A string is wrapped around a solid cylinder with mass M and radius R. The free end of the string is held in place, allowing the cylinder to fall. Recall that the moment of inertia of a solid cylinder rotated about its center is given by MR2/2. All answers to this problem should be symbolic, purely in terms of the variables M, R, and g. (a) Find the linear acceleration (in m/s2) of the cylinder and the tension in the string (in Newtons) as the cylinder falls. (b) Now suppose the cylinder is hollow instead of solid. The moment of inertia of a hollow cylinder rotated about its center is given by MR2. What is the acceleration and tension in this case?

Answers

Answer 1

Answer:

I will use (a / R) for alpha the angular acceleration

T R = I a / R     torque equals angular acceleration for cylinder

M g - T = M a    linear acceleration of center of mass

T = M (g - a) = I a / R^2 from first equation

If I = 1/2 M R^2 then M ( g - a) = M a / 2    from above

or g = 3 a / 2  and a = 2 g / 3

Also we have T = M (g - a) = M (g - 2 g / 3) = g / 3

Substitute I = M R^2 for the hollow cylinder

Looks like a = g/2 for hollow cylinder


Related Questions

Energy Transfer and Temperature Quick Check 1 of 41 of 4 Items Question Use the table to answer the question. Sample Observation 1 The drop of food coloring spreads slowly. 2 The drop of food coloring spreads very quickly. A student places a drop of food coloring into two water samples. Her observations are shown in the table. Which statement best explains the observations in the table? (1 point) The water molecules of sample 1 are moving faster. The water molecules of sample 1 are moving faster. The temperature of sample 2 is close to freezing. The temperature of sample 2 is close to freezing. The temperature of sample 2 is higher. The temperature of sample 2 is higher. The water molecules of sample 1 are transferring more kinetic energy. The water molecules of sample 1 are transferring more kinetic energy.

Answers

Answer: Measure the initial temperature of the water using the thermometer Poke through a food substance measuring 0.5 grams using the needle with the handle. Turn on fire on the burner. Set the food substance on the needle to fire on the burner. Once the food substance starts to burn, place it under the test tube so the water inside it can absorb heat.

Explanation:

Hope this helps!

what is one measurement needed to calculate the speed of an object​

Answers

Answer:

The equation for speed is simple: distance divided by time. You take the distance traveled (for example 3 meters), and divide it by the time (three seconds) to get the speed (one meter per second).

Explanation:

Câu 1. Trường hợp nào dưới đây không phải là vật sáng?

A. Chiếc bút chì đặt trên bàn giữa ban ngày.

B. Chiếc bật lửa rơi giữa sân trường lúc trời nắng.

C. Mặt Trời.

Answers

Answer:

A

Explanation:

A. The pencil is on the table in broad daylight

You are observing a star that is 250 million light years away. From the starlight you are observing now, the appears to be 30 million years old and you determine that the star has a lifetime of 120 million years. How long will it be until Earth receives light from the supernova that occurs at the end of the life of the star

Answers

What ever games your playing it wont work you cant defeat me hahhahha oh I know :O but he can AHHHH :D D: NOOOO IMPOSSIBLE.

A particle of mass m is fired upwards from the surface of a planet of mass M
and radius R with velocity
Show that the maximum height the particle attains is R/3.

Answers

At the maximum height the particles position has been shown as [tex]\frac{R}{3}[/tex].

The given parameters;

mass of the particle, = Mradius of the particle, = Rmaximum height the particle attains = R/3

The velocity of the particle is given as;

[tex]v^2 = \frac{GM}{2R}[/tex]

The total mechanical energy of the particle is given as;

[tex]-\frac{GMm}{R} + \frac{1}{2} mv^2 = - \frac{GMm}{R} + \frac{1}{2} mv^2[/tex]

At maximum height the final velocity of the particle is zero.

