1- A 3m diameter cylinder and a seat with the dimensions shown (figure on the left) are balanced in a pinned

connection at A. f both bodies have a density of 5000kg/m3 and a depth (into the paper) of 1m, then what is the

distance x required for the two bodies to be perfectly balanced on the pinned connection A?

Hint: To incorporate the forces due to the weights of the bodies, break up the body into smaller components

(figure on the right) and place the weights for each respective shape on your FBD.

2. The max speed for the servo shown is 130RPM when connected to 6V. Assume that the gearbox on your servo is able to output a torque of 1.5 kg-cm while turning at this speed. Using the number of teeth on each

gear provided in the table, determine the torque and rotational speed of the output shaft on the DC motor.

gear # teeth

1 10

2 47

3 10

4 38

5 8

6 32

7 7

8 23

HINT: Work backwards from the output shaft and use the equations developed in class that relate the number of

teeth to the torque. When working back from the output shaft to gear 7/6, realize that the “torque” transmitted by

gear 7 is the SAME as the torque transmitted by gear 6 since they are joined. Then, relate the torque of gear 6 to

gear 5 based on their numbers of teeth. Since gears 5 and 4 are actually one piece, the torque in 4 and 5 will be

the same (as was the case for gears 6 and 7). Repeat for the other gears, working your way all the way back to

the DC motor.