Newton’s Laws of MotionNewton’s Laws of Motion

We have studied “kinematics”, or the We have studied “kinematics”, or the description of motion.description of motion.

Now, we look at “dynamics”, the Now, we look at “dynamics”, the causes causes of of motionmotion

A little history –A little history –

Galileo was the first to realize that Galileo was the first to realize that objects in “uniform motion” require objects in “uniform motion” require no “cause” for their motion.no “cause” for their motion.

Only “changes” in motion Only “changes” in motion

------------ accelerations ------ accelerations ------

require a cause: a require a cause: a forceforce

Isaac Newton’s three simple laws are recognized as the foundation for all of physics.

In the early 20th 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 Force is -

A “push” or a “pull” that acts on an objectA “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 A vector - when you pull a cart the force you

exert has both a magnitude (the amount of force) exert has both a magnitude (the amount of force) and a directionand a direction Forces are represented by vector arrowsForces are represented by vector arrows

Measured in units of newtons (N) in the metric Measured in units of newtons (N) in the metric system and pounds (lbs) in the English systemsystem and pounds (lbs) in the English system A newton (N) is the amount of force needed to A newton (N) is the amount of force needed to

accelerateaccelerate

a 1.0 kg mass at a rate of 1.0 m/sa 1.0 kg mass at a rate of 1.0 m/s22.. So a N = kg * m/sSo a N = kg * m/s22

Types of ForcesTypes of ForcesThere are two basic types of forces –There are two basic types of forces –

Contact force - the forces existing betweenContact force - the forces existing betweentwo or more objects in contact withtwo or more objects in contact witheach other. Example – tension, friction, each other. Example – tension, friction, applied force, normal forceapplied force, normal force

Field force - a force exerted through space notField force - a force exerted through space notrequiring contact. Example – gravity,requiring contact. Example – gravity,magnetic forces, electrostatic forcesmagnetic forces, electrostatic forces

Types of Forces, cont.Types of Forces, cont.

Weight – Weight – the force of gravity on a massthe force of gravity on a massW = FW = Fgg = mg (mass * “g” = mg (mass * “g”

acceleration)acceleration)

Normal force – Normal force – when a surface pushes backwhen a surface pushes backThis normal force is always This normal force is always

perpendicularperpendicularto the contact surface. (Fto the contact surface. (FNN))

Tension – Tension – force applied through a rope or chain (T)force applied through a rope or chain (T)

Spring - Spring - the force exerted by a stretched orthe force exerted by a stretched orcompressed spring (Fcompressed spring (Fkk))

Friction – Friction – force resistant to motion acting betweenforce resistant to motion acting betweentwo surfaces (f or Ftwo surfaces (f or Fff))

Force DiagramsForce Diagrams

Also called FBD – “free body diagrams”Also called FBD – “free body diagrams” A diagram whichA diagram which

Uses a dot to represent the center of mass of an objectUses a dot to represent the center of mass of an object Places the tail of the vector on the object and points in Places the tail of the vector on the object and points in

the same direction that the force actsthe same direction that the force acts

A book on a table –A book on a table – FBD –FBD –

The vectors areforces acting onlyon the book.

W (weight force)

FN ( normal force)

Newton’s First LawNewton’s First LawLaw of InertiaLaw of Inertia

Inertia – the tendency of a body at rest to remain at rest or, if Inertia – the tendency of a body at rest to remain at rest or, if in motion, to remain in constant motion (no acceleration)in motion, to remain in constant motion (no acceleration)

Review - acceleration is a change in velocity – either in Review - acceleration is a change in velocity – either in magnitude or direction. So if an object maintains constant magnitude or direction. So if an object maintains constant velocity, its motion never changes, it does not accelerate. velocity, its motion never changes, it does not accelerate. It does not slow down or speed up nor does it change It does not slow down or speed up nor does it change direction.direction.

Sometimes inertia is referred to as “laziness” – and the mass Sometimes inertia is referred to as “laziness” – and the mass of an object is a direct measure of its inertia or laziness. of an object is a direct measure of its inertia or laziness. The more massive something is, it has a greater tendency The more massive something is, it has a greater tendency to be lazy – to not want to change. So a larger accelerating to be lazy – to not want to change. So a larger accelerating force is required to get it to change its motion.force is required to get it to change its motion.

This first law is also called the law of balanced forces.This first law is also called the law of balanced forces.

Newton’s Second LawNewton’s Second LawFFnetnet = m * a = m * a

Law of unbalanced forces Law of unbalanced forces There is a net force which causes the object to There is a net force which causes the object to

accelerate in the direction of the Faccelerate in the direction of the Fnetnet.. Newton expressed this relationship asNewton expressed this relationship as

a = F/ma = F/m

What does this tell us:What does this tell us:For a given force, the acceleration is inversely proportionalFor a given force, the acceleration is inversely proportional

to the mass.to the mass.