[tex]-\frac{GMm}{R} + \frac{1}{2} mv^2 = - \frac{GMm}{R +h}[/tex]

[tex]-\frac{GMm}{R} + \frac{1}{2} m\times \frac{GM}{2R} = - \frac{GMm}{R +h}\\\\-\frac{GMm}{R} + \frac{GMm}{4R} = - \frac{GMm}{R +h}\\\\- \frac{3GMm}{4R} = - \frac{GMm}{R +h}\\\\- \frac{3}{4R} = - \frac{1}{R+ h} \\\\3(R+ h) = 4R\\\\3R + 3h = 4R\\\\3h = 4R - 3R\\\\3h = R\\\\h = \frac{R}{3}[/tex]

Thus, at the maximum height the particles position has been shown as [tex]\frac{R}{3}[/tex].

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Does bouncing or sticking produce more impulse?

Answers

Answer:

yes

Explanation:

Bouncing is a way to increase impulse. Because an object that bounces changes directions the force of impulse must be absorbed then generated by the target object. (Impulse is nearly doubled.)

Name the type of joint present in skull.​

Answers

Answer:

Sutures are nonmoving joints that connect bones of the skull

Explanation:

These joints have serrated edges that lock together with fibers of connective tissue.

Answer:

Immovable fibrous joints are present in our skull

Explanation:

brainliest plz

Thinking Mathematically: Explore the quantitative dependencies of the acceleration upon the speed and the radius of curvature. Then answer the following questions. a. For the same speed, the acceleration of the object varies _____________ (directly, inversely) with the radius of curvature. b. For the same radius of curvature, the acceleration of the object varies _____________ (directly, inversely) with the speed of the object. c. As the speed of an object is doubled, the acceleration is __________________ (one-fourth, one-half, two times, four times) the original value. d. As the speed of an object is tripled, the acceleration is __________________ (one-third, one-ninth, three times, nine times) the original value. e. As the radius of the circle is doubled, the acceleration is __________________ (one-fourth, one-half, two times, four times) the original value. f. As the radius of the circle is tripled, the acceleration is __________________ (one-third, one-ninth, three times, nine times) the original value.

Answers

The expression for the centripetal acceleration allows to find the results for the questions are:

A) The acceleration varies INVERSELY with the radius of curvature.

B) The acceleration varies DIRECTLY with the speed.

C) The acceleration becomes four times greater.

D) The acceleration becomes nine times greater.

E) The acceleration is reduced to half.

F) The acceleration is reduced to a third.

In circular motion there must be an acceleration towards the center of the circle, it is called cenripetal acceleration, in this case all the energy supplied to the system is used to change the direction of the speed even when its magnitude remains constant.

        [tex]a_c = \frac{v^2}{r}[/tex]  

Where [tex]a_c[/tex] the centripetal acceleration, v is the speed and r the radius of curvature of the circle.

Now we can answer the questions about centripetal acceleration.

A) For the same speed, the acceleration varies INVERSELY with the radius of curvature.

B) For the same radius of curvature the acceleration varies DIRECTLY with the speed.

C) The speed is doubled

         v = 2 v₀

         [tex]a_c = \frac{(2v_o)^2 }{r}[/tex]  

         [tex]a_c = 4 \ \frac{v_o^2 }{r}[/tex]  

The acceleration becomes four times greater than the original value

D) The speed is tripled

         v = 3 v₀

         [tex]a_c = 9 \frac{ v_o^2}{r}[/tex]  

Acceleration becomes nine times greater than the original

E) the radius of curvature is doubled

        r = 2 r₀  

        [tex]a_c = \frac{v_o^2}{2 r_o }[/tex]  

        [tex]a_c = \frac{1}{2} a_o[/tex]  

Acceleration is reduced to half the original value

F) The radius of curvature is tripled

       r = 3 r₀

       [tex]a_c = \frac{v_o^2 }{3 r_o} \\ \\a_c = \frac{1}{3} a_o[/tex]  

       

The acceleration is reduced to a third of the initial one.

In conclusion using the expression for the centripetal acceleration we can find the answers for the questions are:

A) The acceleration varies INVERSELY with the radius of curvature.

