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

Which material(s) listed below is an example of a persistent organic pollutant?
(*select all that apply)
Select 4 correct answer(s)
Ricin
PCBs
DDT
Mercury
Arsenic

Answers

Answer:

mercury

arsenic

ricin

ddt

Explanation:

pls mark me as brainliest

Among the materials listed, examples of persistent organic pollutants (POPs) are PCBs (Polychlorinated Biphenyls) DDT (Dichlorodiphenyltrichloroethane). The correct option is (2) and (3).

Persistent Organic Pollutants (POPs) are a class of chemicals that are long-lasting, bioaccumulative, and harmful to humans and wildlife. These pollutants are resistant to degradation and can persist in the environment for long periods of time, resulting in long-distance transport and bioaccumulation in the food chain.

PCBs (Polychlorinated Biphenyls): Once utilized in a variety of industrial applications such as electrical transformers and capacitors, PCBs are now prohibited in many countries due to their toxicity.

DDT (Dichlorodiphenyltrichloroethane): An pesticide that was widely used for agricultural and public health objectives in the past but is now restricted or banned due to its environmental and health effects.

Hence, the correct answer is PCBs and DDT. The correct option is (2) and (3).

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When converted to a household measurement, 9 kilograms is approximately equal to a

Answers

Answer:

D) 19.8 lbs

Explanation:

1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.

1kg is also equal to 2.205 lbs. 9*2.205=19.8416

9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system

a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.

This leaves us with 19.8 lbs

describe in the relationships between all four spheres hydrosphere,atmosphere,biosphere and geosphere support your response with examples​

Answers

Answer:

The spheres interact with one another, and a change in one might result in a change in another. Humans (biosphere) plough the fields with agricultural machinery made of geosphere materials, while the atmosphere (hydrosphere) provides precipitation to water the plants. The biosphere is home to all living organisms on the earth.

Explanation:

don't ask qestionsmm

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

How are Classical and positivist theories similar and different?

Answers

Answer: PLease see Explanation

Explanation:The key idea behind this theory was to use scientific methods to understand criminality and crime. ... The major difference between the two theories are that classical school is mainly based on free will and suggests that crime as a choice, whereas positivism criminology argues that crime is not a choice.

Please get me 5 star and 1 heart

help with this question please.

Answers

Answer: Yes Because it matches with the mass and the amount of force Hope this helps :>

Explanation:

Is my answer correct

Answers

Answer:

it right congratulations

Answer:

A

Explanation:

Simply option A is correct

It's a bit of a common sense question

At the highest point it's velocity will be automatically 0 since it is in rest and so is the acceleration

Indicate whether each of the following statements about car collisions is true or false. Select all that are True.

a. If two identical cars with identical speeds collide head on, the magnitude of the impulse received by each car and each driver is the same as if one car at the same speed had collided head on with a concrete wall.
b. Car 1 has mass m, and car 2 has mass 2m. In a head-on collision of these cars while moving at identical speeds in opposite directions, car 1 experiences a bigger acceleration than car 2.
c. The essential safety benefit of crumple zones (parts of the front of a car designed to receive maximum deformation during a head-on collision) is due to their absorbing kinetic energy, converting it into deformation, and lengthening the effective collision time, thus reducing the average force experienced by the driver.
d. Car 1 has mass m, and car 2 has mass 2m. In a head-on collision of these cars while moving at identical speeds in opposite directions, car 1 receives an impulse of bigger magnitude than that received by car 2. If car 1 has mass m and speed v, and car 2 has mass 0.5m and speed 1.5v, then both cars have the same momentum.

Answers

Answer:

True statements a, b, and c

Explanation:

Answer d is false because in any collision, each object receives the same impulse. Also the momentum of car 1 is mv, while the momentum of car 2 is 0.5m(1.5v) = 0.75mv

The impulse of collision of cars depends on the mass and velocity of the cars. The statements which are true about the car collisions are option a, b, c.

What is impulse?

Impulse is a physical quantity expressed as the product of force and time. The change in momentum mΔV is numerically equals to the impulse F t.

