How can we determine the torque required to perform common school-day tasks?
Introduction. Torque is an important component of rotational dynamics, particularly with respect to an individual's ability to perform mechanical tasks requiring the application of force. Torque is the product of an applied force and the radial distance over which it is perpendicularly applied. The body possesses a fixed position at one end which is able to pivot in response to sufficient applied perpendicularly to the long axis of the body at a selected point. This long axis is essentially a radius line with the fixed pivot serving as the point around which the body is consequently rotated. The radius length is the distance between the pivot and the location of the applied force. Simply stated, torque is the product of an applied force which is producing a rotation and the length of the radius of that rotation which is the distance between the pivot and the applied force. Mathematically torque is expressed as
Torque = Fperpendicular x r
Torque = F x rperpendicular
The calculation of torque with regard to a force which is applied obliquely to the radius of rotation is obtained by
Torque = Fapplied x r x sin(A)
where A is the angle measured between the direction of the applied force and the normal to the radius.
This exercise is designed to provide you with a practical appreciation of torque and its calculation as applied to common tasks in the everyday school setting.
Spring scale (calibrated to 50 N)
1 meter length of fishing line or nylon cord
Wood door jamb block or doorstop
1. You must first calibrate your spring scales to be sure they are in proper working order. Suspending a 1.00 kilogram mass and observing a reading of 9.80 Newtons on your spring scale is sufficient.
2. Next, you must construct a simple device which will permit you to connect your spring scale to the object whose torque you wish to measure. You an accomplish this by tying each end of your fishing line or nylon cord together into a loop. Then create a slip-knot by slipping one looped end of your line between the loop at the opposite end and pulling taut. The noose-like slip-knot should then be placed over door handles, door knobs, and any other attaching point on the object in question. Your spring scale can then be attached to the free end of the loop and the forces then measured.
3. Make sure to use the wooden doorstops to prop doors open slightly to reduce the effects of contact friction and obviate any spontaneous locking mechanisms.
4. Measure the distance from each object's pivot to the point of attachment of your spring scale connector. Record this distance, in meters, in the data table provided.
5. Apply sufficient pulling force to the spring scale/connector assembly so as to just initiate motion. Remember to apply your pulling force perpendicularly to the long axis of the object. The maximum reading revealed by the spring scale equals the applied force. Record this value, in Newtons, in the data table provided.
6. Multiply the applied force and the radius. This value is the torque. Enter this value into the data table.
7. Show all calculations and answer all questions.
1. Which object required the greatest amount of torque to initiate motion? Did you expect that this object would require the greatest amount of torque to operate? Why or why not? Explain.
2. Briefly summarize the principal factors which you believe exert a direct influence over the torque required to operate a mechanism.
3. Briefly explain any reasonable steps which could be taken to reduce the amount of torque required to operate a mechanism.
4. Doors are necessary components of all building structures. Suggest any changes which might be incorporated into the design of a door to minimize the amount of torque that must applied to open them.
5. How did the values of torque obtained from the classroom, science office, cafeteria, and hallway door compare with one another. How do you account for the observed values?
6. Which, if any, required more torque - opening the metal locker door or turning the pencil sharpener. How do you account for the observed values?
7. Calculate the distance from the pivot of the classroom door at which you would have to apply a force equal to your own weight in order to open the door.