Newton’s Laws of Motion Newtonian mechanics (aka Classical mechanics) Forces The ‘cause’ of acceleration (must be vectors) Arise from interactions between objects Contact forces Long range forces Four Fundamental Forces Gravity, Electromagnetism, Weak Nuclear Force, Strong Nuclear Force Units: Newtons Net Force on an object = vector sum of all forces acting on that object Superposition of forces (demo)

Newton’s first law: Inertia A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration. or An object at rest will remain at rest and an object in motion will remain in motion (at constant velocity) unless acted upon by an external force. Inertia: the resistance of an object to changes in it’s motion. Equilibrium: no net force Inertial frame of reference: a frame of reference in which the law of inertia holds A non-accelerating frame of reference vP/A = vP/B + vB/A

Mass is a measure of inertia Relative mass = relative inertia Newton’s second law Mass is a measure of inertia Relative mass = relative inertia mB/mA = vA/vB Force and acceleration: the 2nd Law  F = ma Force units: newton (N) 1 N = 1Kg • 1m/s2 Components  Fx = max  Fy = may  Fz = maz A B vA vB

A horizontal force of 10. 0 N is applied to a 2 A horizontal force of 10.0 N is applied to a 2.00 kg block which is initially at rest on a smooth (i.e. frictionless) level surface. Find the acceleration, speed and displacement of the block after it has gone for 3.00 s. n FA w A mass of 2.00 kg is propelled across a rough horizontal surface with an initial speed 3.00m/s and comes to a rest in a distance of 1.50 m. What is the magnitude and direction of the force of friction which slows the mass?

Weight: the force exerted by earth (via gravity) on an object In free fall, gravity is the only force acting on the object F = ma = mg = w Weight = (mass)(local acceleration of gravity) g varies from 9.78 to 9.82 m/s2 over the surface of the earth g is a vector field! Inertial Mass vs Gravitational mass F = mInerta mgravg = w It is believed that mInert = mgrav for all matter  all things fall at the same rate

english units 1 pound = 1slug ft/s2 (g =32 ft/s2) Some notes on units cgs units 1 dyne = 1g cm/s2 english units 1 pound = 1slug ft/s2 (g =32 ft/s2) 1 kg = weighs 2.2 pounds english engineering units: pounds mass versus pounds force Watch for implied quantities! (weight vs mass!) Example 4.7: A 1.96E4 N car traveling in the +x-direction makes a fast stop. The x-component of the net force acting on it is –1.50E4 N. What is the acceleration?

Newton’s third law: action/reaction When an object exerts a force on a second object, the second object exerts a force on the first of equal magnitude, but opposite direction. The action and the reaction are forces on two different bodies! For every action there is an equal but opposite reaction. Forces arise from interactions! Forces on an Object Action/Reaction reaction force of table on computer reaction force of table on computer force of computer on table weight of computer

Using Newton’s laws Define coordinate system note direction of acceleration use coordinates consistently (+ dir for r, v, F, a) Apply laws to a single body Draw a free body diagram indicate all forces acting on an object in simple diagram Identify known and unknown quantities components with correct sign Use Newton’s laws to relate quantities Check units consistency in your answer

A 200 kg mass is suspended from a chain. what is the weight of the mass? what is the tension in the chain? A 200 kg mass is suspended from a 10 kg chain. what is the weight of the mass? what is the tension at the bottom of the chain? what is the tension in the top of the chain? what is the tension in the middle of the chain?