Journal #21 9/30/09

Most missed question from Chapter 3 Test:

A gazelle is running in a straight line path at a constant velocity of 1340m/min. A cheetah can accelerate from 0m/min to 1820m/min in 3 seconds. What is the average acceleration of the cheetah?

Chapter 4

Forces and Newton’s 3 Laws of Motion

Isaac Newton (1642-1727)

Isaac Newton (1642-1727)

Isaac Newton is without a doubt one of the most influential men in history.Just a few of his accomplishments:• Built the first practical reflecting telescope• Developed a theory of color including the idea

that white light is composed of all colors of the rainbow

• Studied the speed of sound• Developed calculus from scratch!• Defined the 3 Laws of Motion that govern all

objects• Studied the effects of gravity (story about the

apple)

ForceA force is a push or a pull.Force is not a thing in itself, but rather an interaction between two objects.

Force is a vector quantity… direction matters in the answer!

Common Forces

Newton’s First Law

“The Law of Inertia” A body remains at rest or moves in a straight line at a constant speed unless acted upon by a net force.

Objects do not accelerate unless a net force is applied.

Newton’s First LawInertia is a property of an object most closely related to it’s mass (not to be confused with momentum) that explains why objects with greater mass resist a change in motion more than those with a lesser mass.

Net ForceNet force is the vector sum of ALL forces acting on an object. If there is zero net force, then there is

zero acceleration (constant velocity), this is a special case called equilibrium.

If there is a net force, there will be an acceleration. That means that the object will be speeding up, slowing down, or changing direction.

Free Body Diagrams A Free Body Diagram is a simple

drawing that shows the magnitude and direction of all of the force vectors acting on an object.

The length of the arrows in relation to each other is VERY important

Each arrow must point away from the “free body” and be labeled appropriately

The system, the object the force is applied to, is drawn as a shaded circle

Free Body Diagrams Here is an example

of a FBD of a book at rest on a table top.

Fg is acting downward but is “balanced” by FN acting upward.

Results in no net force and zero acceleration

Fg

FN

The book

is drawn as a ball

Common Forces

Free Body Diagrams Here is an example

of a FBD of a box being pulled by a rope at a constant speed on a flat surface.

Fg and FN are still opposite and equal.

FT and Ff are also opposite and equal.

Fg

FN

FTFf

Object is in motion, but not accelerating

Balanced Forces (zero net)

Free Body Diagrams Here is an example

of a FBD of a ball under free fall conditions.

Fg is the only force acting on this object.

The net force is down and the object is accelerating.

Fg

Object is in motion and accelerating

Unbalanced Forces (non-zero net)

HW Questions: P. 89 #1-5

Draw a FBD for the following situations:1. A flowerpot falls freely from a windowsill. (Ignore any

forces due to air resistance.) 2. A sky diver falls downward through the air at constant

velocity. (The air exerts an upward force on the person.)3. A cable pulls a crate at a constant speed across a

horizontal surface. The surface provides a force that resists the crate’s motion.

4. A rope lifts a bucket at a constant speed. (Ignore air resistance.)

5. A rope lowers a bucket at a constant speed. (Ignore air resistance.)

Answers to HW#1 #2

Fg

Fg

Ff

Answers to HW#3 #4

Fg

FT

Fg

FN

FTFf

Answers to HW#5

Fg

FT

Journal #22 10/1/09

Draw a free body diagram for the following situations: A car accelerates from rest on a flat road (there is both

friction from the air and the ground).

The space shuttle just after launch is accelerating upward (include friction from the air)

Newtons’ Second Law

The accel. of an object is directly proportional to the net force acting on the object, and inversely proportional to the mass of the object.

a Fnet

m a m

Fnet

NEWTON'S 2nd LAW

Fa

or amF

aF m

F am

m

F a

m

m

m

m

a1

F a

F a

F aM

M

M

Mass Mass is the amount of matter in

an object (not to be confused with weight)

Also considered a measure of the inertia of an object

measured in SI unit of kilograms (kg)… if mass is given in grams you must convert!

WeightWeight is the downward force upon an object due to acceleration caused by gravity

weight = mass (kg) accel. due to gravity (m/s2)

Fg = mg

measured in Newtons (N)

The weight of a 10 kg brick is...

A) 98 N B) 10 kg C) 9.8 kgD) 10 N E) 98 kg

Newton’s 2nd Law Practice

Two horses are pulling a 100-kg cart in the same direction, applying a force of 50 N each. What is the acceleration of the cart?

A. 2 m/s2

B. 1 m/s2

C. 0.5 m/s2

D. 0 m/s2

Answer B

Reason: If we consider positive direction to be the direction of pull then, according to Newton’s second law,

netnet= ,Since 50 N 50 N 100 N,

Fa F

m

2100 N= = 1m/s

100 kga

netnet= ,Since 50 N 50 N 100 N,

Fa F

m

2100 N= = 1m/s

100 kga

Journal #23 10-02-09

Two friends Mary and Maria are trying to pull a 10-kg chair in opposite directions. If Maria applied a force of 60 N and Mary applied a force of 40 N, in which direction will the chair move and with what acceleration?

