Forces

Force – a push or a pull Contact – a force acting on a body by touching it Long-range – force exerted on a body w/o contact (gravity, magnetic force, electrical force)

Newton’s 2 nd Law The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass. F = ma a = F/mm = F/a Units: kg m/s 2 = Newton (N) Newton's Second Law of Motion

Plot Force Vs. Acceleration for the following carts: cart 1 = m cart 2 = 2m cart 3 = 3m

Net Force – vector sum of all forces acting on a body acceleration = F net /m Only net forces cause accelerations!!

Free-Body Diagrams Include all forces acting on the body Include weight (Wt), the normal force (F n ), or tension if necessary (F T ) Then identify the net force and its direction The direction of the net force indicates the direction of the acceleration of the body

Equilibrium Equilibrium = balance = the sum of all of the forces acting on a body is zero (net force is zero) Static equilibrium = the object is at rest Dynamic equilibrium = the object is moving at constant velocity In each case the net force is zero (there is no acceleration therefore no net force)

Mass versus Weight Mass is the amount of matter in an object and is measured in kilograms Weight is the gravitational force exerted by a large body (Earth) on a mass and is measured in Newtons Wt = m(a) Weights may vary, but mass remains constant

Newton’s 2 nd Law: The Elevator Ride F net = F T + (-Wt) Where F T = the tension force acting upwards and Wt = weight that acts downwards

At rest: F net = 0so: 0 = F T + (-Wt) F T = Wt Accelerating Upward: F net = m(a)so:m(a) = F T + (-Wt) F T = m(a) + mg

Constant Velocity F net = 0so: 0 = F T + (-Wt) F T = Wt Decelerating Upwards F net = m(-a)so:m(-a) = F T + (-Wt) F T = m(-a) + mg

Weightlessness & Apparent Weight Apparent weight – the weight of an object that is sensed as a result of contact forces on it.  For instance, if you were on a scale and someone pushed down on you, the scale would read more  If you and the scale attached were freefalling, it would read zero b/c both would be accelerating in the same direction….ie.: astronauts on the space shuttle orbiting the Earth…the shuttle is freefalling while the astronauts freefall…they “float” b/c of the “apparent forces” Weightlessness- apparent weight is zero. There are no contact forces pushing up on you

Newton’s 1 st Law Newton’s 1 st law states: “an object that is at rest will remain at rest or an object that is moving will continue to move in a straight line with constant speed” unless acted upon by an unbalanced force. Inertia - the tendency of an object to resist change

Examples of Inertia Turning a corner sharply in a car… The Scrambler at the amusement park… Pulling a tablecloth off of a table without disturbing the dishes… The potato on the knife…

Friction Friction – the force that opposes the motion between two surfaces that are in contact. This force is caused by the electromagnetic force b/t the two surfaces.  All surfaces, even smooth are rough at the microscopic level. When surfaces start to move, a weaker kinetic friction results.  The details of this process are still unknown!  We simplify our calculations using a model

Model of Friction This model makes two assumptions: 1.Friction depends on the surfaces in contact 2.Friction does not depend on the area of surfaces in contact Example: a block of wood flat on the desk vs. on its side

Static Friction Static Friction (Starting Friction) – the force that opposes the start of relative motion between two surfaces in contact ***these are maximum values*** When the magnitude of the force exerted exceeds the maximum value of static friction, the object will move Once the object starts to move, the force of friction DECREASES

Kinetic Friction Kinetic Friction (Sliding Friction) – the force exerted on one surface by the other when surfaces are in relative motion ***these values are always less than static friction*** F f kinetic < F f static Other examples: Rolling Friction- less than sliding friction Fluid Friction- friction in a fluid body (gas or liquid)

Force of Friction The magnitude of the frictional force (F f ) is proportional to the magnitude of the force pushing one surface against the other F f kinetic = μ k F N F f static = μ s F N Coefficient of Friction = μ (mu) – proportionality constant for surfaces in contact

Air Resistance ~ Drag When objects move through the air, they experience fluid friction or air resistance As the object accelerates (freefall), air resistance INCREASES Air resistance depends on: 1.Velocity of the object 2.Surface area 3.Shape 4.Density of the fluid

As velocity increases, so does the drag force Eventually, the weight = drag At this point, the body no longer accelerates ~ terminal velocity TERMINAL VELOCITY – the constant velocity that is reached when drag force equals the force due to gravity (dynamic equilibrium)

Newton’s 3 rd Law Newton’s 3 rd Law – all forces come in pairs; equal in magnitude, opposite in direction Interaction Pair (action-reaction pair) = two forces that are in opposite directions and have equal magnitudes ***common misconception*** action-reaction forces act on different objects therefore, equilibrium does not result (the normal force and weight are not action- reaction forces!) YouTube - Newton's 3rd Law - Science Theater 09

Inclines

Hanging Signs Solving using the component method: x = F cos θ y = F sin θ Add the x and y components Use Pythagorean Theorem to find R The magnitude of R is the magnitude of the weight of the sign The direction of the weight is down