Unit Two: Dynamics

Section 1: Forces

Definitions What is the difference between dynamics and

kinematics? What is a force? What can a force do? What

causes a force?

Key Terms: Dynamics Kinematics Force Gravitational Force Electromagnetic Force Strong Nuclear Force Inertia Net Force Normal Force Weight

What is dynamics???

Kinematics: The study of how objects move (velocity, acceleration) Galileo performed experiments that allowed him

to describe motion but not explain motion. Dynamics: The study of why objects

move. The connection between acceleration and its

cause can be summarized by Newton’s 3 Laws of Motion (published in 1687)

The cause of acceleration is FORCE.

Forces What is a force?

A push or a pull

Some forces occur when one object touches another object. Example: If you put your coat on a hook, the hook pulls up

on your coat.

Some forces occur without any physical touch. Example: Gravity pulls downward on anything you drop.

Some forces cause acceleration Example: gravity

Some forces cause stretching, bending, squeezing

4 Types of Forces

1) Gravitational Force: an attractive force that exists between all objects. It is the weakest force. Ex: The moon is held in orbit by the Earth’s

gravity. 2) Electromagnetic Force: forces resulting

from electric charge. This force gives materials their strength, their

ability to bend, squeeze, stretch or shatter. It is very large compared to gravity

4 Types of Forces

3) Strong Nuclear Force: holds the particles in the nucleus of an atom together. It is the strongest force but only acts over the

distance of a nucleus. 4) Weak Force: form of electromagnetic

force. Involved in the radioactive decay of nuclei

Newton’s First Law of Motion- Newton’s Law of Inertia

An object at rest or in uniform motion (ie, constant velocity) will remain at rest or in uniform motion unless acted on by an external force.

Reworded: An object at rest will remain at rest until a force is applied. An object moving at a constant velocity will continue to move at a constant velocity if no force is applied (ie, no acceleration).

Where did this come from?

Galileo performed many experiments and speculated that if a perfectly smooth object were on a perfectly smooth horizontal surface it would travel forever in a straight line.

Newton developed this idea.

Newton’s First Law Example

If an apple is sitting on Mr, Nguyen’s desk, it will remain there until the desk is removed (so gravity acts on it) or someone lifts it up (force).

If a car is driving along a straight road at 100km/h, it will continue to do so (given the car still has gas!) until the brakes are applied (force), there is a turn or the road surface changes (more or less friction).

Net Force

The sum of all vector forces acting on an object.

Example: What are the forces acting on a stopped car? Draw a labeled diagram.

Example: What are the forces acting on a car moving at 100km/h [N]?

Normal Force

A force that acts in a direction perpendicular to the common contact surface between two objects

Example Diagram:

Inertia

Tendency of an object to not change its motion.

Quick Experiment

Materials – cup, card, penny or coin

What to do:

Set up the card on top of the cup and the penny on the card.

Flick the card. What happens to the card? The penny? Why?

Force - Units

F=ma Force units = mass units x acceleration units

F = kg x m/s2

Physicists decided to name 1.00 kg۰m/s2 = 1.00 N

N = Newton = a force that causes a mass of one kilogram to accelerate at a rate of one meter per second squared

Gravitational Forces

Gravitational force decreases as we increase how far we are from the centre of the Earth

It is a non-contact force

Gravitational Forces

Example: Consider the following information and then compare the gravitational force on the SAME OBJECT in each case. A man standing near the equator (distance from

Earth’s centre = 6378 km) A man standing near the North pole (distance

from Earth’s centre = 6357 km) A man standing in the International Space Station

(distance = 6628 km) A man in a space ship past Pluto

Weight Vs. Mass

Weight and mass are NOT THE SAME.

Weight = the force of gravity acting on a mass. Weight can change. It is measured in Newtons (force). Weight = mass x gravitational force Fg = mg

Mass = the quantity of matter an object contains. Mass for the same object is constant. It is measured in kg.

