real springs have mass. will the true period and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? explain

Answers

Answer 1

The frequency will be lower and the time will be longer. The spring must move both its own mass and the mass at the end of the string since it has mass. The frequency and period decrease and lengthen as mass increases.

What impact does mass have on the length of a spring?

A spring-mass system's period is inversely proportional to the square root of the mass and proportionate to the spring constant.

How does mass impact the frequency of springs?

When the mass is twice, the spring constant, oscillator frequency, and motion amplitude are likewise doubled. A vibrating body's frequency falls as its mass rises.

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Related Questions

The kinetic energy of a golf ball is measured to be 143 J. If the golf ball has a mass of 47g. What is its
velocity?

Answers

The velocity of a golf ball with a mass of 47 g and the kinetic energy of a golf ball is measured to be 143 J is 2.44 m/s.

The kinetic energy is the energy obtained when the body is in motion. The kinetic energy equals half of the product of mass and the square of the velocity of the object. The velocity is a vector quantity that defines the speed with a particular direction and the unit of velocity is m/s. The unit of kinetic energy is Joule (J).

From the given,

the mass of a golf ball = 47 g = 0.047 kg

the kinetic energy = 143 J

the velocity of a golf ball =?

K.E = 1/2 (mv²) where m is the mass and v is the velocity.

v² = 143×2 / 0.047

   = 286 / 0.047

  = 6085.10

v² = 6085.1

v = √6

  = 2.44

v = 2.44 m/s.

Thus, the velocity of a golf ball is 2.44 m/s.

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1.A heavy rock and a light rock , both granites , are dropped off the leaning Tower of Pisa . Air resistance is negligible . Which of the following is true? a ) Both rocks will hit the ground at about the same time b ) The lighter rock will hit the ground at about the same time ) The heavier rock will hit the ground first d ) Neither rock will hit the ground

Answers

If two rocks are the same size but one is heavier, the larger rock will fall to the ground first because it has a higher density than the lighter one.

Why does the larger rock not fall more quickly?

Both the gravitational pull and the acceleration are stronger on objects that are heavier. As it turns out, these two processes precisely cancel one another out to produce a falling item with the same acceleration regardless of mass.

When hurled with the same force, how do the accelerations of small and large rocks compare?

The two rocks fall at the same rate because acceleration is dependent on both mass and net force, which in this case is the weight of each rock.

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FILL IN THE BLANK to measure the distance to a star very close to the sun i should use ______ and the distance to a galaxy across the universe i should use ______.

Answers

Answer:

Parallax, Hubbles law

Explanation:

Quizlet

Explain what the following statement means: "Similar to the moon, Mercury and Venus have phases when seen from Earth. "

Please use full sentences

Answers

Being informed that the planets Mercury and Venus, in addition to the Moon, also have phases is one of the joys of studying astronomy. The mechanics underlying the phases as well as the visual experience on these planets are somewhat different.

We observe the phases of these two planetary disks because of the varying position angle between the Earth, Sun, Mercury, and Venus caused by the relative positions of our orbits to one another. When Venus lies between the Earth and the Sun, it appears as a thin crescent in telescopic views as it rotates to the near side. When Venus is far from the Sun, it displays its new phase. The planet may be observed through a telescope at first light because it has an atmosphere.

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A steel ball whose mass is 100 g is rolling at a rate of 2.8 m/sec. What is it’s momentum?

Answers

Answer:

The momentum of the steel ball is 0.28 kg m/sec.

Explanation:

The momentum of an object can be calculated using the formula: momentum = mass x velocity. In this case, the mass of the steel ball is 100 g, which is equivalent to 0.1 kg. The velocity of the ball is 2.8 m/sec. Plugging in the values into the formula, we get:

momentum = 0.1 kg x 2.8 m/sec

momentum = 0.28 kg m/sec

So the momentum of the steel ball is 0.28 kg m/sec.

Why is the choice of a radio pharmaceutical important in radioisotope imaging?

Answers

Answer:

To actually do it what are you referring to comment below I'll assist further

A car slows down from a velocity of 25 m/s to rest in 5.0 seconds. How far did the car travel during that time?

