Transcript Document

Contact forces
- Involve physical contact between
objects.
Field forces:
-No physical contact between
objects
- Forces act through empty space
gravity
electric
magnetic
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.
Newton’s 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
Inertial frame of reference:
-A frame (system) that is not accelerating.
- Newton’s 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?
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.
- Don’t confuse mass and weight (see: bit later).
Newton’s 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.


F  m a
Fx  m ax
Fy m ay
Fz  m az
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 = 1kg·m/s2
Black board example 5.1
(related to HW problem)
F2 = 8.0 N
2 = 60°
F1 = 5.0 N
Two forces act on a hockey puck
(mass m = 0.3 kg) as shown
in the figure.
1 = 20°
(a) Determine the magnitude and direction of the net force acting
on the puck
(b) Determine the magnitude and the direction of the pucks
acceleration.
The force of gravity and weight
• Objects are attracted to the Earth.
• This attractive force is the force of gravity Fg.


Fg  m g
• The magnitude of this force is called the weight of the object.
• The weight of an object is, thus m·g.
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.
Newton’s 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:


F12  F21
Action and reaction forces always act on different objects.
Where is the action and reaction force?
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.
(a) Who experiences the larger force?
(b) Who experiences the larger acceleration?
(c) Who moves away with the higher speed?
(d) Who moves farther while their hands are in contact?
Black board: Free body diagram
• Analyzing forces
• Free body diagram
• Tension in a rope = magnitude of the force that the rope exerts
on object.
Applying Newton’s laws
•
•
•
•
•
•
Make a diagram (conceptualize)
Categorize:
no acceleration: F  0
accelerating object:
F ma
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 Newton’s law for each body and each
coordinate component.  set of equations.
Finalize by checking answers.
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.
Black board example 5.3 (on HW)
A crate of mass m is placed on a frictionless plane of incline = 30.
(a) Determine the acceleration of the crate.
(b) 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?




Black board example 5.4
(on HW)
Attwood’s machine.
Two objects of mass m1 = 2.00 kg and m2 = 4.00 kg are hung over
a pulley.
(a) Determine the magnitude of the acceleration of the two objects and
the tension in the cord.
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
The following empirical laws hold true about friction:
- Friction force, f, is proportional to normal force, n.
f s  s n
fk  k 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 don’t depend on the area of contact.
- s and k don’t 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.
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°.
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
Black board example 5.6
(on HW)
A car is traveling at 50.0 mi/h on a horizontal highway.
(a) 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?
(b) What are the advantages of antilock brakes?