Answer:
the speed (in m/s) of the mass after it has fallen through 1.25 m is 1.968 m/s
Explanation:
Given that :
Mass attached to the free end of the string, m = 423 g = 0.423 kg
Moment of inertia of pulley, I = 0.0352 kg m²
Radius of the pulley, r = 12.5 cm = 0.125 meters
Depth of fallen mass, h = 1.25 m
Acceleration due to gravity, g = 9.8 m/s²
Change in potential energy = mgh
= 0.423 × 9.8 × 1.25
=5.18175 J
From the question, we understand that the change in potential energy is used to raise and increase the kinetic energy of hanging mass and the rotational kinetic energy of pulley.
As such;
where;
is the angular velocity of the pulley
v is the velocity of the mass after falling 1.25 m
where:
replacing into above equation; we have:
Thus, the speed (in m/s) of the mass after it has fallen through 1.25 m is 1.968 m/s