A. The chair will move towards Mary with an acceleration of 2 m/s2.

B. The chair will move towards Mary with an acceleration of 10 m/s2.

C. The chair will move towards Maria with an acceleration of 2 m/s2.

D. The chair will move towards Maria with an acceleration of 10 m/s2.

Answer: C

Reason: Since the force is applied in opposite direction, if we consider Maria’s direction of pull to be positive direction then, net force = 60 N – 40 N = 20 N . Thus, the chair will move towards Maria with an acceleration.

2net 20 N

2 m/s10 kgm

F

WeightLocation Mass

Earth

Moon

OrbitingEarth

18.4 kg

18.4 kg

18.4 kg

180 N

30 N

0 N

1/6 of Earth’s

Mass and WeightOn the Moon, the force of gravity is only 1/6 as strong as on the Earth. (approx. 1.63m/s2)

While orbiting, you are practically weightless but your mass remains unchanged.

Your mass does not depend on where your are. e.g. Earth, Moon, or space

Falling with Air Resistance

Air resistance (drag force) increases with speed and increased cross-sectional area and can be effected by the size and shape of an object.

Terminal VelocityAcceleration = g

Acceleration < g

Acceleration << g

Acceleration = 0

Velocity = 0but motion is about to begin

v increasing downward

v still increasing downwardjust not as rapidly as before

Terminal velocity

mg

mg

mg

mg

F

F

F

Net Force

Terminal Velocity Terminal velocity occurs when the drag force of air

resistance becomes large enough to balance the force of gravity.

At this instant in time, there is no net force — the object stops accelerating (see D below); terminal velocity has been reached.

Newton’s Third Law

Action-Reaction LawTwo forces that make up an interaction pair of forces are equal in magnitude, but opposite in direction and act on different objects.

Newton’s Third LawFor every action, there is always an equal (magnitude) and opposite (direction) reaction.

By “action” or “reaction”, we mean a force.

Action/reaction forces do not act on the same object.

Action: tire pushes on road

Reaction: road pushes on tire

Action: rocket pushes on gases

Reaction: gases push on rocket

Identify at least six pairs of action-

reaction force pairs in the following

diagram:

Question 1If a stone is hung from a mass-less rope, at which place on

the rope will there be more tension?

A. The top of the rope, near the hook.

B. The bottom of the rope, near the stone.

C. The middle of the rope.

D. The tension will be same throughout the rope.

Answer 1Answer: D

Reason: Because the rope is assumed to be without mass, the tension everywhere in the rope is equal to the stone’s weight .

Question 2In a tug-of-war event, both teams

A and B exert an equal tension of 200 N on the rope. What is the tension in the rope? In which direction will the rope move? Explain with the help of Newton’s third law.

Answer 2Team A exerts a tension of 200 N on the

rope. Thus, FA on rope = 200 N. Similarly, FB on rope = 200 N. But the two tensions are an interaction pair, so they are equal and opposite. Thus, the tension in the rope equals the force with which each team pulls (i.e. 200 N). According to Newton’s third law, FA on rope = FB on

rope. The net force is zero, so the rope will stay at rest as long as the net force is zero.

Journal#24 10/5/09

You place a watermelon on a spring scale at the supermarket. If the mass of the watermelon is 4.0kg, what is the reading on the scale in Newtons?

Journal#25 10/6/09

A train engine is accelerating while pulling two box cars of equal mass of 1.0x104-kg. If the acceleration of the cars is 2.0m/s2, with what force must the engine be pulling. (ignore friction from the rails and the air)

Journal#26 10/7/09

A train engine is accelerating while pulling two box cars of equal mass of 1.0x104-kg. There is an opposing frictional force of 2.0x104N acting against the motion. What will be the acceleration of the cars if the engine uses a force of 3.0x104N?

Journal#27 10/8/09

Two train engines are accelerating while pulling two box cars of equal mass of 1.0x104-kg. If EACH engine uses a force of 3.0x104N and the acceleration of the cars is only 2.0m/s2, what is the opposing frictional force acting against the motion?

I Respond Questions # 1

Draw a FBD for the following situations:

A flowerpot falls freely from a windowsill. (Ignore any forces due to air resistance.)

#2 #3 #4

FgFg

Ff

Fg

FN

FTFf

Fg

FT

#1

I Respond Question # 2

A sky diver falls downward through the air at constant velocity. (The air exerts an upward force on the person.

#2 #3 #4

Fg

#1

Fg

Ff

Fg

FN

FTFf

Fg

FT