I need help with this physics problem please The head of a grass string trimmer

Question

I need help with this physics problem please

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 2 550 rev/min in 0.250 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 1 960 rev/min and the grass exerts an average tangential force of 6.85 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

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 = 4.592e-4 kg m^2
= 2550*2/60
E_rot = 1/2 * I *^2 = 16.36 J
Average power = 16.36 / 0.25 = 65.42 W

b) Power = torque x angular speed
Torque = 6.85 * 0.25 Nm
Power = 6.85 * 0.25 * 1960 * 2/60
= 351.3 W

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---