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A 3 kg object attached to a spring oscillates with an amplitude of 15 cm and a period of 2s. At a time t=0.5s, the object's position is x=9.1 cm.


Determine...


a) the spring constant of the spring.


b) the total energy of the system (in joules).


c) the maximum speed of the object.


d) the position of the object as a function of time. Use a cosine function.

Answers

Answer 1

Answer:

Follows are the solution to the given question:

Explanation:

For point a:

[tex]T= 2\pi \sqrt{\frac{m}{k}}\\\\k = \frac{4 \pi^2 m}{T^2}\\\\= \frac{4 \times (3.14)^2 \times 3}{2^2}\\\\=29.578 \ \frac{N}{m}\\\\[/tex]

For Point b:

[tex]E=\frac{1}{2} m a^2 w^2\\\\[/tex]

   [tex]=\frac{1}{2} \times m \times a^2 \times \frac{4\pi^2}{T^2}\\\\=\frac{1}{2} \times 3 \times (0.15)^2 \times \frac{4\times 3.14^2}{2^2}\\\\=0.332 \ J[/tex]

For Point C:

[tex]V_{max}= a w[/tex]

        [tex]= (0.15) \times \frac{2\pi}{T}\\\\= (0.15) \times \frac{2\times 3.14}{2}\\\\=0.471 \frac{m}{s}[/tex]

For point D:

[tex]X= a \sin (wt+ \phi)\\\\0.91=0.15 \sin(\frac{2\pi}{T} \times t+\phi)\\\\0.91=0.15 \sin(\frac{2\times 3.14}{2} \times 0.5+\phi)\\\\0.60 = \sin(3.14 \times 0.5+\phi)\\\\0.60 = \sin(1.57+\phi)\\\\1.57 +\phi =\sin^{-1} 60^{\circ}\\\\1.57 +\phi = 36.86^{\circ}\\\\=35.29^{\circ}\\\\So, X=15 \sin(3.14t+35.29^{\circ}) \ cm[/tex]


Related Questions

The speed of the wooden bar is changed so that the bar hits the water fewer times each second.

What happens to the frequency of the waves produced?

A. Increases
B. Does not change
C. Decreases

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Answer:

c - the frequency of the waves decreases

Is gravitational energy a form of kinetic energy or potential energy? Why do you think that?

Please help due today!!​

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Answer:

When something is lifted, work is done on the object against the pull of gravity. This work is converted to a form of potential energy called gravitational potential energy. When the item falls towards Earth like an apple from a tree, gravitational potential energy is converted into kinetic energy.

what is the difference between a meteor and a meteorite?

1. Meteors are larger than meteorites
2. Meteors come from the Kuiper belt and meteorites originate in the asteroid belt.
3. Meteors are more like comets than meteorites
4. a meteorite is a meteor that impacted the earth.


please help.​

Answers

Answer:

meteorites, meteors are objects that enter Earth's atmosphere from space. But meteors—which are typically pieces of comet dust no larger than a grain of rice—burn up before reaching the ground. ... The term “meteorite” refers only to those bodies that survive the trip through the atmosphere and reach Earth's surface. I believe this is it

Which picture is louder?
A) Bottom picture with greater amplitude
B) Top picture with less amplitude

Help me plssss!!!

Answers

Answer:

A

Explanation:

The amplitude of a sound wave determines its loudness or volume. A larger amplitude means a louder sound, and a smaller amplitude means a softer sound.

Which waves can travel through space?

electromagnetic waves only
mechanical waves only
electromagnetic and mechanical waves
longitudinal and electromagnetic waves

Answers

Answer:

Electromagnetic waves only

Only electromagnetic waves can travel through space. hence option A is correct.

What is Electromagnetic waves ?

Electromagnetic waves are the waves associated with photon. Photons carry  electromagnetic waves. it has both electric field and magnetic field perpendicular to each other.

when input of the Dipole antenna is connected to the electric signals having certain frequency. on first half cycle one pole is on positive potential and other is on negative potential. The pole which is at negative potential attracts all the electrons towards it and the pole which is at positive potential attracts positive holes. In the second half cycle polarity of the poles changes and it happen repeatedly, Due to change in polarity of the dipole of the antenna, electrons in the antenna produces electromagnetic waves which we use it for our radio station and mobile phones.

