Forces and Forces and Momentum Momentum Chapters 4, 5 and 9Chapters 4, 5 and 9

ForceForce

A push or pull exerted on an objectA push or pull exerted on an object It causes a change in velocity (and therefore It causes a change in velocity (and therefore

acceleration)acceleration) SI unit is a newton (N)SI unit is a newton (N) It is a vector quantity (it has magnitude and It is a vector quantity (it has magnitude and

direction)direction) 2 types:2 types:

Contact forcesContact forces Ex. A book on a tableEx. A book on a table

Force fieldsForce fields Ex. Gravity pulling on a falling appleEx. Gravity pulling on a falling apple

Free Body DiagramsFree Body Diagrams A pictorial way to show all the A pictorial way to show all the

forces acting on an objectforces acting on an object Use an arrow for each force on Use an arrow for each force on

the objectthe object Arrowhead points in the direction Arrowhead points in the direction

the force is exertedthe force is exerted Length of the arrow indicates the Length of the arrow indicates the

magnitude of the forcemagnitude of the force Remember to choose your Remember to choose your

coordinate system (which coordinate system (which direction is positive and which direction is positive and which is negative)is negative)

Relating Force and Relating Force and AccelerationAcceleration

More force gives more accelerationMore force gives more acceleration More mass means you need more force More mass means you need more force

to get the same accelerationto get the same acceleration So a = F/m or F = amSo a = F/m or F = am

This is newton’s 2This is newton’s 2ndnd law law Acceleration is directly proportional to the Acceleration is directly proportional to the

force exerted on an object and inversely force exerted on an object and inversely proportional to the mass of an objectproportional to the mass of an object

Using Newton’s 2Using Newton’s 2ndnd Law Law to Calculate Weightto Calculate Weight

Weight is the force of gravity Weight is the force of gravity acting on your massacting on your mass Weight changes from location to Weight changes from location to

location, but mass is constantlocation, but mass is constant

FFgg = ma = magg

aagg = 9.8 m/s = 9.8 m/s22 on the surface of on the surface of

the Earththe Earth The unit for weight is a N The unit for weight is a N

because it is a force exerted on because it is a force exerted on you by the mass of the Earth you by the mass of the Earth (or whatever planet is pulling (or whatever planet is pulling on you)on you)

Net ForceNet Force However, when we talk about However, when we talk about force with Newton’s 2force with Newton’s 2ndnd law, we law, we mean NET forcemean NET force

If forces are in the same plane If forces are in the same plane (or dimension) then they can (or dimension) then they can just be addedjust be added Remember though, if in opposite Remember though, if in opposite

directions then one must be directions then one must be negative according to the negative according to the coordinate system that you’ve coordinate system that you’ve establishedestablished

If the net force on an object is 0, If the net force on an object is 0, then the acceleration with also then the acceleration with also be 0be 0 It is at equilibriumIt is at equilibrium

Newton’s 1Newton’s 1stst Law Law

When there is no net force acting on an object, When there is no net force acting on an object, it will continue to behave in the same mannerit will continue to behave in the same manner An object at rest stays at rest, an object in motion An object at rest stays at rest, an object in motion

remains in motion, unless an outside force acts on itremains in motion, unless an outside force acts on it InertiaInertia

The resistance of a body to changeThe resistance of a body to change Measured in mass (more mass means more inertia)Measured in mass (more mass means more inertia)

A scale measures your weight because the net A scale measures your weight because the net force on you must be zero (a = 0)force on you must be zero (a = 0) The scale actually measures how hard it has to The scale actually measures how hard it has to

push back up on you, not how hard you are pushing push back up on you, not how hard you are pushing downdown

Scale reading are inaccurate when you are Scale reading are inaccurate when you are acceleratingaccelerating

Apparent WeightApparent Weight

FrictionFriction The force that opposes motionThe force that opposes motion 2 types:2 types:

Static frictionStatic friction When an object isn’t moving (v = 0)When an object isn’t moving (v = 0) Starts at 0 and increase as you push harder Starts at 0 and increase as you push harder

until the maximum is exceededuntil the maximum is exceeded Kinetic frictionKinetic friction

When an object is movingWhen an object is moving As long as push equals kinetic friction, the As long as push equals kinetic friction, the

object continues to move at a constant object continues to move at a constant velocityvelocity

