N-1 2/8/2009 © University of Colorado at Boulder Newton's Laws: Forces and Motion A force is a push or a pull. A force is a vector : it has a magnitude and a direction. Forces add like vectors, not like scalars. Example: Two forces, labeled F1 and F2, are both acting on the same object. The forces have the same magnitude 12F F F and are 90o apart in direction: net total 1 2F F F F F     (Fmeans "sum of all the forces on the object") netF 2 F (NOT 2F) Isaac Newton (British, 1642-1727) first figured out the precise relationship between forces and motion “ ... for in those days I was in my prime of age for invention.” Newton's First Law (NI): If the net force acting on an object is zero, then it has constant velocity. netF 0 v constant Newton's Second Law (NII): netF m a (Notice! Fnet, not F, in this equation. There may be many forces acting on an object, but there is only one net force.) The net force on an object causes the object to accelerate (change its velocity). Units of force: 2F m a kg m/s 1 newton = 1 N A force of 1 N is about 0.22 pounds. A small plum weighs about 1 newton. F F Fnet 1 1 45 45 2N-2 2/8/2009 © University of Colorado at Boulder Things to notice about NII: If Fnet = 0, then a = 0 and velocity = constant. (1st Law). The vector a has the same direction asnetF. The magnitude of the acceleration a is proportional to 1/m (at constant Fnet). netF F m a is a vector equation x x y yF m a , F m a Before Newton, everyone thought (incorrectly!): "Force causes motion." WRONG! (You can have motion without any force causing the motion. Example: glider on an air track.) After Newton, "Force causes changes in motion." RIGHT! Definition: The WEIGHT of an object = the force of gravity on the object. W = mg Why? Recall this experimental fact: when object is in free-fall, meaning Fnet = Fgravity , then a = g. So in this situation (free-fall), Fnet = ma Fgrav = mg How big a force is 1 N? If m = 1 kg, W = Fgrav = mg = (1 kg)(9.8 m/s2) = 9.8 N. A kilogram mass has a weight of about 10 N, which is about 2.2 lbs. The pound (lb) is the English unit of force: 1 lb = 4.44 N. Example: Glider on an air track with v = constant OR book at rest on a table. In both cases, a = 0 Fnet = 0 N = force exerted on book by table OR force on glider by air track "normal" means "perpendicular" Since Fnet = 0 N = mg upward force on book exactly cancels downward force on book. How does the table know to exert an upward force that is exactly the right size to cancel the weight of the book? Answer: the table is not perfectly rigid; it is flexible, it is slightly springy. The table is slightly compressed by the weight of the book, and it pushes back on the book, Fgrav = W mass m a = g W = mg N = "normal" forceN-3 2/8/2009 © University of Colorado at Boulder exactly like a compressed spring. The heavier the book, the more the table-spring compresses, and the more it pushes upward on the book. Rules for drawing "Free-body diagram" or force diagram : 0) Draw a blob representing the object. 1) Draw only the forces acting on the object (not the forces which the object exerts on others). 2) Indicate strength and direction of forces on the object by drawing arrows coming out of the object. 3) Use symbols to represent the magnitudes of the forces (Don't worry about +/- signs. The forces arrows show the directions of the forces already.) Example: Object with mass m, hanging by a cord. Magnitude of force exerted by the cord = tension T Three different situations: I. Hanging stationary: velocity v = 0 a = 0 Fnet = 0 T = mg II. Pulled upward with constant velocity v. v = constant a = 0 Fnet = 0 T = mg (again!) same free-body diagram as in case I III. Object is accelerated upward (may be moving upward OR downward!) Question: What is the magnitude of the tension T in the cord? To analyze this situation: Step 1: Draw free-body diagram showing forces (show direction of acceleration off to one side of diagram.) Step 2: Choose a coordinate system and a + direction (always best to choose the direction of the acceleration as the +direction) Step 3: Write down equations x x y yF m a , F m a mg T free-body diagram: v a mg T a +yN-4 2/8/2009 © University of Colorado at Boulder In this example, just the y-equation is needed: +T – mg = ma T = mg + ma = m (a+g) Newton's Third Law (NIII): If body A exerts a force on body B (BA on B by AFF), then B exerts an equal and opposite force on A (AB on A by BFF). BA AB2 forces on 2 different objectsFF Forces always act between pairs of bodies. A force on one body is always being caused by a second body. NIII says that the force from one body on the other is always accompanied by a force from the other on the first, and the two forces of this "action-reaction" pair are always equal in magnitude and opposite in direction. Notice that the 2 forces of the action-reaction pair act on different bodies. Example of equal and opposite forces that are NOT the action-reaction pair of NIII: N = mg (these are NOT the 2 forces of NIII, since both act on the same object.) So which forces make up the action-reaction pairs in this situation ? N force on book due to table N' force on table due to book N N', says NIII mg= force on book due to planet earth (gravity) Book exerts same size force upward on the whole earth. A FAB B FBA mg N Book on a table: N ' N mg mgN-5 2/8/2009 © University of Colorado at Boulder The Story of the Clever Horse and the Cart: Horse says, "No matter how hard I pull on the cart, it will always pull back with an equal-sized force (according to NIII). Therefore, I cannot move the cart so I won't even try!" Farmer's answer: "Your 1st sentence is correct, but irrelevant. Whether or not the cart moves depends only on the forces acting on the cart. The forces on you, the horse, are irrelevant." Free-body diagram of forces on cart: If Fhorse > Ffriction, then the cart will move. The force on the horse from the cart is not relevant. Where are we so far? We have introduced Newton's 3 Laws. Laws are statements which are true always. There are no derivations of Newton's Laws; in particular there is no derivation of Fnet = …