If two identical cars with identical speeds collide head on, the magnitude of the impulse received by each car and each driver is the same as if one car at the same speed had collided head on with a concrete wall. Because they have equal mass and velocity.

The bigger acceleration is experienced by the one which have lighter mass thus car 1 with lower mass experience higher acceleration .

The essential safety benefit of crumple zones (parts of the front of a car designed to receive maximum deformation during a head-on collision) is due to their absorbing kinetic energy.

Converting this energy into deformation, and lengthening the effective collision time, thus reducing the average force experienced by the driver.

The momentum change is proportional to the velocity. The one which have higher velocity is having the higher momentum. Thus car 2 have higher velocity. Thus option d is false.

Therefore, the statements which are true are a, b and c.

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part A
Explain how the students can measure the distance the cars travel.

part B
Explain how the students could measure the time it takes the cars to travel the distance you explained in the first part.

Answers

Answer:

Part A: By using the formula, distance = speed x time

Part B: By using the formula, time = distance ( calculated in the first part) ÷ speed

Câu 1. Trong dao động điều hoà, phát biểu nào sau đây là không đúng ?
A.Cứ sau một khoảng thời gian T (chu kì) thì vật lại trở về vị trí ban đầu.
B.Cứ sau một khoảng thời gian T thì vận tốc của vật lại trở về giá trị ban đầu.
C.Cứ sau một khoảng thời gian T thì gia tốc của vật lại trở về giá trị ban đầu.
Cứ sau một khoảng thời gian T thì biên độ của vật lại trở về giá trị ban đầu

Answers

Answer:

whatttttttttttt

Explanation:

the ಠᴥಠಠᴥಠಠᴥಠಠᴥಠಠᴥಠಠᴥಠಠᴥಠಠᴥಠ

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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You are having a snowball fight with your best friend on a frosty winter day. You are standing on the roof of your 5 m tall house with a 0.4 kg snowball. You drop the snowball downward from rest toward your friend,
who is making snow angels below you. Ignoring air resistance, solve for the gravitational potential energy of
the snowball before it is released.

a) 12.5 J

b) 19.6J

c) 5J

d) 2J

Answers

Answer: B 19.6J

Explanation: The equation for Potential energy is PE=mgh

PE is the potential energy

m=Mass=0.4kg

g=Gravity=9.81m/[tex]s^{2}[/tex]

h=Height=5 metres

(0.4 kg)*(9.81m/[tex]s^{2}[/tex])*(5 metres)=19.62J

Please help with this question, it’s for physical science

Answers

Answer:

s times t

Explanation:

The equation for distance is D = st

Answer:

D is the correct answer (D=S*T)

This is an algebraic law; if you are to move the denominator or numerator to the other side of the equation, you must multiply it by the other side.

S=D/T is the same as D=S*T.

so distance=speed times time.

so if you are going 50 miles per hour, you multiply that times time, say one hour. you get your D distance which is 50 miles.

How can I create a whirlpool of water?​

Answers

Answer:

To make a small scale whirlpool of water, take a cup and fill it with water and stir. It will create a vortex that pulls particles down.

Or you could see this when draining a tub of water.

How do I do these three parts ?what are the answers I’ve been trying for days

Answers

Answer:

Explanation:

ASSUMING the clay is moving horizontally and friction is negligible.

momentum is mass times velocity

9a)

m₁v + m₂(0) = m₁vf + m₂vf

            m₁v = (m₁ + m₂)vf

               vf = m₁v / (m₁ + m₂)

9b)

ASSUMING the positive direction is also the original direction of the clay ball

m₁v + m₂vb = (m₁ + m₂)vf

vf = (m₁v + m₂vb) / (m₁ + m₂)

9c)

vf = (0.37(25) + 4.6(3.4)) / (0.37 +4.6)

vf = (9.25 + 15.64) / 4.97

vf = 5.0080482897...

vf = 5.0 m/s

Shearing is done in case of Processing of __________ ( Silk / Wool / Jute ).​

Answers

Answer:

wool maybe, I was a bit confused in silk and wool but wool

what is the difference between soldering and solder?