Answers

Answer:

\( \boxed{\sf Distance \ travelled = 62.5 \ m} \)

Given:

Initial velocity (u) = 25 m/s

Final velocity (v) = 0 m/s (Rest)

Time taken (t) = 5 seconds

To Find:

Distance travelled by car (s)

Explanation:

From equation of motion of object moving with uniform acceleration in straight line we have:

\( \boxed{ \bold{s = (\frac{v + u}{2} )t}}\)

By substituting value of v, u & t in the equation we get:

\( \sf \implies s = ( \frac{0 + 25}{2} ) \times 5 \\ \\ \sf \implies s = \frac{25}{2} \times 5 \\ \\ \sf \implies s = 12.5 \times 5 \\ \\ \sf \implies s = 62.5 \: m\)

\( \therefore\)

Distance travelled by car (s) = 62.5 m

The distance  car travel during that time is 62.5 meter.

What is acceleration?

Acceleration is the rate at which speed and direction of velocity vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates.

Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.

Initial velocity (u) = 25 m/s

As the car becomes rest, final velocity (v) = 0 m/s (Rest)

Time taken (t) = 5 seconds.

The deceleration of the car: a = (initial speed - final speed)/time interval

= ( 25 m/s - 0 m/s)/5 second

= 5 m/s²

The distance  car travel during that time = ut - at²/2

= 25 × 5.0 meter - (5×5²/2) meter

= 62.5 meter.

Hence, the distance  car travel during that time is  62.5 meter.

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Calculate the acceleration of a bottle rocket that is traveling at a speed of 74 m/s, and then descends at a speed of 89 m/s. It takes the rocket 5 seconds to change its speed.


a) 1 m/s/s


b) 2 m/s/s


c) 3 m/s/s


d) 4 m/s/s

Answers

Answer:Falling objects form an interesting class of motion problems. For example, we can estimate the depth of a vertical mine shaft by dropping a rock into it and listening for the rock to hit the bottom. By applying the kinematics developed so far to falling objects, we can examine some interesting situations and learn much about gravity in the process.

Explanation:

A 200 kg bumper car is moving down the field at a velocity
of 10 m/s when it strikes an identical bumper car that is at
rest. The first car stops after the collision. What is the
velocity of the second car after the collision?

Answers

Answer:

It is 10 m/s

Explanation:

A DNA macromolecule is made up of two strands of DNA, which are connected to form a DNA double helix. The bonds between
the atoms in each strand are covalent bonds. The bonds between the two strands are hydrogen bonds. Which of the following
statements is true about the DNA double helix?

Answers

Answer:

where is the multiple choice?

Given that A=mass number,Z=atomic number and X is the element name. Find 1.Neutron number. 2.element identity. with mass number 54 and proton number 23.​

Answers

The neutron number can be calculated by subtracting the atomic number from the mass number. In this case, 54 - 23 = 31. Therefore, the neutron number is 31.
To determine the element identity, we need to find the element with a mass number of 54 and a proton number of 23. This can be done by looking at the periodic table. Based on these numbers, we know that the element has 23 protons, which places it in the 23rd position on the periodic table. The element with the atomic number 23 is vanadium (V). Therefore, the element identity is vanadium (V).
In summary, for an element with a mass number of 54 and a proton number of 23, the neutron number is 31 and the element identity is vanadium (V).
To determine the neutron number and element identity, you can use the given mass number (A) and proton number (Z).
1. Neutron number:
Neutron number = Mass number (A) - Proton number (Z)
Neutron number = 54 - 23
Neutron number = 31
2. Element identity:
Since the proton number (Z) is also the atomic number, you can use it to identify the element. With an atomic number of 23, the element is Vanadium (V).
In summary, for the element X with mass number 54 and proton number 23, the neutron number is 31, and the element is Vanadium (V).

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When you're super tired and you lose energy, what energy are you actually losing?
I said Physics class, but it's really for Science class.

Answers

Answer:

it is chemical energy

Explanation:

that is the energy used by our body, so it is the one that we will loose. and the energy that we gain is also chemical energy

3 Draw energy transfer diagrams
for:
a) winding up a clockwork car
b) letting a clockwork car run
c) letting a battery-powered car
run.

