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Physics 170 - Mechanics
Lecture 10
Newton’s Laws
Force
Kinematics vs. dynamics: what causes acceleration?
Answer: force.
Force: push or pull
Force is a vector – it has magnitude and direction
The Law of Inertia
You push on an object and it moves. If you
stop pushing an object, does it stop moving?
Only if there is friction! In the absence of
any net external force, an object will keep
moving at a constant speed in a straight line,
or remain at rest.
This is Newton’s 1st Law, and it is also
known as the Law of Inertia.
Motion and Inertial Frames
In order to change the velocity of an object
– in magnitude or in direction – a net force is
required.
An inertial reference frame is one in which
the first law is true. Accelerating reference
frames, e.g., a rotating frame, are not inertial.
Newton’s First Law of Motion
Newton’s 1st Law:
In the absence of external forces, an object
at rest remains at rest; an object in motion
remains in motion.
Inertia
If no force acts on an object, an
inertial reference frame is any frame in
which there is no acceleration on an the
object.
In (a) the plane is flying horizontally
at constant speed, and the tennis ball
does not move horizontally.
In (b) the pilot suddenly opens the
throttle and the plane rapidly gains speed,
so that the tennis ball accelerates toward
the back of the plane.
Inertia is the tendency of mass to
resist acceleration, so that a force must
be supplied to overcome inertia and
produce acceleration.
Mass
Mass is the measure of
how hard it is to change an
object’s velocity.
Mass can also be thought
of as a measure of the
quantity of matter in an
object or the quantity of
inertia possessed by the
object.
One liter of water has a
mass of 1 kg.
Calibrating Spring Force
Two equal weights exert twice the force of
one; this can be used for calibration of a spring:
Acceleration vs. Force
Now that we have a calibrated spring, we can
do more experiments.
Acceleration is proportional to force:
∝
∝
Acceleration vs. Mass
Acceleration is inversely proportional to mass:
∝
∝
Newton’s Second Law of Motion
Combining these two observations gives:
Or, more familiarly:
This is the mathematical expression of
Newton’s 2nd Law of Motion.
Units: Mass has SI units of kg, and acceleration has
SI units of m/s2.
We define the SI unit of force as:
1 newton = 1 N ≡ 1 kg m/s2.
Drawing Force Vectors
Example: Accelerated Mass
m1
A net force of 3.0 N produces an acceleration of 2.0 m/s2 on an object of
unknown mass.
What is the mass of the object?
Newton’s Second Law
Newton’s Second Law of Motion
An object may have several forces acting on it;
the acceleration is due to the net force:
Combining Forces
Forces add vectorially.
Newton’s Second Law of Motion
Free-body diagrams:
A free-body diagram shows every force acting
on an object. To draw a free-body diagram:
 Sketch the forces
 Isolate the object of interest
 Choose a convenient coordinate system
 Resolve the forces into components
 Apply Newton’s second law to each coordinate
direction
Newton’s Second Law of Motion
Newton’s 2nd Law:
An object of a given mass
m subjected to forces F1,
F2, F3, … will undergo an
acceleration a given by:
a = Fnet /m
where
Fnet = F1 + F2 + F3 + …
The mass m is positive,
force and acceleration are
in the same direction.
Example: A Sliding Ice-Cream
Carton
A force exerted by a stretched rubber
band produces an acceleration of 5.0 m/s2
on an ice cream carton of mass 1.0 kg.
When a force exerted by an identical
rubber band stretched the same amount is
applied to a carton of ice cream of mass m2,
it produces an acceleration of 11.0 m/s2.
(a) What is the mass of the second carton?
(b) What is the magnitude of the force
applied by the rubber band?
Example: Three Forces
Moe, Larry, and Curley push on a 752 kg boat, each exerting a 80.5 N force
parallel to the dock.
(a) What is the acceleration of the boat if they all push in the same direction?
(b) What is the acceleration if Moe pushes in the opposite direction from Larry
and Curley as shown?
Example: A Space Walk
You are stranded in space, away from your
spaceship. Fortunately, you have a propulsion unit
that provides a constant net force F for 3.0 s. You
turn it on, and after 3.0 s you have moved 2.25 m.
If your mass is 68 kg, find F.
The Vector Nature of Forces:
Forces in 2D
The easiest way to handle forces in two or
three dimensions is to treat each dimension
separately, as we did for kinematics.