3. An electron moves along the trajectory from i to f as shown.
a) Does the electric potential energy increase, decrease or stay the same? Explain.
b) Is the electron's speed at f greater than, less than or equal to its speed at i? Explain.

Answer:

3rd image, 2nd image, 1st image, 4th image

Explanation:

Not an easy question, tricky one

Electric potential energy is proportional to the magnitude of the charges (the higher the charges, the stronger the Electric potential energy(EPE)) and inversely proportional to the distance between the charges(the longer the distance, the smaller the EPE).  U = kQq/r

EPE is positive in this case due to unlike charges.

Between distance and magnitude of the charges, magnitude of charges play a more significant effect than distance (due to Qq , both the magnitude of Q and q affect the EPE)

Hence. zoom in on the magnitude first.

3rd image has the largest + and -, hence greatest magnitude of charges, therefore highest EPE.

Between 1st and 2nd images, charges have the same magnitude, distance now comes to play. Distance between the charges is smaller for image 2 and the charges experience greater EPE. 1st image, the charges are further, hence smaller EPE.

For the fourth image, the magnitude of the charges is the smallest, hence smallest EPE.

Answer:

0.15 m/s²

Explanation:

Acceleration is rate of change of velocity-time function. We can find acceleration by finding the slope. The slope of graph can be found by:

[tex] \displaystyle{a = \dfrac{ \Delta v}{ \Delta t} \: \to \: \dfrac{v_f - v_i}{t_f- t_i}}[/tex]

Substitute in:

[tex] \displaystyle{a = \dfrac{5 - 2}{40 - 20}} \\ \\ \displaystyle{a = \dfrac{3}{20}} \\ \\ \displaystyle{a = 0.15 \: \text{m/s}^{2} }[/tex]

Therefore, the acceleration is 0.15 m/s²

The reason that Silent Spring was so influential at the time is option D: It was the first time that the public was being made aware of the long-term impacts of pollution.

Silent Spring, a book written by Rachel Carson and published in 1962, was influential at the time because it was the first book to bring awareness to the negative impacts of pesticides on the environment and human health.

Therefore, The book provided evidence and detailed accounts of the harmful effects of pesticides on wildlife and ecosystems, and it argued that the widespread use of pesticides was unsustainable and could have long-term consequences for the environment and human health.

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Answer:

0.48 rad/s

Explanation:

We can use this equation to find the final velocity

[tex]w_f=w_0+at[/tex]

We are given

[tex]w_0=0.16[/tex]

[tex]t=8.0[/tex]

[tex]a=0.04[/tex]

Inserting those numbers into our equation gives us

[tex]w_f=0.16+0.04*8[/tex]

Lets solve for [tex]w_f[/tex].

[tex]w_f=0.16+0.32[/tex]

[tex]w_f=0.48[/tex]

Answer:

666.7 W

Explanation:

Power = P = W/t = 4000 J/6 s = 666.7 W (watts)

The minimum force needed to move the whale along a horizontal ramp, given that the whale has a mass of 1.90×10⁵ Kg is 856520 N

We'll begin by listing out the given parameters from the question. This is shown below:

To obtain the force needed to move the whale, we shall first obtain the normal reaction. This is shown below:

N = mg

N = 1.90×10⁵ × 9.8

N = 1862000 N

Finally, we shall determine the force needed. Details below:

F = μN

F = μN

F = 0.460 × 1862000

F = 856520 N

Thus, we can conclude that the force needed is 856520 N

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The degree of data stability when the measurement is replicated under identical circumstances is known as reproducibility or reliability.

Reproducibility determines how an entire study an experiment can be replicated, whereas repeatability assesses the variation in data made by a single equipment or human under similar circumstances.

Science needs reproducibility because it enables more in-depth investigation, and replication validates our findings. There are several investigations and experiments, which result in a wide range of variables, unforeseen, and things that are either outside your influence or you cannot guarantee.

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Proxima Centauri otherwise known as Alpha Centauri C, is the closest star to our solar system, located about 4.24 light-years away. It was discovered in 1915 by Robert Innes, the director of the Union Observatory in South Africa. Innes identified Proxima Centauri as a possible member of the Alpha Centauri system after noticing that the star had a similar proper motion to Alpha Centauri A and B.

Proxima Centauri was first observed through telescopes, which allowed scientists to study the star's spectra and estimate its distance from Earth. In the following decades, scientists continued to study Proxima Centauri through telescopes, including the Hubble Space Telescope, which provided high-resolution images of the star.

