*Please help* (Will give thanks + Brainliest Answer) A skateboarder is starting at the top of a 50.0 meter hill. At the bottom of the hill the skateboarder is going 25 m/s.
If the mass of the skateboarder is 52 kg, how much energy was lost in the downhill ride?

A) 650 joules

B) 9230 joules

C) 16,250 joules

Answers

Answer 1

Answer:

B

Explanation:

Energy at the top of the hill = energy at the bottom of the hill + energy lost

PE = KE + E

mgh = 1/2 mv² + E

(52 kg) (9.8 m/s²) (50.0 m) = 1/2 (52 kg) (25 m/s)² + E

25480 J = 16250 J + E

E = 9230 J


Related Questions

A system dissipates 12 J of heat into the surroundings; meanwhile, 28 J of work is done on the system. What is the change of the internal energy of the system?

Answers

Answer:

+16 J

Explanation:

We can solve the problem by using the 1st law of thermodynamics:

[tex]\Delta U = Q-W[/tex]

where

[tex]\Delta U[/tex] is the change of the internal energy of the system

Q is the heat (positive if supplied to the system, negative if dissipated by the system)

W is the work done (positive if done by the system, negative if done by the surroundings on the system)

In this case we have:

Q = -12 J is the heat dissipated by the system

W = -28 J is the work done ON the system

Substituting into the equation, we find the change in internal energy of the system:

[tex]\Delta U=-12 J-(-28 J)=+16 J[/tex]

The nucleus contains protons and neutrons. Being positively charged, the protons repel each other. The nucleus should fly apart due to the repulsive force. Yet, the nuclei of most atoms are stable - explain. (5 points)

Answers

this is due to the existence of other forces called the strong nuclear forces that overcomes the repulsion forces between the protons and keeps the nucleons holding to each other also there is a type of energy that is called the nuclear binding energy and this energy also works on binding the components of the nucleus together

Final answer:

The atomic nucleus remains stable despite the repulsion between protons due to the strong nuclear force which is much stronger than the electromagnetic force and acts within a very short range in the nucleus. Further stability is ensured by the conversion of the mass defect into binding energy, and programming of specific numbers of protons and neutrons.

Explanation:

The stability of an atomic nucleus despite the repulsion between positively charged protons is due to a force called the strong nuclear force. This force is significantly stronger than the electromagnetic force causing the repulsion, approximately 100 times stronger, and acts between nucleons (protons and neutrons) within a very short range in the nucleus. That's why protons do not just fly apart as we might expect due to their positive charges. Furthermore, a phenomenon called mass defect, according to Einstein's mass-energy equivalence equation, E = mc², also plays into the nuclear stability. The mass of a nucleus is less than the total mass of its individual protons and neutrons, the 'missing' mass has been converted into the binding energy that holds the nucleus together.

However, not all combinations of protons and neutrons result in a stable nucleus. There are patterns to the stability: nuclei with even numbers of protons or neutrons, or those with 'magic numbers' of nucleons, are especially likely to be stable. Also, it is observed that for higher masses, stable nuclei tend to have more neutrons than protons to reduce the Columb repulsion between protons.

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what is shown in the diagram?


an electromagnet


a generator


a motor


a turbine

Answers

The machine shown in the diagram is generator.

What is generator?

To produce electricity, a generator needs the input in the form of mechanical energy.

The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.

M.E = KE +PE

In order to produce electricity, a generator uses the mechanical energy as the input. It gives the electrical energy as output to light up homes, hotels or industries.

Thus, generator is shown in diagram.

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What is linear speed called when something moves in a circle

Answers

Answer: Tangential Velocity

The tangential velocity [tex]V[/tex] is defined as the angular velocity [tex]\omega[/tex] by the radius [tex]r[/tex] of circular motion. As shown below:

[tex]V=\omega. r[/tex]

Its name is due to the fact that this linear velocity vector is always tangent to the trajectory and is the distance traveled by a body or object in a circular movement in a period of time.

A spring required a force of 5.0 n to compress it 0.1 m. how much work is required to stretch the spring 0.4 m

Answers

Answer:

20N

Explanation:

The force (Hooke's Law) is proportional to the deformation. To extend the spring 4 times longer, you will need 4 times the force. In total, 20 N

The amount of work required to stretch the spring 0.4 m give the data is 4 J

How to determine the spring constant

From the question given above, the following data were obtained

Force (F) = 5 NCompression (e) = 0.1 mSpring constant (K) =?

