1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Karolina [17]
3 years ago
9

A block (mass = 61.2 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1/2MR2 kg · m2, wh

ere M = 14.2 kg is the mass of the pulley and R=1.5 m is its radius ), as the drawing shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of r=R=1.5 m during the block's descent, and the distance of the block at initial position to the floor is 8.0 m. What is the angular velocity in round per minute when the block drops to the floor? Use g = 10 m/s2.
Physics
1 answer:
kolezko [41]3 years ago
8 0

Answer:

The angular velocity is  w = 53.35 \ rounds /minute

Explanation:

From the question we are told that

    The mass of the block is  m = 61.2kg

     The of the pulley is  M = 14.2 kg

      The radius of the pulley is  R = 1.5m

       The radius  of the cord around the pulley is  r = 1.5 m

       The distance of the block to the floor is  d = 8.0 m

         

From the question we are told that the moment of inertia of the pulley is

          I  = \frac{1}{2} MR^2 kg \cdot m^2

Substituting value  

         I = \frac{1}{2}  * 14.2 * (1.5)^2

         I = 15.975 kg \cdot m^2

Using the Newtons law we can express the force acting on the vertical axis as

              ma = mg -T

         =>  T = mg -ma

Now when the pulley is rotated that  torque generated on the massless cord as a r result of the tension T and the radius of the cord around the pulley is mathematically represented as

                  \tau = I \alpha

     Here \alpha is the angular acceleration

           Here \tau is the torque which can be equivalent to

              \tau = T r

  Substituting this above

            Tr = I \alpha      

Substituting for T

         (mg - ma ) r =  I\  r \alpha

Here a is the  linear acceleration which is mathematically represented as

           a = r\alpha

    (mg - m(r\alpha ) ) r =  I\  r \alpha

     mgr = I\alpha  + m(r\alpha ) r

    mgr = \alpha  [ I + mr^2]

   making \alpha the subject

          \alpha  = \frac{mgr}{I -mr ^2}          

   Substituting values

            \alpha  = \frac{61.2 * 1.5 * 9.8}{15.975 + (61.2 ) * (1.5)^2}

             \alpha =5.854 rad /s^2

Now substituting into the equation above to obtain the acceleration

             a = 5.854 * 1.5

                a=8.78 m/s^2

This acceleration is a = \frac{v}{t}

and v is the linear velocity with is mathematically represented as

         v = \frac{d}{t}

Substituting this into the formula acceleration

        a = \frac{d}{t^2}

making t the subject

         t = \sqrt{\frac{d}{a} }

substituting value

      t = \sqrt{\frac{8}{8.78}}

     t = 0.9545 \ s

Now the linear velocity is

       v = \frac{8}{0.9545}

       v = 8.38 m/s

The angular velocity is  

       w = \frac{v}{r}

So

       w = \frac{8.38}{1.5}

        w = 5.59 rad/s

Generally 1 radian is equal to  0.159155 rounds or turns

        So  5.59 radian is  equal to x

Now x is mathematically obtained as

         x = \frac{5.59 * 0.159155}{1}

            = 0.8892 \ rounds

 Also

      60  second =  1 minute

So   1 second  = z      

Now z is mathematically obtained as

         z = \frac{ 1}{60}

            z = 0.01667 \ minute

Therefore

              w = \frac{0.8892}{0.01667}

              w = 53.35 \ rounds /minute

           

You might be interested in
Movement of a molecule against its concentration gradient can occur through Select one or more: a. facilitated diffusion b. pass
uranmaximum [27]

Answer:

The answer to your question is:

Explanation:

There are two kinds of cell transport passive transportation and active transportation.

Passive transportation does not need energy because molecules move from higher concentration to lower concentration.

Active transportation needs energy because molecules moves against concentration.  

a. facilitated diffusion It's an example of passive transportation so this answer is wrong.

b. passive transport Molecules move in favor of concentration so this answer is wrong.

c. osmosis is another example of passive transport so this answer is wrong.

d. simple diffusion it's another example of passive transport, so it's wrong this answer.

e. active transport this is the right answer.

5 0
3 years ago
calculate the value of net force acting on given body?5N acting towards right & 15N force acting towards left on the brick.(
lys-0071 [83]

Answer:

The net force acting on the body is 10N directed to the left.

Explanation:

   Magnitude of force to the right = 5N

   Magnitude of force to the left  = 15N

Net force acting on the object and in what direction;

Solution:

It is the vector sum of all forces acting on a body. This net force is the single force that will replace the forces acting on a body;

  For the problem;

   Net force  = Force to the left + Force to the right

 Let us take left to be negative and right to be positive;

    Force to the left  = -15N

    Net force  = -15N + 5N  = -10N

The net force acting on the body is 10N directed to the left.

4 0
2 years ago
Rose has been working as a receptionist for 20 years. One day, she receives a check in the mail for $750,000—an inheritance from
sergey [27]
The just-world phenomenon is the belief that everything that happens to an individual is due to the individual's actions; in other words, all good and all bad that an individual encounters in the world is deserved by that person. This leads to a victim being blamed with the logic that "they had it coming" and someone who encounters good fortune being praised with "they earned it". Therefore, in this scenario, people will assume that Rose's inheritance is well deserved.<span />
8 0
3 years ago
Read 2 more answers
Which takes longer to reach earth, light from the sun or light from other stars? Explain.
densk [106]
Light from other stars take longer to reach the earth because they are farther than our sun.
4 0
3 years ago
Read 2 more answers
An object releasing energy is evidence of which type of chemical change?
Ray Of Light [21]
Exothermic is the answer to your question
8 0
2 years ago
Other questions:
  • What type of cooling would a scientist determine formed an igneous rock found with large crystals? Slow cooling Medium rate cool
    15·2 answers
  • What does the tilt of Earth on its axis cause?
    6·1 answer
  • According to the chart, which region of the country would be considered the most heavily religious?
    7·1 answer
  • A light ray traveling through medium 1, index of refraction n1n1n_1 = 1.75, reaches the interface between medium 1 and medium 2,
    13·1 answer
  • A plane leaves the airport in Galisteo and flies 160 km at 66.0 ∘ east of north; then it changes direction to fly 260 km at 49.0
    13·1 answer
  • A fighter jet travels 10km at an angle of 30 degrees. He then turns sharply and flies 25 km at an angle of 75 degrees. What is t
    8·1 answer
  • Can I get the answer
    8·1 answer
  • IF YOU MOVE 50 METERS IN TO SECONDS,
    6·1 answer
  • A compass needle acts as a(n)
    9·1 answer
  • Using the periodic table, choose the more reactive nonmetal.<br> Si or N
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!