velocity of

[tex]v_x = 3.8 m/s[/tex]

Therefore, the horizontal distance covered by the man during this time is

[tex]d=v_x t = (3.8)(3.19)=12.1 m[/tex]

So the man lands 12.1 m far from the base of the cliff: therefore, on the lake, so he will survive.

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Answer:

The minimum angle of incidence is, ∅  = 56° 18' 35'' to the normal

Explanation:

Given data,

The distance between the two plane mirror, d = 5 cm

The length of the plane mirror, L = 30 cm

According to the laws of reflection, the angle of incidence is equal to the angle of reflection.

If the laser beam touches each mirror only twice, then the base of the triangle formed is not less than L/2.

Let ∅ be the angle of incidence to the normal. The normal divides the triangle into two equal halves where base becomes L/4.

Therefore,

                        tan ∅ = opp / adj

                                  = (L/4) / d

                                   = (30/4) / 5

                        tan ∅  = 1.5

                               ∅  = tan ⁻¹ (1.5)

                                    = 56° 18' 35''

Hence, the minimum angle of incidence is, ∅  = 56° 18' 35'' to the normal.

Answer:

His weight increases.

Explanation:

                                           W = m x g

Answer:  C. can robots be trained to follow a moral code?

Explanation:

Answer:

Its C

Explanation:

Answer:electric field

Explanation:Because in an electric field, positive charge is directed away and negative charge is directed towards the electric field.

Answer:

an electric field

Explanation:

this field is what is direted to a negative charge

Answer:

A solid is like the tray being shaken slowly and all the marbles moving in their positions, a liquid is like the tray being shaken and the marbles moving around it, and a gas is like the tray being shaken hard and the marbles moving vigorously around it

Explanation:

its b

A solid is like the tray shaken slowly and all the marbles will move in their positions. A liquid is like the tray being shaken and the marbles will move around it. A gas is like the tray being shaken hard and the marbles will move vigorously around it. Therefore, option (B) is correct.

The matter exists in various forms in nature. Some substances have a definite shape such as wood, stone, marbles and some can flow, take the any shape such as water, while there are forms of matter that do not have definite shapes.

In solids, the molecules are very tightly packed and thus solids have a definite and rigid structure. The compact packing of solids indicates that the molecules are too close to each other and the molecules do not show any movement. The kinetic energy of molecules or atoms in the solid is the least or negligible.

In liquids, the molecules are at some distance from each other and they show some movements. Since the molecules show significant movement, so they have significant amount of kinetic energy. The kinetic energy of molecules or atoms in the liquid is more than that of solids.

In gases, the molecules or atoms are farther from each other and thus their molecules show huge movement. The kinetic energy of molecules or atoms in gases is the greatest in comparison to solids and liquids.

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