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Free Fall

•  When an object is falling under the influence of gravity ONLY, it is in “free fall”

•  For each second in free fall, objects gain 9.8 m/s in speed

•  Acceleration in free fall (sometimes called g) is 9.8 m/s2

•  This is often rounded to 10 m/s2

Example: Dropping a ball from rest

After every additional second, ball is going 10 m/s faster

v = g t

Example: Dropping a ball from rest

If speed is increasing, ball falls a larger distance during each successive second of free fall

d = (1/2) g t2

Example: Throwing a ball straight up

•  Velocity and acceleration are initially pointing in opposite directions!

•  Acceleration causes ball to lose 10 m/s every second, until it stops and starts going the other way (down!)

Example: What will the velocity of each ball be after 1 second?

What about air resistance?

•  For most compact objects and for short flights, air resistance is very small

•  If we can’t ignore air resistance, then the object isn’t in free fall anymore! Acceleration will be LESS than 9.8 m/s2

•  More to come…

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Newton’s 2nd Law (Chapter 4)

Force & Acceleration

•  Newton’s First Law of Motion:

Zero Force Constant Velocity

•  Definition of acceleration:

acceleration = change in velocity time interval

Force Implies Acceleration

•  If there’s a net force on an object, the object accelerates

•  Also, if an object accelerates, there must be a net force on it

Net Force Velocity Object not zero not constant accelerates

Acceleration is proportional to Force

•  The larger (or smaller) the force, the greater (or less) the acceleration

•  Double the force -> double the acceleration •  Triple the force -> triple the acceleration •  Half the force -> half the acceleration

•  Acceleration ~ Force

Mass Resists Acceleration

•  The more mass in the object, the more inertia it has

•  More resistance to force -> less acceleration

•  Acceleration ~ 1/mass (inversely proportional)

Acceleration & Mass

•  For a given force, mass and acceleration have opposite behavior

•  Double the mass -> Half the acceleration •  Triple the mass -> One third the

acceleration •  Half the mass -> Double the acceleration

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The more massive the body, the more force you need to

change its motion

 Need a lot of force to move a bowling ball

Only need a little force to move a ping-pong ball

Newton’s 2nd Law of Motion

•  Acceleration ~ Force •  Acceleration ~ 1/(Mass) •  Acceleration depends ONLY on mass and

force

•  Acceleration = (net force) / (mass)

Newton’s 2nd Law of Motion

•  Acceleration and Force are both VECTORS!

•  Newton’s 2nd law is a vector relationship: the directions of force & acceleration are the same!

F = m a

•  Measure mass in kg, acceleration in m/s2, and force in N. 1 N = 1 (kg m)/s2

Example: Solve for Mass

A force of 3 N produces an acceleration of 2.0 m/s2 in a box. What is the mass of the box?

Mass and Weight •  Mass: amount of matter in an object •  Weight: Force of gravity on an object

•  You can be (nearly) weightless, but never massless!

•  Mass: Measured in kg •  Weight: Measured in N (it’s just another

force!)

Weight: W

•  Acts on objects at rest or in motion

•  Always points downward (toward Earth), and acts at the center of mass of the object

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Examples: Weight vs. Mass Free Fall Revisited •  Recall: objects in free fall

have acceleration only due to gravity

•  a = 10 m/s2 •  The force acting on them

is weight or gravity. •  If an object has double the

mass, it also has double the weight

Friction and Air Resistance

•  Friction & air resistance (drag) oppose motion

Friction •  Source of friction is

molecular interaction between solid surfaces.

•  Friction is complicated, and empirical (based on experiments)

•  Friction depends on support force and on properties of the surface.

Friction Examples

•  If you push on a block, which way does friction act?

•  Say you push on the box with a force of 100 N, and the strength of the friction force is also 100 N. Will the box move? What if you push with 150 N?