Electromagnetic waves does not require any medium to travel, it can travel through space(vacuum). Waves travels in the medium but there is no medium in the space, but electromagnetic waves are able to travel in the vacuum so scientist named the space as medium of ether.

Hence option A is correct.

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Can some help me please im confused ‍♀️ !!! I,ll give you BRAINLIES

Answers

Answer:

2 seconds

Explanation:

Do any of the atom diagrams below represent atoms of the same element?



Yes, all the atoms are the same element.

Yes, atom A and atom C are the same element.

Yes, atom A and atom B are the same element.

No, they are all different elements.

Answers

Atom A and atom C are the same element.

A cuboid has sides that are 0.2m, 0.4m and 0.7m. The mass of the cuboid is 0.5kg. Calculate the density.

Answers

Answer:

d= 0.93 kg/m3

Explanation:

density= mass/volume

mass is given

volume= 0.4*0.2*0.7

then fill in the figures

whats the difference between transverse and longitudinal waves?

Answers

Answer:

longitudianl particles are dispelled parrell

Explanation:

transverse perpendicular

C) If your displacement is 19.3m and your final position is 31.8m, what was your initial position?​

Answers

Answer:12.5

Explanation: Subtract

what is tge scientific teem of the ratio between power out to power in (physics)​

Answers

Answer:

In physics, power is the amount of energy transferred or converted per unit time. In the ... Power (physics) ... Angular acceleration / displacement / frequency / velocity. show. Scientists ... Hence the formula is valid for any general situation. ... because they define the maximum performance of a device in terms of velocity ratios

Explanation:

In your lab group you combined salt and water. Then you compared what happens when an egg is placed in tap water versus salt water. You observed that the egg floated in the salt water, but sank on the fresh water. You and your lab partner discuss the cause of this difference and wonder if the combining of the salt and water caused a physical or chemical change. Choose ALL of the evidence that supports that a physical change has occurred.

A) gas was produced

B) the density changed

C) the salt dissolved in the water

D) the salt and the water cannot be separated into their individual molecules

E) the salt and the water can still be separated into their individual molecules

Answers

Answer: the density changed, the salt dissolved in the water, the salt and the water can still be separated into their individual molecules.

Explanation: physical changes are changes in size, shape, or state. Another way to think about a physical change is any change not involving a change in the substance’s chemical identity. You cannot write a chemical equation for salt water because the chemical identity is still salt AND water

trust me i did it

A 1.4 kg coconut falls from rest out of a tree. The instant before it hits the ground, it has a velocity of 6.7 m/s. How high was the coconut initially?

Answers

Answer:

2.29m

Explanation:

Given parameters:

Mass of the coconut  = 1.4kg

Final velocity  = 6.7m/s

Initial velocity  = 0m/s

Unknown:

Height of the coconut initially  = ?

Solution:

To solve this problem, we use one of the kinematics equation. The one given below is the best one to use.

   V²  = U²  + 2gH

V is the final velocity

U is the initial velocity

g is the acceleration due to gravity

H is the height

 So;

            6.7²  = 0²   + (2 x 9.8 x h)

           44.89  = 19.6h

                   h  = 2.29m

help me!
Bill left a hammer out in the rain all day. The next morning it had rust on it.
Oxygen and a metal chemically combine to form rust. What is rust an example of?
O a mixture
• a solution
an element
a compound

Answers

It is a compound yep

Answer:D.Compound

Explanation: internet

A 7.20x10^3 N spacecraft travels away from the Earth. What is its weight when it is a) 6.38×10^3 km
and b) 1.28x10^4 km from the surface of the Earth?

Answers

Answer:

1,252

Explanation:

What is the mass of a bicycle that has 90 kg.m/s of momentum at a speed of 6 m/s?

Answers

Answer:

m = 15 kg

Explanation:

p = m × v

90 = m × 6

6m = 90

m = 90/6

m = 15 kg

A 3.5 kW drill transfers 5 000 kJ of kinetic energy during 15 seconds of use. What is the percentage efficiency of the drill?

