Modified Fall 2012

Chapter 3-4

Force, Mass and Acceleration

Force• Defined as a push or a pull.• Net forces cause acceleration (change in

motion)• Unit of force is the Newton (N)• Net force is the total amount of force acting on

an object1) Can be balanced or unbalanced

a) balanced forces occur when the net force is equal to zero and do no change the motion of the object

b) unbalanced forces when the net force is NOT equal to zero and do change the

motion of the object.

Calculating the Net Force• When the forces are acting in the

same direction, add to get the net force.

2N + 2N = 4N

The above object will accelerate because there is a net force acting on it.

• When the forces are acting in opposite directions, subtract to get the net force.

2N - 2N = 0N

This object will not accelerate because the net force is equal to zero.

Equilibrium occurs when the net force is zero, the object will not change its motion

Calculate the net force

1) 3N 4N

Calculate the net force

1) 3N 4N 7N to the left

2) 2N 2N

Calculate the net force

1) 3N 4N 7N to the left

2) 2N 2N 4N up

3) 3N 4N

3N 4N 1N to the left

3N 4N

7N

3N 4N 1N to the left

3N 4N Force UP 3 + 4 = 7 Force Down = 7

Net Force = Force Up – Force Down

7 – 7 = 0N 7N

5) Which direction will the block move?

5N A

5N

C B

5) Which direction will the block move?

5N A

5N

C B

6) What is the net force on the block?

6N

9N

a) Between 6N and 9Nb) Less than 6Nc) Exactly 9Nd) Greater than 9N

6) What is the net force on the block?

6N To Solve: Use the

Pythagorean theorem.

9N6N

a) Between 6N and 9N 9N

b) Less than 6N a2 + b2= c2

c) Exactly 9N 92 + 62 = c2

d) Greater than 9 81 + 36 = 122 122 = 11 N

Friction – A Force• Defined as a force that results from

the movement of 2 objects in contact.• Caused by the surface irregularities

between the 2 objects.

rough surface smooth surface

has high friction has low friction(carpet) (ice)

• Friction is what causes things to wear outExamples: break pads, erosion

• Friction resists motion

motion of block is to the right

The force of friction acts to the left

• Friction is what enables moving objects to come to rest

Types of Friction1) Static Friction occurs between

surfaces that are not moving. This is the friction you must overcome in order to start motion.a) static friction is the most difficult friction to overcome.

2) Sliding (Rolling) Friction occurs between surfaces that are moving

3) Air Resistancea) friction due to air pushing up on a falling objectb) depends on size, shape, and speed of the object

air resistance gravity

c) Terminal velocity occurs when the force of gravity down equals the air resistance up.1) Highest velocity a falling object will reach

The Absence of Air Resistance

• In the absence of air resistance all objects will fall at the same rate.

• If a hammer and a feather are dropped at the same time on the moon, both will land at the same time because there is no air resistance.

Gravity – Another Force• Is a force that every object exerts on

every other force.• Is the weakest force in nature• The Law of Universal Gravitation The

force of gravity depends on the directly on the masses of the two objects and inversely on the square of the distance between the objects*Increase mass = increase gravity*Increase distance = decrease gravity

Law of Universal Gravitation Formula

Force of mass 2 gravity mass 1

F = G (m1m2)

d2

Universal constant distance squared

Gravity & Weight• Gravity is the force the earth exerts on you• The force of gravity changes with location• Weight is a measure of the force of gravity

acting on a mass• Formula: Weight = mass X gravity

W = m X g• Units:

Weight = Newtons (N)Mass = kilogram (kg)Gravity = m/s2

on earth = 9.8m/s2

W

m g

Mass Weight

DefinitionThe amount of matter in an object

Measure of the force of gravity

on an object

Property

Unit

Mass Weight

DefinitionThe amount of matter in an object

Measure of the force of gravity

on an object

PropertyDoes not change

based on location

Changes based on location

Unit

Mass Weight

DefinitionThe amount of matter in an object

Measure of the force of gravity

on an object

PropertyDoes not change

based on location

Changes based on location

Unit KilogramNewton (SI)

orPound

Newton’s First Law• Two Parts:

1) An object at rest will stay at rest unless a net force acts on it.2) An object in motion will continue in motion in a straight line at the same speed unless a net force acts on it.

• In other words – objects resist changes in motion.

