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Forces and Newton’s First and Second Law
Forces
A force is a _________________ quantity that is typically described as a push or pull. Forces cause changes in
velocities (accelerations)… more specifically, unbalanced forces cause changes in velocities. The newton (N) is
the SI unit for force… the pound is the English unit for force. One pound is about 4.45 newtons.
1 N = 1 kgm/s2
Free-Body Diagrams
Free-body diagrams (FBDs) are graphical representations of objects where all forces acting ON the object are
represented. Forces exerted by the object on other objects are not included in the diagram. FBDs are used
to analyze situations. When you isolate an object, and identify all of the forces acting on it, you can predict how the
object will move.
Newton’s First Law of Motion (Law of Inertia)
A body in motion will remain in motion at a constant velocity, which means constant ________________ and
same _______________, and a body at rest will remain at rest, unless acted upon by an unbalanced force.
Implications of Newton’s First
A body in motion at constant velocity does not necessarily require a force to keep it in motion at constant velocity.
If there were no friction, objects moving along a horizontal surface would not slow down. Any forces acting on a
body at rest or in motion at constant velocity MUST be balanced.
Q1: Which of the scenarios shown below indicates balanced forces?
Inertia is the ___________________ an object has to changes in its motion. Mass is a measure of inertia.
Q2: Which of the objects below has the greatest inertia?
What If There Were An Unbalanced Force??? Newton’s Second Law steps in where Newton’s First Law ends…
If there is an unbalanced force acting on an object, the object will accelerate:
Newton’s Second Law of Motion


 F  ma

a

F

m
F is the summation of forces acting on the object under consideration, meaning you add the forces together
always remembering that forces are vectors. F may also be called the net force, or the unbalanced force. If
there is an unbalanced force acting on an object, the acceleration of the object is directly proportional to the
unbalanced force and inversely proportional to the mass of the object.
Implications of Newton’s Second
Bigger forces yield bigger accelerations on the same mass. The same force accelerates a smaller mass more than
larger mass.
Forces and Newton’s First and Second Law
F vs. a
F vs. a
A toy car (m = 10 kg) is pushed by various
horizontal net forces, F.
Plot the data from the previous table on the
graph below:
F
a
10 N
20 N
30 N
40 N
Identify Each Variable in the Equation:


 F  ma
m vs. a
m vs. a
A net force of 100 N is exerted on objects of
various masses. Complete the table below:
Plot the data from the previous table on the graph
below:
m
a
5.0 kg
10.0 kg
15.0 kg
20.0 kg
Q3: Describe the trend you notice from the F vs. a graph:
Q4: Describe the trend you notice from the m vs. a graph:
Forces and Newton’s First and Second Law
opposite reaction.
Implications of Newton’s Third
If you push/pull on something, it pushes/pulls back on you with an equal but opposite force. These forces do not cancel each other out because
the forces are exerted on different objects. Forces always occur in pairs, called action-reaction pairs.
Newton’s Third Law perplexes, flummoxes, and frustrates some novice users… consider this… if a bug strikes the windshield of a car traveling
70 mph, the force the bug exerts on the car, and the force the car exerts on the car are EQUAL… yes, EQUAL.
Fbug = Fcar
mbug
a m
bug
=
car acar
Objectives for Everyday Forces:
Explain the difference between mass and weight.
Find the direction and magnitude and normal forces.
Use coefficients of friction to calculate frictional forces.
Weight vs. Mass
The mass of an object is the amount of matter contained by the object… that mass doesn’t change, regardless of the position of
the object within the universe. The weight of an object is the magnitude of the force of gravity acting on an object. Weight
changes based on an object’s position in the earth’s gravitational field. The weight of an object near the surface of the earth
may be calculated using:
W = mg
On a free-body diagram, the weight of an object is always represented with a force vector pointing straight down from the center
of mass, towards the center of the earth.
The Normal Force
A normal force (FN) is a force exerted by one object on another in a direction perpendicular to the surface of contact. The
normal force is not necessarily opposite the weight of an object.
Friction
Friction is a force that opposes the relative motion of two surfaces in contact. Friction is really a macroscopic effect caused by a
complex combination of forces at a microscopic level, when two surfaces are in contact.
Static vs. Kinetic Friction
Static friction is the resistive force that opposes the relative motion of two contacting surfaces that are at rest with respect to
each other. Kinetic friction is the resistive force that opposes the motion of two contacting surfaces that are moving across
one another. Kinetic friction (Fk) is less than static friction (Fs). This means that it will take a greater force to overcome static
friction when trying to move a stationary object than it would to overcome kinetic friction when moving the same object once it’s
in motion.
The Normal Force and Friction
The force of friction is proportional to the normal force. The proportionality constant is called the coefficient of friction (), and
the value for the coefficient depends on the surfaces in contact. There are separate coefficients of friction for static (s) and
kinetic friction (k) and these values may be found experimentally. We’ll cover these in greater detail later.
s=Fs,max/FN
k=Fk/FN
There is a table of values for some coefficients of
friction on page 144 of the text book.
Tension
Tension, as it applies to forces, is typically the force that is transmitted through a rope that is taut. Tension forces are always
represented as forces parallel to the rope(s), and always pull away from objects.
Drawing Free-Body Diagrams
 Isolate the object(s) under consideration, and draw a simple shape representing each object.
 Draw and label all external forces acting on the object(s).
Forces and Newton’s First and Second Law