If an object is moving at a constant If an object is moving at a constant velocity (equilibrium), then friction must velocity (equilibrium), then friction must equal the force of the push (net force = 0)equal the force of the push (net force = 0) Not moving is just a special type of Not moving is just a special type of

equilibrium when v = 0equilibrium when v = 0

Calculating FrictionCalculating Friction

Is determined by the material the surface Is determined by the material the surface is made of (measured by the coefficient is made of (measured by the coefficient of friction, of friction, μμss))

Also affected by how hard the materials Also affected by how hard the materials push against each other (measured by push against each other (measured by the normal force, Fthe normal force, FNN)) This is always equal to the weight (mg) of This is always equal to the weight (mg) of

the object, but in a direction perpendicular to the object, but in a direction perpendicular to the surface the object rests onthe surface the object rests on

So, FSo, Ff f = = μμss F FNN

Air Resistance (or Drag)Air Resistance (or Drag)

The frictional force the air exerts on a falling The frictional force the air exerts on a falling object (opposes motion)object (opposes motion)

Can be altered by the objects mass and Can be altered by the objects mass and surface areasurface area More mass, the more drag that can build upMore mass, the more drag that can build up The more surface area, the quicker the drag builds The more surface area, the quicker the drag builds

upup So, heavy, compact objects fall more quickly than So, heavy, compact objects fall more quickly than

light, spread out oneslight, spread out ones When air resistance equals an object’s weight, When air resistance equals an object’s weight,

the net force = 0 and the acceleration = 0 (but the net force = 0 and the acceleration = 0 (but velocity doesn’t)velocity doesn’t) This is the terminal velocity of the objectThis is the terminal velocity of the object

Creating ForcesCreating Forces

When you push on an object, the object When you push on an object, the object actually pushes back on you in an equal actually pushes back on you in an equal and opposite direction (Newton’s 3and opposite direction (Newton’s 3rdrd law) law)

Forces always occur in pairs of equal Forces always occur in pairs of equal magnitude and opposite direction and on magnitude and opposite direction and on 2 different objects that are exerting forces 2 different objects that are exerting forces on each otheron each other Ex. A bat hits a baseball, then the baseball Ex. A bat hits a baseball, then the baseball

must also hit the bat with the same forcemust also hit the bat with the same force

The Same Force ParadoxThe Same Force Paradox If the force on each object is the same, then why don’t If the force on each object is the same, then why don’t

they experience the same effect in the collisionthey experience the same effect in the collision Their masses differ, and therefore they undergo different Their masses differ, and therefore they undergo different

accelerationsaccelerations

If the forces are equal and opposite, why don’t they If the forces are equal and opposite, why don’t they cancel out to a net force of 0cancel out to a net force of 0 Because the forces are on 2 different objects, forces only Because the forces are on 2 different objects, forces only

cancel if they act on the same objectcancel if they act on the same object

Finding Net Force if Vectors Finding Net Force if Vectors Aren’t in the Same Aren’t in the Same DimensionDimension

This can be done graphically This can be done graphically using the tip to tail methodusing the tip to tail method As long as the direction and As long as the direction and

magnitude of a vector remain magnitude of a vector remain unchanged, you can move it unchanged, you can move it anywhereanywhere

Move the tip of one vector so that it Move the tip of one vector so that it touches the tail of anothertouches the tail of another

Draw an arrow connecting the Draw an arrow connecting the exposed tail to the exposed tipexposed tail to the exposed tip

The magnitude and direction of this The magnitude and direction of this line is the combined effect of the 2 line is the combined effect of the 2 vectors (we call this the resultant)vectors (we call this the resultant)

MomentumMomentum

The combined effect of an The combined effect of an object’s mass and it’s object’s mass and it’s velocityvelocity Unit is kgm/sUnit is kgm/s

A change in momentum is A change in momentum is caused by an impulsecaused by an impulse A force acting over a timeA force acting over a time The longer the time, the less The longer the time, the less

force required to cause the force required to cause the same change in momentumsame change in momentum

More impulse results from a More impulse results from a bounce than from a solid hitbounce than from a solid hit

Conservation of Conservation of MomentumMomentum Can be passed between objects, Can be passed between objects,

but cannot be lostbut cannot be lost One object can cause another to One object can cause another to

move after a collision, but it will have move after a collision, but it will have to slow downto slow down

It’s the momentum that’s conserved, It’s the momentum that’s conserved, not the velocitynot the velocity

Is a vector since velocity is a vector Is a vector since velocity is a vector (the sign matters)(the sign matters)

2 collision types:2 collision types: Inelastic – the KE for the system Inelastic – the KE for the system

changeschanges Elastic – the KE for the system Elastic – the KE for the system

remains the same pre and post remains the same pre and post collisioncollision