A cylindrical 4.31 kg pulley with a radius of 0.294 m is used to lower a 6.27 kg bucket into a well. The bucket starts from rest and falls for 3.55 s. The acceleration of gravity is 9.8 m/[tex]s^{2}[/tex]

What is the angular acceleration of the cylindrical pulley?

Answer in units of rad/[tex]s^{2}[/tex]

Answers

Answer 1

Answer:

[tex]24.81\ \text{rad/s}^2[/tex]

Explanation:

M = Mass of cylinder = 4.31 kg

R = Radius of cylinder = 0.294 m

m = Mass of bucket = 6.27 kg

g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]

[tex]\alpha[/tex] = Angular acceleration

a = Acceleration = [tex]\alpha R[/tex]

I = Moment of inertia of cylinder = [tex]\dfrac{MR^2}{2}[/tex]

The force balance of the system is

[tex]mg-T=ma\\\Rightarrow T=m(g-a)[/tex]

For the disk

[tex]TR=I\alpha\\\Rightarrow m(g-a)R=\dfrac{1}{2}MR^2\alpha\\\Rightarrow \alpha=\dfrac{g}{\dfrac{MR}{2m}+R}\\\Rightarrow \alpha=\dfrac{9.8}{\dfrac{4.31\times 0.294}{2\times 6.27}+0.294}\\\Rightarrow \alpha=24.81\ \text{rad/s}^2[/tex]

The angular acceleration of the pulley is [tex]24.81\ \text{rad/s}^2[/tex].


Related Questions

What is the difference between temperature and heat???

Also what is calorimeter and Thermometer​

Answers

Answer:

Difference between heat and temperature in tabular form

Heat vs Temperature

1.Heat is a form of energy that can transfer from a hot body to a cold body. and Temperature is the degree of hotness and coldness of a body.

2.Heat is the total kinetic energy and potential energy obtained by molecules in an object. and Temperature is the average K.E of molecules in a substance.

3.Heat flows from hot body to cold body. It rises when heated and falls down when an object is cooled down and It has a working ability. It does not have the working ability

.

4.Its SI unit is “Joule” and Its SI unit is “Kelvin”.

5.It is measured by the calorimeter and It is measured by the thermometer

.

6.It is represented by “Q”. and It is represented by “T”.

Explanation:

A calorimeter is an object used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. ... A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber.

Suppose that 2 J of work is needed to stretch a spring from its natural length of 24 cm to a length of 42 cm. (a) How much work is needed to stretch the spring from 32 cm to 34 cm

Answers

Answer:

Workdone = 0.025 Joules

Explanation:

Given the following data;

Workdone = 2J

Extension = 42 - 24 = 18 cm to meters = 18/100 = 0.18m

The workdone to stretch a string is given by the formula;

Workdone = ½ke²

Where;

k is the constant of elasticity.

e is the extension of the string.

We would solve for string constant, k;

2 = ½*k*0.18²

2 = ½*k*0.0324

Cross-multiplying, we have;

4 = 0.0324k

k = 4/0.0324

k = 123.46 N/m

a. To find the workdone when e = 32, 34.

Extension = 34 - 32 = 2 to meters = 2/100 = 0.02m

Workdone = ½*123.46*0.02²

Workdone = 61.73 * 0.0004

Workdone = 0.025 Joules

Therefore, the amount of work (in J) needed to stretch the spring from 32 cm to 34 cm is 0.67.

3. Water near the poles receives much less solar energy than the tropical regions and often has water temperatures around 0 degrees Celsius. Why is the water in the polar
regions not completely frozen?
A color
C salinity B density
D phytoplankton

Answers

Answer:

Yes

Explanation:

sdfu8hdfhu8dfghgdfijndfgjknfdgjknfgdjkndfgjkndfgklndfgknldfgklmdfgklmdfgkondfgkjnodfgklndfgklndfglknfgdklndfgklndfgklndfgklndfgklndfgpkmfgdklnfdgyklndklndfgklndfglkngdfklndfgljkngdfklndfglkmdfgh

I think c I’m not sure though :))

Will the 79 kg skier in the figure below slide down if f the coefficient of static friction is 0.25?

