A 220 g mass is on a frictionless horizontal surface at the end of a spring that has force constant of 7.0 Nm-1. The mass is displaced 5.2 cm from its equilibrium position and then released to undergo simple harmonic motion.
At what displacement from the equilibrium position is the potential energy equal to the kinetic energy.

Answers

Answer 1

The work required to stretch the spring by a displacement of 5.2 cm = 0.052 m is

1/2 (7.0 N/m) (0.052 m)² ≈ 0.0095 J

which is stored as potential energy in the spring. When the mass is released, as the spring relaxes, this potential energy is gradually converted into more and more kinetic energy.

Let x be the displacement (relative to the equilibrium position, with 0 < x < 0.052 m) at which this energy is split evenly between potential energy P and kinetic energy K, so that

P + K = 2P = 0.0095 J

or

P ≈ 0.0047 J

At this displacement, the spring is storing

P = 1/2 (7.0 N/m) x²

of potential energy. Solve for x :

1/2 (7.0 N/m) x² ≈ 0.0047 J

x² ≈ (0.0047 J) / (1/2 (7.0 N/m))

x ≈ √((0.0047 J) / (1/2 (7.0 N/m)))

x ≈ 0.037 m = 3.7 cm


Related Questions

Which scientist is credited with having the greatest contribution to early microscopy and was the first to observe and describe single-celled organisms?

Answers

Answer:

Antonie van Leeuwenhoek

Explanation:

If you do 72 J of work in 1.2 seconds, how much power is produced

Answers

Answer:

Explanation:

Power is the rate of doing work

P = 72 / 1.2 = 60 Watts

12. A coconut falls out of a tree 12.0 m above the ground and hits a bystander 3.00 m tall on the top of the head. It bounces
back up 1.50 m before falling to the ground. If the mass of the coconut is 2.00 kg, calculate the potential energy of the
coconut relative to the ground at each of the following sites:
(a) while it is still in the tree,
(b) when it hits the bystandlar on the head,
(c) when it bounces up to its maximum height,
(d) when it lands on the ground,
(e) when it rolls into a groundhog hole, and falls 2.50 m to the bottom of the hole,

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Explanation:

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Vesta is a minor planet (asteroid) that takes 3.63 years to orbit the Sun.
Calculate the average sun -Vesta distance

Answers

Using Kepler's third law, the average sun -Vesta distance is 2.36 AU.

According to Kepler's laws, the square of the period of revolution of planets are proportional to the cube of their average distances from the sun. Hence, we can write; [tex]T^{2} =r^{3}[/tex]

Where;

T = period of the planet

r = average distance of the planet

When;

T =  3.63 years

r = [tex]\sqrt[3]{T^2}[/tex]

r = [tex]\sqrt[3]{(3.63)^2}[/tex]

r = 2.36 AU

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Colette launches an air rocket in the upward, positive direction. It launches with an initial velocity of 25.5 m/s. It accelerates in the downward, negative direction at a rate of 9.81 m/s2. After 3.5 seconds, what is the magnitude of the rocket's displacement?

Answers

Answer:

Give me some hint please

Market researchers were interested in the relationship between the number of pieces in a brick-building set and the
cost of the set. Information was collected from a survey and was used to obtain the regression equation ý =
0.08x + 1.20, where x represents the number of pieces in a set and ŷ is the predicted price in dollars) of a set.
What is the predicted price of a set that has 500 pieces?
$40
$41.20
$600
$6,235

Answers

Plug in 500 for x and solve. 500(0.08) = 40

Then do 40 + 1.2 = 41.20

Answer B

Which force, in real life, will have the least effect on a bowling ball rolling down a lane toward bowling pins?

A) magnetism

B) air resistance

C) gravity

D) friction

Answers

Answer:

Its Friction

Explanation:

the pins are not floating and they are not a magnet and not involved with air

The force, in real life, that will have the least effect on a bowling ball rolling down a lane toward bowling pins is magnetism. The correct option is A.

What is magnetism?

Magnetism is basically the force which indeed magnets exert when they attract or even repel one another. The movement of electric charges resulting in magnetism.

Every substance is composed of tiny units referred to as atoms. Each atom contains electrons, which are charged particles.

To increase stability, the pins themselves have a low center of gravity. Because they are spherical in shape, they can roll and strike other pins in a variety of directions.

The force acting on the bowling ball is friction and air resistance. The friction force is equal to the friction coefficient multiplied by the normal force, and thus mass times acceleration.

Thus, the correct option is A.

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what is the approximate distance from the surface of the earth center 2900km 700km 50000km 6400km

Answers

Answer:

6400km is the closest

Explanation:

Alex is x years old . June is 7years older than Alex . their total combined ages is 29 years . find June,s age . show all work algebraically

Answers

Answer:

18 years

Explanation:

Given,

Let Alex be = x years

Then June will be = (7 + x) years

We know that,

Their total combined age is 29 years

Therefore,

By the problem,

=> x + (7 + x) = 29

=> 2x = 29 - 7

=> 2x = 22

=> x = 22 ÷ 2

=> x = 11

So,

Required age of June is = (7 + x) years

= (7 + 11) years

= 18 years (Ans)

What on earth is equal to 9.8m/s/s

Answers

Answer:

Acceleration due to gravity

What is non examples of enlarged

Answers

reduction

deflation

these are examples of the opposite of enlarged to make something smaller is really the key thing here

Which statement about RNA polymerase is NOT true?

