The head of a grass string trimmer has 100 g of cord wound in a light, cylindric
ID: 1442493 • 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. When switched on, the trimmer speeds up from 0 to 2 750 rev/min in 0.245 s. What average power is delivered to the head by the trimmer motor while it is accelerating? When the trimmer is cutting grass, it spins at 1 930 rev/min and the grass exerts an average tangential force of 8.95 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
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 = 4.592 x 10-4 kg m^2
(You verify this)
= 2750*2/60
E_rot = 1/2 * I *^2 = 19.04 J
Average power = 19.04 / 0.245 = 77.72 W
b) Power = torque x angular speed
Torque = 8.95 * 0.25 Nm
Power = 8.95 * 0.25 * 1930 * 2/60
= 452.22 W
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