Answers

Answer:

1.04%

Explanation:

Given that,

The power of drill = 3.5 kW = 3500 W

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We need to find the percentage efficiency of the drill. It can be given by :

[tex]\eta=\dfrac{P_o}{P_i}\times 100[/tex]

Where

Po and Pi are output and input powers.

[tex]P_o=\dfrac{5000\times 10^3}{15}\\\\=3.34\times 10^5\ W[/tex]

So,

[tex]\eta=\dfrac{3500}{3.34\times10^{5}}\times100\\\\=1.04\%[/tex]

So, the percentage efficiency of the drill is 1.04%.

Which is NOT an example of unbalanced forces acting on an object


A.an acorn falling from a tree

B.a car traveling straight down a road at 40km/h

C.a motorcycle changing speed from 20km/h to 35km/h

D.a truck slowing down as it approaches a red light

Answers

Answer:

C. a motorcycle changing speed from 20km/h to 35km/h

Explanation:

The choice not showing unbalanced forces acting on the object is a motorcycle changing speed from 20km/h to 35km/h.

This change in velocity shows that the body is accelerating during the time interval.

When a body is accelerating, it is changing it's motion and this implies that some unbalanced forces are acting in the body. Unbalanced body changes the state of motion of a body from rest to acceleration or deceleration as the case may be.  

The specific heat capacity of iron is 450.5. A 15.5 kg block of iron with

an initial temperature of 20 degrees Celsius is heated with 250 J. What will

the final temperature of the iron be?

Answers

Answer:

[tex]T_f=20.03^{\circ} C[/tex]

Explanation:

Given that,

The specific heat capacity of iron is 450.5 J/g°C

The mass of block of iron, m = 15.5 kg

Initial temperature, [tex]T_i=20^{\circ} C[/tex]

Heat required, Q = 250 J

We need to find the final temperature of the iron. The formula for heat required is given by :

[tex]Q=mc\Delta T\\\\Q=mc(T_f-T_i)\\\\\dfrac{Q}{mc}=(T_f-T_i)\\\\T_f=\dfrac{Q}{mc}+T_i\\\\T_f=\dfrac{250}{15.5(450.5)}+20\\\\T_f=20.03^{\circ} C[/tex]

So, the final temperature of the iron is [tex]20.03^{\circ} C[/tex].

Some chemical reactions release energy. Others store energy. What important chemical reaction stores energy?

Answers

Chemical energy energy stored in the bonds of chemical compounds. Chemical energy maybe realized during a chemical reaction of in the form of heat

Which explanation BEST supports Newton's second law of motion which states that force = mass x acceleration?

Object Y will accelerate the fastest because it has the largest mass.

Object V will accelerate the slowest because it has the smallest mass.

Object Y will require the most force to move because it has the largest mass.

Object V will require the most force to move because it has the smallest mass.​

Answers

The answer is C. F=ma basically says that force is a function of mass multiplied by acceleration. The first two answers don’t make sense because there’s no necessary relationship between mass and acceleration. And for the last two, the higher the mass, the higher the force needed, therefore C is the correct answer.


Use the motion map to describe the motion of the object.
A motion map. The position line is a long black arrow pointing right, labeled x. Above the line are five dots with a vector pointing away from x that start at x, each one shorter ending in the last dot with no vector. Above that are two yellow vectors pointing toward x between the second and third and third and fourth black dot. Above that are three black dots with vectors pointing toward the origin, x, each with a larger vector. There are three yellow vectors with no black dots pointed toward x starting just above the vertical column of three dots.
Which statements describe what is occurring at
t = 5 seconds? Check all that apply.
The object sped up.
The object slowed down.
The object continued in the same direction.
The object changed direction.
The object came to a complete stop.

Answers

Answer:

The object sped up.

The object changed directions.

Explanation:

Just got the question correct.

Answer:

A & D

The object sped up

The object changed direction

Explanation:

:)

10)A car is moving from rest and attained a velocity of 80 m/s. Calculate the
acceleration of the car after 5 s?