B) The acceleration varies DIRECTLY with the speed.

C) The acceleration becomes four times greater.

D) The acceleration becomes nine times greater.

E) The acceleration is reduced to half.

F) The acceleration is reduced to a third.

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A chemical system is considered to have reached dynamic equilibrium when:__________.
a. the frequency of collisions between the reactant molecules is equal to the frequency of collisions between the product molecules.
b. the rate of production of each of the product species is equal to the rate of consumption of each of the reactant species. c. the rate of production of each of the products is equal to the rate of their consumption by the reverse reaction.
d. the sum of the concentrations of each of the reactant species is equal to the sum of the concentrations of each of the product species.
e. the activation energy of the forward reaction is equal to the activation energy of the reverse reaction.

Answers

Answer:

D

Explanation:

Sum of the concentrations of each of reactant species is equal to the sum of the concentrations of each of the product species

repost!! help need answer

Answers

Answer:

Ask a tutor it is tough

Ask tutor for your betterment

A massive launcher sends a projectile vertically upwards from the surface of a planet of mass M and radius R. You may assume that this planet has no atmosphere. Part A If the projectile is launched at the escape speed, how do the magnitudes of its initial KE and gravitational potential energy (GPE) compare

Answers

Answer:

It can be shown that the potential energy of an object at the surface of the planet would be -G M / R if the potential at infinity is chosen to be zero.

Kinetic energy of G M / R would be required for the escape speed of such an object. The total energy in all such cases is zero.

This can easily be seen by considering the speed of an object falling from infinity towards the planet - the total energy will remain zero if it was zero when the object started to fall.

The potential at infinity is set to zero while the kinetic energy will be [tex]\rm \frac{GM}{R}[/tex] and total energy will be zero.

What is escape speed?

Escape speed is the minimum speed required for a free, non-propelled object to escape from the gravitational pull of the main body and reach an infinite distance from it in celestial physics.

It is proven that if the potential at infinity is set to zero, the potential energy of an item on the planet's surface is [tex]\rm \frac{-GM}{R}[/tex].

The escape speed of such an item would necessitate kinetic energy will be [tex]\rm \frac{GM}{R}[/tex]. In all of these circumstances, the total energy is zero.

Consider the speed of an item falling from infinity towards the planet: if the total energy was zero before the thing began to descend, the total energy will stay zero.

Hence the potential at infinity is set to zero while the kinetic energy will be [tex]\rm \frac{GM}{R}[/tex] and total energy will be zero.

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Câu 20: Chọn câu sai:
A. Công là đại lượng vô hướng B. Công không có tính tương đối
C. Công phụ thuộc vào đường đi D. Công có giá trị đại số

Answers

Answer:

fr

Explanation:

Bài 1. Một vật được đặt trên một mặt phẳng nghiêng hợp với mặt phẳng nằm ngang một góc  = 300.

Answers

Answer:

3q

Explanation:

i just need help plzzzz

Answers

Answer:

I think D it's the correct answer!! Let me know if i'm wrong

Explanation:

The weather that characterizes an area is the O latitude of that area O barometric pressure of that area climate of that area O geography of that area​

Answers

Answer:

climate of that area

Explanation:

A 3 kg drone starts at 5 meter above the ground and reached 25 meter above the
ground. Find the potential energy of the drone. Formula: PE=mghf-hi

Answers

Recall that work is the amount of energy transferred to an object when it experiences a displacement and is acted upon by an external force. It is given a symbol of W and is measured in joules (J).

W=\vec{F}\cdot \Delta \vec{d}

We can use this formula to determine the work done by very specific forces, generating specific types of energy. We will examine three types of energy in this activity: gravitational potential, kinetic, and thermal. Before we start deriving equations for gravitational potential energy and kinetic energy, we should note that since work is the transfer and/or transformation of energy, we can also write its symbol as \Delta E.

Two hicers are 13 miles apart and walking toward each other. They meet in 2 hours. Find the rate of each hiker if one hiker walks 1.7 mph faster than the other.

