Contact forces

1
Contact forces - Involve physical contact
between objects.
2

• Field forces
• No physical contact between objects
• Forces act through empty space

gravity
magnetic
electric
3
Measuring forces

• Forces are often measured by determining the
  elongation of a calibrated spring.
• Forces are vectors!! Remember vector addition.
• To calculate net force on an object you must
  use vector addition.

4

• Newtons first law
• In the absence of external forces
• an object at rest remains at rest
• an object in motion continues in motion with
  constant velocity (constant speed, straight line)
  
• (assume no friction).

Or When no force acts on an object, the
acceleration of the object is zero.
Inertia Object resists any attempt to change is
velocity
5

• Inertial frame of reference
• A frame (system) that is not accelerating.
• Newtons laws hold only true in non-accelerating
  (inertial) frames of reference!

• Are the following inertial frames of reference
• A cruising car?
• A braking car?
• The earth?
• Accelerating car?

6
Mass

• Mass of an object specifies how much inertia
  the object has.
• Unit of mass is kg.
• The greater the mass of an object, the less it
  accelerates under the action of an applied force.
  
• Dont confuse mass and weight (see bit later).

7
Newtons second law (very important)
The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to its mass.
8

• Unit of force
• The unit of force is the Newton (1N)
• One Newton The force required to accelerate a
  1 kg mass to 1m/s2.
• 1N 1kgm/s2

9
Black board example 5.1 (related to HW problem)
F2 8.0 N ?2 60
F1 5.0 N ?1 20
Two forces act on a hockey puck (mass m 0.3 kg)
as shown in the figure.

1. Determine the magnitude and direction of the net
   force acting on the puck
2. Determine the magnitude and the direction of the
   pucks acceleration.

10
The force of gravity and weight

• Objects are attracted to the Earth.
• This attractive force is the force of gravity
  Fg.
• The magnitude of this force is called the
  weight of the object.
• The weight of an object is, thus mg.

The weight of an object can very with location
(less weight on the moon than on earth, since g
is smaller). The mass of an object does not
vary.
11
Newtons third law
For every action there is an equal and opposite
reaction.
If two objects interact, the force F12 exerted by
object 1 on object 2 is equal in magnitude and
opposite in direction to the force F21 exerted by
object 2 on object 1
Action and reaction forces always act on
different objects.
12
Where is the action and reaction force?
13

• Conceptual example
• A large man and a small boy stand facing each
  other on frictionless ice. They put their hands
  together and push against each other so that they
  move apart.
• Who experiences the larger force?
• Who experiences the larger acceleration?
• Who moves away with the higher speed?
• Who moves farther while their hands are in
  contact?

14
Black board Free body diagram

• Analyzing forces
• Free body diagram
• Tension in a rope magnitude of the force that
  the rope exerts on object.

15
Applying Newtons laws

• Make a diagram (conceptualize)
• Categorize no acceleration
• accelerating object
• Isolate each object and draw a free body diagram
  for each object. Draw in all forces that act on
  the object.
• Establish a convenient coordinate system.
• Write Newtons law for each body and each
  coordinate component. ? set of equations.
• Finalize by checking answers.

16
Black board example 5.2 (on HW)
A traffic light weighing 125 N hangs from a cable
tied to two other cables fastened to a support as
shown in the figure. Find the tension in the
three cables.
17
Black board example 5.3 (on HW)

• A crate of mass m is placed on a frictionless
  plane of incline ?? 30?.
• Determine the acceleration of the crate.
• Starting from rest, the crate travels a distance
  d 10.2 m to the bottom of the incline. How long
  does it take to reach the bottom, and what is its
  speed at the bottom?

?
?
?
?
18
Black board example 5.4 (on HW)
Attwoods machine. Two objects of mass m1 2.00
kg and m2 4.00 kg are hung over a pulley.

1. Determine the magnitude of the acceleration of
   the two objects and the tension in the cord.

19
Forces of Friction

• Static friction, fs
• Kinetic friction, fk
• Friction is due to the surfaces interacting with
  each other on the microscopic level.
• sliding over bumps
• chemical bonds

time
20

• The following empirical laws hold true about
  friction
• Friction force, f, is proportional to normal
  force, n.
• ?s and ?k coefficients of static and kinetic
  friction, respectively
• Direction of frictional force is opposite to
  direction of relative motion
• Values of ?s and ?k depend on nature of
  surface.
• ?s and ?k dont depend on the area of contact.
• ?s and ?k dont depend on speed.
• ?s, max is usually a bit larger than ?k.
• Range from about 0.003 (?k for synovial joints
  in humans) to 1 (?s for rubber on concrete). See
  table 5.2 in book.

21
Black board example 5.5 (related to HW)
Measuring the coefficient of static friction A
brick is placed on an inclined board as shown in
the figure. The angle of incline is increased
until the block starts to move.
Determine the static friction coefficient from
the critical angle, ?c, at which the block starts
to move. Calculate for ?c 26.5.
22
Approximate friction coefficients
?s ?k
Rubber on concrete 1.0 0.8
Wood on wood 0.25-0.5 0.2
Waxed wood on wet snow 0.14 0.1
Synovial joints in humans 0.01 0.003
23
Black board example 5.6 (on HW)

• A car is traveling at 50.0 mi/h on a horizontal
  highway.
• If the coefficient of kinetic friction and static
  friction between road and tires on an icy day are
  0.080 and 0.1, respectively, what is the minimum
  distance in which the car can stop?
• What are the advantages of antilock brakes?