Answers

Answer:

Man will not slide down

Explanation:

Given:

Coefficient of static friction = 0.25

Angle = 13°

Computation:

Man will slide down if

tan13° > Coefficient of static friction

Tan 13 = 0.23

So,

0.23 < 0.25

So,

Man will not slide down

please help me please just looking the picture​

Answers

the work done done by that person is less than zero

why is gravity on earth important

Answers

it holds down our atmosphere and the air we need to breathe- it holds our world together!

how is sound produced by using stringed instrument​

Answers

sound vibrations

Explanation:

akechis pancakes

Answer:

By waves

Explanation:

when sound is being produced by string instruments it uses waves to help create that sound


C
D
7
The sun is the original source of
energy for many of our energy
resources
Which energy resource does not
originate from the sun? *
(1 Point)
.
A. Geothermal
B. Hydroelectric
C. Waves
D. Win

Answers

Answer:

geothermal

Explanation:

geothermal energy is the heat energy obtained from within the Earth. Hence not derived from Sun's energy.

If there are 10 Volts across a 5 Ohm resistor, what is the current?

Answers

Answer:

I = 2A

Explanation:

V = IR

10V = I × 5ohms

I = 2A

Answer:

2Ampere

Explanation:

V=IR (ohm's law) so I =[tex]\frac{V}{R}[/tex] =[tex]\frac{10}{5}[/tex]=2Ampere

write the type of energy present in pond water and kerosene?​

Answers

Potential and kinetic energy

The energy present in pond water and kerosene are potential energy and chemical energy respectively.

What is energy?

Energy is a quantifiable quantity in physics that can be transferred from an item to do work. Thus, we might characterise energy as the capacity to engage in any kind of physical action. So, to put it simply, we can define energy as: Energy is the capacity to carry out work.

Energy "can neither be created nor destroyed but can only be changed from one form to another," according to the rules of conservation of energy. The SI unit for energy is called a joule.

In pond, water is stored during rain and stored potential energy whereas in kerosene, carbon molecules have chemical energy and when it burns, chemical energy revels as thermal energy.

Learn more about energy here:

https://brainly.com/question/1932868

#SPJ2

distace x time graph will be ................ if the body is in ununiform motion​

Answers

A non-straight ... possibly a zig-zag, wiggly, curvy, or snaking ... line. But always rising.

Answer:

Uniform: Straight line; Non uniform: Curved.

Explanation:

Have a great day

Which is NOT a way to stay safe from static electricity?

a lightning rod on a building
a metal spike in an airport runway
an anti-static chain on a large truck
a run through an open field during a lightning

plssssssssssss answer not in a meen way but corrrect answer only plsssssssssssss answer correct i will drop a thx and rate yo stars ans give you brainlyest

Answers

a metal spike in an airport runway

A metal spike in an airport runway  is NOT a way to stay safe from static electricity. Hence option C is correct.

What is electricity ?

Electricity is a collection of physical phenomena related with the presence and motion of matter having an electric charge. Both electricity and magnetism are connected to the phenomena of electromagnetic, as defined by Maxwell's equations. Lightning, static electricity, electric heating, electric discharges, and other frequent occurrences are all connected to electricity.

An electric field is created when either a positive or negative electric charge is present. The movement of electric charges results in an electric current and a magnetic field. In most applications, a force of magnitude determined by Coulomb's law operates on a charge. Volts are commonly used to measure electric potential.

Hence option C is correct.

To know more about electricity :

https://brainly.com/question/12791045

#SPJ3.

All of the following are true statements regarding line-voltage thermostats and control wiring except a. An electrician's license is often required to run line-voltage control wiring. b. Line-voltage thermostats must be matched to the voltage and current of the circuit. c. Line-voltage thermostats and controls are not as sensitive as low-voltage thermostats. d. Line-voltage thermostats and controls respond faster than low-voltage thermostats.

Answers

Answer:

c. Line - voltage thermostats and controls are not as sensitive as low - voltage thermostats.

Explanation:

Line voltage thermostat is a regulator which senses the temperature and maintains it to keep the desired level of the voltage. The license in required for the electricians to work on the voltage control wirings. There is technical aspects which an electrician must understand before working on the circuits and voltage lines.

PLZ HELP ILL GIVE RBAINLIEST
Which of the following factors can affect the strength of electric or magnetic fields? (YOU MAY SELECT MORE THAN ONE ANSWER)

Strength of the magnet/electric charge

The material that is creating the field

The mass of the object creating the field

The distance from the source of the field

Answers

All of the above .........

