2Isaac Newton Arguably the greatest physical genius ever. Came up with 3 Laws of Motion to explain the observations and analyses of Galileo and Johannes Kepler.Invented Calculus.Published his Laws in 1687 in the book Mathematical Principles of Natural Philosophy.
3What is Force? A force is a push or pull on an object. Forces cause an object to accelerate…To speed upTo slow downTo change direction
4Newton’s First Law The Law of Inertia. A body in motion stays in motion at constant velocity and a body at rest stays at rest unless acted upon by an external force.This law is commonly applied to the horizontal component of velocity, which is assumed not to change during the flight of a projectile.
5The First Law is Counterintuitive Aristotle firmly believed this.But Physics B students know better!
11Newton’s Second LawA body accelerates when acted upon by a net external force.The acceleration is proportional to the net force and is in the direction which the net force acts.This law is commonly applied to the vertical component of velocity.
12Newton’s Second Law ∑F = ma where ∑F is the net force measured in Newtons (N)m is mass (kg)a is acceleration (m/s2)
13Units of force Newton (SI system) 1 N = 1 kg m /s21 N is the force required to accelerate a 1 kg mass at a rate of 1 m/s2Pound (British system)1 lb = 1 slug ft /s2
14Newton’s Third LawFor every action there exists an equal and opposite reaction.If A exerts a force F on B, then B exerts a force of -F on A.
15Step 1: Draw the problem Working a Newton’s 2nd Law Problem Larry pushes a 20 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N. What is acceleration?20 kgFLFM
16Step 2: Diagram Working a Newton’s 2nd Law Problem Force diagram N FM FLFMFGN20 kgFLFMFGNForce diagramFree Body diagram
17Step 3: Set up equations F = ma Fx = max Fy = may Working a Newton’s 2nd Law ProblemStep 3: Set up equationsF = maFx = maxFy = mayAlways resolve two-dimensional problems into two one-dimensional problems.
18Step 4: Substitute Make a list of givens from the word problem. Working a Newton’s 2nd Law ProblemStep 4: SubstituteMake a list of givens from the word problem.Substitute in what you know.
19Step 5: Solve Plug-n-chug. Calculate your unknowns. Working a Newton’s 2nd Law ProblemStep 5: SolvePlug-n-chug.Calculate your unknowns.Sometimes you’ll need to do kimematic calculations following the Newton’s 2nd law calculations.
20Gravity as an accelerating force A very commonly used accelerating force is gravity. Here is gravity in action. The acceleration is g.
21Gravity as an accelerating force In the absence of air resistance, gravity acts upon all objects by causing the same acceleration…g.
22Gravity as an accelerating force The pulley lets us use gravity as our accelerating force… but a lot slower than free fall. Acceleration here is a lot lower than g.
232-Dimensional problemLarry pushes a 20 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N.a) What is the acceleration?b) What is the normal force?FLFMFGN20 kg
24The problem of weight Are weight and mass the same thing? No. Weight can be defined as the force due to gravitation attraction.W = mg
25Flat surfaces – 1 DN = mg for objects resting on horizontal surfaces.Nmg
26Ramps – 2 D N mg N = mgcos The normal force is perpendicular to angled ramps as well. It’s always equal to the component of weight perpendicular to the surface.N = mgcosNmgcosmgsinmg
27Ramps – 2 D N mg N = mgcos How long will it take a 1.0 kg block to slide down a frictionless 20 m long ramp that is at a 15o angle with the horizontal?N = mgcosNmgcosmgsinmg
28Applied forces affect normal force. frictionapplied forceweightnormalN = applied force
31Friction The force that opposes a sliding motion. Enables us to walk, drive a car, etc.Due to microscopic irregularities in even the smoothest of surfaces.
32There are two types of friction Static frictionexists before sliding occursKinetic frictionexists after sliding occursIn general fk <= fs
33Friction and the Normal Force The frictional force which exists between two surfaces is directly proportional to the normal force.That’s why friction on a sloping surface is less than friction on a flat surface.
34Static Friction fs sN fs : static frictional force (N) s: coefficient of static frictionN: normal force (N)Static friction increases as the force trying to push an object increases… up to a point!
35A force diagram illustrating Static Friction Normal ForceFrictional ForceApplied ForceGravity
36A force diagram illustrating Static Friction Normal ForceBigger Applied ForceBigger Frictional ForceGravity
37A force diagram illustrating Static Friction The forces on the book are now UNBALANCED!Normal ForceFrictional ForceEven Bigger Applied ForceGravityStatic friction cannot get any larger, and can no longer completely oppose the applied force.
38Kinetic Friction fk = kN fk : kinetic frictional force (N) k: coefficient of kinetic frictionN: normal force (N)Kinetic friction (sliding friction) is generally less than static friction (motionless friction) for most surfaces.
39Determination of the Coefficients of Friction Coefficient of Static FrictionSet a block of one material on an incline plane made of the other material.Slowly increase angle of plane until the block just begins to move. Record this angle.Calculate s = tan.
40Determination of the Coefficients of Friction Coefficient of Kinetic FrictionSet a block of one material on an incline plane made of the other material.Slowly increase angle of plane until the block just begins to move at constant speed after giving it a slight tap. Record this angle.Calculate k = tan.