1. Applications of Force ► Anyone who has never made a mistake has never tried anything new. -Albert Einstein Albert EinsteinAlbert Einstein ► Overview  Vector Components  Force Lab  Review of Common Forces (Dynamics)  Free Body Diagrams  Incline Planes  Multi-mass Problems  Static Equilibrium and Torque  Atwood Machine Lab  Momentum and Collisions

2. Vector Components ► Motion is rarely in a straight line. We need to analyze forces and motion that follows curved lines or motion that changes direction abruptly. ► Motion Equations: The Big Four  Uniform motion (constant velocity) ► V = Δd Δt (velocity and displacement) Δt (velocity and displacement)

3. ► Uniformly accelerated motion  A = v 1 – v 2 Δt Δt 1.V = v i + at 2.d = (v 1 + v 2 )t The Big Four 2 3.d = v i t + ½ at 4.v f 2 = v i 2 + 2ad

4. Vector Addition and Subtraction ► In Physics 11 we solved vector problems graphically ► Now we will use trig and right angles in a more precise method vectors at right angles (SOHCAHTOA) rarely vectors are at right angles so we will resolve the vectors into their will resolve the vectors into their components components

5. Vector Addition ► Step 1: resolve all vectors into their x and y components (be careful to indicate if the components are negative or positive – what quadrant they are in) ► Step 2: calculate the total x and y components by addition ► Step 3: draw a summary right angle triangle and use the pythagorean theorem to calculate the hypotenuse (resultant) and angle (direction)

6. Vector Components and Dynamics ► Newton’s 1 st and 2 nd laws of motion are:  An object at rest or in uniform motion will remain at rest or in uniform motion unless acted upon by an external force  F(net) = ma net force is the vector sum of all the forces acting on a body

7. Equilibrium - Stationary ► When the net forces add to zero the body is said to be at equilibrium. ► The force that will counter the net force to make the body stationary is called an equilibriant. ► Problem: calculate the equilibriant for the forces: F 1 – 425 N [E 63° N] F 1 – 425 N [E 63° N] F 2 – 385 N [W 15° N] F 2 – 385 N [W 15° N]