Dynamics: Forces and Motion Along A Line

Force ( ) - a vector quantity that basically affects the motion of the object

- commonly defined as “push” or “pull”Units of Force: SI Unit: newton (N) Gaussian: dyne English: pound (lb)

Net Force ( )- resultant force or sum of all forces acting

on the object.

Net force

Physicists who contributed to the development of force and motion relationship:1. Aristotle (384-322 BC)2. Galileo (2000 years later, approx. 1678)3. Isaac Newton (1687) - Principia (book published)

- “three laws of motion”

Newton’s First LawLaw of Inertia: An object at rest or an object in motion at constant velocity will remain at rest or at constant velocity in the absence of a net force.

• The body remains at rest.• The body moves at constant velocity.

Understanding the First Law:

(a) The driver is forced to move forward. An object at rest tends to remain at rest.

Discuss what the driver experiences when a car accelerates from rest and then applies the brakes.

(b) Driver must resist the forward motion as brakes are applied. A moving object tends to remain in motion.

mass (m)- is a measure of inertia of a body.- synonymous to quantity of matter.

This means that it is constant! * The more mass a body has, the harder it is to change its state of motion.

Newton’s Second Law:• Law of Acceleration: Whenever a net

force acts on an object, it produces an acceleration with a direction the same to the direction of the net force - an acceleration that is directly proportional to the net force and inversely proportional to the mass.

Unit Conversion:1 N = 1 kg m/s2; 1 dyne = 1 g cm/s2

1 lb = 1 slug ft/s2

Acceleration and Force With Zero Friction

Forces

Pushing the cart with twice the force produces twice the acceleration. Three times the force triples the acceleration.

Acceleration and Mass Again With Zero Friction

F F

aa/2

Pushing two carts with same force F produces one-half the acceleration. The acceleration varies inversely with the amount of material (the mass).

Newton’s Third Law• Law of Interaction:To every action

force there must be an equal and opposite reaction force.

Force of

Hands on

Wall

Force of Wall

on Hands

Force of

Floor on

Man

Force of Man on Floor

Force of Ceiling on Man

Force of Man on Ceiling

Action and reaction forces act on different objects.

Newton’s Third LawTwo More Examples:

Action and Reaction Forces Act on Different Objects. They Do Not Cancel

Each Other!

ActionReaction

Action

Reaction

Weight, Normal Force, and TensionWeight (w) – gravitational force

w = mgwhere m = mass of the object

g = acceleration due to gravity

• For practical purposes on the earth, 1 kg = 2.2 lb since g is relatively constant near the surface.• Weight is not constant while mass is!

The force of gravity acts on an object when it is falling.

When the body is at rest on the earth, the gravitational force on it does not disappear.

Why, then, doesn’t the object move?There must be another force to

balance the gravitational force.

Normal force (FN)- contact force that acts perpendicular to

the common surface of contact.

w

FN

w

T

Tension (T )- force of a string, cable, wire running on

the body