a 8.0-m long wire with a mass of 10 g is under tension. a transverse wave for which the frequency is 570 hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. the maximum transverse acceleration of a point on a wire is closest to:______.

Answers

Answer 1

The maximum transverse acceleration of a point on a wire is closest to 47,458.2 m/s²

What is the angular speed of the transverse wave?

The angular speed of the transverse wave is calculated as follows;

ω = 2πf

where;

f is the frequency of the wave

ω = 2πf

ω = 2π ( 570 )

ω = 3,581.4 rad/s

The maximum transverse acceleration of a point on a wire is calculated as follows;

a = ω²A

where;

A is the amplitude of the wave = 3.7 mm = 0.0037 m

a = ω²A

a = (3581.4)²(0.0037)

a = 47,458.2 m/s²

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Related Questions

Please help me with a speech.The topic of my speech is Passion.​

Answers

Answer:

Explanation:

Passion

For me, standing on the summit of Mt Everest was the result of following a process. The process of mountaineering. I love mountaineering. I am passionate about it. I love the months of planning for an expedition, the months of sweating and training to prepare my body physically. The meticulous preparation of my equipment. Most of all I love the huge mental challenge I have to overcome before each climb to confront my own fear. All these reasons are why I climb, they are why I climbed Mt Everest and that is why I continue to climb.

Passion is an enormously powerful force. It gives us the strength to get through hard times and setbacks. It gives us strength to overcome our fears, to ignore what other people think of us, to be disciplined and make sacrifices in pursuit of our dreams. Passionate people do not want to take shortcuts – they consider that ‘learning the process’ is an important part of the journey.

In mountaineering it’s easy to spot those who are not passionate about the process. They want to stand on top of the mountain but they are not really interested in the process of climbing the mountain. I feel for these people. Success without hard work is a hollow, empty feeling. They never last long in the sport.

Just as in life, successful mountaineers are the ones who are passionate. They are not there just to stand on the summit. Their passion gives them the energy to work the hardest, fight the longest, and in the words of Winston Churchill “never, never. never give-up”.

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

HELP PLEASE!!! I HAVE TO GET THIS IN QUICK!!

HELP PLEASE!!! I HAVE TO GET THIS IN QUICK!!

Answers

Acceleration = force/mass
9/3 = 3
Answer is 3 m/s^2. See attached photo.
HELP PLEASE!!! I HAVE TO GET THIS IN QUICK!!

a student thinks that the ball bearing falls through the liquid at a constant speed
explain how you could develop this experiment to determine if the ball bearing falls through the liquid at constant speed

Answers

By measuring the terminal velocity of the ball bearing and knowing the properties of the liquid and the ball bearing, the viscosity of the liquid can be calculated using Stoke's law.

What is the experiment that shows that the ball bearing falls through the liquid at constant speed?

The experiment you are referring to is commonly known as the Stoke's law experiment or the falling ball viscometer experiment.

In this experiment, a ball bearing (usually made of steel or glass) is dropped into a vertical tube filled with a liquid of known viscosity. The ball bearing falls through the liquid under the influence of gravity, but also experiences a viscous drag force due to the resistance of the liquid.

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does the constellation that was highest in the sky now rise earlier or later than it rose last month

Answers

The constellation that was highest in the sky last month will generally rise earlier this month due to the Earth's orbit and axial tilt. Keep in mind that this answer assumes a specific constellation and may vary depending on the time of year and your location on Earth.

The answer to the question "does the constellation that was highest in the sky now rise earlier or later than it rose last month" depends on the specific constellation in question.

If we consider a specific constellation that was highest in the sky last month, it will rise earlier this month. This is because the Earth's axial tilt and its orbit around the Sun cause a shift in the position of the constellations in the night sky throughout the year. As the Earth orbits the Sun, different constellations become visible at different times.

For example, let's say that last month the constellation Orion was highest in the sky. This month, Orion will rise earlier compared to last month. This is because the Earth's orbit has moved our vantage point in space, causing Orion to appear higher in the sky earlier in the evening.

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How do media literacy , information literacy and technology literacy and media and information literacy differ in terms of use?

