The compressor mechanism shown in Figure bellow is driven clockwise by a DC electric motor at a constant rate of 600 rpm. In the position shown, the cylinder pressure is 45 psi. The piston weighs 0.5lb, and the coefficient of friction between the piston and the compressor cylinder is 0.1. The weight of all other links is negligible. At the instant shown, determine the torque required from the motor to operate the compressor. (the piston acceleration is 5378 in/s^2) B 50° 2" (2) 8"

The system shown below is made up of two pulleys attached to the same shaft, with radii ri and re of 0.29 mm and 0.43 mm, respectively. The total mass of the pulley system is 14 kg and its turning radius is 0.26 mm from its center. The mass of block A is 9 kg and the mass of block B is 2 kg. If the coefficient of kinetic friction between block B and the floor is 0.2, find the angular acceleration of the pulley.

A 500 pound weight is attached to a cable that is being lifted by a 10 inch diameter drum.  The 48V DC motor selected has a no-load angular velocity of 800 RPM and a stall torque of 500 inch-pounds.    A gearbox has been designed to spin the drum as quickly as possible.  Assume that there are no friction losses in this system.  The drum is driven by a 72-tooth gear with a diametral pitch of P=8, and is 3D printed such that it has a yield strength in shear of τy = 2500 psi. Assuming that the entire output torque required to turn the drum is produced by the force on one tooth, and that the gear tooth would fail by being sheared off at the pitch circle, determine the required gear face width, b, for a factor of safety of 3.  Note that circular tooth thickness, t, at the pitch circle is π / (2P). Repeat  for a gear made out of 6061 Aluminum (σy = 35 ksi, τy = 20 ksi).   Only do the part for the 6061 gear do not do it for the 3D printed gear

Clutch Mechanism 8. In the clutch mechanism shown, two flat circular disks of radius R are mounted so that they can be brought into contact causing a net frictional force. The contact pressure in general depends on the distance from the center and in one specific case may be modeled buy P(r) = Poe-kr, where k is a constant and r is the distance from the center of the discs. The integral cR F = 2m " P(r)rdr gives the total contact force between the discs. Cross-section a. In your own words explain where this formula comes from.