2. 1.Forces - study of dynamics
a. Force - a push or a pull. It can change
the motion of an object; start or stop
movement; and, change shape of object.
b. Four basic types
(1) gravitational - weakest, attractive
force between objects
(2) electromagnetic - results from basic
property of particles. Large compared
to gravitational
3. (3) strong nuclear forces - holds nucleus
together, limited in range.
• (4) weak nuclear - deals with radiation.
• c. Also classified by how they act
• (1) contact forces act due to physical
contact between objects. Push/pull.
• (2) field forces do not require contact -
such as gravitational forces,
electromagnetic forces, nuclear forces
4. (3) fields - regions around an object that
are influenced by a characteristic of the
object - mass, magnetic, etc.
• d. Unit of Force in the SI system is the
Newton (N)
(1) one newton is the force required to
give a mass of one kilogram an
acceleration of one meter per second
squared.
(2) 1 N = 1 kg-m / s2
derived unit
5. (3) 1 dyne = 1 g-cm/sec2 cgs system
• (4) 1 lb = 1 slug-ft/sec2
British Engineering System
• (5) Conversions
–(a) 1 lb = 4.448 N
–(b) 1 N = 0.225 lb
– c) 1 N = 105 dynes
6. 2.Free-Body Diagrams
a. A technique to use in solving problems
(1) Sketch object under consideration
(2) Draw and label all external forces
acting on object
(a) Assume a direction for each
force. If your selection ends up
negative(-) means it goes the other way
(b) Assume that all forces act at
the center of mass of an object. No
matter where they act they are
shown as acting at the center.
7. (3) forces that the object exerts on other
objects, its surroundings, are not shown. Only
those that act ON the object.
• (4) Rather than drawing a pictorial
representation of an object just show it
as a box, square, or circle.
• (5) Label arrows/forces
• (6) Use a free-body diagram to
determine the net external force acting
on the object.
8. 3.Newton's First Law - Law of Inertia
a. Net external force - combination of all
forces acting on an object, a vector sum.
b. Two parts - body at rest, body in motion
c. “An object at rest will remain at rest,
and an object in uniform motion remains
in uniform motion, unless acted upon by a
net external force.”
9.
10. – d. inertia depends on object's mass, so
mass is the measure of inertia - which is
the tendency of an object not to
accelerate.
• (1) mass is the amount of matter in an
object
• (2) mass also measures the amount of
inertia an object has
11. e. When the net external force acting on an
object is zero, its acceleration is zero.
– (1) NOTE: key concept is net external
force - if it is zero then the object’s
motion is not changing.
– (2) NOTE: motion can be occurring if
the object has a zero net force acting - but
that motion does not change in magnitude
or direction.
12. f. Example: A man is pulling on a sled at an angle
of 35.0o to the horizontal with a force of 500.0
Newtons. The sled has a mass of 25.0 kg.
• If the sled moves at a constant velocity on
level ground, find:
– a. the magnitude of the net force acting
on the sled.
– b. determine the x and y components of
the pulling force.
– c. draw the free-body diagram and show
all the forces acting on the object.
13. • The net force is zero since the object is moving at
a constant velocity.
• Fapplied x = F cos 35o = (500.0N)(.819152)=409.6N
Fapplied y = F sin 35o = (500.0N)(.573576)=286.8N
weight
Force applied
Force Normal
Force Friction
14. g. Equilibrium - net force acting on an object
is zero
• 1. Forces are acting but they cancel each
other out
• 2. Object is at rest or is moving at a constant
velocity - which means its speed is not
changing nor is its direction of motion.
15. 4.Newton's Second Law
a. F = m a but more easily understood by
a = F / m
b. “acceleration is directly proportional to the
net external force applied to the object and
inversely proportional to mass of object.”
c. second law is a vector equation - direction
of acceleration is the same direction as the
net force
16. 5. Newton's Third Law - Action/Reaction
a. forces always occur in pairs.
b. “If two bodies interact, the magnitude of
the force exerted on object 1 by object 2 is
equal to the magnitude of the force
simultaneously exerted on object 2 by
object 1, and these forces are opposite in
direction.”
c. Two bodies, two forces - key is to
recognize what the forces are
17. 6. Mass and Weight
a. weight - due to gravitational force
(1) w = m g (F=ma)
(2) direction is downward
b. mass - amount of matter in an object.
Two types: inertial and gravitational
18. (1) inertial mass - measured using
m = F / a
(a) force needed to accelerate an
object gives mass
(b) difficult to do - frictionless
surface and measuring acceleration
(2) gravitational mass
(a) measured using a pan balance to
compare weights of two objects
(b) unknown mass on one side,
known mass on the other
19. c. essentially different concepts, always
numerically equal. Equality of the two
types is called the "equivalence principle"
d. weight is a vector, mass is a scalar
20. 7. Normal Force - FN
• a. A contact force exerted by one object on
another in a direction perpendicular to the
surface of contact.
