Physics Lab - Torque and Rotational EquilibriumWe will use this virtual experiment to study the concept of torque and the conditions that must be met for a body to be in rotational equilibrium.

Instructions:

- Visit the below web page and review the material on levers and torque. http://dev.physicslab.org/Document.aspx?doctype=3&filename=RotaryMotion_TorqueDefinition.xml

- Next, go to http://www.walter-fendt.de/ph14e/lever.htm

(This is a Shockwave based simulation. If you do not have the Shockwave player, you can download it for free from http://www.adobe.com/products/shockwaveplayer/)

- Complete the below exercises:

Table 1:

For each row in the table below, complete the table to balance the lever. The "arm" is the length that the weight (or group of weights) is from the pivot. The moment is the moment about the pivot caused by the weight (or group of weights) and the distance from the pivot.

Question 1: In table 1, what approach did you use to balance the lever? If you did not use trial and error, what did you use? How were you able to predict what combination of the distance from the pivot and weight would balance the lever?

Question 2: Consider a situation where you were asked to balance a lever with the following conditions:

As you can see, this lever is not balanced because the moment on the right side of the lever is greater than the moment on the left side of the lever. If you were not able to change the weight on the left side or the right side, and you were not able to change the location of the weight on the lever, what else could you change to balance the lever? How would you change it?
A real life lever system

Ships at sea are lever systems - they need to be balanced in two directions: longitudinally (along the length of the ship), transversely (side to side on the ship). The configuration of the ship (whether or not it's balanced) in the longitudinal direction is called "trim" and in the transverse direction is called "list." They are expressed in degrees; for example, a ship with 1° trim by stern is tilted slightly down by the stern.

When we discussed levers previously, we had two types of forces:

(1) A force holding the lever up and allowing both sides of the lever to rotate about that pivot point. We called this the pivot.

(2) A force down on each side of the pivot, which when combined with the distance from the pivot, created a moment arm. In order for the lever to be balanced, the moment arms must be equal on each side.

Consider a very simplified case of USS Constitution. She is 204 ft long. She weighs 2200 metric tons, and we account for that weight by saying that the resultant force acts in one location, which we call the center of gravity. Assume Constitution's longitudinal (lengthwise) center of gravity is located 100 ft from the bow (the front of the ship) and her transverse (side to side) center of gravity is exactly in the midpoint of her beam (the distance from the left side to the right side of the ship when looking head on), which we call the centerline. The "pivot point" is provided by force of buoyancy, which we've discussed in previous lessons. Similar to gravity, we consider all the effects of buoyancy as acting in one location, which we call the center of buoyancy. Assume that the transverse center of buoyancy is located at the centerline, which is same location as the transverse center of gravity. Assume that the longitudinal center of buoyancy is located 102 ft from the bow of the ship (the front of the ship.)

Question 3: Draw a simplified lever system showing the location of the pivot and the weight of USS Constitution. Determine if there is a resultant moment on USS Constitution that should result in trim or list.

Question 4: Constitution was built as a 44 gun frigate in 1797. She's a wooden sail ship, which makes her speed capability particularly sensitive to trim and list. Imagine you are the gunnery officer on Constitution, and you receive the following orders:

- The Captain orders you to onload as many "24 pounders", ammunition for Constitution's long gun, as you can. "24 pounders" weigh 11 kg each.

- The Navigator tells you that the onload must help Constitution achieve even trim and list or come as close to even as possible. If you must put trim or list on the ship, you cannot exceed 5° of trim (by the bow or the stern) or 1° of list (to the left or to the right.)

- You're told by the Supply officer that there are three locations you can use to load the ammunition. These locations and their capacities are listed to below:

Location Capacity (# of "24 pounders" that can fit) Transverse Center of Gravity (TCG) Longitduinal Center of Gravity (LCG)
Forward ammo storeroom 200 2 ft left of centerline 10 ft from the bow

Midships ammo storeroom 10 Centerline 110 ft from the bow

Aft ammo storeroom 120 3 ft right of centerline 199 ft from the bow

Describe your load out plan and how you adhere to the orders from the Captain, the Navigator and the Supply officer. Be sure to include the amount of ammo in each of the above compartments (even if you chose to not include ammo in one or more of them) and the resulting calculation of trim and list. Assume that a moment of 890 ft-ton provides 1° of trim and a moment of 40 ft-ton provides 1° of list.

HINT: Question 4 uses the same principles as the earlier questions - you just have a lever that moves in two dimensions. There are a lot of solutions to this problem. Use the applet to experiment with the lever locations, or set up an Excel spreadsheet similar to Table 1 and tinker with the how much ammunition goes in each compartment and what the end result is in terms of list and trim.