Chapter 4 Notes 4.1-4.4: Motion and Force: Dynamics
4.1 Force
Warm-up: How and why do objects move?
Force – any kind of a push or a pull on an object.
We can exert a force on an object, but it may not move because we cannot equal the force
it takes to move the object. A shopping cart is easy to move, but pushing a car up a hill is
a different story. It’s much more difficult to move.
We can measure the magnitude of a force with a spring scale, but force also has a
direction. It is a vector and can be drawn as an arrow just like we did with vectors in
chapter 3.
4.2 Newton’s First Law of Motion
Aristotle (384-322 B.C.) said that an object is naturally at rest unless a force is applied to
it. He also stated that in order to push a book across the table, you’d have to apply a
continuous force to it. Finally he said that the greater the force, the greater the speed of
the object.
Galileo (1564-1642 A.D.) came up with a very different approach. He said that an object
in motion is just as naturally in motion as it is when it’s at rest.
1. First he observed that it takes a lot of consistent force to move an object along a
rough surface.
2. Second he observed that he could move a heavier object along a smoother surface
with nearly the same force.
3. Third he noticed that if a perfect lubricant was created, then the heavy object
could move across the table without losing speed after the initial force was
applied.
Example – Think about an air hockey table. The puck glides across the table because
there’s almost no friction.
This made Galileo come to the conclusion that if a force is applied to an object and
there is no other frictional force acting on that object, then the object will maintain
its speed in a straight line.
The only problem with this is that Galileo assumed that as the object moved, the force of
the object equaled the frictional force of the surface, making the net force equal to zero.
Newton (1642-1727) took this knowledge and came up with three very important laws of
motion.
The first law or the law of inertia states that every body continues in its state of rest
or of uniform speed in a straight line unless acted on by a nonzero net force.
Inertia – The tendency of a body to maintain its state of rest or of uniform motion in a
straight line.
In some frames of reference, Newton’s first law does not uphold. For example, a cup on
a dashboard stays at rest as long as the car’s velocity is constant. If the car increases its
speed, a person inside the car sees the cup accelerate towards them. There is no force
acting on the cup, but somehow it moved towards the person.
We know that a force was applied to the car which made a net change in the car and the
cup didn’t have a force applied to it, so its speed remained the same. This caused the cup
to move towards the person in the car, but from the perspective of the person in the car,
the cup moved with no forces being applied to it. When we have a frame of reference
glitch like this, we call it a noninertial reference frame. When Newton’s first Law does
hold up we call it an inertial reference frame.
4.3 Mass
Newton used the term mass to describe the quantity of matter.
Mass – measure of the inertia of a body. (In other words, the more mass a body has, the
harder it is to change its state of motion.
The standard units for mass are kilograms.
Mass vs. Weight – Mass is the quantity of matter, but weight is defined as force of
gravity acting upon the object.
Example – If you traveled to space, the acceleration of gravity acting on you is zero, so
your weight is zero (hence the weightlessness), but your mass or (quantity of matter) is
the same.
4.4 Newton’s Second Law of Motion
Newton hypothesized that if a force is acted upon an object, its velocity will change.
Since a change in velocity is an acceleration, Newton said that force is directly
proportional to the acceleration of an object.
He noticed that if you double the force on an object, its acceleration doubles as well. He
also noticed that the acceleration depended on the mass of an object as well.
Example: It’s much easier to push and accelerate a shopping cart without food in it as it
is to accelerate food in it.
Newton’s Second Law states that the acceleration of an object is directly
proportional to the net force acting on it and is inversely proportional to its mass.
The direction of the acceleration is in the direction of the net force acting on the
object.
This can simply be written as:
F = ma
where F equals the net force of the object, m equals the mass of the object, and a equals
the acceleration of the object.
Every force is a vector and units of force are in Newtons ((kg*m)/s2).
Homework – pg. 103-104 Q-1, 3, 4, 5, 7, 9 P 1-7 odd