K = F/ e

K = 5 / 0.1

K = 50 N/m

How to determine the work Spring constant (K) = 50 N/mExtention (e) = 0.4 mWork =?

W = ½Ke²

W = ½ × 50 × 0.4²

W = 25 × 0.16

W = 4 J

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Which of the following best summarizes what we mean by dark matter?Matter for which we have theoretical reason to think it exists, but no observational evidence for its existence.Matter that we have identified from its gravitational effects but that we cannot see in any wavelength of light.Matter that may inhabit dark areas of the cosmos where we see nothing at all.Matter consisting of black holes.

Answers

Answer: Matter that we have identified from its gravitational effects but that we cannot see in any wavelength of light

Dark matter is a type of matter, whose composition is unknown and which corresponds to 80% of the matter in the universe. Its name refers to the fact it does not emit or interact with any type of electromagnetic radiation, being completely transparent throughout the electromagnetic spectrum.  

However, it interacts with the known matter through gravity.  

This means that, like gravity, dark matter can not be observed directly, however its existence is inferred through the movement of the stars and the cosmic dust within the galaxies.

Answer:

5- Normal, 68-dark energy, 27 dark matter

Explanation:

What is the correct composition of the universe, based on theoretical and cosmological observations?

   dark energy

   dark matter

   normal matter

   5 percent

   arrowRight

   68 percent

   arrowRight

   27 percent

   arrowRight

Dude what's the difference between a parallel circuit and a series circuit? Cuz idk ????

Answers

Answer:

-Parallel circuits have multiple branching pathways for electrical current.

-series circuit forms a single path.

Two particles are 15 meters apart. Particle A has a charge of 6.0 • 10-4 C, and particle B has a charge of 5.0 • 10-4 C. The resulting Coulomb force is 12 N. At the same distance, what combination of charges would yield the same Coulomb force?

Answers

We can choose different pairs of values. Here are some examples:

[tex]q'_1 = 3.0 \times 10^{-4}[/tex] C and [tex]q'_2 = 1.0 \times 10^{-3}[/tex] C,

[tex]q'_1 = 1.0 \times 10^{-4}[/tex] C and [tex]q'_2 = 3.0 \times 10^{-3}[/tex] C,

[tex]q'_1 = 1.5 \times 10^{-4}[/tex] C and [tex]q'_2 = 2.0 \times 10^{-3}[/tex] C.

To solve this problem, we'll use Coulomb's Law, given by the formula:

[tex]F = k_e \cdot \frac{q_1 \cdot q_2}{r^2}[/tex]

where:

[tex]F[/tex] is the Coulomb force,[tex]k_e[/tex] is Coulomb's constant (
8.99 × 10^9 N m²/C²),[tex]q_1[/tex] and [tex]q_2[/tex] are the charges on the particles,[tex]r[/tex] is the distance between the charges.

Given:

Coulomb force, [tex]F = 12[/tex] N,[tex]r = 15[/tex] m,[tex]q_1 = 6.0 \times 10^{-4}[/tex] C,[tex]q_2 = 5.0 \times 10^{-4}[/tex] C.

First, we verify the given force with the given charges and distance:

[tex]F = (8.99 \times 10^9) \cdot \frac{(6.0 \times 10^{-4})(5.0 \times 10^{-4})}{(15)^2}[/tex].

Let's simplify this:

[tex]F = (8.99 \times 10^9) \cdot \frac{3.0 \times 10^{-7}}{225}[/tex].

[tex]F = (8.99 \times 10^9) \cdot 1.333 \times 10^{-9}[/tex].

[tex]F = 12[/tex] N (matches the given force).

To find a new combination of charges that yield the same force, we can use different charges, but they must still give the same numerator in the force equation.

Let new charges be [tex]q'_1[/tex] and [tex]q'_2[/tex]. The condition we'll use is:

[tex]q'_1 \cdot q'_2 = 3.0 \times 10^{-7}[/tex] C².

what type of circuit is illustrated?


series circuit


parallel circuit


open circuit


short circuit

Answers

Answer:

Parallel circuit

Explanation:

A parallel circuit is a closed circuit in which current flows and divide in two or more paths and recombining to complete the circuit, each load (light bulb) receives the fully voltage of the batteries in the circuit.

The solubility of most solids _______ as temperatures decreases.

Answers

Answer:

The solubility of most solids decrease as temperatures decreases.

Hope this helps :)

Have a great day !

5INGH

Explanation:

A light goes on immediately when you flip a switch because.

