Download UNIT 2: FORCES, DYNAMICS – YAIZA SCHMÖHE OLLERO 1 UNIT

UNIT 2 (I): FORCES, DYNAMICS 1. FORCE 1.1 Definition Force is any action that can change the state of a body (whether it is resting or moving) or that can deform it. UNITS : NEWTON (N) 1.2 Types of forces There are only 4 forces in Nature: -­‐
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Electromagnetic force: between bodies that are electrically charged (electric force)or between a magnet and iron (magnetic force) Gravitational force: between objects with mass Nuclear weak force: responsible for radiactive desintegrations in the nucleus of the atom. Nuclear strong force: responsible for keeping the nucleus of the atom together (protons and neutrons) 1.3 Forces as vectors Every force can be represented using a vector: like an arrow with -­‐
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Aplication point: where the force is applied to (where the arrow starts) Module or magnitud: intensity of the force (how long the arrow is) Direction: orientation in space (the line that represents the arrow) 1.4 Composing forces When there are several forces acting on a body we can find the NET FORCE or TOTAL FORCE as the overall force acting on the objetc like this: a) same direction  by adding or substracting UNIT 2: FORCES, DYNAMICS – YAIZA SCHMÖHE OLLERO 1 b) different direction R2 = A2 + B2 + 2 AB cosα Note that when the 2 forces (A and B) are perpendicular (α = 90º  cos α = 0) it becomes the Pitagoras law: R2 = A2 + B2 F2 = Fx2 + Fy2 1.5 Decomposing forces Sometimes it´s usefull to write one force (i.e. F) like a sum of 2 different ones (i.e. Fy and Fx): It is useful to decompose F in its vertical (Y) component (Fy) and its horizontal (X) component (Fx) Fx = F . cos α Fy = F . sin α 1.6 Forces and equilibrium: If the overall force acting on a body is ZERO then it´s like there is no force acting on it and the body is in EQUILIBRIUM. 2. NEWTON´S LAWS 2.1 First law  inertia´s law A body will remain at rest or moving at a constant velocity, unless an external force acts upon it (if the net force is not zero) •
An object that is at rest will stay at rest unless an external force acts upon it. 2 •
An object that is in motion will not change its velocity unless an external force acts upon it. 2.2 Second law  fundamental law The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. F = ma where  F is the net force acting on the object,  m is the mass of the object and  a is the acceleration of the object. 2.3 Third law  action and reaction When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body. i.e. a) 2 guys on ice-­‐skates. If one pushes the other, both of them will move b) A swimmer pushes with her legs against the swimming-­‐pool wall and she receives the same force that propelles her forward. 3. APLICATIONS OF NEWTONS LAWS 3.1 Most common forces a) Elastic force Is the force that makes a spring go back to its original place and goes in the opposite direction to the enlargement Fe = K . Δx Hooke´s law Where K is the spring constant and Δx is the extra-­‐lenght of the spring b) Weight Force with which a planet attracts a body with mass. UNIT 2: FORCES, DYNAMICS – YAIZA SCHMÖHE OLLERO 3 W = m . g (towards the centre of the planet!!!) Where g = 9,8 m/s2 on Earth but varies from one planet to another. NOTE: Weight is a force, so is measured in NEWTONS, not kilograms! (mass is different from weight!) c) Normal Support force that any surface does when an object is placed on it so that the object doesn´t sink. The normal force is the reaction of the surface and it is ALWAYS perpendicular to it. d) Tension Force from any string or cable attached to a body e) Friction Contact force that goes ALWAYS against the movement. Ffrict = µ • Fnorm where µ is the friction coeficient 4 3.2 Free body diagram: how to solve problems Whenever you have a dynamics problem, always follow these stops 1-­‐ Isolate the body from its surroundings 2-­‐ Identify all forces that act upon the body 3-­‐ Draw each of these forces with an arrow, each starting at the “gravitacional centre” of the body 4-­‐ Chose 2 axis: X and Y  decompose all forces into these 2 axis and calculate the net force on each axis. 5-­‐ Apply Newton´s law on each axis: a) FR = 0  there would be no movement in this axis b) FR ≠ 0  FR = m.a so there will be movement in this axis we can then compute the “a” for this axis and therefore the velocity and space that the object will move in a certain time. UNIT 2: FORCES, DYNAMICS – YAIZA SCHMÖHE OLLERO 5