In 2016, the European Southern Observatory announced the discovery of an exoplanet orbiting Proxima Centauri, called Proxima Centauri b. This discovery was made using the radial velocity method, which measures the star's small wobbles caused by the gravitational pull of an orbiting planet.

Despite the advances in our understanding of Proxima Centauri, no spacecraft have ever reached this star. The distance between Proxima Centauri and Earth is so vast that it would take tens of thousands of years to reach the star using current propulsion technology.

One potential solution to this problem is the use of interstellar travel, which would allow humans to travel to Proxima Centauri within a human lifetime. There are several proposed methods for interstellar travel, including using a starship propelled by fusion engines or a massive light sail pushed by a beam of lasers. However, these technologies are still in the theoretical stage and have not yet been developed.

There are also many other challenges that must be overcome in order for humans to travel to Proxima Centauri. For example, humans would need to find a way to protect themselves from the high levels of radiation that they would be exposed to during the journey. They would also need to find a way to provide enough food, water, and other resources to sustain themselves for the duration of the trip.

Overall, while it is theoretically possible for humans to travel to Proxima Centauri, it would be a massive undertaking that would require significant technological advancements and the development of new solutions to many challenges.

Sources of Works Cited include:

"Proxima Centauri." Wikipedia, Wikimedia Foundation, 5 Jan. 2021,

"Proxima Centauri b." Wikipedia, Wikimedia Foundation, 20 Nov. 2020,

"Interstellar Travel." Wikipedia, Wikimedia Foundation, 4 Jan. 2021,

Therefore, the correct answer is as given above

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Answer: It is not clear what is the power of 10 in the speed of the bullet but here is a general procedure for the question.

Explanation:

[tex]P_{bullet}=(3.22*10^{-3}kg)*(10^{?}m/s)\\P_{baseball}=P_{bullet}\\[/tex]

Therefore we can write:

[tex](0.151*10^{-3} kg)*v_{baseball}=(3.22*10^{-3}kg)*(10^{?}m/s)[/tex]

From this using the relationship:

[tex]v_{baseball}=\frac{(3.22*10^{-3}kg)*(10^?m/s)}{0.151*10^{-3}kg}[/tex]

I cannot give a precise answer since power of then for speed of the bullet is not clear. But using the above equation you can reach the answer. General form of the equation is therefore:

[tex]v_{baseball}=\frac{P_{bullet}}{m_{baseball}}[/tex]

Where m is the mass of the ball which is 0.151 g.

Acceleration = (change in speed) / (time for the change)

Change in speed = (10,000 m/s) - (5,000 m/s)

Change in speed = 5,000 m/s

Time for the change = 1 minute

Time for the change = 60 sec

Acceleration = (5,000 m/s) / (60 s)

Acceleration =  83-1/3 m/s²

Answer:

800J

Explanation:

W = Fs, Work equals force times displacement

in this case, the force is 400N and the displacement is 2 meters.

The regular SI unit for work is joules

Answer:

1.08 x 10^5 J

Explanation:

First, apply the formula V = IR , where V is the voltage, I is the current and R is the resistance.

R -> 20 ohm (Given)

I -> 3A (Given)

Hence, V = 3 x 20 = 60V (60 volts)

Next, apply the formula E = Pt , where E is the energy produced, P is the power and t is the time in seconds

Furthermore, since P = IV (power = current x voltage)

The formula can be re-expressed as E = VIt

t -> 10 minutes = 600 seconds (don't forget to convert time to seconds!)

Therefore, energy = (60 x 3 x 600) J

                              = 108000 J

                               = 1.08 x 10^5 J (in scientific notation)

Hea produced in the resistance = energy produced in the resistor

                                                      = 1.08 x 10^5 J

Two forces are said to be balanced when their strengths are equal but their directions of action are opposing.

The forces are balanced if the pullers are exerting equal force but going in the opposite direction on either side of the rope.

Forces that are balanced can cancel one another out. The thing stays in place whenever there is a balanced force.

To lift, turn, move, open, close, push, pull, and many other things requires forces. You apply force to a ball when you throw it in order for it to travel through the air. An object can be under the influence of multiple forces at once.

Therefore, Two forces are said to be balanced when their strengths are equal but their directions of action are opposing.

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(a) The magnitude of the car's normal force is 7,792.2 N.

(b) The mass of the car is 795.1 kg.

The weight of the car is calculated by applying Newton's second law of motion as shown below.