For a given mass, the acceleration is directly proportional to For a given mass, the acceleration is directly proportional to the force.the force.

If the forces on an object are If the forces on an object are balancedbalanced, then there , then there is no net force and the object does not accelerate is no net force and the object does not accelerate – it does not change its motion. Mathematically, – it does not change its motion. Mathematically, we see that the vector sum of the forces acting we see that the vector sum of the forces acting on the body in both the horizontal and vertical on the body in both the horizontal and vertical directions is zero.directions is zero.

A car traveling with constant velocity-A car traveling with constant velocity- Fx = F1 + (-)F2 = F1 – F2 = 0

Fy = FN + (-)W = FN – W = 0

FN

F1

W

F2

The sum of all the forces is zero. Theforces balance each other and the objectis in a state of equilibrium.

Fnet = m * a but accel = 0, soFnet = m * 0 = 0

Just hangin’ around - Investigating tension Just hangin’ around - Investigating tension forcesforcesAbsolutely, fundamental and most important concept:Absolutely, fundamental and most important concept:

In equilibrium, the horizontal forces must sum to zeroIn 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 verticalforces. If the weight is 200 N down, there MUST be a 200 N tension up. 200 N - weight and up tension

Theupforcecomesfrom thewall.

Using right triangle geometry,the tension force forms thehypoteneuse.Use this information to find theopposite and adjacent sides.

Thesetwo must beequal andopposite.

Forces on surfaces - tryin’ to be Forces on surfaces - tryin’ to be normalnormal

Be careful – the normal force is ALWAYS perpendicular to the surfaceBe careful – the normal force is ALWAYS perpendicular to the surface

Fn

Fg = mg

Now, raise the surface to create an angled ramp

N

Fg – you need to resolve this weight vector. Make it the hypoteneuse of a right triangle.

By the geometry, these twoangles are equal.

This componentbalances thenormal force.Find it as: mg cos θ

This is the component of the weight actingdownramp.Find it as: mg sin θ

Another situation -Another situation - Draw the FBD Draw the FBD

Determine both horizontal and vertical forcesDetermine both horizontal and vertical forcesFN = 100N

f = 5 N

W = mg = 10 kg * 10m/s2

= 100 N

F = 25 N

Fy = Fn – W = 100 – 100 N = 0 (no motion in the vertical direction)

Fx = F – f = 25 – 5 N = 20 N net force a = F / m so 2 m/s2 = 20 N / 10 kg

May theMay the Net Force Net Force be with be with youyou

Total force acting on an objectTotal force acting on an object Vector sum of all the forcesVector sum of all the forces The unbalanced force referred to in Newton’s Law of MotionThe unbalanced force referred to in Newton’s Law of Motion Net force is equal to the mass of an object times the Net force is equal to the mass of an object times the

acceleration of that object.acceleration of that object.

F = FF = Fnetnet = m * a = m * a

(Remember, in equilibrium an object is at rest or moving with (Remember, in equilibrium an object is at rest or moving with a constant velocity. Either way, acceleration = 0 and there a constant velocity. Either way, acceleration = 0 and there is no net force.)is no net force.)

Force Diagrams (FBD)Force Diagrams (FBD)A ReviewA Review

First case - (1) is in equilibrium (2) is acceleratingFirst case - (1) is in equilibrium (2) is accelerating

N

W

Ff

N

W

F

f

SFy = N – W = 20 N – 20 N = 0 SFx = F – f = 10 N – 10 N = 0 SFx = F-f = 25N – 10 N = 5 N

Fnet = 5 N F net = 0 no acceleration Fnet = ma 5 N = 2 kg (a)

a = 2.5 m/s2

SFy = N – W = 20 N – 20 N = 0

Forces at an angleForces at an angleAny vector at some angle Any vector at some angle must be resolved into must be resolved into

its x and y components.its x and y components.

f

NF

W

Notice - now the Fy works WITH the normal force. Fy = (Fy + N) – WThis means that the normal forceactually decreases. Some of theweight is balanced by the upwardlift of the pulling force.

N

W

f

FNotce – in this diagram, the Fy works WITH the weight. Fy = N – (Fy + W)This means that the normal forceactually increases. There is moredownward force and so the normal mustrespond to remain in equilibrium.

The forward force comes from the x component and is opposite friction.

Newton’s Third LawNewton’s Third LawThird Law deals with action-reaction force pairs.Third Law deals with action-reaction force pairs.

If you push on an object, the object pushes back. The two If you push on an object, the object pushes back. The two forces are equal but opposite in direction. AND – the two forces are equal but opposite in direction. AND – the two forces work on two DIFFERENT objects.forces work on two DIFFERENT objects.