In the motorized rack-and-pinion system in a milling machine, the pinion has 50 teeth an...

In the motorized rack-and-pinion system in a milling machine, the pinion has 50 teeth and a pitch radius of 0.75 in. (Figure P8.21). Over a certain range of its motion, the motor turns at 800 rpm.

(a) Determine the horizontal velocity of the rack.

(b) If a peak torque of is supplied by the motor, determine the pulling force that is produced in the rack and transferred to the milling machine