Mathematically, the formula for Newton's second law of motion is given as;

Ff = μW

where;

The weight of the car is calculated as follows;

W = Ff / μ

W = ( 6,000 N ) / ( 0.77 )

W = 7,792.2 N

Based on Newton's third law of motion, the weight of the car acting downwards is equal to normal force on the car, acting upward.

The mass of the car is calculated as follows;

W = mg

where;

m = W / g

m = ( 7792.2 ) / (9.8)

m = 795.1 kg

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The statement that is correct is that the contents of the cup form a mixture.

Though the question is incomplete but I would try to give you a good explanation as much as I can. We must recall that when we talk about a mixture, we have to note that the term mixture would refer to the combination of two or more substances that do not chemically react together.

In this case, we have been told that we have a water that was pure and then we add dirt to it. It is clear that the water and the dirt do not react in any way hence what we have formed is a mixture.

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Answer:

4.95 m

Explanation:

The rocket's initial kinetic energy is equal to the final gravitational potential energy, so we can set these equal to each other and solve for the additional height the rocket will rise:

KEinitial = KEfinal

1/2 * m * v^2 = m * g * h

Substituting the given values, we have:

1/2 * 9.5 kg * v^2 = 9.5 kg * 9.8 m/s^2 * h

Solving for h, we find that the additional height the rocket will rise is h = 2390 J / (9.5 kg * 9.8 m/s^2) = 4.95 m.

Answer:

Δp=-18799.5kg*m/s

Explanation:

Δv=Vf-Vi

Δv=2.9m/s-18m/s

Δv=-15.1m/s

m*Δv=Δp

1245kg*(-15.1m/s)=Δp

Δp=-18799.5kg*m/s

Extra:

Deriving mΔv=Δp

Δp=Pf-Pi

Δp=m*Vf-m*Vi

Δp=m(Vf-Vi)

Vf-Vi=Δv

Δp=m(Δv) or Δp=mΔv

Answer:

The opposition offered by the conductor to the current flowing through it is known as resistance.

we know,

Resistance is directly proportional to the length of the conductor.Hence,the resistance offered by the long wire will be more than that of the short wire.

Also, Resistance is inversely proportional to the area of cross section of conductor.So,The Resistance in the thick wire will be less than that of the thin wire.

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Important Formulas:
[tex]w=Fd[/tex]

work(measured in joules) = force(measured in newtons) * distance(measured in meters)

__________________________________________________________

Given:

[tex]m=42kg[/tex]

[tex]F=180N[/tex]

[tex]w=2500J[/tex]

[tex]d=?[/tex]

__________________________________________________________

Rearranging work formula to make distance the subject:

[tex]w=Fd[/tex]

[tex]\dfrac{w}{F} =\dfrac{Fd}{F}[/tex]

[tex]d=\dfrac{w}{F}[/tex]

__________________________________________________________

Finding distance:

[tex]d=\dfrac{w}{F}[/tex]

[tex]d=\dfrac{2500}{180}[/tex]

__________________________________________________________

[tex]\fbox{d = 13.89 meters}[/tex]

The horizontal component of the cat's displacement, Dx = 0 m

The vertical component of the cat's displacement, Dy = 12 m

The horizontal component of a vector is the value of that vector acting in the horizontal direction.

The horizontal component of a vector is given as Dx.

Dx = Dcosθ

where;

D is the resultant of the vector

θ is the angle of the vector from the horizontal

The horizontal component of the cat's displacement is:

Dx = 12 * 0

Dx = 0 m

The vertical component of a vector is the value of that vector acting in the vertical direction.

The vertical component of a vector is given as Dy.

Dy = Dsinθ

where;

D is the resultant of the vector

θ is the angle of the vector from the horizontal

The vertical component of the cat's displacement is:

Dy = 12 * 1

Dy = 12 m

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If a longitudinal force exceeding 3000 N is applied. Young's modulus for that object equals DL = 0.0139m.

The greater the modulus, or the lesser elasticity strain that arises from the application of a given stress, the stronger that medium is. Young's modulus, sometimes referred to as mechanical performance, is a metric used to determine how stiff a material is. In other words, it is readily bent or stretched.

Young's modulus really measures a material's ability to withstand changes in length when compressed or under stress along its length. Divide the primary stresses by the strain to get Young's modulus, commonly known also as young's modulus.

