1Chapter 4Newton’s Second Law of Motion22Force and Acceleration• Acceleration is caused by force• We commonly encounter force as a pushing or pulling• We also encounter the force of friction (a resistance caused by rubbing)• Fluids also apply frictional forces (air resistance, etc.)force ~on acceleratiAcceleration is directly related to the amount of force being exerted.33Mass and Weight• Mass – the amount of matter in an object• Weight –the force on or of a mass due to gravity• Mass and weight are often confused:– Astronauts in space are weightless because they feel no gravity but they have lost no matter so they still have that same mass• Do dieters loss weight or mass? What does a bathroom scale measure?–Dieters loss mass. A scale measures weight, but since g is constant, a loss in weight represents a loss of mass.Well, dieters lose both weight and mass… But they are truly losing mass since g has not changed (think of the astronauts in space… Since they are weightless, if they would go on a diet, they would only lose mass).44Newton’s Second Law• “The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object”:• Force is a vector• The unit of force is called a Newton (N)maF =The more mass, the more the object resists acceleration – inertia.If something is inversely proportional, that means that it varies like 1/something.55Free Fall Revisited• Last lecture we discussed free fall – the motion of an object falling only under the influence of gravity• We also discussed that air resistance is a form of friction• So, an object falling in air is not really in free fall (but we often pretend it is since the effect is usually small)If the acceleration of an object is less than g, it is not truly in free fall since there must be a resistive force being applied.66Terminal Velocity• Consider paratrooper:– As the paratrooper’s velocity increases, so does the air resistance. Once the air resistance balances the force of gravity, his velocity is constant.• Terminal velocity is reached when there is zero net force on a falling objectAdd picture of a paratrooper and discuss that the parachute serves to increase the paratrooper’s air resistance so that his fall is slowed faster (preferably before he hits the ground).77The ParatrooperThe acceleration goes in the up direction after the parachute is released because the paratrooper is slowing down, he is not moving up.88Problem Solving: Forces• What is the gravitational force on a 3 kg stone?, a 1 kg stone?–The force on each stone is different:3 kg: 1 kg:BUT they will hit the ground at the same time!NkgF4.29 m/s/s)8.9)(3(==9.8N /s)kg)(9.8m/s1(==FThe force and mass always balance out so that everything falls at the same rate, g.9Chapter 5Newton’s Third Law of Motion1010Forces as Interactions• We have referred to forces as pushes and pulls but a force is more correctly an interactionbetween objects• Sitting in your chair, your weight is a force down on a chair, but since you are not moving, there must be zero net force• For there to be zero net force between you and the chair, the chair must be pushing back up on you!1111Newton’s Third Law• “Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first”• It is not that your chair consciously pushes back on you, it is just that you have not overcome its inertia to make it moveMake the example of how two people leaning together push back on each other without the person making an effort to push back.You cannot touch without being touched.1212Summary of Newton’s Laws•1st: Mass is a measure of inertia•2nd: Acceleration is in the same direction and proportional to force, mass resists acceleration•3rd: Forces always come in pairs; you cannot touch without being touchedThe fact that mass resists accelerations (2nd) is a direct consequence of the 1stlaw.1313More on Vectors• Recall: a vector is a quantity with both a magnitude and direction• All vectors can be broken down into horizontal and vertical components• When you add vectors, you add them head to tail• It does not matter what order you add vectorsComment on how the size of the horizontal and vertical components represent the magnitude of the component vector.1414Adding VectorsRevisit the idea of adding vectors head to tail.1515Adding VectorsIt does not matter what order you add vectors