Today: Dynamics I

Mass, Inertia, Weight

Balanced Forces

Newton’s Laws

Free-body diagrams

Aristotle v. Newton

384 – 322BC 1643 – 1747AD

Aristotle’s Laws of Motion

• Nothing moves unless you push it.  [it is moved by a mover] » Some motion is natural for the sublunar elements,

rectilinear motion to or away from the earth's center for the supralunar quintessence, circular motion

» All other motion is violent, and requires a mover • [Anselm's nth proof of the existence of God] • Because motion exists, there must be a self-moved mover,

i.e. a Prime Mover [later i.d. God]

• There is natural, violent, and local motion; rectilinear and circular motion

• Speed is proportional to motive force, and inversely proportional to resistance. » v = k (F / R)

• There cannot be a vacuum [therefore Natura is a plenum]

• The most Natural state:  Rest [if terrestrial]

Newton’s First Law

Newton’s First Law

Objects in motion tend to stay in motion, and objects at rest tend to stay at rest unless an outside force acts upon them.

Inertia

Kitchen roll

Coin and cup

A hammerhead

Anvil and hammer

Airplanes

Weight?

Zero Net Force(or, a delicious melon)

Newton’s Second Law

The acceleration of an object as produced by a net force is directly proportional to the

magnitude of the net force, in the same direction as the net force, and inversely proportional to the

mass of the object.

Newton’s Second Law in symbols

F = m a

(unit: Newton / kg m s-2)

W = ?

Try:

• A car has a mass of 1000 kg. At one point in its motion, when the combined forces of air resistance and friction (acting backwards) are 500 N, its acceleration is 1.6 m s-2. What forward driving force does it need?

Car (obviously)

Air resistance+ Friction Driving force

Direction of motion

Newton’s Third Law

When body A exert a force on body B, body B exerts a force on body A that is equal in magnitude and opposite in direction

Delicious-melon-on-table

Delicious-melon-on-table-on-planet

Think:

What action-reaction pairs can you think of happening right now?

Free-Body Diagram

Magnet-string-paperclip

Free-body diagrams

• RI boy’s head sleeping on a table• RI boy suspended motionless from a bar hanging from a ceiling by two ropes

• RI boy free-falling from a nest in a tree. Neglect air resistance.

• RI boy gliding from a tree to the ground at constant velocity. Consider air resistance.

Free-body diagrams

• A rightward force is applied to a RI boy in order to move it across a desk with a rightward acceleration.

• Same as above, but constant velocity.• A RI boy rests a backpack on his shoulder. The pack is suspended motionless by one strap from one shoulder.

• A skydiving RI boy is descending with constant velocity. Consider air resistance.

Free-body diagrams

• A force is applied to the right to drag a RI boy across loosely-packed snow with rightward acceleration.

• A RI boy is flying upwards after having been punted by a teacher. Neglect air resistance.

• A car is coasting to the right and slowing down (no RI boys involved).

Conclusion

Mass, Inertia, Weight

Balanced Forces

Newton’s Laws

Free-body diagrams