Chapter 4

Forces in One Dimension

4.1 Force and Motion

Force – A push or a pull exerted on an object. May cause a change in velocity: Speed up Slow down

Any change in velocity is acceleration Therefore a force causes acceleration Forces are vector quantities

Direction Magnitude

Contact Forces

Caused when an object in the external world (an “agent”) touches a system thereby exerting a force upon it

System is the object of interest: A puck hit by a hockey stick A book pushed off the table by a hand

Without an agent and a system, a force cannot exist

Free-body Diagrams

See page 89 Sketch situation Label agent and system Show forces as arrows pointing in the

direction that the force is applied Indicate which way is positive (usually

up!)

Force and Acceleration

The greater the force, the greater the resulting acceleration

They are directly proportional Newton’s Second Law states that

a = F/m F = ma

F is measured in newtons (N) 1 N = 1kg.m/s2

Net Force (Fnet)

Vector sum of all forces See Figure 4-5 page 92

Newton’s First Law

An object that is at rest will remain at rest and an object that is moving will continue to move in a straight line with constant speed, if and only if the net force acting on the object is zero

Also known as inertia (the tendency of an object to resist any change in motion)

Equilibrium

If no net forces are acting on an object is said to be at equilibrium

4.2 Using Newton’s Second Law

Fg = mg Fg (Force of gravity) is weight

Fg is always (-) Weight is always (-)

Weight changes with location because gravity differs…that’s why we weigh less on the moon

Mass does not change with location because it doesn’t depend on gravity

Apparent Weight

Equal to the weight of the object plus the net force acting on it

See Problem 2 on page 99 Weightlessness is a factor of apparent

weight. This does not mean that the object has no weight, rather there are no upward contact forces acting on it.

Fscale = mg + ma (going up) Fscale = mg – ma (going down)

Drag Force

Drag force is experienced by any object moving through a fluid Gas (like air) Liquid (like water)

The magnitude of the drag force increases with the speed of the object moving through the fluid

Terminal Velocity

Object is dropped and accelerates as gravity acts upon it

As the velocity increases, so does the drag force of the air acting against gravity

When gravity pulling down equals drag force pushing up the object stops accelerating

This constant and final velocity is called “terminal velocity”

4-3 Interaction Forces

Newton’s Third Law All forces come in pairs FAonB = -FBonA

Interaction pair Also called action-reaction pair Two forces that are opposite in direction

but equal in magnitude

Example: Action-Reaction Pair

Forces of Ropes & Strings

Tension – a force exerted by a string or rope Is equal to the weight of the object

hanging on the rope/string Fnet = Sum of the positive force of a rope

pulling up and the negative force of gravity pulling down

Fnet = FT + (-Fg)

Normal Force

Perpendicular contact force exerted by one surface on another

May be equal to the weight of an object or… Less than the weight if an additional

upward force is exerted More than the weight if an additional

downward force is exerted See Figure 4-16 on page 107