Chapter 4 The Laws of Motion. Forces Usually think of a force as a push or pull Usually think of a...

Chapter 4Chapter 4

The Laws of MotionThe Laws of Motion

ForcesForces

Usually think of a force as a push Usually think of a force as a push or pullor pull

Vector quantityVector quantity May be contact or field forceMay be contact or field force

Contact and Field ForcesContact and Field Forces

Newton’s First LawNewton’s First Law

If no forces act on an object, it If no forces act on an object, it continues in its original state of continues in its original state of motion; that is, unless something motion; that is, unless something exerts an external force on it, an exerts an external force on it, an object at rest remains at rest and object at rest remains at rest and an object moving with some an object moving with some velocity continues with that same velocity continues with that same velocity.velocity.

Newton’s First Law, cont.Newton’s First Law, cont. External forceExternal force

any force that results from the interaction any force that results from the interaction between the object and its environmentbetween the object and its environment

Alternative statement of Newton’s Alternative statement of Newton’s firstfirst LawLaw When there are no external forces acting When there are no external forces acting

on an object, the acceleration of the on an object, the acceleration of the object is zero.object is zero.

Inertia – proportional to Inertia – proportional to massmass

Is the tendency of an object to Is the tendency of an object to continue in its original motioncontinue in its original motion

Newton’s Second LawNewton’s Second Law

The acceleration of an object is directly The acceleration of an object is directly proportional to the net force acting on it proportional to the net force acting on it and inversely proportional to its mass.and inversely proportional to its mass.

F and a are both vectorsF and a are both vectors

Can also be applied three-dimensionallyCan also be applied three-dimensionally

Gravitational ForceGravitational Force

Mutual force of attraction between Mutual force of attraction between any two objectsany two objects

Expressed by Newton’s Law of Expressed by Newton’s Law of Universal Gravitation:Universal Gravitation:

221

g r

mmGF

WeightWeight

The magnitude of the gravitational The magnitude of the gravitational force acting on an object of mass force acting on an object of mass mm near the Earth’s surface is called near the Earth’s surface is called the weight the weight ww of the object of the object w = m gw = m g is a special case of Newton’s is a special case of Newton’s

Second LawSecond Law g g can also be found from the Law can also be found from the Law

of Universal Gravitationof Universal Gravitation

Newton’s Third LawNewton’s Third Law

If two objects interact, the force FIf two objects interact, the force F1212 exerted by object 1 on object 2 is exerted by object 1 on object 2 is equal in magnitude but opposite in equal in magnitude but opposite in direction to the force Fdirection to the force F2121 exerted exerted by object 2 on object 1.by object 2 on object 1. Equivalent to saying a single isolated Equivalent to saying a single isolated

force cannot existforce cannot exist

Newton’s Third Law cont.Newton’s Third Law cont.

FF1212 may be called may be called the the actionaction force force and Fand F2121 the the reactionreaction force force Actually, either Actually, either

force can be the force can be the action or the action or the reaction forcereaction force

The action and The action and reaction forces reaction forces act on act on differentdifferent objectsobjects

Some Action-Reaction Some Action-Reaction PairsPairs

n and n’n and n’ n is the n is the normalnormal

force, the force the force, the force the table exerts on the table exerts on the TVTV

n is always n is always perpendicular to perpendicular to the surfacethe surface

n’ is the reaction – n’ is the reaction – the TV on the tablethe TV on the table

n = - n’n = - n’

More Action-Reaction pairsMore Action-Reaction pairs

FFgg and F and Fgg’’ FFgg is the force the is the force the

Earth exerts on Earth exerts on the objectthe object

FFgg’ is the force ’ is the force the object exerts the object exerts on the earthon the earth

FFgg = -F = -Fgg’’

Forces Acting on an ObjectForces Acting on an Object

Newton’s Law uses Newton’s Law uses the forces acting the forces acting onon an object an object

n and Fn and Fgg are acting are acting on the objecton the object

n’ and Fn’ and Fgg’ are ’ are acting on other acting on other objectsobjects

Free Body DiagramFree Body Diagram

Must identify all the forces acting Must identify all the forces acting on the object of intereston the object of interest

Choose an appropriate coordinate Choose an appropriate coordinate systemsystem

If the free body diagram is If the free body diagram is incorrect, the solution will likely be incorrect, the solution will likely be incorrectincorrect

EquilibriumEquilibrium

An object either at rest or moving An object either at rest or moving with a constant velocity is said to with a constant velocity is said to be in be in equilibriumequilibrium

The net force acting on the object The net force acting on the object is zerois zero

or 0 F

0Fx 0Fy

Solving Equilibrium Solving Equilibrium ProblemsProblems

Make a sketch of the situation described Make a sketch of the situation described in the problemin the problem

Draw a free body diagram for the Draw a free body diagram for the isolated object under consideration and isolated object under consideration and label all the forces acting on itlabel all the forces acting on it

Resolve the forces into x- and y-Resolve the forces into x- and y-components, using a convenient components, using a convenient coordinate systemcoordinate system

Apply equations, keeping track of signsApply equations, keeping track of signs Solve the resulting equationsSolve the resulting equations

Equilibrium Example – Equilibrium Example – Free Body DiagramsFree Body Diagrams

Inclined PlanesInclined Planes

Choose the Choose the coordinate system coordinate system with x along the with x along the incline and y incline and y perpendicular to perpendicular to the inclinethe incline

Replace the force Replace the force of gravity with its of gravity with its componentscomponents

Slide 19

Fig. P4.41, p. 110

Static Friction, ƒStatic Friction, ƒss

Static friction acts Static friction acts to keep the object to keep the object from movingfrom moving

If F increases, so If F increases, so does ƒdoes ƒss

If F decreases, so If F decreases, so does ƒdoes ƒss

ƒƒss µ n µ n

Kinetic FrictionKinetic Friction

The force of The force of kinetic friction kinetic friction acts when the acts when the object is in motionobject is in motion

ƒƒkk = µ n = µ n

Click toview animation.

Click toview animation.

Fig. P4.34, p. 109

Click toview animation.

Click toview animation.