Answers

Answer:

The outline of the energy transfer are;

a) Kinetic energy → Clockwork spring → Potential energy

b) Potential energy in clockwork car → Clockwork spring coil unwound → Clockwork car run

c) Chemical potential energy → Batteries in the car → Electric motors → Kinetic energy

Please find attached the drawings of the energy transfer created with MS Visio

Explanation:

The energy transfer diagrams are diagrams that can be used to indicate the part of a system where energy is stored and the form and location to which the energy is transferred

a) The energy transfer diagram for the winding up a clockwork car is given as follows;

Mechanical kinetic energy is used to wind up (turn) the clockwork car such that the kinetic energy is transformed into potential energy and stored in the wound up clockwork as follows;

Kinetic energy → Clockwork spring → Potential energy

b) Letting a wound up clockwork car run results in the conversion of mechanical potential energy into kinetic (energy due tom motion) energy as follows;

Potential energy in clockwork car → Clockwork spring coil unwound → Clockwork car run

c) The energy stored in the battery of a battery powered car is chemical potential energy. When the battery powered car runs, the chemical potential energy produces an electromotive force which is converted into kinetic energy as electric current flows from the batteries

Therefore, we have;

Chemical potential energy → Batteries in the car → Electric motors → Kinetic energy

3 Draw energy transfer diagramsfor:a) winding up a clockwork carb) letting a clockwork car runc) letting
3 Draw energy transfer diagramsfor:a) winding up a clockwork carb) letting a clockwork car runc) letting
3 Draw energy transfer diagramsfor:a) winding up a clockwork carb) letting a clockwork car runc) letting

Is it possible to accelerate a massive object to the speed of light in a real situation? Explain your answer.
Yes, it is possible. Velocity is the product of acceleration and time, and therefore all objects can reach the speed of light if accelerated long enough.
No, it is not possible. Accelerating a massive object to the speed of light would require infinite energy.
Yes, it is possible. Objects may be accelerated up to but not beyond the speed of light because it is the ultimate speed limit.
No, it is not possible. As an object's length contracts towards zero, the work that can be done on it also approaches zero.

Answers

No, it is not possible. Accelerating a massive object to the speed of light would require infinite energy. The correct answer is b).

According to Einstein's theory of relativity, as an object with mass approaches the speed of light, its relativistic mass increases. This means that as the object's speed gets closer to the speed of light, its mass increases, making it harder and harder to accelerate further.

As an object with mass accelerates, its kinetic energy increases, and according to classical physics, kinetic energy is given by the equation

KE = 1/2 mv².

As the object approaches the speed of light, its mass increases, which means that more and more energy is required to continue accelerating it.

In fact, as an object with mass approaches the speed of light, its relativistic mass becomes infinite, which implies that an infinite amount of energy would be needed to reach or surpass the speed of light.

Therefore, it is not possible to accelerate a massive object to the speed of light in a real situation due to the requirement of infinite energy.

The correct answer is b)

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Assertion: In domestic electric circuits, the metallic body is connected to the earth wire, which

provides a low-resistance conducting path for the current.

Reason: It ensures that any leakage of current to the metallic body of the appliance keeps its

potential to that of the earth, and the user may not get a severe electric shock. pls fast

Answers

The earth connection offers protection in case of an electrical fault.

An electric circuit is a path provided for the flow of current. Usually metallic conductors carry electric current in a circuit. Circuits have an earth connection. The essence of the earth connection is to provide protection from possible electric shocks. The earth connection provides a pathway by which current can flow to the earth in event of a fault in the circuit.

Hence, from the statement in the reason and assertion, we can conclude that the reason is an explanation for the assertion in the question.

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Calculate the power required to move a 2,000-kilogram automobile to the top of a 100-meter hill in 15. 0 seconds. Express the power both in



units of watts and horsepower.

Answers

The power required to move the automobile to the top of the hill is 130,666.67 watts or 175.41 horsepower.

The power required to move an object can be calculated using the formula: power = work / time.

First, let's calculate the work done in lifting the automobile to the top of the hill. The work done against gravity is given by the formula: work = force × distance.

The force required to lift the automobile is equal to its weight. The weight of an object is given by the formula: weight = mass × acceleration due to gravity.

Substituting the given values, we have: weight = 2,000 kg × 9.8 m/s^2 (acceleration due to gravity) = 19,600 N.