• b. normal is a mathematical term meaning
the force is perpendicular.
• c. a reaction force - but one that does act on
an object.
21. 8. Friction
a. A force that opposes the motion of two
objects that are touching each other
b. An electromagnetic force resulting from
temporary attractions between the
contact points of the two surfaces
c. friction always acts parallel to the
surfaces in contact and in a direction
opposing motion
22. d. Two main types
(1) Static Friction - force of friction
resisting the start of motion. Varies in
magnitude depending on the applied force
trying to start motion.
(2) Kinetic (Sliding) Friction - force
resisting existing motion
(3) Static friction is always larger than
sliding friction
(4) We will work mainly with kinetic
friction
23. e. Coefficient of Friction (µ) = Ff / FN
(1) FN represents the normal force. The
force pulling the surfaces together. It is
always perpendicular to the surfaces in
contact.
(2) Ff is the force of sliding friction. It is
parallel to the surfaces in contact and in the
opposite direction from motion
24. f.Example: a box being pulled at a constant
speed over a level surface.
FN
FApplied
Fweight
Ff
25. (1) since constant speed - no
acceleration, forces are balanced
(2) not moving off surface so sum of
forces in y direction is equal to 0
(3) force of friction depends only on the
nature of the surfaces in contact and
Normal Force.
(4) coefficient of friction (µ) is
independent of the surface areas in
contact and the velocity of the object
26. g. Example: A smooth wooden block is placed on
a smooth wooden tabletop. A force of 14 N is
necessary to keep the 40N object moving at a
constant speed.
(1) Find coefficient of friction (µ)
(2) If a 20.0N weight is placed on the
block what force will be required to
keep the block and weight moving at a
constant velocity.
27. Given:
W = 40N
FA = 14N
Ff = 14N since
constant velocity
FN = 40N, since object
not being raised
Ff = µ FN
FN = 40N
Ff =14N
W = 40N
F =14N
28. 9. Net Force Causes Acceleration
a. Net force is the vector sum of all forces
acting on a body
Fnet = Fapplied + Ffriction
b. Ex: Consider a mass of 50 kg sitting on a
frictionless surface. A force of 100N is
applies. Find a.
29. Given: m =50kg F = m a
FAPPLIED = 100N A = F /
m
Ffriction = 0
a = 2 m/s2
c. If in the above problem µ is 0.2, find a.
30. Ffriction = µ FN = 0.2 (50kg x 9.8 m/s2) and it
opposes motion of applied force
FNet = 100N + (-98N) =2N a=.04m/s2
Ffriction = 98N
Fapplied = 100N
31. d. Student Problem. A shopper in a
supermarket cart pushes a loaded cart
with a horizontal force of 10.0N. If the
cart has a mass of 30.0 kg, how far will it
move in 3 sec, starting from rest if
(1) you ignore friction
(2) if the shopper places his 30.0 N
child in the cart before he pushes it?
33. e. Elevator Problems
(1) elevator at rest - weight reading on the scale is
from the normal force of the scale pushing back
up on the object which is pushing down due to
gravity
(2) with elevator at rest, aY = 0 and ΣFY = 0
scale
weight
normal force
ΣFY = 0 = FN - W
FN = W
34. (3) elevator moving up, aY = +n & ΣFY =m aY
weight
normal force
ΣFY = m aY = FN - W
FN = apparent weight=
= W + m aY
35. (4) elevator moving down, aY = -n & ΣFY =-m aY
weight
normal force
ΣFY = -m aY = FN - W
FN = apparent weight=
= W - m aY
36. 10. Terminal Velocity
a. constant velocity when Fdrag = W
b. Air resistance is a frictional force
c. depends on the density of air, size and
shape of the object, and speed of motion
37. 11. Two-body Problems
a. To solve a problem involving two or
more bodies write F = ma for each body
separately, having first decided which
direction of motion you want to designate
as positive.
b. Both objects will have same
acceleration, just different directions
38. c. Example: Two masses are tied to
opposite ends of a massless rope, and the
rope is hung over a massless and
frictionless pulley. Find the acceleration
of the masses.
39. (1) 15 kg mass falls,
turns CW, so
designate down as
positive motion for 15
kg object and upward
as positive for 10 kg
object.
(2) Draw freebody
diagrams
(3) Note tension is the
same throughout the
rope
10 kg
15 kg
40. (4) T - 98N = 10kg (a)
147N - T = 15kg (a)
two equations with two
unknowns “T” and “a”
T
T
w = 98 N W = 147 N
