Forces and Newton’s Laws of Motion

1
Chapter 4

• Forces and Newtons Laws of Motion

2
Forces and Newtons Laws of Motion

• Forces
• Newtons Three Laws of Motion
• The Gravitational Force
• Contact Forces (normal, friction, tension)
• Application of Newtons Second Law
• Apparent Weight

3
Net Force
The net force is the vector sum of all the forces
acting on a body.
The net force is the resultant of this vector
addition.
Bold letters represent vectors. The units of
Force are Newtons, or the abbreviation N, which
represent the SI units kg-m/s2
4
Free Body Diagrams
The free body diagram (FBD) is a simplified
representation of an object, and the forces
acting on it. It is called free because the
diagram will show the object without its
surroundings i.e. the body is free of its
environment. We will consider only the forces
acting on our object of interest. The object is
depicted as not connected to any other object
it is free. Label the forces appropriately. Do
not include the forces that this body exerts on
any other body. The best way to explain the free
body diagram is to describe the steps required to
construct one. Follow the procedure given
below. (1) Isolate the body of interest. Draw a
dotted circle around the object that separates
our object from its surroundings. (2) Draw all
external force vectors acting on that body. (3)
You may indicate the bodys assumed direction of
motion. This does not represent a separate force
acting on the body. (4) Choose a convenient
coordinate system.
5
Free Body Diagram
The force directions are as indicated in the
diagram. The magnitudes should be in proportion
if possible.
6
Newtons First Law of Motion Inertia and
Equilibrium
Newtons 1st Law (The Law of Inertia) If no
force acts on an object, then the speed and
direction of itsmotion do not change.
Inertia is a measure of an objects resistance to
changes in its motion. It is represented by the
inertial mass.
7
Newtons First Law of Motion
If the object is at rest, it remains at rest
(velocity 0). If the object is in motion, it
continues to move in a straight line with the
same velocity.
No force is required to keep a body in straight
line motion when effects such as friction are
negligible.
An object is in translational equilibrium if the
net force on it is zero and vice versa.
Translational Equilibrium
8
Newtons Second Law of Motion Net Force, Mass,
and Acceleration
Newtons 2nd Law The acceleration of a body is
directly proportional to the net force acting on
the body and inversely proportional to the bodys
mass.
Mathematically
This is the workhorse of mechanics
9
Newtons Second Law of Motion
An objects mass is a measure of its inertia.
The more mass, the more force is required to
obtain a given acceleration.
The net force is just the vector sum of all of
the forces acting on the body, often written as
?F.
If a 0, then ?F 0. This body can have
Velocity 0 which is called static equilibrium,
or Velocity ? 0, but constant, which is called
dynamic equilibrium.
10
Newtons Third Law of Motion Interaction Pairs
Newtons 3rd Law When 2 bodies interact, the
forces on the bodies, due to each other, are
always equal in magnitude and opposite in
direction. In other words, forces come in pairs.
Mathematically
designates the force on object 2 due to object 1.
11
Types of Forces
Contact forces Normal Force Friction Tension Gr
avitational Force
12
Contact Forces
Contact forces these are forces that arise due
to of an interaction between the atoms in the
surfaces of the bodies in contact.
13
Normal Forces
Normal force this force acts in the direction
perpendicular to the contact surface.
14
Normal Forces
Example Consider a box on a table.
FBD for box
Apply Newtons 2nd law
This just says the magnitude of the normal force
equals the magnitude of the weight they are not
Newtons third law interaction partners.
15
Frictional Forces
Friction a contact force parallel to the contact
surfaces.
Static friction acts to prevent objects from
sliding.
Kinetic friction acts to make sliding objects
slow down. Sometimes called Dynamic friction.
16
Frictional Forces
17
Tension
This is the force transmitted through a rope
from one end to the other.
An ideal cord has zero mass, does not stretch,