RNA polymerase reads a template strand of DNA 5' to 3'

RNA polymerase binds to a promoter region to initiate transcription

RNA polymerase adds a ribonucleotide to the 3' end of a growing RNA molecule

During transcription of a gene, RNA polymerase reads only one strand of DNA

Please explain!

Answers

Answer:

RNA polymerase reads a template strand of DNA 5' to 3'

Explanation:

RNA polymerase is the enzyme accountable for the transcription of the DNA. It shows one coast of the DNA and transcribed within the RNA. It combines the nucleotide to the 3' conclusion of the expanding series of the RNA. It commences the method by connecting to the promoter area of the gene. The enzyme increases nucleotide, not ribonucleotide.

Therefore, A. RNA polymerase reads a template strand of DNA 5' to 3' is false.

Answer:

RNA polymerase reads a template strand of DNA 5' to 3'.

Explanation:

RNA synthesis is less processive during elongation than during initiation. Synthesis begins with the polymerase binding two rNTP molecules. The polymerase frequently releases the nascent transcript before it reaches 8-10 nucleotides in length.

Option B.
Consider a setup in which two springs are attached to a mass in parallel.
Convince yourself that in this setup, the compression of each spring must be the same. Using
this fact, derive the effective spring constant for springs in parallel
This is asking, "ll1 replace the two springs by a single imaginary spring, what would its spring
constant be such that the force stays the same?" Your answer should only depend on k, and k

Answers

Answer:

it would be...

Explanation:

An object moves 45m due East and then 15m due West, the total distance is

Answers

Answer:30m east

Explanation: 45m-15m=30m, which cancels out the one to the west. All that is left is 30m east.

Is this a test/quiz btw?

60 POINT!!!!!!
PLEASE HELP THIS WORK IS VERY IMPORTANT FOR ME
IF YOU GIVE ME THE CORRECT ANSWER I WILL GIVE YOU THE CROWN!!
Miranda found four different bottles filled with unknown pure liquids. She measured the mass, volume, and boiling point of these liquids, and calculated the density which are displayed in Table 1.

What conclusion can you make on whether any of the liquids are the same. Explain based on the information in the table.

Answers

Answer:

Samples 2 and 4 are the same liquid

Explanation:

Samples 2 and 4 should be the same liquid because they have the same density as well as the same boiling point. The mass and volumes given do not matter in this case, however they could be used to calculate the density which was already given.

The liquid  present in sample 2 and 4 is same as according to forces of attraction they have same density and boiling points.

What are forces of attraction?

Forces of attraction is a force by which atoms in a molecule  combine. it is basically an attractive force in nature.  It can act between an ion  and an atom as well.It varies for different  states  of matter that is solids, liquids and gases.

The forces of attraction are maximum in solids as  the molecules present in solid are tightly held while it is minimum in gases  as the molecules are far apart . The forces of attraction in liquids is intermediate of solids and gases.

The physical properties such as melting point, boiling point, density  are all dependent on forces of attraction which exists in the substances.

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A Scooter has a mass of 250 kg. A constant force is exerted on it for 6.0 s. During the time the force is exerted, the scooter increases its speed from 6.00 m/s to 280 m/s. What is the magnitude of the force exerted on the scooter

Answers

Answer:

917 N

Explanation:

917 N, this is your answer!!

Glad to help.

 what is the difference between repelling and attracting

Answers

Answer:

Attracting means pulling toward you and repelling means pushing away

Explanation:

Answer: Repelling is when something will not connect with another object. The force will cause a repel between the two objects. Attracting is when something is attracted or being pulled to another object.

Explanation: Hope this helps!

A meter stick is attached to one end of a rigid rod with negligible mass of length l = 0.302 m. The other end of the light rod is suspended from a pivot point, as shown in the figure below. The entire system is pulled to a small angle and released from rest. It then begins to oscillate. A meter stick hung from a rod of length l. The rod is attached to the ceiling. The rod and meter stick extend downward in a straight line making a small angle with the vertical. (a) What is the period of oscillation of the system (in s)? (Round your answer to at least three decimal places.)

Answers

The period of oscillation of the system nearest to three decimal places

= 1.092 seconds

The period of an oscillation occurring in a system is the time taken to complete one cycle.

The formula that is used to calculate the period of oscillation (T) is

                = 2π√[tex]\frac{l}{g}[/tex]

But,

π = 3.14159 (constant)

g= 10m/s² (acceleration due to gravity)

l = 0.302 m

Therefore T = 2 × 3.14159 × √[tex]\frac{0.302}{10}[/tex]

                    = 6.28318 x √0.0302

                    = 6.28318 x 0.17378

                    = 1.09189s

                    = 1.092 seconds ( to the nearest three decimal places)

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Write a question you would like to see on a quiz to calculate NET FORCE.

Answers

Answer:

How do you find the net force?

Explanation:

i think this is want you asked for?

1
2) Mighty Mouse can lift seven mammoths with a total mass of 525 kg. Using the acceleration of
gravity, find the total WEIGHT that Mighty Mouse is lifting. (answer: 5250 N)

Answers

Answer:

5250N

Explanation:

Weight= Mass × acceleration due to gravity

= 525kg × 10m/s^2

= 5250N

Acceleration of a car that speeds from 4.3 m/s to 12.9 m/s in 2 seconds

Answers

Explanation:

let v1 = 4.3 m/s

v2 = 12.9 m/s

t = 2 seconds

v2 = v1 + at

12.9 = 4.3 + a×2

2a = 12.9 - 4.3 = 8.6

a = 8.6/2

a = 4.3 m/s^2

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