Answers

Answer:

Soldering is a technique or a process to bond metals with the help of solder. Solder is a metal alloy with a low melting point and is often regarded as the base metal for soldering. The piece or structure that is being bonded together does not get hot enough to melt and this is where solder (base metal) comes into play and creates the connection.

Explanation:

Hope this helps :)

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And have an amazing day <3

Give him brainly ;) he deserves it

Which graph uses bars to show data that are broken into intervals?
O A. Scatter plot
O B. Bar graph
O C. Box-and-whisker plot
O D. Histogram

Answers

Answer:

A. scatter plot?

Explanation:

I dont really know if I'm right... sorry.

Um cubo fechado com 1 m3 de um líquido (d=0,8;  =21 000 kgf/cm2

) é submetido a um aumento de pressão de

20107 N/m2

. Calcule, no Sistema Internacional, as seguintes grandezas:

a) massa final;
b) peso final;
c) volume final;
d) massa volúmica final;
e) peso volúmico final.

Answers

Answer:

a. massa final

Explanation:

eu escolhi isso porque essa é a resposta espero que ajude você pode me dar uma ideia?

How long does it take light from a camera to travel to the face of someone standing 7 meters away?

Answers

The time taken for the light to travel from the camera to someone standing 7 m away is 2.33×10¯⁸ s

Speed is simply defined as the distance travelled per unit time. Mathematically, it is expressed as:

Speed = distance / time

With the above formula, we can obtain the time taken for the light to travel from the camera to someone standing 7 m away. This can be obtained as follow:

Distance = 7 m

Speed of light = 3×10⁸ m/s

Time =?

Time = Distance / speed

Time = 7 / 3×10⁸

Time = 2.33×10¯⁸ s

Therefore, the time taken for the light to travel from the camera to someone standing 7 m away is 2.33×10¯⁸ s

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What is the mass of an object that is experiencing a net force of 225 N and an acceleration of 3.0 m/s^2?​

Answers

Answer:

Mass of a object 75 Kilograms

Explanation:

Net force acting on an object, [tex]Fnet = 225N[/tex]

Acceleration produced, [tex]a = 3.0m/s^2[/tex]

According to Newton's second law :

F = m a

[tex]M =\frac{F}{a}[/tex]

[tex]m =\frac{225N}{300m/s^2}[/tex]

[tex]m= 75 Kg[/tex]

So, the mass of an object is 75kg.

Hence, this is the required solution.

Answer:

75 kg.

Explanation:

Net Force

[tex]\sf \longmapsto F_{net} = 225N[/tex]

Acceleration produced

[tex]\sf \longmapsto \: a = 3 .0 m / {s}^{2}[/tex]

According to Newton's 2nd Law –

F = m•a

[tex]\sf \longmapsto \: M = \frac{F}{A} [/tex]

[tex]\sf \longmapsto \: M = \frac{225N}{300m/s ^{2} } [/tex]

[tex]\sf \longmapsto \: M = \: 75 \: kg[/tex]

Therefore, the mass of an object is 75 kg.

Adam and Bobby are twins who have the same weight. Adam drops to the ground from a tree at the same time that Bobby begins his descent down a frictionless slide. If they both start at the same height above the ground, how do their kinetic energies compare when they hit the ground

Answers

Answer:

They are the same.

Both have potential energy of M g H   and that is the energy that will be converted to kinetic energy for each twin,

a block starts from rest and begins sliding down an incline. The block reaches a speed of 12 meters per second as it slides a distance of 50 meters. calculate the blocks rate of acceleration

Answers

Vf² = V₁² + 2ad

(12 m/s) ² = (0 m/s) ² + 2 (a) (50m)

a = 1.44 m/s ²

Answer:

[tex]\boxed {\boxed {\sf 1.44 \ m/s^2}}[/tex]

Explanation:

We are asked to find the block's rate of acceleration.

