Question 8: Unspooling Thread (100 points) A 110 g spool of thread with a 4.2 cm radius is held up by a peg through its center and allowed to freely rotate. Assume the thread is ideal (i.e., it does not stretch or slip, and its mass is negligibly small). A 160 g needle is tied to the loose end of the thread. The needle is dropped, and it accelerates to the floor as the thread unwinds. Find the tension in the thread and the magnitude of the acceleration of the needle as it falls.

Answers

Answer 1

Answer:

   a = 7.29 m / s²,      T = 0.40 N

Explanation:

To solve this exercise we must apply Newton's second law to each body

The needle

              W -T = m a

              mg - T = ma

The spool, which we will approach by a cylinder

             Σ τ = I α

             T R = I α

the moment of inertia of a cylinder with an axis through its center is

             I = ½ M R²

angular and linear variables are related

            a = α R

            α = a / R

we substitute

           T R = (½ M R²) a / R

            T = ½ M a

we write our system of equations together

              mg - T = m a

                      T = ½ M a

we solve

              m g = (m + ½ M) a

              a = [tex]\frac{m}{m + \frac{1}{2} M} \ g[/tex]

let's calculate

              a = [tex]\frac{0.160}{0.160 + \frac{1}{2} 0.110} \ 9.8[/tex]

              a = 7.29 m / s²

now we can look for the tension

              T = ½ M a

              T = ½ 0.110 7.29

               T = 0.40 N


Related Questions

A wave has a wavelength of 1.5 meters and period of 0.083s. What is the waves speed?

Answers

Oh yeah sweetie I just don’t got to go to

Pls help ASAP
Imagine that Maritans launch a rocket toward the Earth at a great speed. While the
rocket is traveling toward us, it will appear
than it actually is.
O more blue
darker
larger
more red

Answers

Answer:

The rocket will appear larger than it actually is

An organ pipe open at both ends has a length of 0.80 m. If the velocity of sound in air is 340 m/s, what is the frequency of the second harmonic of this pipe

Answers

Answer:

the frequency of the second harmonic of the pipe is 425 Hz

Explanation:

Given;

length of the open pipe, L = 0.8 m

velocity of sound, v = 340 m/s

The wavelength of the second harmonic is calculated as follows;

L = A ---> N   +  N--->N   +   N--->A

where;

L is the length of the pipe in the second harmonic

A represents antinode of the wave

N represents the node of the wave

[tex]L = \frac{\lambda}{4} + \frac{\lambda}{2} + \frac{\lambda}{4} \\\\L = \lambda[/tex]

The frequency is calculated as follows;

[tex]F_1 = \frac{V}{\lambda} = \frac{340}{0.8} = 425 \ Hz[/tex]

Therefore, the frequency of the second harmonic of the pipe is 425 Hz.

The frequency of the second harmonic of the pipe is 425 Hz.

What is the frequency?

Frequency is the number of oscillations per second in the sinusoidal wave.

Given is length of the open pipe, L = 0.8 m, and velocity of sound, v = 340 m/s

The wavelength of the second harmonic is represented as

L = A → N   +  N→N   +   N→A

where, L is the length of the pipe in the second harmonic, A represents antinode of the wave, N represents the node of the wave

Length = λ/4 +λ/2 +λ/4

Length = λ

The frequency is calculated

frequency = speed of light / wavelength

Put the values, we get

f = 340/0.80

f = 425 Hz

Therefore, the frequency of the second harmonic of the pipe is 425 Hz.