Young's modulus Y= stress/strain

= (F/A) /(DL/L)

F=3000N,

A=0.54 cm²,

L=2.5cm,

Y=0.1 Gpa

0.1 * 10⁹ = (3000/(0.54* 10⁻⁴) (2.5 ⋆ 0.01/DL)

DL = 0.0139m

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The value of mA is the equation of conservation of linear momentum is determined as mA = [ mB (vBi - vBf) ] / [  (vAf - vAi ) ].

The principle of conservation of linear momentum states that in a closed or isolated system, the total momentum of the system is always conserved.

Mathematically, the formula for the principle of conservation of linear momentum is given as;

Pi = Pf

where;

mAvAi + mBvBi = mAvAf + mBvBf

where;

To find the value of mA, we will make mA the subject of the formula as follow;

mAvAf  - mAvAi = mBvBi - mBvBf

mA (vAf - vAi ) = mB (vBi - vBf)

mA = [ mB (vBi - vBf) ] / [  (vAf - vAi ) ]

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Answer:

2 nitrogen and 1 oxygen,

Explanation:

N2=2 nitrogen

O= a single element

If an object is moving and the sum of all the vector forces on it is zero, then the object will move at a constant speed. The correct option is c.

A force's magnitude and direction are both represented by a force vector. This contrasts with expressing the force's magnitude alone, which is known as a scalar quantity.

Typically, a vector is represented by an arrow that points in the direction of the force and has a length proportionate to the strength of the force.

Therefore, the correct option is c, move at a constant speed.

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The option that correctly states what happen to the kinetic energy and the momentum of the two-cart system as a result of the collision compared to those quantities before the collision is

B) Kinetic energy: Increases; Magnitude of Momentum: Stays the same

The energy an object has as a result of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force.

Since the elastic potential energy that was initially stored in the compressed spring has now been converted into kinetic energy, the system's total energy should be conserved. As a result, the system's kinetic energy increases. As a result, the system's kinetic energy rises.

The magnitude of the two-cart system's net momentum remains constant because there is no outside force acting on it, which implies that the system's overall momentum should be conserved.

Therefore, the correct option is B.

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Explanation:

Mass of the football = 0.49 kg

Initial velocity of the ball ,u= 0 m/s

Final velocity of the ball ,v= 44 m/s

time of contact ,t = 0.028 seconds

First law of motion:

v=u+at

44 m/s=0+a\times 0.028 sec44m/s=0+a×0.028sec

a=1,571.42 m/s^2a=1,571.42m/s

2

force=mass\times acceleration=0.49 kg\times 1,571.42 m/s^2=769.99Nforce=mass×acceleration=0.49kg×1,571.42m/s

2

=769.99N

The magnitude of the force exerted by the ball on the kicker's foot is of 769.99 Newtons.

The perpendicular force that a surface applies to an item is known as the normal force. FN = m ⋅ g

The perpendicular force that a surface applies to an item is known as the normal force. For instance, if you place a book on a table, a gravitational force will cause it to fall. The table pulls on the book in order to counterbalance this force and keep it from dropping. The normal force, often known as the opposing force, is denoted by the symbols FN F N or  NN. "N" stands for the normal force unit (Newton).

A common illustration of Newton's third rule of motion is the normal force.

When one object applies force to another, the other applies a force in the opposite direction and of equal magnitude to the first object (action equals reaction).

Therefore, the force applied by the item to the surface is equal to the normal force. The calculations change according to the surface's slope.

The formula is as follows for an object laying on a flat surface:

FN = m ⋅ g

where

The mass of an object is m.

Gravitational acceleration is denoted by g.

The normal force (FN F N ) for an item on a flat surface is equal to its gravitational force, according to Newton's third law ( WW).

The formula is as follows for an object laying on a flat surface:

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The goal kick strikes a defender racing at 5 m/s away from a goalkeeper in the back. The ball was moving at a speed of 70 m/s if it weighed 500g and the player's mass was 70k.

The goalkeeper extends the amount of time he has to hold the ball by pulling his hands back. He lessens the force (rate of change of momentum) the football exerts on him by lengthening the time.

A vector quantity, momentum. A body's momentum is equal to P=m.v if it is travelling at a speed of v while having mass m. P=mv describes the magnitude of the momentum. Because momentum is a function of mass and velocity, its unit is the product of those two quantities.

By using conservation of momentum,

Initial momentum = Final momentum

(5 x 70) + (v x 0.5) = (5.5 x 70) + (0 x 0.5)

350 + 0.5v = 385 + 0

0.5v = 35

v = 70 m/s

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