a solid cylinder with a mass of 4.5 kg, a radius of .017 m, an initial velocity

Question

a solid cylinder with a mass of 4.5 kg, a radius of .017 m, an initial velocity of 0m/s, an initial angular velocity of 0.0 rads/s and an initial height of 3.6 m, rolls down an incline until it hits the bottom where its height is 0 m.

1.what is the cylinders moment of inertia..

2. what is the cylindars initial transitional kinetic energy.

3. what is the cylinders initial rotational kinetic energy.

4. what is the cylinders initial gravitational potential energy.

5. what is the cylinders final gravitational potential energy.

6. what is the cylinders final velocity.

7.what is the cylinders final angular velocity.

8. what is the cylinders final transitional kinetic energy.

9. what is the cylinders final rotational energy.

10. what is the cylinders total final mechanical energy?

Explanation / Answer

m =4.5 kg, r=0.17 m , hi =3.6 m, hf =0, wi =0,vi=0

1) I =(2/5)mr^2 =(2/5)(4.5*0.17*0.17)

I =0.052 kg.m^2

2) Kit = 0

3) Kir =0

4) Ui=mghi =(4.5*9.8*3.6) = 158.76 J

5) Uf =0

6) From conservation of energy

Kf+Uf =Ui+Ki

(1/2)mv^2 +(1/2)Iw2 = mgh

v = rw

v =[10gh/7]1/2 = [10*9.8*3.6/7]1/2

v= 7.1 m/s

7) w =v/r =7.1/0.17 = 41.76 rad/d

8) Kft = (1/2)mv2 = (1/2)(4.5)(7.1)2

Kft =113.4 J

9) Kfr = (1/2)Iw^2 =(1/2)(0.052*41.76*41.76)

Kfr = 45.36J

10) Ui = 158.76 J

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