• Inertia is the ability of an object to resist changes in its motion.1) depends on mass

a) the more mass = the more inertia

Tennis Ball Bowling Ball

• Newton’s 1st Law is known as the Law of Inertia.

Newton’s 2nd Law• Relates force and mass to

acceleration.• Formula:

acceleration = force a = F mass m

• Units: Force (N) mass (kg)

acceleration (m/s2)

(We will solve some sample problems later )

F

a m

• Formula tells us:1) Net forces cause acceleration.

a) force and acceleration are directly proportional.

1) F = A (Big Force = Big Acceleration)2) f = a (Little Force = little Acc)

2) mass resists acceleration.a) mass and acceleration are

inversely proportional1) M = a (Big mass = little

acceleration)2) m = A (small mass = big acc)

Newton’s 3rd Law• States for every action there is an

equal and opposite reaction.• Relates forces as pairs. Each force pair

is made up of an action force and a reaction force.Example: Student sitting in chairAction force: Student pushes down on chairReaction force: Chair pushes up on student

State the reaction force• Action force: Bat hits ball

Reaction force:

State the reaction force• Action force: Bat hits ball

Reaction force: Ball hits bat• Action force: You push a box to the

rightReaction force:

State the reaction force• Action force: Bat hits ball

Reaction force: Ball hits bat• Action force: You push a box to the

rightReaction force: Box pushes you to the left

• Action force: Book pushes down on tableReaction force:

State the reaction force• Action force: Bat hits ball

Reaction force: Ball hits bat• Action force: You push a box to the

rightReaction force: Box pushes you to the left

• Action force: Book pushes down on tableReaction force: Table pushes up on book

• Remember, Newton’s 3rd Law states that forces are EQUAL and opposite.

• Since forces are equal, that means that you can only apply a force to an object that an object can apply to you.

Check Understanding - Newton’s Three Laws

1) Imagine a place in the cosmos far from all gravitational and frictional forces. Suppose an astronaut in that place throws a rock. The rock will:

a) gradually stopb) continue in the same direction and the same speed

2) A 2-kg object is moving horizontally with a speed of 4 m/s. How much force is required to keep the object moving with the same speed and in the same direction?

Zero. Think about if friction could be eliminated~once an object is in motion, it will continue in motion at a constant velocity (same speed and straight line). Newton’s 1st Law INERTIA

Remember Galileo postulated that if friction could be entirely eliminated an object in motion would continue to move

3) Mac and Tosh are arguing in the cafeteria. Mac says that if he throws his jello with a greater speed, it will have greater inertia. Tosh argues that inertia does not depend on speed, but rather on mass. With whom do you agree?

Tosh

4) If you were in a weightless environment in space, would it require a force to set an object in motion?

Yes. Newton’s 1st law states: an object at rest will remain at rest unless a net force acts on it.

5) Mr. Wegley spends most Sunday afternoons at rest on the sofa watching football games and consuming large quantities of food. What effect (if any) does this situation have upon his inertia?

His inertia will increase. As he eats, he will increase his mass. As his mass increases so does his inertia.

6) When a bug and a car have a collision, both experience the same force. Which object, the bug or car, will have little change in its motion? Why?

The car will have very little change in its motion because it has more inertia.

7) While driving Anna Litical observed a bug striking the windshield of a car. The bug hits the windshield and the windshield hits the bug. Which of the two forces is greater:A) The force on the bugB) The force on the carC) Neither

C. Newton’s 3rd Law – equal and opposite forces

Momentum• Inertia in motion• Formula:

momentum = mass X velocityp = m X v

(momentum) (velocity) (mass)

Unitsmomentum = kg*m/smass = kgvelocity = m/s

p

m v

• Mass and momentum are directly proportional.1) increase mass = increase momentumExplains why a bike is easier to stop than a car traveling at the same speed.

Bike Car

p = mv p = mv

• Velocity and momentum are directly proportional1) increase velocity = increase momentumExplains why a slow moving bike is easier to stop than a fast moving bike

Slow Bike Fast Bike

p = mv p = mv

The Law of Conservation of Momentum

• States: As long as interacting objects are not influenced by outside forces (like friction), the total momentum does not change.Momentum is transferred between objects

Collisions• Examples of the Law of

Conservation of Momentum• Two types:

1) Elastic objects bounce off one another ex: billiard balls2) Inelastic collisions objects stick together ex: car crashes