Answers

Answer:

Explanation:

Let r be the rate of the slower walker in mph

[r + (r + 1.7)](2) = 13

    (2r + 1.7)(2) = 13

         4r + 3.4 = 13

                  4r = 9.6

                    r = 2.4 mph

            r + 1.7 = 4.1 mph        

If the law allows abortion based on sex, should we also allow abortion based on race, ethnicity, or skin color? Briefly explain why you believe this is right or wrong.

Answers

Answer:

No because you don't have to be black or white you don't have to be a pacific race to just get it like lets say for example a asian person come in and they want to get a abortion but the doctor say no then that person can end up killing her self or when the baby is born she could end you know doing something bad. But no you do not have to be a pacific person to just get it

Explanation:

25. Which of the following cannot be broken down into smaller parts through ordinary chemical means?
a. Nitrogen
b. Protein
C. Salt
d. Sugar

Answers

Answer:

the correct answer is sugar

I think it’s Sugar!!!!!

Describe the shape of the earth besides round and tell me how it rotates​

Answers

Answer:

The Earth is in hydrostatic equilibrium pretty much. Which is to say that if it were entirely liquid it would still be the same shape ignoring minor differences like mountain ranges that are in any case indistinguishable on the large scale.

A spinning liquid sphere will flatten out somewhat at the axis poles and expand somewhat in its equatorial region and that’s the way the Earth is.

Hope it wirks

A box is 30 cm wide, 40 cm long and 25 cm high. Calculate the volume of the box in cubic centimeter.

A) 3,000
B) 30,000
C) 15,000
D) 1,200

Answers

Answer:

The correct answer would be A: 3,000.

Explanation:

To find the volume of a box, you have to do l * w * h. You multiply 30, 40, and 25 which gives you an answer of 3,000 cubic centimeters.

How can wind, coiled wire, and magnets be used together to generate electricity?

Answers

Answer:

b

Explanation:

hope helpful

have a great day

A boy of mass 43.2 kg runs and jumps onto a stationary skateboard.The boy lands on the skateboard with a horizontal velocity of 4.10 m/s.The skateboard has a mass of 2.50 kg.
Using ideas about conservation of momentum, calculate the combined
velocity of the boy and skateboard just after the boy lands on it.

Answers

Answer:

= 3.87 m/s

Explanation:

Since momentum is conserved, momentum right before and after the boy jumps onto the skateboard should be the same.

Initial momentum = momentum of boy = 43.2 x 4.10 = 177 kg·m/s

Final momentum = momentum of boy and skateboard = (43.2 + 2.50) x v = 45.7v

177 = 45.7v

v = 177 / 45.7 = 3.87 m/s

(Hope this helps can I pls have brainlist (crown)☺️)

The combined velocity of the boy and the skateboard just after the boy lands on it will be equal to 3.87 m/s.

What is momentum?

Momentum is the product of a particle's mass and velocity. Being a vector quantity, momentum possesses both direction and magnitude. According to Isaac Newton's second equation of motion, the force applied on a particle is equivalent to the temporal rate at which momentum changes. 

According to Newton's second law, the product of the energy and the time interval is equal to the shift in momentum if a constant force acts on a molecule for a specified amount of time.

Momentum should be the same both before and after the boy gets onto the skateboard because it is preserved.

Initial momentum = momentum of boy

= 43.2 × 4.10 = 177 kg m/s

Final momentum = momentum of boy as well as skateboard

= (43.2 + 2.50) × v = 45.7 v

177 = 45.7 v

v = 177 / 45.7 = 3.87 m/s

Therefore, the combined velocity of boy and skateboard is 3.87 m/s.

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A baseball is traveling with a velocity of 12 m/s at an angle of 45 above
horizontal. What is the velocity of the ball after two seconds?

Answers

Focus on the ball. Do you see you? Keep following it. Put all your energy into watching it and then unlock your third eye. With that you'll be able to determine your question.

can anyone heelp me pls

Answers

Answer:

Lotion - Semisolid

Suspension - Liquid

Capsule - Solid

Lotion - Semisolid

Suspension - Liquid

Capsule - Solid



Please mark as brianliest answer.