Answers

Answer:

Media literacy creates a conscious awareness, the ability to understand, analyze, the messages various media like the newspapers, the radio, that is for the consumer, and it also promotes how best media create information for production.

While information literacy and technology literacy differs from other literacy asked in the question above, as information literacy and technology could be used when describing getting information through adequate research and further dishing out this available information so as to effectively use the information with the aim to solve problems, create awareness, or educate, through technologies such as for example, email.

Lastly, media and information literacy differ in terms of use from the other two explained above, as media and information literacy describes discerning information credibility, accuracy, and objectivity of sources they come from, and it shows people how important it is to have credible information to make informed judgments and the ethical use of the information they consume.

A dog walks 40. m west, then 10. m east and then 50. m south. What is the
distance and displacement traveled?

Answers

The distance is 40+10+50 = 100m
Displacement = square root ( 30^2 + 50^2)

The total distance traveled by the dog is 100 m and the displacement of the dog is 58.31 m.

The given parameters;

Initial position of the dog, 40 m westSecond position of the dog, 10 m eastFinal position of the dog, = 50 south

The displacement of the dog is the change in its initial position and the final position.

The resultant of the dogs position in x-direction: = 40 m - 10 m = 30 m

The resultant of the dogs position in y-direction: 50 m

The magnitude of the displacement;

R² = 30²  + 50²

R² = 3400

R = √3400

R = 58.3 m

The distance covered by the dog is the sum of all the positions of the dog.

Distance = 40 m + 10 m + 50 m

Distance = 100 m.

Thus, the total distance traveled by the dog is 100 m and the displacement of the dog is 58.31 m.

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Solve for the resultant displacement of the two vectors: A = 2.3 km at 45 degrees B = 4.8 km at 90 degrees

Answers

Answer:

The resultant of the vector is 6.63 km

Explanation:

Given;

vector A = 2.3 km 45°

vector B = 4.8 km 90°

The vectors in the x - direction is given by;

Aₓ = 2.3 km Cos 45° = 1.6263 km

Bₓ = 4.8 km Cos 90° = 0

The sum of the vectors in x -direction is given by;

∑X =  1.6263 km + 0 = 1.6263 km

The vectors in the y - direction is given by;

Ay = 2.3 km Sin 45 = 1.6263 km

By = 4.8 km Sin 90° = 4.8 km

The sum of the vectors in y -direction is given by;

∑Y =  1.6263 km + 4.8 km = 6.4263 km

The resultant vector is given by;

R = √(X² + Y²)

R = √[(1.6263)² + (6.4263)²]

R = 6.63 km

Therefore, the resultant of the vector is 6.63 km

The resultant displacement of the two vectors A and B is 6.63 Km and this can be determined by using the given data.

Given :

The two vectors: A = 2.3 km at 45 degrees B = 4.8 km at 90 degrees.

In order to determine the resultant displacement, first, determine the vector in x-direction:

\(\rm A_x=2.3cos45=1.6263 \;Km\)

\(\rm B_x=4.8cos90=0 \;Km\)

Now, the sum of the vectors is given by:

\(\rm \sum X=1.6263+0=1.6263\;Km\)

In order to determine the resultant displacement, first, determine the vector in y-direction:

\(\rm A_y=2.3sin45=1.6263 \;Km\)

\(\rm B_y=4.8sin90=4.8 \;Km\)

Now, the sum of the vectors is given by:

\(\rm \sum Y = 1.6263+4.8=6.4263\)

Now, the resultant vector is given by:

\(\rm R = \sqrt{X^2+Y^2}\)

\(\rm R=\sqrt{(1.6263)^2+(6.4263)^2}\)

R = 6.63 Km

The resultant displacement of the two vectors A and B is 6.63 Km.

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A ball is launched straight out from a 20 meter tall cliff. It is launched horizontally at 7.5 m/s.

a. How long is the ball in the air?
b. How far does it land from the cliff?

Answers

Answer:

b. how far does it land from the cliff

Build your paper cup telephone system?

Answers

To Build your paper cup telephone system do the following:

Two cups, some inelastic string, thread, or fishing line, two paper clips, and a pencil or sewing needle are needed to make a paper cup phone.

Use a pencil or sewing needle to make a hole in the bottom of each cup, then thread a string through each hole to make a paper cup phone.

