Ph101: Fundamentals of Physics Laboratory1

Instructor: Tony Zable

Laboratory #8: Torque

Purpose:

  • To examine the torques acting upon a New York Balance
  • To determine the mass of a meter stick using balanced torques

Apparatus:

A New York Balance, which consists of:

  1. a center stand with cast iron base
  2. a meter stick, a knife edge clamp
  3. a 50 gram mass
  4. a 100 gram mass

Procedure:

Part 1: Fulcrum in the center

1) Set up the balance with the fulcrum clamp set on the 50 centimeter mark. This is the center of the meter stick (and also the center of mass for the meter stick). The clamp should be mounted with the screw on the bottom. If the ruler does not balance, slightly move the fulcrum clamp towards the lower side until it does balance.

2) Attach a small loop of string to the 100 gram mass and it hang from the 40 cm mark on the meter stick. Next, attach a small loop of string to the 50 gram mass and it hang from the 99 centimeter mark. What happens?

Question: The force being exerted on 100 gram side of the fulcrum is greater that the force being exerted on the 50 gram side, so why does this occur?

3) Move the left hanger with the 100 gram weight outwards, away from the fulcrum until the ruler is again balanced. How is this possible? A 100 gram weight is perfectly balancing a 50 gram weight, thus there must be another important quantity in this calculation. This quantity is the distance of the force from the fulcrum. Recall from lecture that torque is equal to force times moment arm (in this case, the distance from the force to the fulcrum). Calculate the “clockwise” torque and the “counterclockwise” torque. Do these values agree? If not, then why is the ruler balanced?

4) Take a long look at your setup and try to figure out what you have missed. When you do, recalculate the torques, and compare them to one another. Do they agree?

5) So, for all practical purposes, the ruler is balanced. Whenever we have a smaller force (50 gram weight) that is moving a larger force, we have mechanical advantage. But in physics, just as in life, you never get anything for free. In order to gain this mechanical advantage, we must sacrifice distance. Go back to your setup, and rock the arm up and down. You can clearly see that the 50 gram mass is moving approximately twice the distance as the 100 gram mass. When the left side goes down one centimeter, the right side goes up two centimeters. Actually, this is just an approximation. The true value of the mechanical advantage is given by the ratio of the mass on the left side to the mass on the right side. Calculate the mechanical advantage.

Part 2: Fulcrum off–center

1) Set up the apparatus in a slightly different manner. Place 100-gram and 50-gram mass back at the 1 and 99 centimeter marks, respectively.

2) Balance the ruler by moving the FULCRUM towards the heavier weight. The screw will have to be loosened slightly so that the ruler can be slid through the clamp, but try to keep some tension on the screw so the ruler stays in place. When the ruler is balanced, tighten the screw on the fulcrum.

3) Calculate the “clockwise” and “counterclockwise” torques acting on the ruler. Notice that, once again, your torques does not balance, but your ruler does. What is the difference between the “clockwise” and “counter-clockwise” torques?

4) Welcome to the real world of physics. Quite often, theoretical equations are difficult to duplicate due to unconsidered factors like friction, static electricity, air currents, etc. In this case we have forgotten to include one force. This “missing” force is responsible for the difference in torque determined in (3). Look at your setup and try to deduce which force you have forgotten.

4) It turns out the missing force is the weight of the meter stick itself. The torque difference is due to this force as it is applied at the center of mass for the meter stick. Do you recall where the center of mass is for the meter stick? Where is it?

5) Use the distance from the center of mass to the fulcrum to determine the mass of the meter stick. (If you cannot figure it out how to do this, your instructor would be happy to help!)

6) Now, measure the mass of the meter stick with a gram scale.

7) How do your mass values from (5) and (6) compare to one another. Do they agree?

8) Calculate the % Error for these mass values.

Part 3: Questions & Summary

1) Suppose you are an animal trainer at a circus. You have a very strong, very light, wooden plank. You want to balance a 4200. kg elephant on a see-saw using only your own body weight. Suppose your body has a mass of 70. kg. The elephant is to stand 2 meters from the fulcrum.

a) What is the torque produced by the elephant on the see-saw?

b) How far from the fulcrum must you stand in order to balance the elephant?

c) How long must the plank be for both you and the elephant to be at opposite ends while it is balanced? Neglect the mass of the balance.

2) Write a CONCLUSION summarizes what you have learned in this experiment!