Torque: Force at a Distance©01



Torque©01

Experiment 3

Objective: To discuss the topics of force, distance and center of mass and they relate to torque.

DISCUSSION:

Torque is defined as a force acting on an object that changes the objects angular momentum. You use it everyday in such motions as opening and shutting a door or opening the top of your ThinkPad computer. In Figure 1, we see a common application of torque. To tighten a bolt, a hand pulls on a wrench with a force, F, at a distance λ. The amount of torque, τ , applied to the bolt is simply

[pic] (1)

Figure 1. The torque exerted by a hand and

wrench can tighten or loosen a bolt.

Note that this formula is only true if F and λ are perpendicular, as they are in this case.

Another common application of torque is that of the lever. Here, a small amount of force can be used to move a large object. The torque that the person exerts on the right side of the pivot is [pic]. The torque on the left side of the pivot will be the same (but in the opposite direction). This means that because λ2 is smaller than λ1, F2 must be larger than F1. Thus, the person is able to amplify the force applied to the rock by using the lever.

Figure 2: A person uses a lever to amplify the force applied in order to move the rock.

A final example is what you will be doing in lab today. Using the concept of torque, you will be balancing a meter stick at different pivot points, an example of which is shown in Figure 3. The torque on the right must be balanced by an equal torque on the left in order for the stick to balance. The forces are provided by the weight of the masses, [pic] , and you must figure out the lengths needed to balance the stick. When the pivot is at the center of mass, you can ignore the mass of the meter stick, as seen in Figure 3.

Figure 3: A meter stick is balanced on a pivot as the center of mass by equal torques on both sides.

However, when the pivot is NOT at the center of mass, the meter stick’s own weight creates a torque and must be taken into consideration. Figure 4 shows such a configuration. The equation for picture would be:

(2)

Figure 4: A meter stick is balanced on a pivot not at the center of mass by equal torques on both sides.

EXERCISES:

Using the masses given, calculate the forces provided by the masses. Place the meter stick on the pivot at the given location. Then, by adjusting how far the masses are hung from the pivot, balance the meter stick. The meter stick is considered ‘balanced’ when it is perfectly horizontal. Finally, calculate the torque on both sides, using Equation 2 where necessary.

Questions:

1. Did the right side torque equal the left side torque in each case? Why or why not.

2. Which give a larger torque, 0.050kg, 0.02m from the pivot or 0.020kg, 0.05m from the pivot?

3. If you have a torque of 100N•m on the right side of the stick and a torque of 150N•m on the left, what happens to the stick when you let go of it?

Mass of meter stick: kg

Pivot Point |mleft |Fleft

= mleft×g |mright |Fright

= mright×g |λleft |λcm |λright |τleft

= Fleftt×λleft |τcm

= Fcm×λcm |τright

= Fright×λright | |0.50m |0.050kg | |0.050kg | | | | | | | | |0.50m |0.100kg | |0.050kg | | | | | | | | |0.40m |0.050kg | |0.050kg | | | | | | | | |0.25m |0.200kg | |0.020kg | | | | | | | | |0.10m |0.700kg | |0.010kg | | | | | | | | |

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