To keep the thread from coming away from the cups, secure each end with a paper clip. One person should speak into one cup, and you should listen through the other.

Pull the string taut. With the cups, you can talk to someone up to 100 feet away.

A string phone functions quite similarly to a landline. Talking into the cup causes the bottom to vibrate as sound waves are transmitted within the cup by your voice.

The other cup's bottom receives the vibrations that are transmitted to the string, across it, and into it. The second cup vibrates as a result of the sound waves transmitting your voice's audio.

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water has a density of 1.94 slug>ft3 . what is the density expressed in si units? express the answer to three significant figures

Answers

The density of water expressed in SI unit is 1000.3 kg/m³

Density is defined as the ratio of mass per unit volume.

Also it is a measurement that compares the amount of mass an object has to its volume. An object with a large amount of mass in a given volume has a high density.It is denoted by a Greek symbol 'ρ'.Mathematically, ρ = (M/V),

where M is the mass of the object and V is the volume occupied by the object

It has the SI unit of kg/m³.

As we know that 1 slug = 14.593 kg

So 1.94 slug = 1.94 × 14.593 kg

Also 1 ft³ = 0.0283 m³

On converting slug/ft³ to kg/m³

= (1.94 slug/ ft³) * (14.593/1 slug) * (1/0.0283 )

= 1000.3 kg/m³

Therefore the density in SI unit is 1000.3 kg/m³.

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When you push a 1.85-kg book resting on a
tabletop, you have to exert a force of 2.10 N to
start the book sliding. Once it is sliding, however,
you can use a force of only 1.01 N to keep the
book moving with constant speed.
What is the coefficient of static friction between the book and the laptop?
What is the coefficient of kinetic friction between the book and the tabletop?

Answers

Answer:

Given:

mb=2.05 kgmb=2.05 kg Mass of the book

fs=2.45 Nfs=2.45 N Static friction

fk=1.50 Nfk=1.50 N Kinetic friction

2. Write "PE" or KE" next to the types of energy
gravitational
sound
chemical
nuclear
radiant
thermal
elastic
electrical

Answers

Gravitational- PE
Sound- KE
Chemical- PE
Nuclear- PE
Radiant- KE
Thermal- KE
Elastic- PE

An arrow of mass 0.0306 kilograms is placed on a bow, and the string is drawn back 0.591 meters with an average force of 141 newtons. With what speed does the arrow leave the bow? Include units in your answer. Answer must be in 3 significant digits.

Answers

\(\begin{gathered} m=0.0306\text{ kg} \\ F=141\text{ N} \\ x=0.591\text{ m} \\ v=\text{?} \\ F=ma \\ \text{Solving a} \\ a=\frac{F}{m}=\frac{141N}{0.0306\text{ kg}}=4607.8m/s^2 \\ v^2=v^2_o+2ax \\ The\text{ arrow stars from rest},hence_{} \\ v_o=\text{ 0 m/s} \\ v^2=2ax \\ v=\sqrt{2ax} \\ v=\sqrt{(2)(4607.8m/s^2)(0.591\text{ m})} \\ v=73.8\text{ m/s} \\ \text{The spe}ed\text{ is }73.8\text{ m/s} \end{gathered}\)

ability of the muscles to function effectively and efficiently without undue fatigue​

Answers

Answer:

Physical fitness can be defined as the “ability to carry out daily tasks with vigor and alertness, without undue fatigue, and with ample energy to enjoy leisure-time pursuits and to meet unforeseen emergencies”

Explanation:

Help pls and. No links pls

Help pls and. No links pls

Answers

Answer:

the answer to this question will be False

Answer:

false.......,.....,...........

You get yourself a new mirror so that you can admire yourself in the morning. When you open the box, you notice that it is only ½ your height. You think to yourself "This is no good! Now I can't see all of me!" You put it up anyway and realize that you can see your entire body in it. How can this be?

Answers

Answer:

Because you stand at a distance from the mirror at which your entire body shows.

Explanation:

Since the mirror is a plain mirror, the distance of the object from the mirror is also the distance of the image from the mirror. Also since the magnification is 1 for a plane mirror because the height of the image equals the height of the object. Since the magnification always equals 1, for you to be able to see your entire body, you must stand at a distance from the mirror such that your height equals the image height.

