Apr 20, 2023 Physics 1 (Garcia) SJSU
Chapter 4 Newton’s Second Law
of Motion
How does an object move when a force acts on it?
Apr 20, 2023 Physics 1 (Garcia) SJSU
Force & Acceleration
Newton’s First Law of Motion,
Zero Force Constant Velocity
Definition of Acceleration,
(Acceleration) = (Change in Velocity)
(Time interval)
implies
(same as uniform motion)
Apr 20, 2023 Physics 1 (Garcia) SJSU
Force Implies Acceleration
From those two results we have that,
Net Forcenot Zero
ObjectAccelerates
implies impliesVelocity
not Constant
So if there’s a net force on an object, that implies that the object accelerates.Also have that if an object accelerates, that implies that there’s a net force.
Force Causes Acceleration
• Net Force-The combination of all forces that act on an object
• The acceleration of an object is directly related to the net force on an object (force and acceleration change in the same direction)
Apr 20, 2023 Physics 1 (Garcia) SJSU
More Force, More Acceleration
The greater the net force on an object, the greater the acceleration of that object.
Apr 20, 2023 Physics 1 (Garcia) SJSU
Acceleration Goes As Force
Larger the net force, greater the acceleration
Double the Force
Triple the Force
Half the Force
impliesDouble the Acceleration
Triple the Acceleration
Half the Acceleration
implies
implies
Acceleration “goes as” Force
Force “goes as” Acceleration.
Mathematically, we write
Force ~ Acceleration.
Apr 20, 2023 Physics 1 (Garcia) SJSU
Check Yourself
You push on a crate with 100 Newtons of force. If the friction force is 100 Newtons, does the crate accelerate?
Does that mean that the crate is not moving?
Apr 20, 2023 Physics 1 (Garcia) SJSU
Check Yourself (cont.)
Now push with 150 N; friction is still 100 N. Does the crate accelerate?
A friend helps push with an additional 150 N. By how much does acceleration increase?
Apr 20, 2023 Physics 1 (Garcia) SJSU
More Mass, Less Acceleration
The greater the mass of an object, the less it accelerates when acted on by a force.
Mass Resists Acceleration
• Acceleration is inversely proportional to mass– Inversely-the 2 values change in opposite
directions• As mass increases, acceleration decreases for a
given force• As mass decreases, acceleration increases for a
given force
Apr 20, 2023 Physics 1 (Garcia) SJSU
Mass & Acceleration
For a given force, greater mass, smaller the acceleration
Double the Mass
Triple the Mass
Half the Mass
impliesHalf the Acceleration
Third of the Acceleration
Double the Acceleration
implies
implies
Acceleration goes as
the inverse of mass. Mathematically, we write,
Acceleration ~ 1/(Mass).
Apr 20, 2023 Physics 1 (Garcia) SJSU
Check Yourself
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NOFRICTION
Newton’s Second Law
• Also called the Law of Acceleration
• The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction of the net force, and is inversely proportional to the mass of the body.
or
A=F/M
Apr 20, 2023 Physics 1 (Garcia) SJSU
Newton’s Second Law of Motion
Acceleration goes as net Force.
Acceleration goes as inverse of Mass.
Acceleration only depends on Force and Mass.
Acceleration is in the direction of the net Force.
(Acceleration) = (Net Force)
(Mass)
Apr 20, 2023 Physics 1 (Garcia) SJSU
Weight on Earth
From the Chapter 2, acceleration of gravity on Earth is 10 meters per second per second. (Notation: g = 10 m/s2 )
From Newton’s Second Law,
(Force) = (Mass) X (Acceleration)
For example, weight (force of gravity) for 1 kg is
( 10 Newtons ) = ( 1 kg ) X ( 10 m/s2 )
1 kg
10 N
Apr 20, 2023 Physics 1 (Garcia) SJSU
Demo: Elevator Cable
Tension in elevator cable depends on acceleration
10 N
1 kg
Zero acceleration
15 N
1 kg
5 m/s2 upward( ½ g upward)
5 N
1 kg
0 N
1 kg
5 m/s2 downward( ½ g downward)
10 m/s2 downward(Free fall)
Apr 20, 2023 Physics 1 (Garcia) SJSU
Free Fall Acceleration
Newton’s Second Law explains why all objects fall with same acceleration.
