A light rope is wrapped several times around a large wheel of radius 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis. The free end of the rope is tied to a suitcase of mass 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.5 m/s when it reaches the ground. Calculate (a) the angular velocity of the wheel when the suitcase reaches the ground and (b) the moment of inertia of the wheel.

Answer :

Answer:

a)  ω = 8.75 rad/s

b) I = 12.9 kgm^2

Explanation:

Given data:

Radius of the wheel r = 0.400 m

Speed of the suitcase v = 3.50 m/s

Height h = 4.00 m

Mass of the suitcase m = 15 kg

a) To determine angular velocity of the wheel when the suitcase reaches the ground is

we know that ,         ω = v / r

ω = (3.50 m/s) / (0.400 m )

    ω = 8.75 rad/s

b) From the conservation of energy

  we have         KEi + Ui = KEf + Uf

where KEi , KEf are initial and final kinetic energies and Ui and Uf are initial and final potentail energies.  

We know that KEi = 0 and Uf   = 0

             Ui = KEf

           mgh = (1/2)mv^2 + (1/2) Iω^2

I = moment of inertia of wheel to determined

15×9.8×4 = (1/2) (15)(3.5)^2 + (1/2) I (8.75)^2

Calculating we get                  

I = 12.9 kgm^2

A force that acts on a body moving in a circular path and is directed toward the center around which the body is moving.

According to the question, The formula is used to find the omega is:-

[tex]w =\frac{v}{r}[/tex]

[tex]w= \frac{3.50}{0.400}[/tex]

Hence, the omega is ω = 8.75 rad/s

From the conservation of energy  we have  KEi + Ui = KEf + Uf

where Kei, KEf are initial and final kinetic energies and Ui and Uf are initial and final potential energies.  

We know that KEi = 0 and Uf   = 0

So, therefore the Ui = KEf

Hence [tex]mgh = \frac{1}{2}mv^{2} + \frac{1}{2} Iw^{2}[/tex]

After putting the value:-

[tex]15*9.8*4 = \frac{1}{2}*15*3.5^{2} + \frac{1}{2}*I*8.75^{2}[/tex]

Hence the value of I is[tex]12.9 kgm^2[/tex]

For more information, refer to the link:-

https://brainly.com/question/21338592