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Honors Physics 1Class 03 Fall 2013

Force

Newton’s Laws

Everyday Forces

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Newton’s Laws

Mechanics laws are hard to observe because there are confounding forces, such as friction and drag.

1rst Law – A body will continue to move with constant velocity unless a net force acts on it.

2nd Law – F=ma (We need to define inertial mass and force. We should write acceleration as second derivative of position.)

3rd Law – Force is necessarily the result of interaction between two systems.

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Questions

What is a force?

What is mass?

What is an isolated body?

How do we measure acceleration?– Inertial reference frame.

When are Newton’s Laws true? Are there any special conditions?

Note: Newton’s Laws are easy to apply when dealing with “point” masses, but not for fluids.

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Simplifications

We will start by treating physical objects as particles.

Particle: an object for which internal structures and motions can be ignored or all of whose parts move in the same way.

Force: the interaction of an object with its environment in ways that can influence the motion of the object.

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Inertial systems

If the net force on an object is zero, then it is possible to find a set of coordinate systems, or reference frames, in which that body has no acceleration.

Inertial frames are defined by the sentence above.

The laws of Physics are the same in all inertial frames.

Inertial frames are related by x’=x+vt+d

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Forces and accelerations are related in the same way in different inertial

reference frames

0

0 0

0

Consider the motion of an object in one reference frame.

; ( )

Now allow '

'' ( )

'' 0

F ma v v t

x x v t

dx dxv v v t v

dt dtdvdv dv

a adt dt dt

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Mass

The mass of an object is a quantitative measure of the resistance of an isolated body to acceleration for a given net applied force.

standard

standard

x

x

m a

m a

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Types of Forces

There are four (maybe five) “fundamental” forces

- strong nuclear, - weak nuclear, - electromagnetic, - gravity - + maybe “dark”.

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Everyday forces in mechanics

Contact (Normal and/or Tension)

Gravity

Electromagnetic

Friction

Drag

Spring

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Using Newton’s Laws

1) Mentally divide the system of objects into smaller systems, until the forces and motion of each can be analyzed.

2) Draw a force diagram for each mass.A. represent each object as a point mass or simple symbol.

B. Draw a force vector on each mass for each force acting on the mass.– Convention: Label forces with subscripts indicating which body the force is

acting on and which one the force is exerted by:

– FAB is the force on A due to B

» Draw only forces acting on the object.

3. Choose a coordinate system

4. Take care to address interactions

5. Carefully consider and include constraints on the motion. (Sometimes constraints are trivially included, sometimes not.)

6. Keep track of which variables are known, which are unknown, and what is the goal of your calculation.

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Free-Body Diagrams

1. Draw the object as a box or a circle, detached from everything else. (“free-body”)

2. Draw and label the force arrows acting on the

object, with all tails on the object. 3. It helps to put the coordinate axes in the diagram

to remember which direction is positive. 4. If you know the direction of the acceleration it is

often helpful to pick that as one coordinate axis.

N

W = mg

F P

a Y

X

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Normal force

The normal force FN acts perpendicular to the point of contact between two objects.

When two objects are in contact and remain in contact, the normal force is equal to the force that the object exerts on the surface.

mg

FN

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Tension

When a cord (or spring, cable, wire, chain, band…) is attached to a body and pulled taut, the cord pulls on the body with a force T that is directed away from the body. This is called the tension force.

mg

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Friction

If we attempt to slide a body over a surface, the motion is resisted by bonding between the two surfaces. This friction force is directed along the surface and is opposite to the intended motion.

The magnitude of the friction force depends on the normal force between two surfaces and on the nature of the surfaces.

mg

FN

FAppliedFF

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Friction vs Applied Force

Frictional

Force

Applied Force

Static Friction Kinetic Friction

Starting Friction

Motion begins

(usually less than starting friction)

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Coefficient of Friction

( )F

The friction force is equal to the applied force parallel to

a surface until the applied force exceeds the critical friction force.

The critical friction force is given by:

F

static frictiS N

S

crit F

( )F

on coefficient (0 to 1, typical= 0.2)

Once the object is sliding, the force opposing motion is

F

kinetic friction coefficient (0 to 1, typical = 0.1)k N

k

moving F

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Illustration of Newton’s 3rd Law

Reaction force of table on book

Force of book on table

Reaction forces of floor on table

Forces of table on floor

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Example 1: Two astronauts – tug of war

Unequal strengths (A>B), unequal masses (A>B). Mass of rope can be neglected.

Find their motion if each pulls on the rope as hard as he can.

Make a sketch. Draw forces on each object.

Things to note:– Each astronaut can only apply force to the rope.– Make a sketch and force diagram– Newton’s third law applies between rope and each astro.

– If rope mass is negligible then FAB=FBA

– Forces must be equal and opposite. B must let rope slip and A can’t exert max force.

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Activity

The motion of an asteroid is measured by the crew of two space ships. Crew 1 observes that the asteroid moves with v=1000m/s. Crew 2 observes that the asteroid moves with v=2000 m/s.

Can they both be making their measurement from an inertial frame?

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Activity

The motion of an asteroid is measured by the crew of two space ships. Crew 1 observes that the asteroid moves with v=1000m/s+10m/s2. Crew 2 observes that the asteroid moves with v=2000 m/s+20m/s2. The asteroid has a mass of 106 kg.

Do both crews measure the same force on the object.

Can both crews be in a inertial frame?

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Activity – Motion with constraints

Frictionless pulley and table.

Only net external force=gravity on mass 2.

Rope massless and fixed length.

Find acceleration of mass 1.