0 2 4 6 8 10 12 14 16

0

10

20

30

40

50

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70Mean = 10.8 (68%)Sigma = 3 (20%)

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Class 10 - Force and Motion IClass 10 - Force and Motion IChapter 5 - Wednesday September 16thChapter 5 - Wednesday September 16th

•Force and acceleration

•Newton's first law

•Force and mass

•Newton's second law

•Some particular forces

Reading: pages 87 thru 99 (chapter 5) in HRWReading: pages 87 thru 99 (chapter 5) in HRWRead and understand the sample problemsRead and understand the sample problemsAssigned problems from chapter 5: Assigned problems from chapter 5: 24, 26, 34, 38, 44, 46, 52, 56 (due Sun. Sept. 24, 26, 34, 38, 44, 46, 52, 56 (due Sun. Sept. 26)26)

What causes acceleration?What causes acceleration?

Linguistic arguments:Linguistic arguments:•Some sort of interaction - loosely speaking, a push Some sort of interaction - loosely speaking, a push or a pull on an object.or a pull on an object.

•We call this a We call this a forceforce, which can be said to act on a , which can be said to act on a body.body.

•Examples of forces:Examples of forces:

Normal or "contact force"Normal or "contact force"

Gravitational forceGravitational force

Electromagnetic forceElectromagnetic force

Weak and strong nuclear forcesWeak and strong nuclear forces

We'd better be We'd better be more scientific more scientific about this...about this...

Before NewtonBefore Newton•Friction and air resistance have a tendency to Friction and air resistance have a tendency to distort our appreciation of the nature of forces.distort our appreciation of the nature of forces.

•Think of a motor boat or a car: their engines Think of a motor boat or a car: their engines constantly do work (i.e. generate driving forces) in constantly do work (i.e. generate driving forces) in order to maintain a constant velocity.order to maintain a constant velocity.

•This led people to believe, before Newton, that a This led people to believe, before Newton, that a force was necessary to keep a body moving at force was necessary to keep a body moving at constant velocity, and that the natural state of a constant velocity, and that the natural state of a body was when it was stationary - body was when it was stationary - this leads to some this leads to some very interesting philosophical questions.very interesting philosophical questions.

But hang on a minute.... What But hang on a minute.... What happens if we remove all resistance happens if we remove all resistance to motion, i.e. friction and air to motion, i.e. friction and air resistance?resistance?

Newton's first lawNewton's first lawIf no force acts on a body, then the body's If no force acts on a body, then the body's velocity cannot change; that is, it cannot velocity cannot change; that is, it cannot accelerate.accelerate.An object at rest tends to stay at rest and an An object at rest tends to stay at rest and an object in motion tends to stay in motion with the object in motion tends to stay in motion with the same speed and in the same direction unless same speed and in the same direction unless acted upon by an unbalanced force.acted upon by an unbalanced force.

•Therefore, according to Newton, the car traveling at Therefore, according to Newton, the car traveling at constant velocity experiences no net or unbalanced constant velocity experiences no net or unbalanced force. force.

•That is, the engine forces it one way, and friction That is, the engine forces it one way, and friction exactly balances this force by opposing the motion exactly balances this force by opposing the motion with an equal and opposite force.with an equal and opposite force.

•Friction is a somewhat mysterious force, though we Friction is a somewhat mysterious force, though we will learn to deal with it in the next chapter.will learn to deal with it in the next chapter.

ForceForce

•We declare that: a force of 1 Newton is that force We declare that: a force of 1 Newton is that force required to accelerate our standardized mass (1 Kg) required to accelerate our standardized mass (1 Kg) at a rate of 1 m.sat a rate of 1 m.s-2-2. .

•A reference defines the Kg, and the above definition A reference defines the Kg, and the above definition defines force.defines force.

Definition (Definition (there is no proof!there is no proof!):):

total ii

F F

•Force is a vector. Thus, forces add like vectors. This Force is a vector. Thus, forces add like vectors. This is something one has to test by experiment.is something one has to test by experiment.

•Forces obey the "principle of superposition.“Forces obey the "principle of superposition.“

Free-body diagramsFree-body diagrams

F 2

F 1

F 3

S

0F

F 2

F 1

F 3

•The forces shown above are what we call "external The forces shown above are what we call "external forces."forces."

