Oscillating Beans

Puzzle supplied by Purdue Mechanical Engineering Ambassadors.

The bottom of a vertical, massless spring is 88.0 cm above the floor. When a 660 gram can of beans is hung on the end of the spring and moved to equilibrium, the end of the spring is stretched until it is 76.0 cm above the floor. The beans are then lifted up from their equilibrium position until the top of the can is 80.0 cm above the floor and released.

  • (A) What is the spring constant of the spring?
  • (B) Determine the equation of motion for the velocity of the can of beans as a function of time.
  • (C) At what height above the floor will the acceleration of the beans be equal to acceleration of gravity?
  • (D) How fast are the beans moving exactly 3.80 seconds after they are released ? Are the beans above or below the equilibrium position?
  • (E) How much work did it take to set the beans in motion?
  • (F) How long does it take the beans to move from lowest position above the floor to their highest position above the floor?
  • (G) What is the speed of the beans when they are 73.0 cm above the floor?

 

Congratulations to David W. Hanna (BSME ’58), who submitted the correct solution.

Solution to "Will James Bond Escape?"

Due to the length of the solution, please see an abbreviated version below. If you would like the complete calculation, please check here.

  • The total weight of the raft (empty raft + James Bond + anchor) = 1,040 pounds.
  • The weight of the anchor is 489.8 pounds.
  • The depth of the water displaced by the total weight of the raft is 1.852 feet.
  • The total volume of water surrounding the raft is 44.963 ft3 and the volume of water initially surrounding the raft is 12.963 ft3.
  • When the anchor is thrown overboard, the volume of water surrounding the raft is 6.858 ft3 and the raft and James rise 0.44 ft to a height of 7.94 ft.
  • Bottom line, James Bond does not make it out of the pit!

 

(David W. Hanna solved the puzzle correctly, but he also gets extra credit for pointing out that we had the wrong title [Torque Troubles] on the puzzle.)