The distance the automobile is lifted is 100 meters.

Therefore, the work done against gravity is: work = 19,600 N × 100 m = 1,960,000 J (joules).

The time taken to reach the top of the hill is given as 15.0 seconds.

Now, we can calculate the power using the formula: power = work / time.

power = 1,960,000 J / 15.0 s = 130,666.67 W (watts).

To convert watts to horsepower, divide the power in watts by 746 (1 horsepower = 746 watts).

power in horsepower = 130,666.67 W / 746 = 175.41 hp (horsepower).

Rounding to two decimal places, the power required to move the automobile to the top of the hill is approximately 130,666.67 watts or 175.41 horsepower.

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The  to problem of calculating the power required to move a 2,000-kilogram automobile to the top of a 100-meter hill in 15.0 seconds is given

Given, Mass of the automobile, m = 2000 knight of the hill, h = 100 time, t = 15.0 the gravitational potential energy of the automobile when at the bottom of the hill is equal to the work done in lifting it up the hill

.W = mgh= (2000 kg) (9.81 m/s²)

(100 m)= 1,962,000 J

Power is defined as the rate at which work is done, or the work per unit time. Therefore,

Power = Work / Time= 1,962,000 J / 15.0 s

= 130,800 WIn horsepower, Power = (130,800 W) / (746 W/hp)

= 175.3 hp

Therefore, the required power to move a 2,000-kilogram automobile to the top of a 100-meter hill in 15.0 seconds is 130,800 W or 175.3 hp.

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Please help me!!!.......​

Please help me!!!.......

Answers

Answer: its a

Explanation:

Look at the diagram of the male reproductive system. Name the parts

Answers

The testes are the primary male reproductive organs responsible for producing testosterone.

How to explain the parts

Vas Deferens: Also known as the ductus deferens, it is a muscular tube that carries mature sperm from the epididymis to the ejaculatory ducts.

Seminal Vesicles: These glands produce a fluid rich in fructose and other nutrients, which helps nourish and provide energy to the sperm.

Prostate Gland: It is a walnut-sized gland that produces a milky fluid containing enzymes, proteins, and other substances that contribute to se men formation.

Cowper's Glands: These small glands secrete a clear, alkaline fluid that lubricates the urethra and neutralizes any acidic urine remnants, creating a favorable environment for sperm.

Urethra: This is a tube that runs  serves as a passage for both urine and semen, though not at the same time.

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Look at the diagram of the male reproductive system. Name the parts

the separation of white light into its component colors is

Answers

Answer:

Retraction

I hope this helps:)

The separation of white light into its component colors is called "dispersion." This phenomenon occurs due to the interaction of light with a medium, such as a prism or a droplet of water.

When white light passes through a medium, such as a prism, the different wavelengths of light that make up white light refract (or bend) at different angles as they enter and exit the prism. This bending of light is known as refraction. The degree of refraction depends on the wavelength of light, with shorter wavelengths being refracted more than longer wavelengths.

As a result of this differential refraction, white light is spread out or dispersed into a spectrum of colors, known as a rainbow. The spectrum includes colors ranging from violet (which has the shortest wavelength) to blue, green, yellow, orange, and red (which has the longest wavelength).

This dispersion of white light into its component colors is the basis for various optical phenomena, such as rainbows, prismatic effects, and the color separation in devices like spectrometers or cameras that use prisms or diffraction gratings to analyze light.

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. sand runs from a hopper at a constant rate dm dt onto a horizontal conveyor belt that is driven at a constant speed v by a motor. a) find the power needed to drive the belt. b) compare your answer to part (a) with the rate of change of kinetic energy of the sand. can you account for the difference?

Answers

Power Transmission and Efficiency of Belts. Calculate the efficiency of power transfer of belts. Featured Links. As can be used to express the torque at the driven wheel or pulley

(a). Where T = (F₂ - F₁) r a. torque, or

T (Nm) f = force (N)

Belts: Efficiency in Power Transmission Classical V-belts are usually worn separately, especially in the sizes A and B. Due to financial burdens and inefficiencies, the bigger C, D, and E sizes are typically not employed in single-belt drives. The use of multiple A or B belts is a more cost-effective option than using a single-belt C, D, or E segment.

