Question

According to the shop manual, when drilling a 11.8mm--diameter hole in wood, plastic, or aluminum, a drill should have a speed of 1400 rev/min.
1) For a 11.8mm--diameter drill bit turning at a constant 1400 rev/min , find the maximum linear speed of any part of the bit.
2) Find the maximum radial acceleration of any part of the bit.

Answer 1

Answer:

a) v max = 0.1376 m,/s

b) a max = 3.212 m/s^2

Explanation:

a) To find the maximum linear sped of any part of the bit, you use the following formula:

$v=\omega r$       (1)

v: linear speed

w: angular velocity of the bit = 1400 rev/min

r: distance to the center of the bit

You can observe that for r=rmax you obtain the maximum linear speed.

rmax = diameter/2 = 11.8mm/2 = 5.9mm

Before you replace the values of w and r in the equation (1), you convert to appropriate units:

$\omega=1400rev/min*\frac{1min}{60s}=23.333\frac{rev}{s}$

Then, you obtain:

$v_{max}=\omega r_{max}=(23.333rev/s)(5.9mm)=137.666\frac{mm}{s}$

$v_{max}=137.666\frac{mm}{s}*\frac{1m}{1000mm}=0.1376\frac{m}{s}$

the maximum linear speed of the bit is 0.1376 m/s

b) The maximum radial acceleration is given by:

$a_r_{max}=\frac{v_{max}^2}{r_{max}}\\\\a_{rmax}=\frac{(137.666mm/s)^2}{5.9mm}=3212.222\frac{mm}{s^2}\\\\a_{rmax}=3212.222*\frac{mm}{s^2}*\frac{1m}{1000mm}=3.212\frac{m}{s^2}$

the maximum radial acceleration is 3.212 m/s^2