A. conductors allow electrons to travel extremely quickly from the power source to the light

B. tightly bound electrons are already present in the conductors that make up the circuit

C. loosely bound electrons are already present in the wire conductors that make up the circuit

Answers

The light turns on immediately due to loosely bound electrons in the conductors that quickly propagate the electrical signal nearly at the speed of light, causing an instantaneous chain reaction and creating a current. The correct option is: C. loosely bound electrons are already present in the wire conductors that make up the circuit.

A light goes on immediately when you flip a switch because loosely bound electrons are already present in the wire conductors that make up the circuit. These electrons move through the circuit quickly, initiating a nearly instantaneous chain reaction that allows the current to flow and the light to turn on almost immediately.

This movement is much quicker than the drift velocity of the electrons, which is the average speed at which they move through the conductor. Instead, the signal that causes the electrons to start moving travels at a fraction of the speed of light, which is why we perceive the light turning on without noticeable delay.

How do you do this question?

Answers

Answer:

Explanation:

All the bulbs with have the same resistance.

Let the resistance of the Bulbs all = R

Bulb 1 will get all of the current running through it. There will be a voltage drop of Ed1 = I * R and the voltage left over will be seen by some combination of bulbs 2,3 and 4.

The current will be divided between 2R and R. 2R will get the smaller amount of current, and R will get the larger amount. There will be 3 parts in total.

So 2 and 3 will experience 1/3 I,   while the  other bulb will get 2/3 I.

The initial voltage is E

The voltage drop seen by bulbs 2,3 and 4 is E - I*R

Bulb 4 will see the entire voltage of E - I*R

Since it sees 2/3 * I The power dissipated by 4 is P4 = (E - I*R) * (2/3)I

Each of the other bulbs see (E - IR) * (1/3 I)/2 as their power dissipation.

So here's the answer.

P1>P4 > (P2 - P3)

P2 = P3 if there is such an answer in C.

Which phrase does not describe a mineral?
A. Specific chemical consumption B. Organic solid C. Crystal structure D. Naturally occurring

Answers

The answer is A) specific chemical consumption

A should be the answer

A girl and a boy are riding on a merry go round that is turning at a constant rate. The girl is near the outer edge, and the boy is closer to the center. Who has greater tangential acceleration?Both the girl and boy have the same nonzero tangential accelerationThe boy has greater tangential accelerationBoth the girl and the boy have zero tangential accelerationThe girl has greater tangential acceleration

Answers

Answer:

The girl has greater tangential acceleration

Explanation:

The angular acceleration ([tex]\alpha[/tex]) of the merry go round is equal to the rate of the change of the angular velocity, [tex]\omega[/tex]:

[tex]\alpha = \frac{d\omega}{dt}[/tex]

Since all the points of the merry go round complete 1 circle in the same time, the angular velocity of each point of the merry go round is the same, and so all the points also have the same angular acceleration.

The tangential acceleration instead is given by

[tex]a_t = \alpha r[/tex]

where

[tex]\alpha[/tex] is the angular acceleration

r is the distance from the centre of the merry go round

Since the girl is near the outer edge and the boy is closer to the centre, the value of r for the girl is larger than for the boy, so the girl has greater tangential acceleration.

Tim adds salt as he starts to heat a pot of water to cook pasta. When the water is boiling, he notices the salt has dissolved

Answers

Answer:

The salt is dissolved by the water and heat. If the pot isn't boiling, the salt wouldn't dissolve, it would stay undissolved.

The diagram below illustrates the law of reflection.

Which is the angle of reflection?

A

B

C

D

Answers

C Is the angle of reflection. The reflected ray is consistently in the plane determined by the incident ray and perpendicular to the surface at the point of reference of the incident ray.

What is the law of reflection?

The law of reflection specifies that upon reflection from a downy surface, the slope of the reflected ray is similar to the slope of the incident ray.

When the light rays descend on the smooth surface, the angle of reflection is similar to the angle of incidence, also the incident ray, the reflected ray, and the normal to the surface all lie in a similar plane.

Hence,C Is the angle of reflection.

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The diagram shows a person holding a bow and arrow.


Which will most likely increase the kinetic energy in this system?

pulling farther back on the string
releasing the string
holding the arrow higher
decreasing the mass of the arrow

Answers

Answer:

releasing the string

Explanation:

In a bow-arrow system, the potential energy stored by pulling the string backwards gets converted to kinetic energy when the string is released. Thus, more the string is pulled backwards, more potential energy would be stored. When the string is released, the potential energy reduces and converts to kinetic energy. Therefore, by releasing the string, the kinetic energy increases.