•They act on the "system" They act on the "system" SS..

•SS may represent a single object, or a system of rigidly may represent a single object, or a system of rigidly connected objects. We do not include the internal connected objects. We do not include the internal forces which make the system rigid in our free body forces which make the system rigid in our free body diagram.diagram.

Inertial reference framesInertial reference framesAn inertial reference frame is one in which An inertial reference frame is one in which Newton's laws hold.Newton's laws hold.

Simply put: this is a frame which is not Simply put: this is a frame which is not accelerating.accelerating.

PB BAPA PB

dv dva a

dt dt

*PA PBF F

*Assuming we define mass in the same way in all inertial frames*Assuming we define mass in the same way in all inertial frames

•Newton's laws do not apply in accelerating frames.Newton's laws do not apply in accelerating frames.

•They must also be modified in relativistic and quantum They must also be modified in relativistic and quantum limitslimits

What is mass?What is mass?

•On earth, we use the fact that the acceleration due to On earth, we use the fact that the acceleration due to gravity is gravity is approximatelyapproximately constant for all objects, and constant for all objects, and characterize an “effective” mass according to the force characterize an “effective” mass according to the force needed to balance the earth's gravitational force.needed to balance the earth's gravitational force.

•We call this "weight", We call this "weight", as measured in Newtons (v. as measured in Newtons (v. imp!)imp!)

•In outer space, everything is weightless, but not In outer space, everything is weightless, but not massless!!massless!!

This is not a trivial question!This is not a trivial question!

Mass is simply the characteristic of a body that Mass is simply the characteristic of a body that relates a force on the body to the resulting relates a force on the body to the resulting accelerationacceleration•This is how one has to measure mass in outer space.This is how one has to measure mass in outer space.

•No static method works, because there is no basis for No static method works, because there is no basis for comparison, e.g. hanging or spring balances, which comparison, e.g. hanging or spring balances, which depend on g.depend on g.

•YOUR MASS DOES NOT CHANGE IN OUTER YOUR MASS DOES NOT CHANGE IN OUTER SPACE!!!SPACE!!!

Newton's second lawNewton's second lawThis law was developed through systematic This law was developed through systematic experimentationexperimentation1) We calibrate our force apparatus by accelerating our 1) We calibrate our force apparatus by accelerating our

standard mass by 1, 2, 3, etc.. m.sstandard mass by 1, 2, 3, etc.. m.s-2-2. .

2) We then apply a standard force of 1 N to a range of 2) We then apply a standard force of 1 N to a range of objects, and measure their acceleration.objects, and measure their acceleration.

3) We then look for the relationship between force, mass 3) We then look for the relationship between force, mass and acceleration.and acceleration.

And the result:And the result: net 5 1ii

F F ma

net, net , net ,, ,x x y y z zF ma F ma F ma •We may treat the components separately.We may treat the components separately.•Mass is a scalar quantity.Mass is a scalar quantity.•1 N = (1 Kg)(1 m.s1 N = (1 Kg)(1 m.s-2-2) = 1 Kg.m.s) = 1 Kg.m.s-2-2

Some particular forcesSome particular forces

•During free fallDuring free fall

Gravity:Gravity:ja g

jF ma mg

•This is always true at the surface of the earth, and will This is always true at the surface of the earth, and will usually be the case for problems worked in this class.usually be the case for problems worked in this class.

•In other words, even when a mass is stationary on the In other words, even when a mass is stationary on the surface of a table, gravity still acts downwards with a surface of a table, gravity still acts downwards with a magnitude equal to magnitude equal to mgmg..

•This leads to the concept of a normal force: for the This leads to the concept of a normal force: for the mass on the table to remain stationary, the table must mass on the table to remain stationary, the table must exert an upward force on the mass so as to exactly exert an upward force on the mass so as to exactly balance the force due to gravity.balance the force due to gravity.

Normal forceNormal force

g

g y

y g y

N F ma

N F ma

N ma F m a g

if 0g yN F mg a Weight (a force!):Weight (a force!):•In the above example, the internal forces within the In the above example, the internal forces within the table supply the normal force.table supply the normal force.

•If we hold the mass in a stationary state, we must If we hold the mass in a stationary state, we must supply the force. This is the sensation of weight, i.e.supply the force. This is the sensation of weight, i.e.

NewtonsgW F mg