Answer: By keeping a distance away from the mirror.

Explanation:

If it's a plane mirror, it's possible to see your entire body by keeping distance away from the mirror. The distance of the object away from the mirror is equal to the distance of the image away from the mirror.

13. A distant quasar is found to be moving away from the earth at 0.80 c . A galaxy closer to the earth and along the same line of sight is moving away from us at 0.60 c .
What is the recessional speed of the quasar, as a fraction of c, as measured by astronomers in the other galaxy?

Answers

The recessional speed of the quasar, as a fraction of c, as measured by astronomers in the other galaxy, is 0.33.

The recessional speed of the quasar, as measured by astronomers in the other galaxy, can be calculated using the relativistic Doppler formula:

v = (c * z) / (1 + z)

where v is the recessional speed of the quasar, c is the speed of light, and z is the redshift of the quasar. The redshift can be calculated using the formula:

z = (λobserved - λrest) / λrest

where λobserved is the observed wavelength of light from the quasar and λrest is the rest wavelength of that light.

Assuming that the rest wavelength of the light emitted by the quasar is known and that the observed wavelength has been measured, we can calculate the redshift z. From the question, we know that the quasar is moving away from the earth at 0.80 c. Since the speed of light is constant, the observed wavelength of light from the quasar will be shifted to longer (redder) wavelengths due to the Doppler effect. This means that λobserved will be greater than λrest. Using the formula above, we can calculate the redshift z:

z = (λobserved - λrest) / λrest = (cobserved - crest) / crest = 0.80

where cobserved and crest are the observed and rest wavelengths of light from the quasar, respectively.

Now we can use the Doppler formula to calculate the recessional speed of the quasar as measured by astronomers in the other galaxy. Let's call this speed v'. We know that the other galaxy is also moving away from us, but at a slower speed of 0.60 c. This means that the observed wavelength of light from the quasar in that galaxy will be shifted to longer wavelengths by a smaller amount than the observed wavelength on earth. We can use the same formula to calculate the redshift z' in the other galaxy:

z' = (λobserved' - λrest) / λrest

where λobserved' is the observed wavelength of light from the quasar in the other galaxy.

Since the quasar is moving away from the other galaxy, we know that z' will be positive, but we don't know its exact value. However, we can use the fact that the galaxy and the quasar are moving away from each other to set up an equation relating z and z'. The relative velocity between the galaxy and the quasar can be calculated by subtracting their recessional speeds:

vrel = v - 0.60c = 0.20c

where v is the recessional speed of the quasar as measured on earth. We can use the relativistic Doppler formula again to relate this velocity to the redshift:

vrel = (c * (z - z')) / (1 + z')

Substituting the values we know, we get:

0.20c = (c * (0.80 - z')) / (1 + z')

Solving for z', we get:

z' = 0.50

Now we can use the Doppler formula to calculate the recessional speed of the quasar as measured in the other galaxy:

v' = (c * z') / (1 + z') = (c * 0.50) / 1.50 = 0.33c

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What is 98.907 rounded to 1 significant figure?

Answers

The answer to the digits rounded to one significant figure is 100.

Significant figures are the most important figures in a number of digits.

The closer a digit is to the beginning of a number, the more important  or significant  it is.

But, the rule for rounding up a set of numbers to the first significant or to one significant figure is that:

If the next number is 5 or more, we round up.If the next number is 4 or less, we do not round up.

From the numbers 98.907, 9 is the most significant digit followed by 8.

8 is greater than 5 so we should round up by adding one to 9 making the number 100.

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A proton moves perpendicularly to a magnetic field that has a magnitude of 6.48 x10 -2 T. A magnetic force of 7.16 x 10 -14 N is acting on it. If the proton moves a total distance of 0.500 m in the magnetic field, how long does it take for the proton to move across the magnetic field? If the magnetic force is directed north and the magnetic field is directed upward, what was the proton’s velocity?

Answers

(a) It takes approximately 7.75 x 10^-11 seconds for the proton to move across the magnetic field. (b) The proton's velocity is approximately 1.29 x 10^5 m/s directed east.

