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1 Physics 218 LAB: TORQUES and STATIC EQUILIBRIUM Name Section Number Team Number Introduction One purpose of this lab is to introduce you to quantity called torque or, as engineers cail it, moment of a force. It is a somewhat complicated object that will be defined in general later in course. The simple definition is that torque exerted by a force on some object is product of a force times distance from point at which force acts to some reference point. There is a direction or sense associated with a torque and, for simple cases considered in this lab, this just means that torque is tending to rotate object eir clockwise or counterclockwise. The force must be perpendicular to line from point of contact to reference point or this definition needs to be modified. Only this special case will be considered here. In this lab you will verify following statement: In order for an object to be in static equilibrium, i.e. to remain at rest if it is initially at rest, sum of torques on object must be zero. This is in addition to condition studied in previous lab, namely that sum of forces on object must be zero. The Apparatus You will have a meter stick which has a hanger on it so that it can be balanced on a stand. This hanger will be referred to as pivot hanger. The hanger has a knife edge and stand has a groove into which knife edge fits. There are additional hangers, that can be placed at any points on meter stick, on which you can hang various masses. The force being exerted on meter stick by a hanging mass m1 has magnitude mg. (This will also be covered later in lecture.) First Step Slide hanger to 50 centimeter mark and place knife edge on grooves on stand. (You should attach hangers with adjustment screw on bottom. Although this is somewhat inconvenient, system works much better this way.) If meter stick does not remain horizontal move hanger slightly until it does. Moving hanger one way will make imbalance worse, while or way makes it better. Note hanger s location when stick remains at rest. Since forces on stick must add to zero and stand can only exert a force on knife edge, it follows that effect 1

2 of gravity on meter stick is a single force, acting down at point on meter stick above knife edge. This does not determine magnitude of force of gravity, just its location. The location is called center of gravity. The mass of meter stick will be determined later. Second Set Of Experiments Leave hanger at center of gravity of meter stick, so that it can pivot on stand about that point. Put two more hangers on meter stick, one on each side of pivot. Hang different weights on se two hangers and slide m around until positions are located such that meter stick remains horizontal, at rest. Write down sizes and positions of two hanging masses. Also weigh a hanger to determine and record its mass. Set 1. Repeat this procedure two more times with different sets of masses and again note ir sizes and positions. Set 2. Set 3.

3 Analysis For each of sets of masses and positions you found above, you are to show that condition for static equilibrium, is in fact satisfied. Here vector sign on torque, r, just means that if torque tends to rotate clockwise about pivot it is considered positive while tending to rotate counterclockwise is negative. Since force exerted by stand and force exerted by gravity act right at pivot point, ir corresponding torques about this point are zero. (Don t forget to include torque due to gravitational force on hangers.) Set 1. Clockwise torque= Set 2. Clockwise torque= Set 3. Clockwise torque= Third Experiment You can use condition for static equilibrium to determine mass of meter stick. Move pivot hanger from center of gravity and fasten it at 40 cm mark. Remove one of or hangers and move remaining one, with some known mass on it, until static equilibrium is obtained. (You may have to change mass on hanger 3

4 to achieve this.) The two torques about pivot must cancel. Since distances to pivot can be measured and mass on hanger is known, mass of meter stick can be determined. Calculation of Meter Stick Mass Fourth Experiment Put pivot hanger at 40 cm mark and put one hanger and mass to left of it and one, with a different mass, to right. Adjust positions of se two hangers until static equilibrium is achieved. (You may have to use different masses as this will not work for every choice of two masses.) Calculate sum of torques about pivot point.

5 Now use condition point. at pivot that = 0 to find force being exerted on meter stick mark Now calculate sum of and 70 cm mark. torques about or reference points, such as 20 cm You should have verified following statement: point. If an object is in static equilibrium, sum of torques is zero for any reference You might try to prove that this is true analytically.