Chapter 4 Forces in One Dimension

4.1 Force and Motion Force – A push or a pull exerted on an object. May cause a change in velocity:  Speed up  Slow down Any change in velocity is acceleration Therefore a force causes acceleration Forces are vector quantities  Direction  Magnitude

Contact Forces Caused when an object in the external world (an “agent”) touches a system thereby exerting a force upon it System is the object of interest:  A puck hit by a hockey stick  A book pushed off the table by a hand Without an agent and a system, a force cannot exist

Free-body Diagrams See page 89 Sketch situation Label agent and system Show forces as arrows pointing in the direction that the force is applied Indicate which way is positive (usually up!)

Force and Acceleration The greater the force, the greater the resulting acceleration They are directly proportional Newton’s Second Law states that  a = F/m  F = ma F is measured in newtons (N) 1 N = 1kg. m/s 2

Net Force (F net ) Vector sum of all forces See Figure 4-5 page 92

Newton’s First Law An object that is at rest will remain at rest and an object that is moving will continue to move in a straight line with constant speed, if and only if the net force acting on the object is zero Also known as inertia (the tendency of an object to resist any change in motion)

Equilibrium If no net forces are acting on an object is said to be at equilibrium

4.2 Using Newton’s Second Law Fg = mg Fg (Force of gravity) is weight  Fg is always (-)  Weight is always (-) Weight changes with location because gravity differs…that’s why we weigh less on the moon Mass does not change with location because it doesn’t depend on gravity

Apparent Weight Equal to the weight of the object plus the net force acting on it See Problem 2 on page 99 Weightlessness is a factor of apparent weight. This does not mean that the object has no weight, rather there are no upward contact forces acting on it. Fscale = mg + ma (going up) Fscale = mg – ma (going down)

Drag Force Drag force is experienced by any object moving through a fluid  Gas (like air)  Liquid (like water) The magnitude of the drag force increases with the speed of the object moving through the fluid

Terminal Velocity Object is dropped and accelerates as gravity acts upon it As the velocity increases, so does the drag force of the air acting against gravity When gravity pulling down equals drag force pushing up the object stops accelerating This constant and final velocity is called “terminal velocity”

4-3 Interaction Forces Newton’s Third Law  All forces come in pairs  F AonB = -F BonA Interaction pair  Also called action-reaction pair  Two forces that are opposite in direction but equal in magnitude

Example: Action-Reaction Pair

Forces of Ropes & Strings Tension – a force exerted by a string or rope  Is equal to the weight of the object hanging on the rope/string  F net = Sum of the positive force of a rope pulling up and the negative force of gravity pulling down  F net = F T + (-F g )

Normal Force Perpendicular contact force exerted by one surface on another May be equal to the weight of an object or…  Less than the weight if an additional upward force is exerted  More than the weight if an additional downward force is exerted  See Figure 4-16 on page 107