(a) To calculate the time it takes for the proton to move across the magnetic field, we can use the equation for the magnetic force on a charged particle:

F = qvB,

where F is the magnetic force, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field.

F = 7.16 x 10^-14 N,

B = 6.48 x 10^-2 T,

d = 0.500 m (distance traveled by the proton).

From the equation, we can rearrange it to solve for time:

t = d/v,

where t is the time, d is the distance, and v is the velocity.

Rearranging the equation:

v = F / (qB),

Substituting the given values:

v = (7.16 x 10^-14 N) / (1.6 x 10^-19 C) / (6.48 x 10^-2 T)

= 1.29 x 10^5 m/s.

Now, substituting the values for distance and velocity into the time equation:

t = (0.500 m) / (1.29 x 10^5 m/s)

= 7.75 x 10^-11 seconds.

Therefore, it takes approximately 7.75 x 10^-11 seconds for the proton to move across the magnetic field.

(b) The proton's velocity can be calculated using the equation:

v = F / (qB),

where v is the velocity, F is the magnetic force, q is the charge of the particle, and B is the magnetic field.

F = 7.16 x 10^-14 N,

B = 6.48 x 10^-2 T.

Substituting the given values:

v = (7.16 x 10^-14 N) / (1.6 x 10^-19 C) / (6.48 x 10^-2 T)

= 1.29 x 10^5 m/s.

Therefore, the proton's velocity is approximately 1.29 x 10^5 m/s directed east.

(a) It takes approximately 7.75 x 10^-11 seconds for the proton to move across the magnetic field.

(b) The proton's velocity is approximately 1.29 x 10^5 m/s directed east.

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6. A scientist wants to calculate the density of an
object that is the shape of a rectangular prism.
She will find its density based on its mass and
volume. Which procedure should she use?
A. 1. Use a balance to measure the object's
mass.
2. Use a scale to weigh the object.
3. Calculate the density.
1. Weigh the object using a scale.
2. Calculate the density from the weight.
C. 1. Measure the object's dimensions using a
ruler.
2. Use the dimensions to calculate the
object's volume.
3. Use a balance to measure the object's
mass.
4. Calculate the density.
D. 1. Add the object to a water-filled
graduated cylinder.
2. Use the results to calculate the object's
volume.
3. Use the volume to calculate the density
of the object.

Answers

Answer:

C

Explanation:

Density = mass / volume

  so she will need to calculate both the volume ( by measuring dimensions to calculate)  and finding the mass by using a balance   .... then calculate the density

When do a 1000kg car and a 2000kg truck have the same momentum

Answers

Answer:A 1000 kg car and a 2000 kg truck have the same momentum when the car is travelling at twice the speed of the truck, i.e. 38 m/s.

When a 1000kg car and a 2000kg truck have the same momentum, the speed of 1000 kg car is twice that of the  2000kg truck.

What is momentum?

The product of a particle's mass and velocity is its momentum. Being a vector quantity, momentum possesses both magnitude and direction. According to Isaac Newton's second equation of motion, the force applied on a particle is equal to the time rate of change of momentum.

As  a 1000kg car and a 2000kg truck have the same momentum,

1000 kg × v₁ = 2000 kg × v₂

v₁ = 2v₂

Hence, the speed of 1000 kg car is twice that of the  2000kg truck.

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a 35.7 kg girl and a 57.6 kg boy are on the surface of a frozen lake, 11.5 m apart. using a rope, the girl exerts a horizontal 4.35 n force on the boy, pulling him toward her. calculate the magnitude of the girl's acceleration.

Answers

The magnitude of the girl's acceleration is determined as 0.12 m/s².

What is the magnitude of the girl's acceleration?

The magnitude of the girl's acceleration is calculated by applying Newton's second law of motion as follows;

F (net) = ma

where;

m is the mass of the girla is the acceleration of the girl

The mass of the girl = 35.7 kg

The net force on the girl = 4.35 N

The magnitude of the girl's acceleration is calculated as;

a = F / m

a = 4.35 N / 35.7 kg

a = 0.12 m/s²

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An object that is moving in uniform circular motion will definitely have a large acceleration if it is

Answers

If a circular motion is accelerated, it will undoubtedly have a high Turning at a rapid rate.