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Red light of wavelength 630 nm passes through two slits and then onto a screen that is 1.3 m from the slits. The center of the 3rd order bright band on the screen is separated from the central maximum by 0.90 cm. a) What is the frequency of the light, the slit separation, and the angle of the 3rd order bright band

Answers

Answer:

a) f = 4.76 10¹⁴ Hz, b) d = 2.73 10⁻⁴ m, c) θ = 6.923 10⁻³ rad

Explanation:

a) In this problem the frequency of light is asked, let's use the relationship between the speed of the wave, its wavelength and its frequency

           c = λ f

           f = c /λ

           f = [tex]\frac{3 \ 10^8}{630 \ 10^{-9}}[/tex]

           f = 4.76 10¹⁴ Hz

b) slit separation (d)

the expression for the constructive interference of the double-slit experiment is

          d sin  θ = m λ

let's use trigonometry

          tan θ = y / L

          tan θ = [tex]\frac{sin \theta}{cos \theta}[/tex]

in general the angles are small, so we can approximate

          tan θ = sin θ

          tan θ = y/L

we substitute

          d y / L = m λ

          d = m L λ / y

we calculate

          d = 3  1.3  630 10⁻⁹ /0.90 10⁻²

          d = 2.73 10⁻⁴ m

c) the angle

           tan θ = y / L

           θ = tan⁻¹ y / L

           θ = tan⁻¹ 0.9 10⁻² / 1.3

           θ = tan⁻¹ 6,923 10⁻³

let's find the angle in radians

           θ = 6.923 10⁻³ rad

   

What is the approximate surface temperature of the 'White Dwarfs'?.
2,500-5,000 K
5,000-10,000
10,000-15,000 K
15,000 K-35,000 K

Answers

Answer:

5,000-10,000 K

Explanation:

make me your brainlist pls

What is the speed of a ball that is attached to a string and swings in a horizontal circle of radius 2.0 m with the central acceleration of 15 m/s^2?

Answers

Answer:

5.48 m/s.

Explanation:

Use the formula a=v^2/r.

Audrey, an astronomer is searching for extra-solar planets using the technique of relativistic lensing. Though there are believed to be a very large number of planets that can be found this way, actually finding one takes time and luck; and finding one planet does not help at all with finding planets of other stars in the same part of the sky. Audrey is good at it, and finds one planet at a time, on average once every three months. a.) Find the expected value and

Answers

Answer:

- the expected value is 8

- the standard deviation is 2.8284

Explanation:

Given the data in the question;

The model N(t), the number of planets found up to time t, as a poisson process,

∴ N(t) has distribution of poisson distribution with parameter (λt)

so

the mean is;

λ = 1 every month = 1/3 per month

E[N(t)] = λt

E[N(t)] = (1/3)(24)

E[N(t)] = 8

Therefore, the expected value is 8

For poisson process, Variance and mean are the same,

Var[N(t)] = Var[N(24)]

Var[N(t)] = E[N(24)]

Var[N(t)] = 8

so the standard deviation will be;

σ[N(24)] = √(Var[N(t)] )

σ[N(24)] = √(8 )

σ[N(24)] = 2.8284

Therefore, the standard deviation is 2.8284

a disk of radius 25 cm spinning at a rate of 30 rpm slows to a stop over 3 seconds. what is the angular acceleration?
b. how many radians did the disk turn while stopping?
c. how many revolutions?​

Answers

Answer:

too many

Explanation:

A wave has a frequency of 67 Hz and a wavelength of 7.1 meters. What is the speed of this
wave?

Answers

the answer hopes this helped

Answer:

475.7 m/s

Explanation:

Given,

Frequency ( f ) = 67 Hz

Wavelength ( λ ) = 7.1 m

To find : Speed ( v ) = ?

Formula : -

v = f λ

v

= 67 x 7.1

= 475.7 m/s

Therefore,

the speed of the wave is 475.7 m/s.

I need help with this

Answers

Explanation in File!

Chris used a non plane mirror to check out an box resting on a shelf. He wanted to find
the focal length of the mirror. The image of the box was located 15 cm behind the mirror
and the box was placed 19 cm from the mirror.

Answers

1/f=1/15 - 1/19
Then get the reverse it will be the focal length

Chris used a non-plane mirror to check out a box resting on a shelf, the focal length of the mirror is mathematically given as

f=8.38cm

What is the focal length of the mirror?

Question Parameter(s):

The image of the box was located 15 cm behind the mirror

and the box was placed 19 cm from the mirror.

