Final answer:
The torque on the driven shaft in a chain drive system with a driver sprocket of 24 teeth and a driven sprocket of 72 teeth, given a driver shaft torque of 633 ft-lbs, is 1899 ft-lbs.
Step-by-step explanation:
If a chain drive system has a driver sprocket with 24 teeth and a driven sprocket with 72 teeth, and the driver shaft exerts 633 ft-lbs of torque, then we can calculate the torque on the driven shaft. The torque on the driven shaft is found by using the principle that in a chain drive, the torque ratio is inversely proportional to the speed ratio, which is determined by the sizes (number of teeth) of the two sprockets.
The speed ratio is given by the size of the driver sprocket over the size of the driven sprocket (24/72 = 1/3), which means the driven sprocket turns at one-third the speed of the driver sprocket. Because power (which is torque times angular speed) must be conserved (ignoring losses), the torque on the driven sprocket must be three times that of the driver's torque, since the speed is one-third.
Therefore, the torque on the driven shaft will be 633 ft-lbs × 3 = 1899 ft-lbs.