We are given the final velocity, initial velocity, and distance. Therefore, we will use the following kinematic equation:

[tex]{v_f}^2={v_i}^2+2ad[/tex]

The block starts at rest or 0 meters per second. The block reaches a final velocity of 12 meters per second. The distance traveled is 50 meters.

[tex]v_i[/tex]= 0 m/s [tex]v_f[/tex]= 12 m/s [tex]d[/tex]= 50 m

Substitute the values into the formula.

[tex](12 \ m/s)^2 = (0 m/s)^2 + 2a (50 \ m)[/tex]

Solve the exponents.

(12 m/s)² = 12 m/s * 12 m/s = 144 m²/s²(0 m/s)² = 0 m/s * 0 m/s = 0 m²/s²

[tex]144 \ m^2/s^2= 0 m^2/s^2 + 2a (50 \ m)[/tex]

The 0 can be subtracted from both sides, or simply canceled.

[tex]144 \ m^2/s^2 = 2a (50 \ m)[/tex]

Multiply 2 and 50 meters.

[tex]144 \ m^2/s^2 = (2 *50 \ m)* a[/tex]

[tex]144 \ m^2/s^2 = (100 \ m)* a[/tex]

We are solving for a, so we must isolate the variable. It is being multiplied by 100 meters. The inverse of multiplication is division, so we divide both sides by 100 meters.

[tex]\frac {144 \ m^2/s^2}{100 \ m}= \frac{(100 \ m)*a}{100 \ m}[/tex]

[tex]\frac {144 \ m^2/s^2}{100 \ m}=a[/tex]

[tex]1.44 \ m/s^2 =a[/tex]

The block's rate of acceleration is 1.44 meters per second squared.

2. Calculate; The acceleration of any object due to Earth's gravity is -9.81 m/s. For every
second an object falls, its velocity changes by 9.81 meters per second. For several different
times on the table, multiply the time by the acceleration
A. What do you notice:
I

Answers

As the time of motion increases, the velocity of the object increases downwards.

The given parameters;

acceleration due to gravity, g = -9.81 m/s²velocity of the object, v₀ = 9.8 m/s

The final velocity of the object at different time is calculated as follows;

when the time = 1 second;

v = v₀ - gt

v = 9.8  - 9.8(1)

v = 0

when the time = 2 second;

v = v₀ - gt

v = 9.8 - 9.8(2)

v = -9.8 m/s

when the time = 3 second;

v = v₀ - gt

v = 9.8 - 9.8(3)

v = -19.6 m/s

Thus, we can conclude that as the time of motion increases, the velocity of the object increases downwards.

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can anyone heelp me pls pls

Answers

Answer:

Lotion : semisolid

Suspension : liquid

capsule : solid

Explanation:

how much work is done by a crane that lowers 1000 N of material a distance of 150 m?

Answers

Answer:

Force= 1000 Newtons. Distance= 150 metres. Work= 150000 Joules. So, the work done by crane that lowers 1000 Newton's of a material a distance of 150 meters is 150000 Joules.

why do the star constellations seem to move across the sky

Answers

Answer: These apparent star tracks are in fact not due to the stars moving, but to the rotational motion of the Earth. As the Earth rotates with an axis that is pointed in the direction of the North Star, stars appear to move from east to west in the sky.

Explanation: why do the star constellations seem to move across the sky

Answer:

because the world moves around and around rotating in a circle and circling around the sun so as we move the stars stay the same but to our view it looks like their moving but in reality we are.

Explanation:

Gravity will apply a different amount of force to objects with different mass. The force of gravity can also be called
a. weight.
b. inertia.
c. kilograms.
d. resistance.
e. Mass

Answers

Answer:

E.Mass

Explanation:

Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases.

WILL GIVE BRAINLIEST
An object with mass m dropped from height H, after travelling a distance and emerged horizontally from the bottom of the track with a velocity v and height of h. what is The work done due to friction while traveling through the track. could someone also please explain the difference between h and H

Answers

Answer:

I think d

Explanation:

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        

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