Generally, the equation for the focal length is mathematically given as

1/f=1/u+1/v

Therefore

1/f=1/15+1/19

f=8.3823529cm

In conclusion,  the focal length of the mirror

f=8.3823529cm

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if 400g is 1kg find the ratio in the simplest form​

Answers

2:5

Explanation:

400g : 1kg

400g: 1000g

4 : 10

2 : 5

Are all harmful effects of smoking reversible? Explain your answer.

Answers

I don’t think so, becuase is a big damage that can’t be repaired easily

true or false

The Total electric potential due to two or more charges is equal to the algebraic sum of the potentials due to the individual charges.

Answers

Answer:

i guess the answer is false

A spring has a spring constant of 450 N/m. How much must this spring be stretched to store 49 J of potential energy?

Answers

Answer:

W = 1/2 K x^2

x^2 = 2 * W / K = 2 * 49 J / (N/m)  = .218 / m^2

x =  .467 m

Please help me with this question. Every help is appreciated.

Answers

Answer:

Change in KE = +1.96×10^4 J while the change in ME = 0 J

here is a clever kitchen gadget for drying lettuce leaves after you wash them. It consists of a cylindrical container mounted so that it can be rotated about its axis by turning a hand crank. The outer wall of the cylinder is perforated with small holes. You put the wet leaves in the container and turn the crank to spin off the water. The radius of the container is 10.7 cm. When the cylinder is rotating at 1.65 revolutions per second, what is the magnitude of the centripetal acceleration at the outer wall

Answers

Answer:

11.5 m/s²

Explanation:

The centripetal acceleration, a = rω² where r = radius of cylinder = 10.7 cm = 0.107 m and ω = angular speed = 2πN where N = number of revolutions per second = 1.65 rev/s

So, a = rω²

a = r(2πN)²

a = 4π²rN²

substituting the values of the variables into the equation, we have

a = 4π²rN²

a = 4π²(0.107 m)(1.65 rev/s)²

a = 4π²(0.107 m)(2.7225 rev²/s)²

a = 4π² × 0.2913075 mrev²/s)²

a = 11.5 m/s²

Someone help me like please thank you

Answers

The car should have less kinetic energy.
They are both going the same speed, but the truck is bigger and heavier. The more mass an object has, the more kinetic energy it has. There is more mass being moved, so it makes more kinetic energy. The car does not have as much mass, so it makes less kinetic energy compared to the truck.

Good luck with the rest of your test or quiz :)

Please help me with this review question.

Answers

Answer:

28.7%

Explanation:

efficiency = work output /work input × 100

A car driver spends 3hrs driving at an average speed of 80km/hr, stops for 30 minutes to
have some rest, and then drives at an average speed of 90km/hr for 2 hours.
Calculate the average speed during the whole journey​

Answers

Answer:

The average speed throughout the journey was 76.36 kilometers per hour.

Explanation:

Given that a car driver spends 3hrs driving at an average speed of 80km / hr, stops for 30 minutes to have some rest, and then drives at an average speed of 90km / hr for 2 hours, to determine the average speed during the whole journey the following calculation must be performed:

80 km / h x 3 = 240 km

90 km / h x 2 = 180 km

240 + 180 = 420 km

3 + 2 + 0.5 = 5.5 hours

420 / 5.5 = 76.36

Thus, the average speed throughout the journey was 76.36 kilometers per hour.

b. Calculate the kinetic energy of the car for group A.

Answers

Answer: Kinectic Energy (KE) is equal to half of an object's mass (1/2*m) multiplied by the velocity.

Explanation: If an object with a mass of 10 kg (m=10 kg) is moving at a velocity of 5 meters per second (v=5 m/s), the kinetic energy is equal to 125 Joules, or (1/2* 10 kg) * 5 m/s^2.

Help me please with both questions?