In belt drives, the input pulley transmits forces to the belt, which then transfers those forces back to the output pulley. Effective force or circumferential force F c are other names for the force that needs to be transferred from one pulley to the next.

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If the person's velocity is changing is the person
accelerating

Answers

Answer:

a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction.

The slope of the line on a position vs. time graph reveals information about an object's velocity. The magnitude (numerical value) of the slope is equal to the object's speed and the direction of the slope (upward/+ or downward/-) is the same as the direction of the velocity vector. Apply this understanding to answer the following questions.
a. A horizontal line means
b. A straight diagonal line means
c. A curved line means
d. A gradually sloped line means
e. A steeply sloped line means​

The slope of the line on a position vs. time graph reveals information about an object's velocity. The

Answers

The correct answer is as follows:

a. A horizontal line means zero velocity.

b. A straight diagonal line means constant velocity.

c. A curved line means changing velocity.

d. A gradually sloped line means slow velocity.

e. A steeply sloped line means​ fast velocity.

Briefing:

The velocity of an object is represented by the slope of a location graph. Thus, the slope's value at a given instant corresponds to the object's velocity at that precise moment.

An object's distance from its beginning position at any given moment since it began moving is displayed on a position-time graph. The greater the slope of the line and the faster the object's speed changes, the steeper the line is.

The Position-Time graph exists the graph where the time t and the particle's instantaneous position x exists shown on the y-axis and x-axis, respectively.

The correct answer is as follows:

a. A horizontal line means zero velocity.

b. A straight diagonal line means constant velocity.

c. A curved line means changing velocity.

d. A gradually sloped line means slow velocity.

e. A steeply sloped line means​ fast velocity.

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The net force on a vehicle that is accelerating at a rate of 1.8 m/s2 is 2100 N. What is the approximate mass of the vehicle in kg? Round your answer to the nearest kilogram

Answers

Solution

Given,

Force(F)= 2100N

Acceleration (a)=1.8m/s^2

Mass(m)= ?

Wo know that ,
Force = mass*acceleration
or, F= m*a
or, 2100= m*1.8
or , 2100/1.8 = m
:. m = 1166.67N

The net force on a vehicle that is accelerating at a rate of 1.8 m/s2 is 2100 N. The approximate mass of the vehicle in kg is 1166.67kg.

What is force ?

The word "force" has a clear definition. At this level, calling a force a push or a pull is entirely appropriate. A force is not something an object "has in it" or that it "contains." One thing experiences a force from another. There are both living things and non-living objects in the concept of a force.

The vector sum of the forces exerted on a particle or object is known as the net force. The original forces' impact on the motion of the particle is replaced by the net force, which is a single force.

Force ( F ) is 2100N

Acceleration ( a ) is 1.8m/s²

Mass(m)= ?

According to formula;

Force = mass × acceleration

F= m × a

2100 = m × 1.8

2100 / 1.8 = m

Therefore, m = 1166.6kg.

Thus, The net force on a vehicle that is accelerating at a rate of 1.8 m/s2 is 2100 N. The approximate mass of the vehicle in kg is  1166.67kg.

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Please solve this
Question 4 The sound intensity of the pin drop is about \( 1 / 30000 \) of the sound intensity of a normal conversation. What is the decibel level of a pin drop? (4 Points)

Answers

The decibel level of a pin drop is -47.8 dB. The negative sign indicates that the pin drop sound is significantly quieter than the reference sound intensity.

For the decibel level of a pin drop,

dB = 10 × log10(I/I₀)

Where I is the sound intensity being measured and I₀ is the reference sound intensity,

Sound intensity = 1 / 3000

I/I₀ = 1/30000

log₁₀(I/I₀) = log₁₀(1) - log₁₀(30000) = 0 - log₁₀(30000) = -4.78

dB = 10 × (-4.78) = -47.8

Hence, the decibel level of a pin drop is -47.8 dB. the negative sign indicates that the pin drop sound is significantly quieter than the reference sound intensity.

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In a study conducted by a University of Illinois researcher, the football team at Unity High School in Tolono, IL was equipped for an entire season with helmets containing accelerometers. Information about every impact in practice and in games was sent to a computer present on the sidelines. The study found that the average force on a top of the head impact was 1770 N and endured for 7. 78 milliseconds. Using a head mass of 5. 20 kg and presuming the head to be a free body, determine the velocity change experienced in such an impact

Answers

The velocity change experienced on a top of the head impact is calculated to be 2.65 m/s.