Gravitational forces are always straight down, toward the center of the earth.
Normal forces are always perpendicular to the surfaces in contact.
Frictional forces are always drawn in the direction opposing motion, parallel to the surfaces in contact.
Tensile forces are always drawn away from the objects.
How to Solve Problems




Draw an appropriate free-body diagram, correctly labeling all forces acting on the object.
Establish a convenient coordinate system. The direction of the object’s motion should be aligned with an axis.
Resolve all forces into components parallel and perpendicular to the object’s motion.
Write equations using Newton’s Second Law for each dimension. The sum of the forces perpendicular to the object’s motion
should = 0.
 Solve for unknown variables.
Equilibrium is defined as a state in which there is no change in a body’s motion, meaning that the body is either at rest, or
moving with constant ______________ (in a straight line with constant speed). According to Newton’s First and Second Laws
of Motion, the net force (F) acting on an object in equilibrium must be _______________. That means that if there are any
forces acting on the object, they must be balanced.
1.
A 15-kg box is at rest on the floor. Sketch the free-body diagram on the box to the far right:
FBD
(a)
(b)
(c)
(d)
Is the box accelerating vertically?
Y
Is the box accelerating horizontally?
Y
Write the equation(s) for F
What is the magnitude of the weight? Of FN?
2.
N
N
m1
A 15-kg box is being pulled at constant velocity across floor by force F = 25 N. Sketch the FBD:
(a) Is the box accelerating vertically?
Y
N
(b) Is the box accelerating horizontally?
Y
N
(c) Write the equation(s) for F, and calculate the magnitude of
all of the forces acting on the box.
3.
m1
FBD
m1
F = 25 N
m1
A 15-kg box is being pulled with constant velocity across the floor by force F = 25 N (as shown). Sketch the FBD:
(a) Is the box accelerating vertically?
Y
N
(b) Is the box accelerating horizontally?
Y
N
(c) Write the equation(s) for F, and calculate the magnitude of
all of the forces acting on the box.
F = 25 N
m1
35
FBD
m1
Forces and Newton’s First and Second Law
4.
A 15-kg box is at rest on an incline as shown. Sketch the FBD:
(a) Is the box accelerating parallel to the incline?
Y
N
(b) Is the box accelerating perpendicular the incline?
Y
N
(c) Write the equation(s) for F, and calculate the magnitude of all of the
forces acting on the box.
30
FBD
m1
m1