Forces and the Laws of Motion Fresistance Fforward Fground-on-car Fgravity

Force A force is a push or a pull on an object An object’s motion will change with time if the forces acting on it are unbalanced Change in motion  change in velocity Change in velocity  acceleration If the forces are balanced the object’s motion will not change No change in motion  velocity is constant Velocity is constant  acceleration is zero

Force (cont.) There are two kinds of force: Contact forces Field forces Contact forces happen when objects touch Field forces act at a distance Gravity Electrostatic forces Magnetic forces

Force (cont.) Force is a vector To find out if the forces on an object are balance or unbalanced, we must add them as vectors A free-body diagram shows all the forces on an object Fresistance Fforward Fground-on-car Fgravity

Newton’s First Law An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless the object experiences a net external force “At rest” means zero velocity “Net force” means the forces are unbalanced and do not add up to zero “External force” means the force comes from outside the object itself

Newton’s First Law (cont.) The tendency of an object with mass to resist a change in motion is called inertia Newton’s first law is called the law of inertia: it says that without a net force an object’s motion will remain unchanged Mass gives objects the property of inertia The greater the mass, the greater the inertia

Equilibrium If all of the forces acting on an object add to zero, the object is in equilibrium The forces acting on the object are balanced Net force equals zero Equilibrium means zero acceleration The object is at rest, or The object is moving with constant velocity

net force = mass  acceleration Newton’s Second Law The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass: a = F/m F = ma net force = mass  acceleration

Newton’s 2nd (cont.) F is the vector sum of all external forces acting on the object Net force (F) and acceleration (a) are in the same direction When a is zero, F is zero, and vice versa a = 0  F = 0 The net force (F) is sometimes called Fnet

Unit of Force: The Newton Because F = ma, force has units of mass (kg) times acceleration (m/s2) Define the newton, N, as 1 N = 1 (kgm)/s2 One newton is about 0.225 pounds of force One pound of force is about 4.45 N

Example of Newton’s 2nd: Two boys are pulling on a 5.2-kg wagon in opposite directions. B1 is pulling to the right with a force of 38 N, and B2 is pulling to the left with a force of 17 N. What is the wagons acceleration? F = F1 – F2 = 38 N – 17 N = 21 N (to the right) m = 5.2 kg a = F/m = (21 N)/(5.2 kg) = 4.0 m/s2 (to the right)

Component Version of 2nd Law The equation F = ma is not very useful as is! We often use this equation in component form to solve problems: Fx = max Fy = may where Fx = sum of forces in x-dir. = x-comp of F Fy = sum of forces in y-dir. = y-comp of F ax = x-comp of accel. ay = y-comp of accel.

Example

Newton’s Third Law The magnitude of the force exerted on Object 1 by Object 2 is equal to the magnitude of the force exerted on Object 2 by Object 1, and these two forces are opposite in direction The two forces act on different objects: One force acts on Object 1 The other acts on Object 2 Field forces also exist in pairs Example: Earth/Moon System Force on Earth is same size as force on Moon F

Everyday Forces Ff The three most common forces: Weight, Fg Normal Force, FN Friction Force, Ff Ff FN

Weight Weight is the force of Earth’s gravity on an object Symbol: Fg Direction: toward the center of the Earth Magnitude: Fg = mg where g = 9.80 m/s2 on the surface of Earth Weight is a “field force” (no contact required)

Normal Force Normal Force is the contact force of a surface on an object Symbol: FN Direction: perpendicular to the surface Magnitude: Is determined by analyzing the y-direction  FN Fg Ff

Friction Force Friction force is caused by surfaces sliding over each other Symbol: Ff Direction: Opposite the motion of the object Magnitude: If object is sliding, Ff = FN where  = coefficient of kinetic friction Air resistance is a form of friction (it always opposes the motion)

Example A box of books is being dragged across the ground ( = 0.81) by a rope (FA = 170 N, 33 from horizontal). If m = 15 kg, calculate ax. Fx = FAcos  Ff = max  ax = (FAcos  Ff) We would be done except we don’t know Ff How do we get Ff? m = 15 kg ax = ? FA = 170 N   = 33  = 0.81 FA Fg FN Ff 1 m

Fy = FAsin + FN  Fg = may = 0  FN = Fg  FAsin = mg  FAsin = (15 kg)(9.8 m/s2)  (170 N)sin(33) = 54.4 N Ff = FN = (0.81)(54.4 N) = 44.1 N ax = [(170 N)cos(33)  44.1 N] = 6.6 m/s2 1 (15 kg)