A massless string is wrapped around a cylinder of mass 0.400 kg and radius 0.100 m. The string is attached to the ceiling. The cylinder is released. As it falls, the string unwinds. What is the magnitude of the acceleration of the cylinder as it falls in m/s2?
A.3.27
B.6.54
C.4.91
D.7.61
E.9.81
2 answers
A.3.27 i'm 100% sure :D
B
For the cylinder moment of inertia (rotational inertia) is I = m•R²/2,
v =ω•R = > ω= v/R
PE =KE
m•g•h = m•v²/2 +I•ω²/2 = m•v²/2 + (m•R²/2) • ( v/R)²/2 =
= 3•m•v²/4, =>
v² = 4•g•h/3
From kinematics:
v² = 2•a•h, therefore
4•g•h/3 = 2•a•h,
a =4•g/6 = 2•g/3 = 9.8•2/3 = 6.54 m/s² .
Note! Mass and radius are unnecessary for solution
For the cylinder moment of inertia (rotational inertia) is I = m•R²/2,
v =ω•R = > ω= v/R
PE =KE
m•g•h = m•v²/2 +I•ω²/2 = m•v²/2 + (m•R²/2) • ( v/R)²/2 =
= 3•m•v²/4, =>
v² = 4•g•h/3
From kinematics:
v² = 2•a•h, therefore
4•g•h/3 = 2•a•h,
a =4•g/6 = 2•g/3 = 9.8•2/3 = 6.54 m/s² .
Note! Mass and radius are unnecessary for solution
1 answer