Final answer:

option A. Pulling back further on the bowstring increases the kinetic energy in the system. This is due to the added work, translated into kinetic energy when the string is released, accelerating the arrow to a higher speed.

Explanation:

The kinetic energy in this system will most likely increase by pulling farther back on the string. Kinetic energy is the energy of motion, and in this case, it's the energy that the arrow will have as it moves. When you pull back further on the bowstring, you are applying more work (force times distance) to the arrow. This additional work is transformed into kinetic energy when the string is released, causing the arrow to move at a higher speed, thus, the total kinetic energy of the arrow increases.

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A pilot flies in a straight path for 1 hour and 30 min. she then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 hours in the new direction. if she maintains a constant speed of 685 miles per hour, how far is she from her starting position?

Answers

Answer:

The answer is 2,388.56

Explanation:

A pilot flies in a straight path for 1 hour and 30 min. she then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 hours in the new direction. if she maintains a constant speed of 685 miles per hour. and she will be 1486.65 miles far from the starting position.

To find the distance from the starting position of the pilot after the course correction:

Calculate the distance traveled in the new direction using trigonometry.Then, use the Pythagorean Theorem to find the total distance from the starting point.

The pilot is approximately 1486.65 miles from her starting position.

Gamma rays x rays visible light and radio waves are all types of

Answers

Answer:

Electromagnetic waves

Explanation:

Electromagnetic waves are waves that consist of oscillating electric and magnetic fields, that oscillate perpendicularly to each other and perpendicularly to the direction of propagation of the wave (for such a reason, these waves are also called transverse waves).

Electromagnetic waves always travel in a vacuum at the same speed, called speed of light:

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

and they are classified into 7 different types, according to their frequency. From lowest to highest frequency, we have:

Radio waves

Microwaves

Infrared

Visible light

Ultraviolet

X-rays

Gamma rays

Therefore, gamma rays, x-rays, visible light and radio waves are all types of electromagnetic waves with different frequencies.

What does each item used in the experiment represent in the actual greenhouse effect on Earth? For instance, the light used in the experiment represents the Sun. What does the bottom of the box, air in the box, and plastic wrap each represent in the greenhouse effect?

Answers

The light represents the sunlight.

The bottom of the box represents the surface of the Earth.

The air in the box represents the atmosphere.

The plastic wrap represents the part of the atmosphere where the Greenhouse gases are and influence the temperature.

So we have a box, air in it, plastic wrap, and directed light on it. The bottom of the box represents the surface of the Earth. The light that is directed towards it gets partially through the plastic wrap, reaching the bottom of the box and warming it up. As it warms up, the bottom of the box starts to radiate heat and returns it upwards through the air that represents the atmosphere. Then that heat reaches the plastic wrap, but it is not able to move through it, thus the air starts to warm up more and more, giving us a nice simplified example of how this process works.

The law of reflection is quite useful for mirrors and other flat, shiny surfaces. (this sort of reflection is called specular reflection). however, you've likely been told that when you look at something, you are seeing light reflected from the object that you are looking at. this is reflection of a different sort: diffuse reflection. in this problem, you will see how diffuse reflection actually arises from the same law of reflection that you are accustomed to for reflections from mirrors.

Answers

Specular reflection is a mirror-like reflection where light reflects at specific angles, occurring on smooth surfaces and obeying the law of reflection. Diffuse reflection is when light scatters in many directions after hitting a rough surface, allowing us to see objects from different angles. Both types of reflection are explained by the same fundamental law of reflection.

Diffuse vs. Specular Reflection

When light reflects off a surface, the nature of the reflection is determined by the surface's texture. Specular reflection occurs when light strikes a smooth surface, like a mirror, causing light rays to reflect at specific angles maintaining the image's appearance. This type of reflection follows the law of reflection, where the angle of incidence is equal to the angle of reflection. Conversely, diffuse reflection happens when light hits a rough surface, such as paper or clothing. Here, the variance in surface angles causes light to scatter in multiple directions, which enables us to see the object from various perspectives without a distinct reflection of the light source.

Figures referenced in the provided text illustrate these concepts by comparing the predictable reflection from a mirror (specular) with the scattered light from a rough surface (diffuse). This scattering effect of diffuse reflection is what allows us to view nonluminous objects from any angle. It's important to understand that both types of reflections are governed by the law of reflection; it's the surface texture that dictates whether the light is reflected in a singular direction or scattered.

