A massless string is wound around a solid cylinder that has a radius of 0.31 m a

Question

A massless string is wound around a solid cylinder that has a radius of 0.31 m and a mass of 12.66 kg. The free end of the string is tied to a block of mass 4.22 kg which hangs straight down. At t = 0, the cylinder is allowed to spin about an axis through its center and the block falls, unwinding the string. Assume that the cylinder spins without friction. What is the acceleration of the block? Opts Incorrect. Submissions to practice problems are not permanently recorded. Tries 4/99 Previous Tries What is the tension in the part of the string that extends between the cylinder and the block? Opts Tries 0/99 What is the angular acceleration of the cylinder? Opts Tries 0/99 What is the tension in the part of the string that extends between the cylinder and the block? Opts Tries 0/99 What is the angular acceleration of the cylinder? Opts Tries 0/99 What is the tangential acceleration of a point on the edge of the cylinder? Opts Tries 0/99

Explanation / Answer

(a) For the cylinder moment of inertia (rotational inertia) is I = m•R²/2,
v =•R = > = v/R
PE =KE
m•g•h = m•v²/2 +I•²/2 = 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

(b) T- mg= - ma

T= mg- ma

T= 4.22(9.8-6.54)=13.76 N

(c) angular acceleartion= alpha= a/r=6.54/0.31=21.1 rad/sec^2

(d) a= alpha r = 21.1 (0.31)= 6.54 m/s^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.