What happens when something moves uniformly in a circle?

When an object travels along a circular path at a constant speed, it is said to be in uniform circular motion (UCM).So because object's direction was constantly shifting, the velocity doesn't really remain constant along with the speed.To maintain a circular course, the object must speed up toward the the circle's center.

Is the rate of acceleration constant in uniform circular motion?

As the particle moves in a circle, its direction of acceleration is continuously changing since it is continually moving toward the center.As a result, it is variable.

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Find the average circumference of the two balloons with each amount of sugar. Show your work.
No sugar:
Some sugar:
More sugar:

Answers

The average circumference of the two balloons for each amount of sugar are as follows; No sugar: 31.4 cm Some sugar: 34.54 cm More sugar: 40.84 cm

The circumference of a balloon is given by the formula;

C = 2πr

where r is the radius of the balloon. We can find the average circumference of the two balloons for each amount of sugar as shown below. No sugar: The circumference of the balloon with no sugar is given by

C1 = 2πr1

We can find the average circumference of the two balloons as follows;

Average circumference = (C1 + C1)/2 = (2πr1 + 2πr1)/2= 2πr1= 2 × 3.14 × 5= 31.4 cm

(to one decimal place)Some sugar: The circumference of the balloon with some sugar is given by

C2 = 2πr2

We can find the average circumference of the two balloons as follows; Average circumference

= (C1 + C2)/2 = (2πr1 + 2πr2)/2= (2 × 3.14 × 5) + (2 × 3.14 × 6)/2= 2 × 3.14 × 5.5= 34.54 cm

(to two decimal places)More sugar: The circumference of the balloon with more sugar is given by

C3 = 2πr3

We can find the average circumference of the two balloons as follows; Average circumference

= (C2 + C3)/2 = (2πr2 + 2πr3)/2= (2 × 3.14 × 6) + (2 × 3.14 × 7)/2= 2 × 3.14 × 6.5= 40.84 cm (to two decimal places)

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If you throw a ball up with a velocity of 7 m/s, how long will it take for the ball to reach
the top of its path?

Answers

Answer:

42secs

Explanation:

v=u-gt

0=7-10t

10t=7

t=7/10

t=7/10*60

t=42


A pack of dogs are pulling a wooden sled and rider of combined mass
of 238 kg across dry snow. How much force do the dogs need to apply
to cause the sled to begin to move?

Answers

Answer:

FN=-Fg -> Fg=mg -> Fg = 238 kg*9.8 m/s^2 ->

Fg = -2432.4 so FN = 2432.4 -> FF = μs*FN ->

FF = 0.22*2332.4 N -> FF = 513.128 ->

Fapplied > 513.128 N

Explanation:

...

How do you draw a free-body diagram of an object that is attached to a string moving in uniform circular motion? What forces do you draw?

Answers

Answer:Whenever an object experiences uniform circular motion there will always be a net force acting on the object pointing towards the center of the circular path. This net force has the special form  , and because it points in to the center of the circle, at right angles to the velocity, the force will change the direction of the velocity but not the magnitude.

It's useful to look at some examples to see how we deal with situations involving uniform circular motion.

Example 1 - Twirling an object tied to a rope in a horizontal circle. (Note that the object travels in a horizontal circle, but the rope itself is not horizontal). If the tension in the rope is 100 N, the object's mass is 3.7 kg, and the rope is 1.4 m long, what is the angle of the rope with respect to the horizontal, and what is the speed of the object?

As always, the place to start is with a free-body diagram, which just has two forces, the tension and the weight. It's simplest to choose a coordinate system that is horizontal and vertical, because the centripetal acceleration will be horizontal, and there is no vertical acceleration.

The tension, T, gets split into horizontal and vertical components. We don't know the angle, but that's OK because we can solve for it. Adding forces in the y direction gives:

This can be solved to get the angle:

In the x direction there's just the one force, the horizontal component of the tension, which we'll set equal to the mass times the centripetal acceleration:

We know mass and tension and the angle, but we have to be careful with r, because it is not simply the length of the rope. It is the horizontal component of the 1.4 m (let's call this L, for length), so there's a factor of the cosine coming in to the r as well.

