Question 401.
A 11 kg solid steel cylinder with a 10 cm radius is mounted on bearings so that it rotates freely about a horizontal axis. Around the cylinder is wound a number of turns of a fine gold thread. A 1.0 kg monkey named Fred holds on to the loose end and descends on the unwinding thread as the cylinder turns.
Compute Fred's acceleration (m/(s^2)) and the tension in the thread (N).
Answer 401.
Net force on the monkey,
mg - T = ma, where a = acceleration of the monkey and T = tension in the thread
=> 9.81 - T = a ... ( 1 )
Torque acting on the cylinder w.r.t. to its axis
= (moment of inertia of the cylinder) * (its angular acceleration) = 0.1 T
=> (1/2) * 11 * (0.10)^2 * α = 0.1 T
Also, α * 0.1 = a
=> (1/2) * 11 * (0.10)^2 * a/(0.10) = 0.1 T
=> 5.5a = T ... ( 2 )
Solving ( 1 ) and ( 2 ),
a = 9.81/6.5 = 1.51 m/s^2
T = 5.5a = 5.5 * 1.51 N = 8.376 N.
Link to YA!
A 11 kg solid steel cylinder with a 10 cm radius is mounted on bearings so that it rotates freely about a horizontal axis. Around the cylinder is wound a number of turns of a fine gold thread. A 1.0 kg monkey named Fred holds on to the loose end and descends on the unwinding thread as the cylinder turns.
Compute Fred's acceleration (m/(s^2)) and the tension in the thread (N).
Answer 401.
Net force on the monkey,
mg - T = ma, where a = acceleration of the monkey and T = tension in the thread
=> 9.81 - T = a ... ( 1 )
Torque acting on the cylinder w.r.t. to its axis
= (moment of inertia of the cylinder) * (its angular acceleration) = 0.1 T
=> (1/2) * 11 * (0.10)^2 * α = 0.1 T
Also, α * 0.1 = a
=> (1/2) * 11 * (0.10)^2 * a/(0.10) = 0.1 T
=> 5.5a = T ... ( 2 )
Solving ( 1 ) and ( 2 ),
a = 9.81/6.5 = 1.51 m/s^2
T = 5.5a = 5.5 * 1.51 N = 8.376 N.
Link to YA!
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