Relative MotionRelative Motion You are swimming across a 50m wide river in

which the current moves at 1 m/s with respect to the shore. Your swimming speed is 2 m/s with respect to the water. You swim across in such a way that your path is a straight perpendicular line across the river.– How many seconds does it take you to get across?

2m/s1m/s50m

s25250 a)

s50150 b)

s29350 c)

s35250 d)

What Causes Acceleration?What Causes Acceleration? Group 1 Go on the internet and find newtons laws.

Physicsclassroom.com might be good. Be prepare to discuss them.

Group 2 Devise an experiment to test what is important in horizontal acceleration. You have a bowling ball, and tennis ball as equipment. (don't drop the bowling ball) List the things that effect the acceleration as you push a ball.

Group 3 Discuss moving the contents of your house what would you least like to move and why?

Group 4 Push against the wall. Tell me all the things that are pushing and being pushed. (Their are more than you think.)

The Laws of MotionThe Laws of Motion Isaac Newton (1642 - 1727) published Principia

Mathematica in 1687. In this work, he proposed three “laws” of motion:

Law 1: An object at rest tends to stay at rest and object in motion tends to stay in motion.

Law 2: For any object, FFNET = FF = maa

Law 3: Forces occur in pairs: FFA ,B = - FFB ,A (For every action there is an equal and opposite reaction.)

ForceForce We have an idea of what a force is from everyday life. Physicist must be precise.

– A force is that which causes a body to accelerate.(See Newton’s Second Law)

– A Force is a push or a pull.– A Force has magnitude & direction (vector).– Adding forces is like adding vectors

FF1 FF2

aaFF1

FF2

aa

FFNET

FFNET = maa

Force …Force … We will consider two kinds of forces Contact force: (physical contact between objects)

– This is the most familiar kind.– Kicking a ball– I push on the desk.– The ground pushes on the chair...

Field Forces (Non-Contact): (action through “empty” space)

– Moon and Earth– Gravity– Electricity

On a microscopic level, all forces are non-contact (Hun????)

Contact forces:Contact forces:

Objects in contact exert forces.

Convention: Fa,b means “the force acting on a due to b”.

So Fhead,thumb means “the force on the head due to the thumb”.

FFhead,thumb

An ExampleAn Example

FB,E = - mB g

EARTH

FE,B = mB g

Consider the forces on an object undergoing projectile motion

FB,E = - mB g

FE,B = mB g

Action at a distanceAction at a distance

Gravity:

We’ll come back to this later. Just remember you don’t have to touch to push

MassMass We have an idea of what mass is from everyday

life.

Physicist must be precise. – mass (for this class) is a quantity that specifies how

much inertia an object has.(See Newton’s First Law)

Mass is an inherent property of an object.

Mass and weight are different quantities.weight is a force.

Newton’s First LawNewton’s First LawAn object subject to no external forces moves

with a constant velocity if viewed from an inertial reference frameinertial reference frame.

– If no forces act, there is no acceleration.

The above statement can be thought of as the definition of inertial reference frames.– An IRF is a reference frame that is not accelerating

(or rotating) with respect to the “fixed stars”.– If one IRF exists, infinitely many exist since they are

related by any arbitrary constant velocity vector!

Newton’s Second LawNewton’s Second LawThe acceleration of an object is directly

proportional to the net force acting upon it. The constant of proportionality is the mass.

UnitsThe units of force are kg m/s2 = Newtons (N)The English unit of force is Pounds (lbs)

Ex: weight is a force W=mg

Mass vs. WeightMass vs. WeightAn astronaut on Earth kicks a bowling

ball and hurts his foot. A year later, the same astronaut kicks a bowling ball on the moon with the same force.

His foot hurts...

(a) more

(b) less (c) the same

Ouch!

Mass vs. WeightMass vs. WeightTHE SAME!!!!

If I stand on earth and hit myself in the head with a hammer it hurts. If I do the same thing in space I think you can imagine that it would still hurt.

Ouch!

Mass vs. WeightMass vs. WeightWow!

That’s light However the weights of the bowling

ball and the astronaut are less:

Thus it would be easier for the astronaut to pick up the bowling ball on the Moon than on the Earth.

W = m gMoon gMoon < gEarth

Newton’s Second Law...Newton’s Second Law...

Components of F = ma : FX = maX

FY = maY

Suppose we know m and FX , we can solve for aX and apply the things we learned about kinematics over the last few weeks:

tavv

ta21

tvxx

xx0x

2xx00

+=

++=

Example: Pushing a Box on Example: Pushing a Box on Ice.Ice.

A skater is pushing a heavy box (mass m = 100 kg) across a sheet of ice (horizontal & frictionless). He applies a force of 50N in the i direction. If the box starts at rest, what is its speed v after being pushed a distance d=10m ?

FF

v = 0

m a

ii

Force and accelerationForce and acceleration A force F acting on a mass m1 results in an acceleration a1.

The same force acting on a different mass m2 results in an acceleration a2 = 2a1.

If m1 and m2 are glued together and the same force F acts on this combination, what is the resulting acceleration?

(a)(a) 2/3 a1 (b)(b) 3/2 a1 (c)(c) 3/4 a1

F a1

m1 F a2 = 2a1

m2

F a = ? m1 m2

Newton’s Second LawNewton’s Second LawA constant force is exerted on a cart that is initially at rest on

an air table. The force acts for a short period of time and gives the cart a certain final speed.

Air Track

CartForce

For a second shot, I can apply a force only half as large (I’m getting tired). To reach the same final speed, for how long must I apply the force ?

A) 4 x as long B) 2 x as long C) Same timeD) 1/2 as long E) 1/4 x as long

Talk about Quadratic and Talk about Quadratic and linear relationships linear relationships

tavv

ta21

tvxx

xx0x

2xx00

+=

++=

Newton’s 3Newton’s 3rdrd Law Law

For every action there is an equal and opposite reaction

Newton’s Third LawNewton’s Third LawA fly gets smushed onto the windshield of a speeding bus.

The force exerted by the bus on the fly is,A) greater thanB) the same asC) less thanthat exerted by the fly on the bus.