Simple Nature - Light and Matter

1. It always relates exactly two forces, not more.2. The two forces involve exactly two objects, in the pattern Aon B, B on A.3. The two forces are always of the same type, e.g., friction andfriction, or gravity and gravity.Directions of forcesWe’ve already seen that momentum, unlike energy, has a directionin space. Since force is defined in terms of momentum, forcealso has a direction in space. For motion in one dimension, wehave to pick a coordinate system, and given that choice, forces andmomenta will be positive or negative. We’ve already used signs torepresent directions of forces in Newton’s third law, F AB = −F BA .There is, however, a complication with force that we were ableto avoid with momentum. If an object is moving on a line, we’reguaranteed that its momentum is in one of two directions: the twodirections along the line. But even an object that stays on a linemay still be subject to forces that act perpendicularly to the line.For example, suppose a coin is sliding to the right across a table, h,and let’s choose a positive x axis that points to the right. The coin’smotion is along a horizontal line, and its momentum is positive anddecreasing. Because the momentum is decreasing, its time derivativedp/ dt is negative. This derivative equals the horizontal force offriction F 1 , and its negative sign tells us that this force on the coinis to the left.But there are also vertical forces on the coin. The Earth exertsa downward gravitational force F 2 on it, and the table makes anupward force F 3 that prevents the coin from sinking into the wood.In fact, without these vertical forces the horizontal frictional forcewouldn’t exist: surfaces don’t exert friction against one anotherunless they are being pressed together.To avoid mathematical complication, we want to postpone thefull three-dimensional treatment of force and momentum until section3.4. For now, we’ll limit ourselves to examples like the coin, inwhich the motion is confined to a line, and any forces perpendicularto the line cancel each other out.Discussion QuestionsA Criticize the following incorrect statement:“If an object is at rest and the total force on it is zero, it stays at rest.There can also be cases where an object is moving and keeps on movingwithout having any total force on it, but that can only happen when there’sno friction, like in outer space.”g / A swimmer doing the breaststroke pushes backward againstthe water. By Newton’s third law,the water pushes forward on him.h / A coin slides across a table.Even for motion in onedimension, some of the forcesmay not lie along the line of themotion.Section 3.2 Force In One Dimension 149