When a guitar is tuned to adjust it pitch what is it that is changed?

A) its wavelength
B) Its frequency
C) Its amplitude
D) its linear density

Answers

Answer:

B) Its frequency

Explanation:

The pitch of sound heard depends on its frequency of the sound wave. Frequency refers to how fast the sound wave is oscillating. A high frequency sound wave has a high pitch while a low frequency sound wave has a low pitch.The faster the sound wave oscillates the higher the pitch. For instance, a guitar with a big heavy string will vibrate slowly and thus create a low pitch.

When a guitar is tuned to adjust its pitch, B) its frequency is changed.

The frequency determines how high or low we perceive the sound (or pitch) to be. This adjustment is achieved by tightening or loosening the tension on the strings, which alters the rate at which the string vibrates.

Frequency is the number of vibrations per second of the string and is measured in Hertz (Hz). Higher tension on the string increases the vibration rate, leading to a higher pitch, while lower tension decreases the vibration rate, resulting in a lower pitch.

So, the frequency is key in changing the pitch of the guitar string, not the wavelength, amplitude, or linear density. The correct answer is B.

Which is an example of the conversion of gravitational potential energy into kinetic energy? a sliding hockey puck an idling car a swimming fish a falling raindrop

Answers

A falling raindrop.

The reason why it's because mass of a raindrop is under influence of gravity pushing it down towards earth surface. When it hit the surface kinetic energy is released.

Answer:

a falling raindrop

Explanation:

Kinetic energy depends on the mass and the velocity of an object.

Potential energy depends on the mass of an object an how high it is.

A raindrop initially has potenial energy because of its high above the ground, when is falling it has a velocity, and having a velocity means it now has kinetic energy.

By falling, the raindrop exchange potential energy for kinetic energy, as it falls, its potential energy is lower since it is at a lower altitud.

And also when it falls it accelerates towards the ground wich makes it have grater velocity and by analogy greater kinetic energy.

Which of the following happens when the rate of forward motion of a glacier is slower than the rate of ablation? A. The glacier remains stationary B. The glacier sheds an iceberg C. The glacier advances D. The glacier retreats

Answers

The glacier retreats when the rate of forward motion of a glacier is slower than the rate of ablation

Answer: D

Explanation:

The Glacial ice moves with respect to the gravity, glacial ice always flows downwards in response to gravitational force and the front line of the glacier is either calving or melting into water which is also referred as shedding icebergs.

When the rate of flow of the glacier is quicker than the rate of melting or ablation, the advancing end of the glacier moves forward. Whereas, the rate of forward motion of the glacier is about the same as the rate of defrosting, the glacier edge doesn't intend to move at all, and if the rate of glacier's flow lacks behind the rate of defrosting, then it retreats (moves backward).

Answer:

Explanation:

The glacier retreats

Biological systems use free energy based on empirical data that all organisms require a constant energy input. The first law of thermodynamics states that energy can be neither created nor destroyed. For living organisms, which of the following statements is an important consequence of this first law?

A) The entropy of an organism decreases with time as the organism grows in complexity.
B) The organism must ultimately obtain all necessary energy for life from its environment.
C) The energy content of an organism is constant except for when its cells are dividing.
D) Organisms are unable to transform energy from the different states in which it can exist.

Answers

Answer:

B

Explanation:

Final answer:

The first law of thermodynamics states that energy can neither be created nor destroyed, only transformed. Thus, organisms must obtain all necessary energy for life from their environment. This is because they cannot create their own energy from scratch because of this law.

Explanation:

The first law of thermodynamics states that energy cannot be created or destroyed, but only transformed. In biological systems, energy is constantly being transformed within organisms, as well as being exchanged with the environment. This principle is crucial for organisms to maintain their life processes like growth, reproduction, and movement.

In the context of the choices, statement B is the most relevant. The organism must ultimately obtain all necessary energy for life from its environment. Organisms get energy from the environment in the form of nutrients or sunlight because energy cannot be created from nothing due to the first law of thermodynamics. Whether an organism is a plant using sunlight in photosynthesis, or an animal eating food and using cellular respiration to extract energy, they are harnessing the energy originally sourced from their environment.