Given that,

Average force = 1770 N

Mass m = 5.2 kg

Time t = 7.78 milliseconds = 7.78 × 10⁻³ s

From impulse-momentum theorem, we know,

J = Fav Δt = Δp = m Δv

Fav Δt = m Δv

Making Δv as subject, we have,

Δv = Fav Δt /m

Placing the values in the above equation, we have,

Δv = Fav Δt /m = (1770 × 7.78 × 10⁻³)/5.2 = 2.65 m/s

Thus, the velocity change experienced on a top of the head impact is calculated to be 2.65 m/s.

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Star X has lines of ionized helium in its spectrum, and star Y has bands of titanium oxide. Which is hotter

Answers

Hotter is Star X. Ionized helium lines are highest at high temperatures (> 30,000 K), whereas titanium oxide lines are brightest at low temperatures (3000 K), according to the study Absorption Lines in Stars of Different Temperatures. Star X must therefore be hotter than Star Y. A higher amount of electron excitation.

The creation of excimers are two other methods of making helium reactive. Helium that has been ionized (He+), also referred to as He II, is a very high energy substance capable of removing one electron from any other element. One electron only exists in a single, ionized helium atom.

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1. Under what conditions can chemical
properties be observed

Answers

Chemical properties are observed when matter or substance changes to form a new kind of matter or substance.

What is Chemical properties?

This is the term used to describe the ability of a substance or matter to react and form new substance. Chemical properties are used during chemical reaction to be able to control the reaction and get a certain product

we can conclude that chemical properties are observes during chemical reaction to ascertain the new substance or matter to be formed

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Which equation best represents the intensity of light coming out of a secondpolarizing filter is equal to the intensity of polarized light coming out of a firstpolarizing filter multiplied by the cosine, squared, of the angle between thepolarizing axes of the two filters?

Which equation best represents the intensity of light coming out of a secondpolarizing filter is equal

Answers

Let the angle between the polarizing axes of the two filters be

\(\theta\)

Let the intensity of polarized light coming out of the first polarizing filter be I1.

Then the intensity of the second polarizing filter will be

\(I_2=I_1cos^2\theta\)

Thus, the correct option is B.

now assume that the surface is rough (that is, not frictionless). you perform the experiment and observe that the second spring only compresses a distance d2/2. how much energy, in joules, was lost to friction?

Answers

Assuming the surface is frictionless, the energy lost to friction would be 0 Joules.

Energy lost due to Friction

Friction is the force that resists motion between two objects that are in contact with each other. In the experiment, friction is the force that resists the motion of the second spring as it compresses a distance of d2/2. Since the surface is rough, it provides a strong resistance to the motion of the spring, thus leading to a loss of energy.

However, if the surface had been frictionless, then the second spring would have compressed a distance of d2, as there would be no resistance to its motion. This means that no energy would have been lost to friction, as there would not have been any friction present in the system.

In conclusion, friction is the force that is responsible for the loss of energy in this experiment. When the surface is rough, the friction between the surface and the second spring is strong, leading to a loss of energy. However, when the surface is frictionless, the friction between the surface and the second spring is not present, thus no energy is lost to friction.

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3 examples of newtrons 2 law

Answers

Explanation:

1) Kicking a ball.

2) Capture the ball by hand.

3) Push a car.

