WORK AS A DOT PRODUCT OF VECTORS
 

The preceding formula is not quite complete because, as you should know by now, both force and displacement are vector quantities. How can we multiply two vectors? Fortunately, in this case it is easy because the force and displacement vectors generally point in the same direction when work is done. It turns out that the dot product provides the answer we need. Work is a scalar, therefore, and is equivalent to
w = F . q
where F is the force vector, represented as newtons in a certain direction, and q is the displacement vector, represented as meters in a certain direction. The directions of F and q are almost always the same. Note the dot symbol here (.), which is a heavy dot so that the dot product of vectors can be distinguished from the ordinary scalar product of variables, units, or numbers, as in kg . m²/s².
As long as the force and displacement vectors point in the same direction, we can simply multiply their magnitudes and get a correct result for work done. Just remember that work is a scalar, not a vector.
 

مواضيع ذات صلة

أنظمة لأكثر من جسيم واحد

كمية التحرك الزاوية والقوة المركزية

الحركة الدورانية

امثلة عن الاتزان الاستاتيكي للأجسام الممتدة

الاتزان الاستاتيكي للأجسام الممتدة

تعريف العزم

تذبذبات صغيرة لبندول

اعتبارات الطاقة في الحركة التوافقية البسيطة

الحل الهندسي للمعادلة التفاضلية للحركة التوافقية البسيطة، دائرة المرجع

الحل باستخدام حساب التفاضل والتكامل

قانون هوك والمعادلة التفاضلية للحركة التوافقية البسيطة

القدرة ووحدات الشغل