Air Resistance •  Source of drag is molecules of gas (or liquid)

striking a moving object. •  Drag force depends on:

– Size (area) of the object – Speed of the object

•  Larger the size or speed, larger the drag. •  Also depends on shape of object, density of gas or liquid

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Terminal Speed •  Speed of falling objects

increases until drag force balances weight.

•  When forces balance, zero acceleration -> constant velocity.

•  Speed for which air resistance balances weight is called terminal speed.  

Newton’s Third Law

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force back on the first. Forces come in pairs!

Action-Reaction

Pairs

???  

???  

???  

???  

The Moon and Earth pull on each other with equal strength

and in opposite directions

Earth

Moon

Fg Fg

You and Earth pull on each other with equal strength and

in opposite directions

Earth

Fg

Fg

Wait, I thought I understood this stuff! Shouldn’t Earth feel less gravity from me? I’ve got

a lot less mass than Earth!

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The more massive the body, the more force you need to change its motion

Earth

Fg

Fg

Which one will move more: You or Earth?

a (acceleration) = F (force) m (mass)

Discussion: The stubborn donkey

A very lazy donkey is hitched to a cart, but refuses to move. He says: “because of Newton’s third law, if I pull on the cart then the cart will pull on me with a force that is equal in strength & opposite in direction. So I will never be able to pull the cart.” How would you convince the donkey that he’s wrong?

Walking, running, or jumping

•  For a person walking, running, or jumping, the three main forces on the person are: – Gravity (Downward) – Support of the floor (Upward) – Frictional force of the floor (Horizontal)

•  Only these forces can accelerate the person. •  Gravity is constant but the force exerted by

the floor can increase in reaction to the person exerting a force on the floor.

Important:

Action force and reaction force NEVER cancel, because they act on different

objects!!!

This is why we need to remember the force of the ground on the donkey.

Summary of Newton’s Laws 1 (Inertia): Object at rest will stay at rest, and an object in uniform motion will stay in uniform motion unless acted upon by a force. 2 (F=ma): An object’s acceleration is proportional to the force and in the same direction as the force, and inversely proportional to its mass. 3 (Pairs): When one object exerts a force on a second object, the second object exerts an equal and opposite force back on the first.

Adding Forces: More Vectors

•  Combining forces in the same or opposite directions: add or subtract!

•  But when forces act in many different directions, we have to consider the angle.

•  Sum of two or more vectors: resultant

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Vector Addition: Parallelogram Rule

Special Case: For vectors at right angles, resultant R = √(X2 + Y2)

X

Y

R

Ranking: Net Force

As seen from above, a stubborn tree stump is pulled by a pair of ropes, each with a force of 200 N but in different directions. Which one experiences the weakest net force?

Momentum & Impulse •  Momentum = mass x velocity

– units: (kg m)/s – p = mv

•  Impulse: how much force applied over how much time?

•  Impulse = Force x time interval

•  Objects have momentum, but impulses act on objects

Which of the four balls has the biggest momentum?

Which of the four balls has the smallest momentum? Impulse Changes Momentum

Impulse is related to momentum:

change in momentum = Impulse or

Mass x (change in velocity) = Force x (time interval)

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Increasing Momentum

•  Say you want to hit a baseball, and get it going as fast as possible.

•  You want to apply as big a force as you can, AND for as long a time as possible.

Decreasing Momentum

•  If you had to jump out of a burning building, which would be better: landing on the pavement, or landing on a stack of mattresses?

Change in momentum -> same in both cases Impulse -> same in both cases Remember: Impulse = force x time

Car Safety

•  It’s all about trying to maximize TIME of impact on the driver/passengers!

Seatbelts Airbags Crumple zones

Crate is pushed across the floor for 3 seconds, starting at rest with net force shown. Which crate has the

largest impulse delivered?

Crate is pushed across the floor for 3 seconds, starting at rest with net force shown. Which crate has the

largest change in momentum?

Crate is pushed across the floor for 3 seconds, starting at rest with net

force shown. Find the final speed of each box after 3 seconds.