Answers

Answer:

question #1 is A

Question #2 is C

Explanation:

The answer for number 1 is A

As altitude decreases, what happens to
air pressure?
A. increases
B. decreases
C. stays the same
D. not enough information to tell

Answers

Answer:

A. Increases

Explanation:

As altitude decreases, the amount of gas molecules in the air increases - the air becomes less dense. As altitude increases, the amount of gas molecules in the air decreases—the air becomes less dense.

Answer:

It decreases so it is B

Explanation:

As altitude rises, air pressure drops.

The liquid emerges into a vertical jet as it drains from the container, with the velocity profile in the jet remaining uniform. The outlet of the container is located 2.0 m above ground, and the radius of the emerging liquid jet changes with vertical distance from the bottom of the container as it accelerates under the action of gravity. Neglecting viscous losses and surface tension effects in the liquid jet, what is the velocity of the water jet as it strikes the ground when the container begins to drain

Answers

Answer:

6.26 m/s

Explanation:

Since we are neglecting viscous losses and surface tension effects in the liquid jet, by conservation of energy, the potential energy loss of the jet = kinetic energy gain of the jet

So, mgh = 1/2mv² where m = mass of water in jet, g = acceleration due to gravity = 9.8 m/s², h = height of outlet = 2.0 mand v = velocity of liquid jet

So, mgh = 1/2mv²

gh = 1/2v²

v² = 2gh

v = √(2gh)

v = √(2 × 9.8 m/s² × 2.0 m)

v = √(39.2 m²/s²)

v = 6.26 m/s

the number of perpandicular components of a force is

Answers

answer. 2 components

one directed upwards, and the other directed rightwards

Question 10 (10 points)
Listen
In an ionic solution, 5.0x1015 negative ions with charge -e pass to the right each
second while 8.0x1015 positive ions with charge +2e pass to the left. What are the
magnitude and direction (+ or -) of current in the solution? (to the right is the +
direction, to the left is the - direction)
Note: Your answer is assumed to be reduced to the highest power possible.
Your Answer:
x10
Answer
units

Answers

Answer:

Please I do not understand the instructions given at the end of the question

A go-cart is traveling at a rate of 25 m/sec for 20 seconds. How far will the go cart travel?

Answers

Answer:

Distance travel by go-cart = 500 meter

Explanation:

Given:

Speed of go cart = 25 m/s

Time travel = 20 seconds

Find:

Distance travel by go-cart

Computation:

Distance = Speed x time

Distance travel by go-cart = Speed of go cart x Time travel

Distance travel by go-cart = 25 x 20

Distance travel by go-cart = 500 meter

Which of the following would NOT be
considered a pollutant?
A. carbon monoxide
B. sulfur dioxide
C. oxygen
D. smoke

Answers

Answer:

Answer: Oxygen

Explanation:

Oxygen would not be considered as a pollutant

Answer:

Hey there the answer is C. Oxygen

Explanation:

Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as well as with other compounds. After hydrogen and helium, oxygen is the third-most abundant element in the universe by mass. At standard temperature and pressure, two atoms of the element bind to form dioxygen, a colorless and odorless diatomic gas with the formula O 2. Diatomic oxygen gas constitutes 20.95% of the Earth's atmosphere. Oxygen makes up almost half of the Earth's crust in the form of oxides. Hope this helps! Have a great day!

On the map, which major plate is flanked by the red sea rift and the Minor Arabian Plate?


A:#1 North American Plate

B:#3 South American Plate

C:#5 Eurasian Plate

D:#2 African Plate

Answers

Answer:

D:#2 African Plate

Explanation:

The African Plate is flanked by the Red sea rift and the minor African plate.

The Red sea rift is a small part of a greater line of rifts known as the Great African Rift Valley. The rift valley is making several small lakes all through Africa and it will eventually split up the African continent.

The Red sea lift is the divergent boundary between the African plate and the Arabian plate. It means that the two plates are moving apart or spreading apart.

What is a transfer of energy called?
A. Displacement
B. Acceleration
C. Work
D. Torque

Answers

Your answer is c, work
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