Rearranging this to solve for the speed gives:

which gives a speed of v = 5.73 m/s.

Example 2 - Identical objects on a turntable, different distances from the center. Let's not worry about doing a full analysis with numbers; instead, let's draw the free-body diagram, and then see if we can understand why the outer objects get thrown off the turntable at a lower rotational speed than objects closer to the center.

In this case, the free-body diagram has three forces, the force of gravity, the normal force, and a frictional force. The friction here is static friction, because even though the objects are moving, they are not moving relative to the turntable. If there is no relative motion, you have static friction. The frictional force also points towards the center; the frictional force acts to oppose any relative motion, and the object has a tendency to go in a straight line which, relative to the turntable, would carry it away from the center. So, a static frictional force points in towards the center.

Summing forces in the y-direction tells us that the normal force is equal in magnitude to the weight. In the x-direction, the only force there is is the frictional force.

The maximum possible value of the static force of friction is

As the velocity increases, the frictional force has to increase to provide the necessary force required to keep the object spinning in a circle. If we continue to increase the rotation rate of the turntable, thereby increasing the speed of an object sitting on it, at some point the frictional force won't be large enough to keep the object traveling in a circle, and the object will move towards the outside of the turntable and fall off.

Why does this happen to the outer objects first? Because the speed they're going is proportional to the radius (v = circumference / period), so the frictional force necessary to keep an object spinning on the turntable ends up also being proportional to the radius. More force is needed for the outer objects at a given rotation rate, and they'll reach the maximum frictional force limit before the inner objects will.

Explanation:

A dart with a mass of 0.6 kg is thrown at 10.8 m/s and sticks into a 1.9 kg apple hanging
on a string. What is the velocity of the dart and apple just after the dart is embedded?

Answers

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To find the velocity of the dart and apple just after the dart is embedded, we can use the principle of conservation of momentum. According to this principle, the total momentum of a closed system (such as the dart and apple) is constant, meaning that the total momentum before and after an interaction (such as the dart being thrown) must be the same.

The momentum of an object is equal to its mass times its velocity, so the total momentum of the dart and apple before the dart is thrown is:

p1 = (0.6 kg)(10.8 m/s) + (1.9 kg)(0 m/s) = 6.48 kg*m/s

After the dart is thrown, the total momentum of the dart and apple is:

p2 = (0.6 kg)(v) + (1.9 kg)(v) = 2.5v kg*m/s

Since the total momentum before and after the interaction must be the same, we can set p1 equal to p2 and solve for v:

6.48 kgm/s = 2.5v kgm/s

v = 6.48 kgm/s / 2.5 kgm/s

v = 2.592 m/s

The answer is 2.592 m/s.

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Answer: To find the velocity of the dart and apple after the dart is embedded, you can use the principle of conservation of momentum. This principle states that the total momentum of an isolated system remains constant, unless acted upon by an external force.

In this case, the dart and apple form an isolated system, so their total momentum must remain constant.

The momentum of the dart before it is embedded is given by the formula p = mv, where p is momentum, m is mass, and v is velocity. The momentum of the dart is therefore 0.6 kg * 10.8 m/s = 6.48 kg*m/s.

After the dart is embedded, the total momentum of the dart and apple is also 6.48 kg*m/s. We can find the velocity of the combined system using the same formula, p = mv. The mass of the combined system is the sum of the masses of the dart and apple, or 1.9 kg + 0.6 kg = 2.5 kg.

Substituting these values into the formula, we get:

p = mv

6.48 kg*m/s = 2.5 kg * v

v = 2.592 m/s

This is the velocity of the dart and apple after the dart is embedded.

A box with a mass of 100.0 kg slides down a ramp with
a 50 degree angle.
What is the weight of the box?
N
What is the value of the normal force? Round the
answer to the nearest whole number.
N
What is the acceleration of the box? (Disregard friction
and air resistance.) Round the answer to the nearest
tenth.
m/s2

Answers

Answer:

Weight of the box? 980 N

Value of the normal force? 630 N

Acceleration of the box? 7.5 m/s^2

Explanation:

I got the answer right

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