CHAPTER 3

RELATIVE VELOCITY

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?

CHAPTER 4

FORCES & LAWS OF MOTION

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!!!

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.

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.

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

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

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

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.

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.

DO NOW

A 2.26 kg book is dropped from a height of 1.5 m.

a.) What is the book’s acceleration?

b.) What is its weight in Newtons?

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

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.

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.

YOU TRY

INDEPENDENTLY:

Work on 1, 3 & 4 on pg. 133

NEWTONS 2ND LAW

Force is proportional to mass and acceleration.

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

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.

To put it more simply …

ΣF=ma

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?

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 FORCE IS 100 NEWTON'SWHAT IS THE ACCELERATION OF THE SYSTEM?WHAT IS THE FORCE BETWEEN 1 AND 2?

CONNECTED MASS EXAMPLE 1

IF BLOCK ONE HAS A MASS OF 20 KG AND BLOCK 2 HAS A MASS OF 35 KG WHAT IS THE ACCELERATION OF THE SYSTEM?

CONNECTED MASS EXAMPLE 2

IF BLOCK ONE HAS A MASS OF 10 KG, BLOCK 2 HAS A MASS OF 15 KG, AND BLOCK 3 HAS A MASS OF 20KG WHAT IS THE ACCELERATION OF THE SYSTEM? IGNORE FRICTION

FRICTION

• Friction ALWAYS opposes motion – always in the opposite direction of the NET FORCE.

• There are two different types of friction: Static Friction & Kinetic Friction

STATIC FRICTION

• The resistive force that keeps an object from moving.

• Usually, the static friction of the object is equal to in magnitude but opposite in direction to the applied force.

KINETIC FRICTION

• The retarding frictional force on an object in motion is called the force of kinetic friction.

• Kinetic frictional forces arise from complex interactions at the microscopic level between contacting surfaces.

CALCULATING FRICTION

• The force of friction is proportional to the normal force.

• Friction also depends upon the surfaces in contact.

• The force of friction depends upon the composition and qualities of the surfaces in contact.

• The quantity that expresses the dependence of frictional forces on the particular surfaces in contact is called the coefficient of friction.

CALCULATING FRICTION

Ff=μFn

Ff= Force of Friction

μ= coefficient of friction

Fn = Normal Force

COEFFICIENT OF FRICTION

μk= coefficient of kinetic

friction

μs= coefficient of static

friction

EXAMPLE

A 24 kg crate initially at rest on a horizontal floor requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor.

YOU TRY

• A 25 kg chair initially at rest on a horizontal floor requires a 365 N horizontal force to set it in motion. Once the chair is in motion, a 327 N horizontal force keeps it moving at a constant velocity.

A. Find the coefficient of static friction between the chair and the floor

B. Find the coefficient of kinetic friction between the chair and the floor

ELEVATOR PROBLEM