Respuesta :
Answer:
c. V = 2 m/s
Explanation:
Using the conservation of energy:
[tex]E_i =E_f[/tex]
so:
Mgh = [tex]\frac{1}{2}IW^2 +\frac{1}{2}MV^2[/tex]
where M is the mass, g the gravity, h the altitude, I the moment of inertia of the pulley, W the angular velocity of the pulley and V the velocity of the mass.
Also we know that:
V = WR
Where R is the radius of the disk, so:
W = V/R
Also, the moment of inertia of the disk is equal to:
I = [tex]\frac{1}{2}MR^2[/tex]
I = [tex]\frac{1}{2}(5kg)(2m)^2[/tex]
I = 10 kg*m^2
so, we can write the initial equation as:
Mgh = [tex]\frac{1}{2}IV^2/R^2 +\frac{1}{2}MV^2[/tex]
Replacing the data:
(5kg)(9.8)(0.3m) = [tex]\frac{1}{2}(10)V^2/(2)^2 +\frac{1}{2}(5kg)V^2[/tex]
solving for V:
(5kg)(9.8)(0.3m) = [tex]V^2(\frac{1}{2}(10)1/4 +\frac{1}{2}(5kg))[/tex]
V = 2 m/s