Describe what causes the planets to stay in orbit around the Sun

Answers

Answer:

Gravitional pull or gravity

Explanation:

Its that simple

four particles connected by rigid rods of negligible mass where y1 = 5.70 m. the origin is at the center of the rectangle. The system rotates in the xy plane about the z axis with and angular speed of 5.60 rad/s. a) calculate the moment of inertia of the system about the z axis. b) Calculate the rotational kinetic energy

Answers

The definition of moment of inertia and kinetic energy we can find the results for the questions are:  

          a) The moment of inertia is: I = 32.49 kg m²

          b) The kinetic energy is: K = 509.4 J

a) The moment of inertia is a scalar quantity that has the same function as mass, it is given by

             I = m r²

       

They indicate that the length of the bar is y₁ = 5.70 m, if the two rigid bars form the square that supports the masses, the distance from the center to the end where each mass is:  

            r = y₁ / 2

             r = 5.70 / 2 = 2.85 m

The moment of inertia of the system is.

         I = 4 m r²

Let's calculate.

        I =4 m 2.85²

        I = 32.49m kg m²

If we assume that the mass of each point particle is:

        m = 1 kg

   

         I = 32.49 kg m²

b) They ask for the rotational kinetic energy, if the angular velocity is.

           w = 5.60 rad / s

The kinetic energy for rotational motion is.

         K = ½ I w²

Let's calculate.

          K = ½ 32.49 5.60²

          K = 509.4 J

In conclusion with the definition of moment of inertia and kinetic energy we can find the results for the questions are:

          a) The moment of inertia is: I = 32.49 kg m²

          b) The kinetic energy is: K = 509.4 J

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The following question has two parts. First, answer part A. Then, answer part B.

Part A:
Why did the author most likely choose the title “Breaking Barriers” for this text?

A.
to show that Elizabeth worked hard to make people like her

B.
to show that Elizabeth accomplished things never done before

C.
to show that Elizabeth proved to be smarter than those around her

D.
to show that Elizabeth tried to show she was the better than other doctors

Part B:
Which sentences from the text best support your answer in part A? Select two options.

A.
“Elizabeth loved learning, and she developed a passion for reading.”

B.
“When Elizabeth was 11 years old, her family moved to America.”

C.
“When she was just 16, she became a teacher.”

D.
“Finally, the Geneva Medical College in New York accepted her as a student.”

E.
“When people in town ignored the woman with the strange ambition, Elizabeth treated them in a polite, quiet manner.”

F.
“She became the first woman in the country to obtain a medical degree.”

Answers

Answer:

for part A the answer is D and for part B the answer is F

Which can occur during a physical change? (SELECT ALL THAT APPLY!.)
The amount of energy within a substance can change.
The shape of a piece of matter can change.
The chemical reaction produces a new substance.
The atoms of the substance can permanently change.

Answers

Answer:

C, B, and D are ones i think i know that can occur during a physical change

Explanation:

A water rocket uses an amount of water and pressurized air to send a plastic rocket several feet into the air. As the water and air rush out the tail end of the rocket, the rocket shoots into the air. Which statement explains the rocket's motion?

Answers

Answer:

D.

For every action there is an equal and opposite reaction.

Explanation:

im doing the same one lol

For every action there is an equal and opposite reaction explains the rocket's motion.

What is rocket?

A rocket is indeed a vehicle that accelerates by employing jet propulsion rather than the surrounding air. A rocket engine generates thrust by reacting to high-speed exhaust. Since rocket engines run solely on fuel carried within the vehicle, a rocket may travel in space.

A water rocket uses an amount of water and pressurized air to send a plastic rocket several feet into the air. As the water and air rush out the tail end of the rocket, the rocket shoots into the air. For every action there is an equal and opposite reaction explains the rocket's motion.

Therefore, for every action there is an equal and opposite reaction explains the rocket's motion.

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