According to Newton’s
If the force is
held constant
the relationship between
mass and acceleration is
direct/inverse.
If the mass is
held constant
the relationship between
force and acceleration is
direct/inverse.
If the acceleration is
held constant
the relationship between
mass and force is
direct/inverse.
nd
2
Law
In this situation . . .
Mass
• Amount of matter in an
object
• Is always constant at any
place and time
• Is measured in kilograms
• Is measured using a balance
• Is an intrinsic property of an
object and is independent of
any external factor
Weight
• Force which a given mass
feels due to the gravity at its
place
• Depends on gravity at the
place
• Is measured in Newtons
• Is measured using a scale
• Depends on:
– Mass of the object
– Mass of the object that is
attracting it
To calculate weight:
When you know the mass use ΣF = ma
If standing on the Earth (no friction force),
acceleration due to gravity is 9.8 m/sec/sec
Mass = 65.0 kg
Weight on earth?
Weight on the moon?
Weight on Jupiter?
Free Fall
Falling without air resistance
∑F=ma
Gravity is the only force acting upon the
object causing the object to change it’s
velocity
 Acceleration (change in velocity) due to
gravity on earth is 9.8 m/sec/sec for all objects
That means . . . When an object is in free fall it
will be increasing its velocity 9.8 m/sec every
second
Free Fall on the Moon
a = 9.8 m/sec/sec
Free Fall neglecting friction – which
object – the elephant or the featherwill hit the ground first
True or false:
 The elephant and the feather each have the same
force of gravity
 The elephant has the greatest acceleration
(change in velocity)
 On earth, all objects (whether an elephant or a
feather) have the same force of gravity
 The elephant and the feather have the same
acceleration (change in velocity) due to gravity
Free fall cont.
 In the absence of air resistance, the elephant
and the feather land at the same time.
 The force of gravity experienced by an object
is dependent upon the mass of that object.
RULE: all objects (regardless of their mass)
experience the same acceleration
(change in velocity) when in a
state of free fall
Free Fall
Draw a velocity vs. time graph
v
Draw an acceleration vs. time
graph
a
t
t
-9.8 m/s/s
Slope = -9.8 m/s/s
Acceleration of fall is less when
air resistance (drag) acts
Air resistance is the result of collisions of
the object's leading surface with air
∑F=ma
molecules.
Fluid friction (air drag) depends on two
things: surface area & speed
The greater the surface area, the greater the
friction
As an object falls, the friction increases as
the speed increases
Falling with Air Resistance
Falling with air resistance
Because a is not zero
the balls are speeding
up, friction increases
Because a is not zero
the balls are still
speeding up, friction
gets bigger
ΣF = 0
a=0
Because a = 0 ball no
longer speeds up; ball
will travel at that speed
the rest of the way down
(terminal velocity)
Same size, different mass
ΣF = ma
ΣF & m are directly related
bigger mass = bigger weight
a (change in velocity) = 9.8 m/sec/sec
ΣF on each ball decreases
ΣF and a are directly related
smaller ΣF = smaller a
Balls are still speeding
up but not as much as
they were before
ΣF is smaller than
before so a is smaller
Ball will continue to
speed up but not as
much as it was before
Terminal Velocity
Draw a velocity vs. time graph
v
Draw an acceleration vs. time
graph
a
t
t
Lab 4 Air Resistance
• Purpose: Does changing the mass of a falling object
affect the velocities observed on the motion graphs?
• Method:
• Materials: motion detector on ceiling; laptop; coffee
filters
• Hypothesis:
• Procedure:
• Data: 5 different velocity vs. time graphs
• Analysis: analyze motion on graphs and label with
descriptions of motion (ie where is the terminal
velocity)
• Conclusion:
Which object - the elephant or the
feather - will hit the ground first?
True or false:
 The elephant encounters a smaller force of air
resistance than the feather and therefore falls
faster.
 The elephant has a greater acceleration (change in
velocity) due to gravity than the feather and
therefore falls faster.
 Both elephant and feather have the same force
of gravity, yet the feather experiences a greater
air resistance.
 The feather has a smaller force of gravity so
friction equals the force of gravity sooner
causing a net force of zero (no acceleration);
whereas the elephant has a net force that is not
zero and will continue to speed up.
What is the acceleration for A?
What is the acceleration for B?
What is the acceleration for C?
What is the acceleration for D?
Which encounters the greater force of air
resistance—a falling elephant or a falling
feather?
Two smooth balls exactly the same size, one made of
wood and the other made of iron, are dropped from a
high building to the ground below. The ball to
encounter the greatest force of air resistance on the
way down is the:
a) wooden ball
b) iron ball
c) ... both the same
As she falls faster and faster through the air,
her acceleration (change in velocity)
a) increases
b) decreases
c) remains the same
What will be the acceleration (change in velocity)
of a rock thrown straight upward at the moment it
reaches the tippity-top of its trajectory (no air)?
Chapter 3 Review
1. On a long alley a bowling ball slows down as it rolls. Is
any horizontal force acting on the ball? How do you
know?
2. What is the net force on a 1-N apple when you hold it at
rest above your head? What is the net force on it after you
release it?
3. A bear that weighs 4000 N grasps a vertical tree and
slides down at constant velocity. What is the friction
force that acts on the bear?
4. Two basketballs are dropped from a high building through
the air. One ball is hollow and the other filled with rocks.
Explain in detail the fall of the two balls.
Review
6. Upon which will air resistance be greater; a sheet of falling paper or
the same paper wadded into a ball if they have both reached terminal
velocity? (Careful!)
7. Aristotle claimed the speed of a falling object depends on its weight.
We now know that objects in free fall, whatever their weights, undergo
the same gain in speed. Why does weight not affect acceleration?
8. Why is it that a cat that accidentally falls from the top of a 50-story
building hits the ground no faster than if it falls from the 20th story?
End of Chapter Exercises
1. What is the net force on a bright red Mercedes convertible traveling
along a straight road at a steady speed of 100 km/h?
2. Your empty hand is not hurt when it bangs lightly against a wall.
Why is it hurt if it does so while carrying a heavy load? Which of
Newton's laws is most applicable here?
3. When a junked car is crushed into a compact cube, does its mass
change? Its weight? Its volume? Explain.
4. If it takes 1 N to push horizontally on your book to make it slide at
constant velocity, how much force of friction acts on the book?
5. A parachutist, after opening the chute, finds herself gently floating
downward, no longer gaining speed. She feels the upward pull of
the harness, while gravity pulls her down. Which of these two
forces is greater? Or are they equal in magnitude?
1. Why will a sheet of paper fall slower than one that is wadded
into a ball?
2. How does the force of gravity on a raindrop compare with the
air drag it encounters when it falls at constant velocity?
3. How does the gravitational force on a falling body compare
with the air resistance it encounters before it reaches terminal
velocity? After?