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What happens to the acceleration when the velocity is zero

Answers

Answer:

It's easy to fall into the temptation to say that when the velocity is zero, then the acceleration is also zero. But wait! To answer this question we need to bring out the concept of instantaneous velocity. This type of velocity stands for a specific moment, a specific instant of time, that is, [tex]t=1, \ t=2, \ t=3, \ t=3.2 \ t=4.5[/tex]. If so, then acceleration may not be zero when velocity is zero. For example, suppose you throw an object upward, when it is at the top of the travel the instantaneous velocity is zero because it changes from positive to negative value and there is a moment when it must be zero, but yet there is a constant acceleration by the Earth's gravity at that moment. Even though the velocity at that stationary moment is zero, it doesn't imply the acceleration must be zero, so it has a value and in this case is [tex]-9.8m/s^{2}[/tex]

Using kinetic theory explain why a tire is more likely to blow out during a trip in the summer than during one in the winter

Answers

the hotness of the ground would mostly likely make the tire blow out

Matthew throws a ball straight up into the air. It rises for a period of time and then begins to drop. At which points in the ball's journey will gravity be the greatest force acting on the ball?

Answers

the time it begins to drop

Gravity is a force that acts on the ball throughout its entire journey. However, the point at which gravity is the greatest force acting on the ball is at the highest point of its trajectory.

The gravity of the ball

This is the point where the ball momentarily stops before changing direction and starts to fall back down.

When the ball reaches its highest point, its vertical velocity becomes zero, and for an instant, it is motionless before it starts to fall due to the force of gravity. At this point, gravity is the only force acting on the ball, and it is pulling it downward with the maximum force, trying to bring it back to the ground.

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what is the voltage drop across the 20.0 resistor?

Answers

120.0v drop across the 20.0 resistor

Answer:

120.0v drop across the 20.0 resistor

Explanation:

A mass moves back and forth in simple harmonic motion with amplitude A and period T.(a) In terms of A, through what distance does the mass move in the time T? ?A(b) Through what distance does it move in the time 5.00T? ?A(c) In terms of T, how long does it take for the mass to move through a total distance of 2A? ?T(d) How long does it take for the mass to move through a total distance of 7A? ?T(e) If the objects undergoes simple harmonic motion with a period T. In the time 5T/2 the object moves through a total distance of 16D. In terms of D, what is the object's amplitude of motion? ?D

Answers

(a) 4A

In a simple harmonic motion:

- The amplitude (A) is the maximum displacement of the system, measured with respect to the equilibrium position

- The period (T) is the time needed for one complete oscillation, so for instance is the time the system needs to go from position x=+A back to x=+A again

Therefore, we have that in one time period (1T) the distance covered is 4A. In fact, during one period (1T), the system:

- Goes from x=+A to x=0 (equilibrium position) --> distance covered: A

- Goes from x=0 to x=-A --> distance covered: A

- Goes from x=-A to x=0 (equilibrium position) --> distance covered: A

- Goes from x=0 to x=+A --> distance covered: A

So, in total, 4A.

(b) 20A

Since the system moves through a distance of 4A in a time interval of 1T, we can set a proportion to see what is the distance covered in the time 5.00 T:

[tex]1 T : 4 A = 5T : d[/tex]

Solving for d, we find

[tex]d=\frac{(4A)(5T)}{1 T}=20A[/tex]

So, the distance covered in the time 5.00 T is 20 A.

(c) 0.5 T

Since the system moves through a distance of 4A in a time interval of 1T, we can set a proportion to see the time t that the system needs to move through a total distance of 2A:

[tex]1 T : 4 A = t : 2A[/tex]

Solving for t, we find

[tex]t=\frac{(2A)(1T)}{4 A}=0.5 T[/tex]

So, the time needed for the system to move through a total distance of 2A is 0.5T (half period).

(d) 7/4 T

As before, since the system moves through a distance of 4A in a time interval of 1T, we can set a proportion to see the time t that the system needs to move through a total distance of 7A:

[tex]1 T : 4 A = t : 7A[/tex]

Solving for t, we find

[tex]t=\frac{(7A)(1T)}{4 A}=\frac{7}{4}T[/tex]

So, the time needed for the system to move through a total distance of 2A is 7/4 T

(e) 8/5 D

In a time of [tex]\frac{5}{2}T[/tex], the distance covered is 16D.

We also now that the distance covered in 1T is 4A.

So we can find the distance covered in a time of [tex]\frac{5}{2}T[/tex] in terms of A:

[tex]1T:4A = \frac{5}{2}T:d\\d=\frac{(4A)(\frac{5}{2}T)}{1T}=10A[/tex]

And we know that this distance must correspond to 16D, so we can find a relationship between A and D:

[tex]10A=16D\\A=\frac{16}{10}D=\frac{8}{5}D[/tex]

Other Questions
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