Newton’s Laws of Motion We have studied “kinematics”, or the description of motion. Now, we look at “dynamics”, the causes of motion

A little history – Galileo was the first to realize that objects in “uniform motion” require no “cause” for their motion. Only “changes” in motion accelerations require a cause: a force

Isaac Newton’s three simple laws are recognized as the foundation for all of physics. In the early 20 th century, however, it was discovered that Newton’s laws must be modified for objects moving near the speed of light (relativistic physics) or for objects on the atomic level (quantum physics). But for us, Newton’s laws are supreme !!!

A Force is - A “push” or a “pull” that acts on an object A “push” or a “pull” that acts on an object Something that is caused by an “agent” Something that is caused by an “agent” A vector - when you pull a cart the force you exert has both a magnitude (the amount of force) and a direction A vector - when you pull a cart the force you exert has both a magnitude (the amount of force) and a direction Forces are represented by vector arrows Forces are represented by vector arrows Measured in units of newtons (N) in the metric system and pounds (lbs) in the English system Measured in units of newtons (N) in the metric system and pounds (lbs) in the English system A newton (N) is the amount of force needed to accelerate A newton (N) is the amount of force needed to accelerate a 1.0 kg mass at a rate of 1.0 m/s 2. So a N = kg * m/s 2 So a N = kg * m/s 2

Types of Forces There are two basic types of forces – Contact force - the forces existing between two or more objects in contact with each other. Example – tension, friction, applied force, normal force Field force - a force exerted through space not requiring contact. Example – gravity, magnetic forces, electrostatic forces

Types of Forces, cont. Weight – the force of gravity on a mass Weight – the force of gravity on a mass W = F g = mg (mass * “g” acceleration) Normal force – when a surface pushes back Normal force – when a surface pushes back This normal force is always perpendicular to the contact surface. (F N ) Tension – force applied through a rope or chain (T) Tension – force applied through a rope or chain (T) Spring - the force exerted by a stretched or Spring - the force exerted by a stretched or compressed spring (F k ) Friction – force resistant to motion acting between two surfaces (f or F f ) Friction – force resistant to motion acting between two surfaces (f or F f )

Force Diagrams Also called FBD – “free body diagrams” Also called FBD – “free body diagrams” A diagram which A diagram which Uses a dot to represent the center of mass of an object Uses a dot to represent the center of mass of an object Places the tail of the vector on the object and points in the same direction that the force acts Places the tail of the vector on the object and points in the same direction that the force acts A book on a table –FBD – The vectors are forces acting only on the book. W (weight force) F N ( normal force)

Newton’s First Law Law of Inertia Inertia – the tendency of a body at rest to remain at rest or, if in motion, to remain in constant motion (no acceleration) Review - acceleration is a change in velocity – either in magnitude or direction. So if an object maintains constant velocity, its motion never changes, it does not accelerate. It does not slow down or speed up nor does it change direction. Sometimes inertia is referred to as “laziness” – and the mass of an object is a direct measure of its inertia or laziness. The more massive something is, it has a greater tendency to be lazy – to not want to change. So a larger accelerating force is required to get it to change its motion. This first law is also called the law of balanced forces.

Newton’s Second Law F net = m * a Law of unbalanced forces Law of unbalanced forces There is a net force which causes the object to accelerate in the direction of the F net. There is a net force which causes the object to accelerate in the direction of the F net. Newton expressed this relationship as Newton expressed this relationship as a = F/m What does this tell us: For a given force, the acceleration is inversely proportional to the mass. For a given mass, the acceleration is directly proportional to the force.

If the forces on an object are balanced, then there is no net force and the object does not accelerate – it does not change its motion. Mathematically, we see that the vector sum of the forces acting on the body in both the horizontal and vertical directions is zero. A car traveling with constant velocity-  F x = F 1 + (-)F 2 = F 1 – F 2 = 0  F y = F N + (-)W = F N – W = 0 FNFN F1F1 W F2F2 The sum of all the forces is zero. The forces balance each other and the object is in a state of equilibrium. F net = m * a but accel = 0, so F net = m * 0 = 0

Just hangin’ around - Investigating tension forces Absolutely, fundamental and most important concept: In equilibrium, the horizontal forces must sum to zero In equilibrium, the horizontal forces must sum to zero and - the vertical forces must sum to zero. and - the vertical forces must sum to zero. 200 N Find all the horizontal and vertical forces. If the weight is 200 N down, there MUST be a 200 N tension up. 200 N - weight and up tension The up force comes from the wall. Using right triangle geometry, the tension force forms the hypoteneuse. Use this information to find the opposite and adjacent sides. These two must be equal and opposite.

Forces on surfaces - tryin’ to be normal Be careful – the normal force is ALWAYS perpendicular to the surface FnFn F g = mg Now, raise the surface to create an angled ramp N F g – you need to resolve this weight vector. Make it the hypoteneuse of a right triangle. By the geometry, these two angles are equal. This component balances the normal force. Find it as: mg cos θ This is the component of the weight acting downramp. Find it as: mg sin θ

Another situation - Draw the FBD Draw the FBD Determine both horizontal and vertical forces Determine both horizontal and vertical forces F N = 100N f = 5 N W = mg = 10 kg * 10m/s 2 = 100 N F = 25 N  F y = Fn – W = 100 – 100 N = 0 (no motion in the vertical direction)  F x = F – f = 25 – 5 N = 20 N net force a = F / m so 2 m/s 2 = 20 N / 10 kg

May the Net Force be with you Total force acting on an object Total force acting on an object Vector sum of all the forces Vector sum of all the forces The unbalanced force referred to in Newton’s Law of Motion The unbalanced force referred to in Newton’s Law of Motion Net force is equal to the mass of an object times the acceleration of that object. Net force is equal to the mass of an object times the acceleration of that object.  F = F net = m * a (Remember, in equilibrium an object is at rest or moving with a constant velocity. Either way, acceleration = 0 and there is no net force.)

Force Diagrams (FBD) A Review First case - (1) is in equilibrium (2) is accelerating N W F f N W F f SF y = N – W = 20 N – 20 N = 0 SF x = F – f = 10 N – 10 N = 0 SF x = F-f = 25N – 10 N = 5 N F net = 5 N F net = 0 no acceleration F net = ma 5 N = 2 kg (a) a = 2.5 m/s 2 SF y = N – W = 20 N – 20 N = 0

Forces at an angle Any vector at some angle  must be resolved into its x and y components. f N F W Notice - now the Fy works WITH the normal force.  Fy = (Fy + N) – W This means that the normal force actually decreases. Some of the weight is balanced by the upward lift of the pulling force. N W f F Notce – in this diagram, the Fy works WITH the weight.  Fy = N – (F y + W) This means that the normal force actually increases. There is more downward force and so the normal must respond to remain in equilibrium. The forward force comes from the x component and is opposite friction.

Newton’s Third Law Third Law deals with action-reaction force pairs. If you push on an object, the object pushes back. The two forces are equal but opposite in direction. AND – the two forces work on two DIFFERENT objects.