forces. force – a push or a pull contact – a force acting on a body by touching it long-range...

Forces

Force – a push or a pull

• Contact – a force acting on a body by touching it

• Long-range – force exerted on a body w/o contact (gravity, magnetic force, electrical force)

Newton’s 2nd Law

• The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass.

F = ma a = F/m m = F/a

Units: kg m/s2 = Newton (N)

Newton's Second Law of Motion

Plot Force Vs. Acceleration for the following carts:cart 1 = m

cart 2 = 2mcart 3 = 3m

Net Force – vector sum of all forces acting on a body

acceleration = Fnet/m

Only net forces cause accelerations!!

Free-Body Diagrams

• Include all forces acting on the body

• Include weight (Wt), the normal force (Fn), or tension if necessary (FT)

• Then identify the net force and its direction

• The direction of the net force indicates the direction of the acceleration of the body

Equilibrium

• Equilibrium = balance = the sum of all of the forces acting on a body is zero (net force is zero)

• Static equilibrium = the object is at rest

• Dynamic equilibrium = the object is moving at constant velocity

• In each case the net force is zero (there is no acceleration therefore no net force)

Mass versus Weight

• Mass is the amount of matter in an object and is measured in kilograms

• Weight is the gravitational force exerted by a large body (Earth) on a mass and is measured in Newtons

• Wt = m(a)

• Weights may vary, but mass remains constant

Newton’s 2nd Law: The Elevator Ride

Fnet = FT + (-Wt)

Where FT = the tension force acting upwards and Wt = weight that acts

downwards

At rest:

Fnet = 0 so: 0 = FT + (-Wt)

FT = Wt

Accelerating Upward:Fnet = m(a) so: m(a) = FT + (-Wt)

FT = m(a) + mg

Constant VelocityFnet = 0 so: 0 = FT + (-Wt)

FT = Wt

Decelerating UpwardsFnet = m(-a) so: m(-a) = FT + (-Wt)

FT = m(-a) + mg

Weightlessness & Apparent Weight

• Apparent weight – the weight of an object that is sensed as a result of contact forces on it.

For instance, if you were on a scale and someone pushed down on you, the scale would read more

If you and the scale attached were freefalling, it would read zero b/c both would be accelerating in the same direction….ie.: astronauts on the space shuttle orbiting the Earth…the shuttle is freefalling while the astronauts freefall…they “float” b/c of the “apparent forces”

• Weightlessness- apparent weight is zero. There are no contact forces pushing up on you

Newton’s 1st Law

Newton’s 1st law states: “an object that is at rest will remain at rest or an object that is moving will continue to move in a straight line with constant speed” unless acted upon by an unbalanced force.

Inertia - the tendency of an object to resist change

Examples of Inertia

• Turning a corner sharply in a car…

• The Scrambler at the amusement park…

• Pulling a tablecloth off of a table without disturbing the dishes…

• The potato on the knife…

Friction

Friction – the force that opposes the motion between two surfaces that are in contact. This force is caused by the electromagnetic force b/t the two surfaces.

All surfaces, even smooth are rough at the microscopic level. When surfaces start to move, a weaker kinetic friction results.

The details of this process are still unknown! We simplify our calculations using a model

Model of Friction

This model makes two assumptions:

1.Friction depends on the surfaces in contact

2.Friction does not depend on the area of surfaces in contact

Example: a block of wood flat on the desk vs. on its side

Static Friction

Static Friction (Starting Friction) – the force that opposes the start of relative motion between two surfaces in contact

***these are maximum values***

When the magnitude of the force exerted exceeds the maximum value of static friction, the object will move

• Once the object starts to move, the force of friction DECREASES

Kinetic Friction

Kinetic Friction (Sliding Friction) – the force exerted on one surface by the other when surfaces are in relative motion

***these values are always less than static friction***

Ff kinetic < Ff static

Other examples:

Rolling Friction- less than sliding friction

Fluid Friction- friction in a fluid body (gas or liquid)

Force of Friction

• The magnitude of the frictional force (Ff) is proportional to the magnitude of the force pushing one surface against the other

Ff kinetic = μk FN Ff static = μs FN

Coefficient of Friction = μ (mu) – proportionality

constant for surfaces in contact

Air Resistance ~ Drag

When objects move through the air, they experience fluid friction or air resistance

As the object accelerates (freefall), air resistance INCREASES

Air resistance depends on:1. Velocity of the object2. Surface area3. Shape4. Density of the fluid

• As velocity increases, so does the drag force

• Eventually, the weight = drag

• At this point, the body no longer accelerates ~ terminal velocity

TERMINAL VELOCITY – the constant velocity that is reached when drag force equals the force due to gravity (dynamic equilibrium)

Newton’s 3rd Law

Newton’s 3rd Law – all forces come in pairs; equal in magnitude, opposite in direction

Interaction Pair (action-reaction pair) = two forces that are in opposite directions and have equal magnitudes

***common misconception*** action-reaction forces act on different objects therefore, equilibrium does not result

(the normal force and weight are not action-reaction forces!)

YouTube - Newton's 3rd Law - Science Theater 09

Inclines

Hanging Signs

Solving using the component method:

x = F cos θ y = F sin θ

• Add the x and y components • Use Pythagorean Theorem to find R• The magnitude of R is the magnitude of the

weight of the sign• The direction of the weight is down