Answers

Explanation:

the velocity graph of a ball mass 20mg moving along a straight line

16m/s^2

Explanation:

initial velocity (u) =0

final velocity (v) =80

acceleration =?

Now,

acceleration = (v-u)/t

=(80-0)/5

= 80/5

= 16m /s^2

A woman standing on the ground watches an airplane fly by a mountain on a clear summer day. Her reference point for the moving plane would be:

a. There is no reference point
b. The ground
c. The mountain
d. A person in the plane

Answers

D I THINK Hope I helped hav ea good day anjajsgbsnsba

A 136 kg defensive lineman is about to tackle a 100 kg quarterback. Right before impact, the lineman is moving north at 6.0 m/s and the the quarterback is moving north at 1.0 m/s. Determine the speed and direction of the two players immediately after the tackle.

Answers

Answer:

Explanation:

We shall apply law of conservation of momentum .

Momentum before impact = momentum after impact

Since they are moving towards the same direction , their momentum will add up .

Total momentum before impact

= 136 x 6 + 100 x 1 = 916 kg m/s .

Total mass of lineman and quarterback = 236 kg , if their velocity after impact be v

their momentum = 236 v

According to law of conservation of momentum

236 v = 916

v = 3.88 m /s

Both of them will move with velocity of 3.88 towards the north .

How would a speed vs. time line graph appear if an airplane moved at a
positive acceleration?

Answers

Answer:

Explanation:

Acceleration is the time rate of change, or the rate, of the velocity. Therefore, the slope y/x of a speed vs time graph would give the acceleration. If the acceleration is said to be positive, the graph would be a straight line that is at a constant increase over time.

What are all of the physics rules?

Answers

Answer:

f this bs

Explanation:

no i will not answer this

Answer: PLEASE GIVE BRIANLIEST

1. Archimedes Principle

2. Avogadro’s Law

3. Ohm's Law

4. Newton’s Laws (1642-1727)

5. Coulomb’s Law (1738-1806)

6. Stefan’s Law (1835-1883)

7. Pascal’s Law (1623-1662)

8. Hooke’s Law (1635-1703)

9. Bernoulli's Principle

10. Boyles's Law

11. Charles's Law

12. Kepler's Law

13. Law of conservation of energy

14. Tyndall effect

15. Graham’s Law

Which part of the electromagnetic spectrum is nearest to radio waves?

X-rays
microwaves
gamma rays
ultraviolet light

Answers

Answer:

i believe it is the microwaves that is closest to the radio waves.

Explanation:

The microwaves are the part of the electromagnetic spectrum is nearest to radio waves.

What is meant by electromagnetic spectrum?

The range of all EM radiation arranged from high to low frequency (short to long wavelength) according to their frequency or wavelength. is known as the electromagnetic spectrum (EM).

Here,

The visible light from a bulb in your home and the radio waves from a radio station are two examples of electromagnetic radiation. Radiation is energy that travels and disperses as it does.

The properties of the electromagnetic spectrum include the ways in which signals can propagate and how much data they can carry. Signals delivered at higher frequencies typically propagate more quickly but can carry more data in a given amount of space.

The electromagnetic spectrum begins with the lowest frequency radio waves and moves up in frequency and down in wavelength from there. Radio waves are followed by visible light, infrared radiation, and lastly microwaves.

Hence,

The microwaves are the part of the electromagnetic spectrum is nearest to radio waves.

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Is this right? Please help me

Answers

Answer:

It would be C

Explanation:

The brain operates on two levels, one of them is unconscious.

This would be definitely C


I NEED HELP ASAP!!!!!!!
A balloon has a volume of 25.0 L at a pressure of 98.7 kPa. Will the new volume be more or less that 25.0 L whe
the pressure is 51.2 kPa?

Answers

Answer:

It will be more

Explanation:

Pressure and volume relationships between gases is given by the Boyle's law.

According to this law, we know that:

  "the volume of a fixed mass of a gas varies inversely as the pressure changes if the the temperature is constant".

So, the higher the pressure on a body, the lower it's volume and vice versa.

Since we set off at a higher pressure and wants to end at a lower pressure, the volume of the gas will increase more.

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