The head of a grass string trimmer has 100 g of cord wound in a light, cylindric
ID: 2189507 • Letter: T
Question
The head of a grass string trimmer has 100 g of cord wound in a light, cylindrical spool with inside diameter 3.00 cm and outside diameter 18.0 cm as shown in the figure below. The cord has a linear density of 10.0 g/m. A single strand of the cord extends 16.0 cm from the outer edge of the spool. (a) When switched on, the trimmer speeds up from 0 to 2 450 rev/min in 0.175 s. What average power is delivered to the head by the trimmer motor while it is accelerating? (b) When the trimmer is cutting grass, it spins at 2 095 rev/min and the grass exerts an average tangential force of 9.10 N on the outer end of the cord, which is still at a radial distance of 16.0 cm from the outer edge of the spool. What is the power delivered to the head under load?Explanation / Answer
a) Average power = total energy imparted / time Total energy = rotational + translational energy Rotational energy = 1/2 inertia * ?^2 Inertia, I = inertia of wounded cord + extended cord This involves inertia of annulus + rod using parallel axis theorem I = 4.659e-4 kg m^2 (You verify this) ? = 2700*2p/60 E_rot = 1/2 * I *?^2 = 18.62 J The extended cord also has linear translation v = ? * 0.17 E_tr = 1/2 m v^2 = 1.85 J E_total = 20.47 J Average power = 20.47 / 0.185 = 110.66 W b) Power = torque x angular speed Torque = 8.75 * 0.25 Nm Power = 8.75 * 0.25 * 2160 * 2p/60 = 494.8 W
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