UNIT 4

RELATIVE VELOCITY & NEWTONS LAWS

FRAMES OF REFERENCE

• Velocity measurements differ in different frames of reference.

• Observers using different frames of reference would generally not agree on some features of motion.

RELATIVE VELOCITY

• Write down all information that was given in the problem and that you want to know in the forms of velocities with some kind of subscript.

EXAMPLE PG 108 SAMPLE 3F

A boat heading north crosses a wide river with a velocity of 10 km/hr relative to the water. The river has a uniform velocity of 5.0 km/hr due east. Determine the boat’s velocity with respect to an observer on the shore.

YOU TRY!

(pg 109 #1)

A passenger at the rear of a train traveling at 15 m/s relative to Earth throws a baseball with a speed of 15 m/s in the direction opposite the motion of the train. What is the velocity of the baseball relative to Earth as it leaves the throwers hand?

4.1: CHANGES IN MOTION

• Force: a push or pull exerted on an object.

• Forces cause a change in velocity.• Force is a VECTOR QUANTITY.• SI unit of force is the Newton (N).• Forces can act through contact or at a

distance

CONTACT VS FIELD FORCES

• Contact Forces – result from physical contact between two objects

• Usually easy to identify• A physical push or a pull

• Field Forces – do not involve physical contact between two objects

• Example: Electric Force, GRAVITY!!!

THE MASTERMIND

• In the 1630s, GALILEO – yes not Newton – realized that a block sliding on a perfectly smooth surface would slide forever in the absence of an applied force.

NEWTON

• In 1687, Newton further developed the concepts that were initially developed by Galileo which has now come to be known as Newton’s 1st Law of Motion

NEWTON’S FIRST LAW

An object at rest remains at rest, and an object in

motion stays in motion, unless acted upon by an

outside force.

NEWTON’S FIRST LAW, CONTINUED

External force

• any force that results from the interaction between the object and its environment

Alternative statement of Newton’s First Law

• When there are no external forces acting on an object, the acceleration of the object is zero.

LAW OF INERTIA

• Newton’s 1st Law came to be known as the “Law of Inertia”

• Inertia = tendency of an object to not accelerate

• The more mass something has, the harder it is to …

• Slow it down …if it is already moving• Get it to start moving … if it is at rest

MASS

A measure of the resistance of an object to changes in its motion due to a force

Scalar quantity

SI units are kg

Inertia is an other name for mass

http://www.youtube.com/watch?v=NYSgd1XSZXc

WEIGHT VS. MASS

• Mass = the amount of matter something has.

• Weight = the magnitude of the force of gravity acting on an object.

**You need mass to calculate weight.

MASS ≠ WEIGHT

WEIGHT VS. MASS

Weight is not an inherent property of an object

• mass is an inherent propertyWeight depends upon location

THE FORCE OF GRAVITY

• The force of gravity as we talk about it in everyday life is called WEIGHT.

• We will call the force of gravity Fg.

• We can calculate the force of gravity using the following formula.

Fg= mgFg= Force of Gravity, measured in Newtons (1 N= 0.22 lb)

m= mass, measured in Kilograms

g= acceleration due to gravity, -9.8 m/s2

EXAMPLE

A bag of sugar has a mass of 2.26 kg. What is its weight?

YOU TRY!

If a the mass of Mickey Mouse is 24 kg. Calculate Mickey’s weight on Earth.

DO NOW

Calculate the Weight of the following objects:

1) A stack of textbooks with mass of 150 kg.

2) A bucket of water with mass of 45.2 kg

3) A ruler with a mass of 0.25 g.

4) A pile of papers with a mass of 2.3 g.

NEWTONS 2ND LAW

The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to an object’s mass.

All motion is caused by a force applying to a mass causing acceleration!

To put it more simply …

ΣF=ma

NEWTONS 2ND LAW

Force is proportional to mass and acceleration.

Newton’s 2nd Law relates Force, Mass and Acceleration

EXAMPLE

Roberto and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book toward Roberto. If the net external force acting on the book is 2.6 N to the right, what is the book’s acceleration?

YOU TRY

The net eternal force on the propeller of a 3.2 kg model airplane is 7.0 N forward. What is the acceleration of the airplane?

TRY: Pg. 138 #2-5

FBD: FREE BODY DIAGRAMS

• Helps analyze a situation

• Isolate an object and the forces acting on that object.

• FBDs are used to show all the external forces acting on an object.

HOW TO FBD

1. Draw your object as single point. (forces are assumed to act on a single point at the center of an object)

2. Draw and label vector arrows representing all external forces acting on the object.

3. Make sure you are only drawing the forces acting on the object and NOT the forces that the object acts on other things.

4. When finished, an FBD can be used to find the net external force on an object.

CALCULATING NET FORCE

In order to calculate the net force we must first do the following …

1. Identify a coordinate system

2. Draw a FBD of the system

3. Draw a chart breaking up our forces

4. Add all the forces in the x-direction set them equal to the “net force”

5. Repeat step three for the y-direction.

EXAMPLE 2

Derek leaves his physics book on top of a drafting table that is inclined at 35 degrees. The free body diagram (on the board) shows the forces acting on the book. Find the net external force acting on the book, determine whether the book will remain at rest in this position.

EXAMPLE

A crate is pulled to the right with a force of 82 N, to the left with a force of 115 N, upward with a force of 565 N and downward with a force of 236 N.

a.) Find the net external force in the x direction

b.) Find the net external force in the y direction

c.) Find the magnitude and direction of the net external force on the crate.

THE NORMAL FORCE

• The Normal Force= a force exerted by one object on another in a direction perpendicular to the surface of contact.

FN

Fg

EXAMPLE

A block of mass 26 kg is sitting stationary on a 1 m high table. Calculate the block’s weight and normal force.

NEWTON’S 3RD LAW

• Forces always exist in pairs

• When two objects interact with one another, the forces they mutually exert on each other are called an action-reaction pair.

NEWTON’S 3RD LAW

For every action there is an equal and opposite

reaction.

NEWTON’S 3RD LAW

• Action and reaction forces each act on different objects.

• Field forces also exist in pairs.

ACTION REACTION EXAMPLE 1

WHAT IS THE ACCELERATION OF THE SYSTEM? WHAT IS THE FORCE BOX 1 PROVIDES ON BOX 2? WHAT ABOUT BOX 2 ON BOX 1?

ACTION REACTION EXAMPLE BOX 1 HAS A MASS OF 30KGBOX 2 HAS A WEIGHT OF 196NTHE PUSH FORCE IS 100 NEWTON'SWHAT IS THE ACCELERATION OF THE SYSTEM?WHAT IS THE FORCE BETWEEN 1 AND 2?