4. A sodium ion has a +1 relative atomic charge which indicates it has one more proton than electron.
This ion is placed in a 4.00 NC electric field. Remember, the charge of one relative atomic charge is 1.60 x 10-19


a. Calculate the force applied to a single sodium ion in this electric field.

Answers

Answer:

a

Explanation:

What happens when you move two
objects far apart from each other?
A. The force of gravity increases.
B. The force of gravity decreases.
C. Distance does not affect the force of gravity.
D. The friction between the two objects will increase.

Answers

Answer:

b

Explanation:

B. The force of gravity decreases

Four monitoring wells have been placed around a leaking underground storage tank. The wells are located at the corners of a 1-ha square. The total piezometric head in each of the wells is as follows: NE corner, 30.0 m; SE corner, 30.0 m; SW corner, 30.6 m: NW corner 30.6 m. Determine the magnitude and direction of the hydraulic gradient.

Answers

Answer:

direction : West to East

magnitude : 6.0 * 10^-3

Explanation:

Given data :

Four ( 4 ) monitoring wells

location of wells = corners of 1-ha square

Total piezometric head in each well ;

NE corner = 30.0 m ;

SE corner = 30.0 m;

SW corner = 30.6 m;

NW corner = 30.6 m.

Calculate for  the magnitude and direction of the hydraulic gradient

first step ; calculate for area

Area = ( 1 -ha  ) ( 10^4 m^2/ha )

        = 1 * 10^4 m^2

Distance between the wells = length of side

      = √( 1 * 10^4 ) m^2

      = 100 m

Direction of Hydraulic gradient is from west to east because the total piezometric head in the west = Total piezometric head in the east

Next determine The magnitude of the hydraulic gradient

= ( 30.6 - 30 ) / 100

= 6.0 * 10^-3

A young parent is dragging a 65 kg (640 N) sled (this includes the mass of two kids) across some snow on flat ground, by means of a rope attached to the sled. The rope is at an angle of 30 degrees with respect to the ground and the tension in the rope is 160 N. The sled is moving at a constant velocity of 1.5 m/s.
(a) Draw and label all forces acting on the kids + sled system. Indicate the relative size of each force by scaling the length of each force arrow appropriately
(b) Calculate the normal force acting on the system
(c) Calculate the force of friction acting on the system.
(d) Calculate the coefficient of friction between the sled and the snow.

Answers

Answer:

b) N = 560 N, c)  fr = 138.56 N, d)  μ = 0.247

Explanation:

a) In the attachment we can see the free body diagram of the system

b) Let's write Newton's second law on the y-axis

              N + T_y -W = 0

              N = W -T_y

let's use trigonometry for tension

             sin θ = T_y / T

             cos θ = Tₓ / T

             T_y = T sin θ

             Tₓ = T cos θ

we substitute

              N = W - T sin 30

we calculate

              N = 640 - 160 sin 30

              N = 560 N

c) as the system goes at constant speed the acceleration is zero

X axis

              Tₓ - fr = 0

               Tₓ = fr

we substitute and calculate

              fr = 160 cos 30

              fr = 138.56 N

d) the friction force has the formula

             fr = μ N

             μ = fr / N

we calculate

             μ = 138.56 / 560

             μ = 0.247

Expository essay "Climate change in Fiji"​

Answers

Answer: Climate change poses to the tourism development in Fiji islands. It shows the adverse effects of the changing climate and the dangers pose by the tourism activities and also pose a major hazard for the local people in the region. It also deals with the dangerous carbon emissions and CO2 effect on the landscape, food, water, energy.

The pacific is the world`s largest ocean with a surface area of 175 million sq km and constitutes for 40% of the planet`s waters. Located in the tropical latitudes, it covers more than half the globe`s circumference. Temperature of the surface water in the western tropical regions is always more than 28 ÌŠC over a depth of several hundred meters. This makes up the world`s storage of thermal energy for exchange with atmosphere. Here the interaction between atmosphere and ocean is most extreme and influences the climate not only regionally but planet-wide. The nations of the pacific are obscured human settlements absorbed in this vast fluid universe. The ocean is the most important factor controlling the environment and life.

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