and the tension is the same throughout the cord.
18
Example (text problem 4.77) A pulley is hung
from the ceiling by a rope. A block of mass M is
suspended by another rope that passes over the
pulley and is attached to the wall. The rope
fastened to the wall makes a right angle with the
wall. Neglect the masses of the rope and the
pulley. Find the tension in the rope from which
the pulley hangs and the angle ?.
FBD for the mass M
Apply Newtons 2nd Law to the mass M.
19
Example continued
Apply Newtons 2nd Law
FBD for the pulley
This statement is true only when ? 45? and
20
Gravitational Forces
Gravity is the force between two masses. Gravity
is a long-range force. No contact is needed
between the bodies. The force of gravity is
always attractive!
r is the distance between the two masses M1 and
M2 and G 6.67?10?11 Nm2/kg2.
21
Gravitational Forces
Let M1 ME mass of the Earth.
Here F the force the Earth exerts on mass M2.
This is the force known as weight, w.
Near the surface of the Earth
22
Gravitational Forces
Note that
is the gravitational force per unit mass. This
is called the gravitational field strength. It
is also referred to as the acceleration due to
gravity.
What is the direction of g?
What is the direction of w?
23
Gravitational Forces
Example What is the weight of a 100 kg astronaut
on the surface of the Earth (force of the Earth
on the astronaut)? How about in low Earth orbit?
This is an orbit about 300 km above the surface
of the Earth.
On Earth
In low Earth orbit
The weight is reduced by about 10. The
astronaut is NOT weightless!
24
Applying Newtons Second Law
The one equation everyone remembers!
Sumof the forces acting on the objects in the
system
m is the System Mass
a is the System Response
This equation is just the tip of the iceberg of
the mechanics problem. The student will need to
anlyze the forces in the problem and sum the
force vector components to build the left hand
side of the equation.
25
Applying Newtons Second Law
Example A force of 10.0 N is applied to the
right on block 1. Assume a frictionless surface.
The masses are m1 3.00 kg and m2 1.00
kg. Find the tension in the cord connecting the
two blocks as shown.
Assume that the rope stays taut so that both
blocks have the same acceleration.
26
FBD for block 2
FBD for block 1
Apply Newtons 2nd Law to each block
27
Example continued
(1)
These two equations contain the unknowns a and
T.
(2)
To solve for T, a must be eliminated. Solve for
a in (2) and substitute in (1).
28
Pick Your System Carefully
Include both objects in the system. Now when you
sum the x-components of the forces the tensions
cancel. In addition, since there is no friction,
y-components do not contribute to the motion.
29
Apparent Weight
Stand on a bathroom scale.
FBD for the person
Apply Newtons 2nd Law
30
Apparent Weight
The normal force is the force the scale exerts on
you. By Newtons 3rd Law this is also the force
(magnitude only) you exert on the scale. A scale
will read the normal force.
is what the scale reads.
When ay 0, N mg. The scale reads your true
weight.
When ay ? 0, N gt mg or N lt mg.
In free fall ay -g and N 0. The person is
weightless.
31
Apparent Weight
Example (text problem 4.128) A woman of mass 51
kg is standing in an elevator. The elevator
pushes up on her feet with 408 newtons of force.
What is the acceleration of the elevator?
FBD for woman
Apply Newtons 2nd Law
(1)
32
Apparent Weight
Example continued
Given N 408 newtons, m 51 kg, g 9.8
m/s2 Unknown ay
Solving (1) for ay
The elevator could be (1) traveling upward with
decreasing speed, or (2) traveling downward with
increasing speed. The change in velocity is
DOWNWARD.
33
Force Summary
Friction Opposes motion Proportional to normal
force Non-conservative Static dynamic Normal
Forces Perpendicular to surface at point of
contact. Magnitude needed to maintain equilibrium
Tension No mass No stretching Pulleys
Massless No friction (bearing) Tension in rope
continuously changes direction
34
Summary

• Newtons Three Laws of Motion
• Drawing free body diagrams
• Contact forces versus long-range forces
• Different forces (gravity, friction, normal,
  tension, air resistance)
• Application of Newtons Second Law