Ratio of weight/mass always the same since weight depends on mass.
Analogy with ratio of circumference / diameter always equals pi (3.1415…).
Apr 20, 2023 Physics 1 (Garcia) SJSU
Demo: Drop the Sheet
A flat sheet of paper falls slowly because of air resistance.
What happens if we place it on top of a book, blocking the air from reaching it?
AirResistance
Weight
Apr 20, 2023 Physics 1 (Garcia) SJSU
Friction and Air Resistance
Friction and air resistance are forces opposing motion.
Apr 20, 2023 Physics 1 (Garcia) SJSU
FrictionOrigin of friction is molecular interaction between
solid surfaces.
Friction is complicated.
Friction depends on support force and on properties of the surface.
Basic properties of friction first established by Leonardo da Vinci.
Apr 20, 2023 Physics 1 (Garcia) SJSU
Air Resistance (Drag)Origin 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, etc.
Apr 20, 2023 Physics 1 (Garcia) SJSU
Air Resistance on a Falling Object
Gravity force on an object (i.e., weight) is constant but air resistance depends on an object’s speed.
As a falling object gains speed, the resistance force gets larger so the net force decreases.
Net force is sum of:Weight (downward)Resistance (upward)
Apr 20, 2023 Physics 1 (Garcia) SJSU
Check Yourself
Golf ball has more mass than a ping-pong ball. Force of gravity is greater on: golf ball, ping-pong ball, or the same?
The two balls are the same size; when speeds are equal, drag force is greater on which ball?
Which ball falls faster (which has greater acceleration)?
GolfBall
PingpongBall
Drag
Weight
Apr 20, 2023 Physics 1 (Garcia) SJSU
Terminal SpeedSpeed of falling objects increases until drag force
balances weight.
When forces balance, zero acceleration so constant velocity.
Speed for which air resistance balances weight called terminal speed.
High terminal speed(better open the chute!)
Low terminal speed(large area of chute)
Apr 20, 2023 Physics 1 (Garcia) SJSU
Demo: Drop the CatCats seem to have an uncanny ability to survive
falls from high places. For example, cats have been known to survive falls of up to 32 stories. By contrast, dogs rarely survive falls of more than six stories. Humans usually die when they fall from such heights.
From: www.animalhealthcare.ca
In a study of cats that had fallen from up to 32 stories, an interesting finding emerged: while the rate of injury in cats seemed to increase linearly depending on the length of the fall, after seven stories, the rate of injury seemed to level off! In other words, the survival rate and severity of injuries were no more severe in a cat that fell seven stories than in one that fell 32 and in some cases, injuries were even less!
Apr 20, 2023 Physics 1 (Garcia) SJSU
Demo: Drop the Cat (cont.)After further study, the reasons for this discrepancy
became clear. When a person falls from a building, maximum speed or "terminal velocity" (120 mph) is reached after 32 stories. Cats, on the other hand, achieve terminal velocity at 60 mph after falling only five stories!
Until a cat reaches terminal velocity, it will experience acceleration and tend to reflexively extend its limbs, making it more susceptible to injuries. However, when a cat reaches terminal velocity, its vestibular system (i.e. the organs of balance) become less stimulated, causing the cat to relax. It will then orient its limbs more horizontally (splay-legged), thereby increasing air drag in much the same way a parachute does. In this posture, the force of impact also appears to become more evenly distributed.
Apr 20, 2023 Physics 1 (Garcia) SJSU
Mass: Quantity of matter in an objectWeight: Force of gravity on an object
Mass is a universal property.Weight depends on gravity
(different on Moon).
Mass is the measure of inertia.Metric unit for mass is the kilogram.Metric unit for weight is Newton (since it’s a force)
Mass & Weight
Earth Moon
Weight