Chapter 4 Forces and Newton s Laws of Motion 4 1 The concepts of force and mass Definitions Force what hurts Force is what makes things interact with each other Contact force easier to see Mass kg not the same as weight Weight what you don t want to see when you step on a scale Your weight will be different if you are on the moon Mass is the intrinsic property of something Doesn t change from one planet to another Noncontact force more general than we feel Gravity electric magnetic force cell phone remote 1 4 2 Newton s First Law of Motion An object continues to be at rest or moving with the same velocity both magnitude and direction without experiencing a force No force no change inertia measured by its mass Engines breaks forces to cause change in velocity 4 3 Newton s Second Law F ma Looks simple but hard to calculate vectors Break it down to components Fx max Fy may Solve the two components independently Once ax and ay are known we can use kinematics in two dimensions to solve the problems completely 2 Example Gravitational Force m2 F2 1 F1 2 m1 r F1 2 F2 1 G m1m 2 r2 M earth 5 98 x 10 24 kg and R earth 6 38 x 106 m G 6 673 x 10 11 N m2 kg2 F1 2 F2 1 G m1m 2 r2 G 6 673 x 10 11 N m2 kg2 universal constant on earth or anywhere else Direction along line connecting the masses attractive Example two 1 kg masses separated by 1 m Force 6 67 x 10 11 N very weak but this holds the universe together 3 4 4 Newton s Third Law Example Rita accelerates a 0 4 kg ball from rest to 9 m s during the 0 15 s in which her foot is in contact with the ball What average force does she apply to the ball during the kick If object 1 and object 2 interact the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1 F12 F21 Equivalent to saying a single isolated force cannot exist F12 may be called the action force and F21 the reaction force 4 Equilibrium Equilibrium Example An object either at rest or moving with a constant velocity is said to be in equilibrium The net force acting on the object is zero since the acceleration is zero F 0 5 Normal Force Normal Definition the direction perpendicular to a surface FN w book at rest on table weight w mg table support with FN FN normal force force exerted by surface on object FN is always perpendicular to surface and outward FN w 0 FN w this is NOT always true 6 Where is the normal force Tension T FN2 FN1 Tension force exerted by a rope or string Magnitude same everywhere in rope Not changed by pulleys Direction same as direction of rope 7 Example a Example If the elevator s full load m 10 000 kg what s the tension in the cable when it pulls up the elevator with a 5 m s2 T Both truck trailer have the same acceleration Ftotal ma T w ma y T w ma w T mg ma T m g a 10 000 9 8 5 T 148 000 N a Determine the tension T which pulls the trailer T T Fx T m2ax 27000 0 78 21000 N b Determine the force D that propels the truck Fx D T m1ax D m1ax T 8500 0 78 21000 28000 N 8 Multiple Objects Draw free body diagrams for each object Apply Newton s Laws to each object Find out the given quantities Solve the equations Connected Objects Apply Newton s Laws separately to each object The magnitude of the acceleration of both objects will be the same The tension is the same Solve the simultaneous equations 9 4 6 Forces of Friction Ignore friction find the acceleration fk kFN 10 Kinetic Friction Frictional force parallel to surface Magnitude is proportional to normal force fk k FN k coefficient of Kinetic friction 11 Static Friction fs s FN s coefficient of static friction Static friction can be any value up to sFN Direction always opposes the tendency of motion Don t drive without it 12