Newton’s Laws of Motion

1. 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)

2. 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

3. B B A A vB vA • 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

4. 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?

5. 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

6. 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?

7. 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

8. 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

9. 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?