(a)
The equations of the motion:
- of the cylinder
Iε =M
Ia/R =TR
T= Ia/R²
- of the object
m₂a=m₂g-T
m₂a=m₂g- Ia/R²
a(m₂+ I/R²) =m₂g
a= m₂g/ (m₂+ I/R²)
(b)
T= Ia/R²=Im₂g/ R² (m₂+ I/R²)=
=Im₂g/(m₂R²+ I)
(c)
h=v²/2a =>
v= sqrt{2ha} =
=sqrt { 2hm₂g R²/(m₂R² + I)}
A light inflexible cable is wrapped around a cylinder of mass m1 , radius R , and moment of inertia about the center of mass Ic . The cylinder rotates about its axis without friction. The cable does not slip on the cylinder when set in motion. The free end of the cable is attached to an object of mass m2 . The object is released from rest at a height h above the floor. You may assume that the cable has negligible mass. Let g be the acceleration due to gravity.
(a) Find the acceleration a of the falling object. Express your answer in terms of m2, R, Ic and g (enter m_2 for m2, R for R, I_c for Ic and g for g).
a=
(b) Find the tension T in the cable. Express your answer in terms of m2, R, Icm and g (enter m_2 for m2, R for R, I_c for Ic and g for g).
T=
(c) Find the speed v of the falling object just before it hits the floor. Express your answer in terms of m2, R, Icm, h and g (enter m_2 for m2, R for R, I_c for Ic, h for h and g for g).
1 answer