Which set of weights will the strong man be able to lift faster?

Not exactly a challenging question, eh? Isaac Newton figured out that this relationship between force F, mass m and acceleration a could be expressed mathematically: F = ma Which is the same as a = F/m And m = F/a

 If there is a net force on an object, the object accelerates. ◦ Its acceleration is directly proportional to the net force ◦ Its acceleration is inversely proportional to the object’s mass ◦ Its acceleration is in the same direction as the net force.

 If the net force doubles, the acceleration doubles.  If the net force triples, the acceleration triples.  If the net force is half as much, the acceleration is half as much.  Etc.

 If the object’s mass doubles, its acceleration will be half as much.  If the object’s mass triples, its acceleration will be one-third as much.  If the object’s mass is half as much, its acceleration doubles.  Etc.

 Mass measures the inertia of an object.  All objects made of matter have inertia - that is, they resist accelerations (Newton’s First Law), but some objects resist more than others.  Mass is a scalar quantity.  SI unit of mass is the kilogram (kg).

 In symbols: a = F net m F net = ma F net m a

A = F/m A = (80 N)/(0.045 kg) A = … ~ 1800 m/s 2

F = ma F = (0.08 kg)(200 m/s 2 ) F = 16 N

m = F/a m = (80 N)/(120 m/s 2 ) m = 0.67 kg

30 kg Force Applied = 300 NForce Friction = 25 N What is the net (overall) force acting on this object? What happens to the object as a result – what is its acceleration?

30 kg Force Applied = 300 NForce Friction = 25 N Net force = Force Applied – Force Friction = -25 N N Net Force = 275 N 25 N 300 N 275 N

30 kg Force Applied = 300 NForce Friction = 25 N Net Force = 275 N Acceleration = Net Force mass Acceleration = 275 N 30 kg Acceleration = 9.1 m/s 2

Net Force = (500 N – 80 N) = 420 N to the right Acceleration = Net Force/mass Acceleration = (420 N)/(30 kg) Acceleration = 14 m/s 2 30 kg Force Applied = 500 NForce Friction = 80 N

Net force = 255 N N – 18 N Net force = 432 N Acceleration = Net force/mass Acceleration = (432 N)/(25 kg) Acceleration = m/s 2 25 kg Force Applied = 195 N Force Friction = 18 N Force Applied = 255 N

 There are 2 major preconceptions to address: ◦ Mass is not the same as weight. ◦ Force is not the same as pressure.

 Mass is a property of an object that measures how much it resists accelerating.  An object is difficult to accelerate because it has mass.

 Weight is a force - an interaction between 2 objects involving a push or a pull. One of these objects is typically VERY big - the Earth or the Moon, for instance.  Weight is NOT a property of an object.

 The weight of an object depends on the object’s mass. ◦ In fact, an object’s weight is directly proportional to the object’s mass.  The weight of an object also depends on the object’s location. ◦ In fact, an object’s weight is directly proportional to its free fall acceleration, g at its current location.

 In symbols: W = mg W m g

 Since W = mg, the weight of a 1 kg object is: ◦ W = (9.8 m/s 2 )(1 kg) = 9.8 N on Earth ◦ W = (1.6 m/s 2 )(1 kg) = 1.6 N on the Moon

 We typically think that an object is difficult to accelerate because it is heavy (has weight) - but it is heavy because it has mass.  So, objects are difficult to accelerate because they have mass.

 Force determines how much an object will accelerate.  Pressure determines how that acceleration will feel.

 The pressure exerted on an object depends on:  The force exerted on the object.  In fact, pressure is directly proportional to force.  The area over which the force is applied. ◦ In fact, pressure is inversely proportional to area.

 A force of 1 N applied over an area of 1 m 2 exerts a pressure of 1 Pascal.  Another common unit of pressure is pounds per square inch (lb/in 2 ).

 In symbols: P = F A F AP

 Video clips: ◦ Newton’s Law 2 on FMA Newton’s Law 2 on FMA ◦ Newton’s 2 nd Law of Motion (1) Newton’s 2 nd Law of Motion (1) ◦ Newton’s 2 nd Law of Motion (Hewitt) Newton’s 2 nd Law of Motion (Hewitt) ◦ How acceleration is produced (Hewitt) How acceleration is produced (Hewitt)  Interactive: ◦ pushing an elephant pushing an elephant ◦ Online text with occasional self-quizzes Online text with occasional self-quizzes