9/5/2006PHY 101 Week21 The Laws of Motion …or, Newtonian mechanics

9/5/2006PHY 101 Week22 1.The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0. 2.Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma. 3.Action and reaction. For every action there is an equal but opposite reaction. Newton’s Laws of Motion

9/5/2006PHY 101 Week23 Newton’s second law

9/5/2006PHY 101 Week24 Newton’s second law of motion F = m a F = force acting on the moving object, a vector m = mass of the moving object a = acceleration of the moving object, a vector If the force is known, Newton’s second law states how the object (on which the force is acting) accelerates: What is “force?” What is “mass?”

9/5/2006PHY 101 Week25 Force and acceleration are vectors. A vector has both magnitude and direction.

9/5/2006PHY 101 Week26 Three kinds of acceleration m slows down m speeds up m changes direction

9/5/2006PHY 101 Week27 UNIFORM CIRCULAR MOTION

9/5/2006PHY 101 Week28 Example The “string tension” is the strength of the force exerted by the string at either end. Centripetal acceleration (Christian Huygens,1673) Therefore, the force on m is

9/5/2006PHY 101 Week29 Analyze free fall including air friction The aerodynamic drag force (C) depends on the size, shape and surface roughness; it is about the same for both balls. The gravitational acceleration (g) is independent of mass. Effect of air is inversely proportional to mass: heavy --- small effect of air light --- large effect of air

9/5/2006PHY 101 Week210 Newton’s third law

9/5/2006PHY 101 Week211 Which vehicle exerts a greater force ― the tow truck or the car?

9/5/2006PHY 101 Week212 1.The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0. 2.Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma. 3.Action and reaction. For every action there is an equal but opposite reaction. Newton’s laws of motion Action means force.

9/5/2006PHY 101 Week213 force on B due to A force on A due to B Newton’s third law We will see than this is very hard to accept! It is just not common sense. That is why it took a great genius like Newton to figure it out. Whenever one object exerts a force on another object, the second object exerts an equal but opposite force on the first object. Forces always occur like this, in pairs. For every action there is an equal but opposite reaction.

9/5/2006PHY 101 Week214 Example – A collision

9/5/2006PHY 101 Week215 Universal Gravitation --- an example of Newton’s third law

9/5/2006PHY 101 Week216 The Earth pulls the apple down (“action”). The apple pulls the Earth up (“reaction”). The two forces are equal (but opposite).

9/5/2006PHY 101 Week217 When does a scientific theory become an accepted fact?

9/5/2006PHY 101 Week218 The truck pulls to the right. According to Newton’s third law, the car pulls to the left with an equal force. So how can they start moving, or accelerate? A puzzle: Resolution: Consider each part separately, and don’t forget that other forces are also acting.

9/5/2006PHY 101 Week219 Harold Edgerton’s high speed photograph of Wes Kessler kicking a football. The force exerted by the ball on the toe (reaction) is equal to the force exerted by the toe on the ball. Really hard to accept!

9/5/2006PHY 101 Week220 Momentum, p = mv Total momentum is conserved: Proof

9/5/2006PHY 101 Week221 The four fundamental forces Gravity Electromagnetic Strong nuclear force Weak nuclear force unified by Maxwell’s theory not really a force, but an interaction that causes certain radioactive decays comes from QCD, the interaction of quarks and gluons

9/5/2006PHY 101 Week222 FIN

9/5/2006PHY 101 Week223 Newton’s second law and calculus differential equation Isaac Newton invented calculus to solve the equation of motion – to calculate motion for the force that is acting. Generally, calculus is the mathematics that describes continuous change.