Other Questions
PLEASE SOLVE THIS FOR MEEEE What is a null and alternative hypothesis example? What property of matter is most responsible for the fact that sound travels at different speeds through different materials?. 1. How would you simplify and solve this equation? What steps would you use? *y - 3(2y - 7) = 76 A train is traveling at 55m/s begins to slow down as it approaches a bend in the tracks. If it travels around the bend at a speed of9 m/s and it takes 49 s to properly slow down, what distance does the train travel while slowing down? What kind of function is f/x )? G x? Find the measure of angle bplease help:) Lens Co manufactures lenses for use by a wide range of commercial customers. The company has two divisional manager who has overall responsibility for all aspect of running their division and the divisions are currently treated as investment centres. Each manager, however, has an authorization limit divisions the photographic division (P) and the optometry division (O). Each of the division is run by a of GHe 15,000 per item for capital expenditure and any item costing more than this must first be approved by head office. During the year, head office made a decision to sell a large amount of the equipment in division P and replace it with more technologically advanced equipment. It also decided to close one of Division O's factories in a country deemed to be politically unstable with the intention of opening a new factory elsewhere in the following year. Both divisions trade with overseas customers choosing to provide these customers with 60 days credit to encourage sales. Due to difference in exchange rates between the time of invoicing the customers and receiving the payment 60 days later, exchange gains and loses often occur. The cost of capital for Lens Co is 12% per annum. The following data relates to the year ended 30 November 20X6 Revenue Gains on sale of equipment Direct labour Direct material Divisional overheads Trading profit Exchange gain/(loss) Exceptional costs for factory closure Allocated head office costs Net divisional profit Depreciation on uncontrollable assets Included in divisional overhead Division P GHC 000 14,000 400 14,400 (2,400) (4,800) (3.800) 3,400 (200) (680) 2.520 320 Page 3 of 5 Division O GHC 000 18,800 18,800 (3,500) (6,500) (5,200) 3,600 460 (1,800) (1,040) 1,220 (Total 15 marks) 460 Division P GHc 000 Non-current assets controlled by the division No-current assets controlled by head office Inventories Trade receivables Overdraft Trade payables 15,400 3,600 1,800 6,200 500 5,100 Division O GHC 000 20,700 5,200 3,900 8,900 7,200 To date, managers have been paid a bonus based on return on investment (ROI) achieved by their division. However, the company is considering whether residual income would be a better method. a. Calculate the return on investment (ROI) for each division for the year ended 30 November 20X6. ensuring that the basis of the calculation makes it a suitable measure for assessing the divisional manager's performance. (4 b. Explain why you have included or excluded certain items in calculating the ROI in question (a) above, stating any assumptions you have made. (4marks) c. Briefly discuss whether it is appropriate to treat each of the division of Lens Co as investment centres. d. Discuss the problems involve in using ROI to measure the managers performance. (4marks) (3marks) (15 marks) 1cm^3 of hydrochloric acid of ph 2 is made up to a volume of 10 cm^3 with distilled water. state the ph of the new solution. thankyou A spherical liquid drop of radius R has a capacitance of C = 4me,R. If two such drops combine to form a single larger drop, what is its capacitance? A. 2 C B. 2 C C. 23 C D. 23 The width of a rectangle with area 55in^2 depends on its length. write the formula that describes the width of the rectangle as a function of its length. (screenshot attached if you need to see the problem better) Assignment on queueing Theory I) The mean time between arrivalsof customers in a bank is 4 minutes. If a customer has alreadyarrived in the bank,a) What is the probability that the next arrival wil The _______________________________ established the principle of self-government in New England and also demonstrated the social contract in early-America. On October 1, Swifty's Painting Service borrows $101000 from National Bank on a 3-month, $101000, 4% note. The entry by Swifty's Painting Service to record payment of the note and accrued interest on January 1 is Ejercicio 5. En el ao 1985 fue puesto en rbita el primer satlite de Mxico, el Morelos 1. Dicho satlite orbitaba la Tierra a una altura de 35 800 km (35.8 x10^6 m).a) Obtenga el radio de la rbita del satlite (r = R +h)b) Calcule la velocidad del Morelos 1c) Obtenga el periodo de rotacin en horasd) Cul es el valor de la intensidad del campo gravitacional en la rbita del Morelos 1? Do you think AIDS/HIV is a global health crisis? Why or why not? Why do you think more progress hasnt been made on curing this disease? Grant can buy 6-packs of table-tennis balls for $2.10 or 9-packs of table-tennis balls. for $2.88. Grant wants to buy 18 table- tennis balls. How much more will he spend if he buys only 6-packs of table-tennis balls? Show work in which one of the following cases is the displacement of the object directly proportional to the elapsed time? For open book tests, you dont need to know everything, just where to find everything. please select the best answer from the choices provided t f A parent brings a 6-year-old to the clinic and informs the nurse that the child is tired all the time, even though the child sleeps 7 to 8 hours each night. what is the best response by the nurse?