Examples of Weight Problems

Mr. Nguyen’s dog Pi has a mass of 17kg. What would Pi’s weight be:

A) On Earth? B) On Jupiter (where g = 25.9 m/s2) C) On the Moon (where g = 1.64 m/s2)

Examples of Weight Problems

A student standing on a scientific spring scale on Earth finds that he weighs 825N. Find his mass.

Friction

A contact force Electromagnetic Force (between surface

atoms of objects touching)

Friction

There are 2 types of friction: Static Frictional Force

When you start to move an object from rest Larger than Kinetic Frictional Force due to Inertia ųs

Kinetic Frictional Force Exists when the object is moving ųK

Friction

The strength of friction depends on… Surface materials Magnitude of forces pressing surfaces together

The strength of friction DOES NOT depend on… Surface area Velocity of object moving

Coefficient of Friction

“Stickiness value” ų (symbol mu) ų has no units

Formula: Ff = ųFN

Remember: FN = - Fg

Friction Example

During the winter, owners of pickup trucks often place sandbags in the rear of their vehicles. Calculate the increased static force of friction between the rubber tires and wet concrete resulting from the addition of 200. kg of sandbags in the back of the truck.

Friction Example 2

A horizontal force of 85N is required to pull a child in a sled at constant speed over dry snow to overcome the force of friction. The child and sled have a combined mass of 52 kg. Calculate the coefficient of kinetic friction between the sled and the snow.

Tug of War

Sometimes we have more than 1 force acting on an object (like in a tug of war).

What are the forces at work in a tug of war? What direction are the forces? If your team wins, what does that mean about

the forces? If your team loses, what does that mean

about the forces? What other forces are there on the players?

Free Body Diagrams

We usually use a box or small circle to represent the object.

The size of the arrow is reflective of the magnitude of the force.

The direction of the arrow reveals the direction in which the force acts.

Each force arrow in the diagram is labelled to indicate the type of force.

Use math symbols to show equality if needed.

What can you tell about these forces???

Free Body Diagram Examples

1. A book is at rest on a table top. Diagram the forces acting on the book.

Frames of Reference

Imagine you are driving in a car. Does it feel like you have moved?

If you are watching from the road, how does your frame of reference change?

Newton’s Second Law

Newton’s first law states that there an object does not accelerate unless a force is applied to the object.

But how much will an object accelerate when there is a net force? The larger the force the larger the acceleration. Therefore acceleration is directly proportional to mass.

Acceleration also depends on mass. The larger the mass, the smaller the acceleration. Therefore acceleration is inversely proportional to mass.

Newton’s Second Law- Newton’s Law of Motion The acceleration of a body is directly proportional to

the net force and inversely proportional to its mass. Force = mass x acceleration F = ma

A net force acting on an object causes it to accelerate. The larger the mass of an object, the smaller the acceleration. We say that a massive body has more INERTIA than a less massive body.

The acceleration is in the same direction as the force.

Newton’s Second Law Examples

Ex. 1: What net force is required to accelerate a 1500. kg race car at +3.00m/s2?

Newton’s Second Law Examples

Ex. 2: An artillery shell has a mass of 55 kg. The shell is fired from a gun leaving the barrel with a velocity of +770 m/s. The gun barrel is 1.5m long. Assume that the force, and the acceleration, of the shell is constant while the shell is in the gun barrel. What is the force on the shell while it is in the gun barrel?

Newton’s Third Law

When one object exerts a force on a second object, the second object exerts a force on the first that is equal in magnitude but opposite in direction.

These forces are called action-reaction forces. Ex: If you push against a wall, you don’t go through

it as the wall “pushes back”.

Only the forces on an object determine its acceleration.

Mass versus Weight

Friction

Inertial Frame of Reference

A frame of reference that is at rest or moving at a constant velocity.

Example: You moving in a car on cruise control.

Example: You sitting at your desk. Newton’s Laws of Motion are valid here!

Non-inertial Frame of Reference

An accelerating frame of reference Example: When you suddenly stop in a car. Newton’s Laws of Motion do not apply!