Transcript Newton_s_Laws

Newton’s Laws
Inertia
Force
Action Reaction
Isaac Newton (1642-1727)
• Life & Character
– Born at Woolsthorpe in
Lincolnshire (England)
– entered Cambridge
University in 1661
– Professor of
Mathematics in 1669
and Natural
Philosopher
– President of the Royal
Society of London in
1703 until death.
Scientific achievements
• GRAVITATION
– calculated the relative
masses of heavenly
bodies from their
gravitational forces,
calculated the force
needed to hold the
Moon in its orbit book:
Principia I and III
(1687)
• MECHANICS
– calculated the
centripetal force
needed to hold a
stone in a sling,
and the relation
between the
length of a
pendulum and
the time of its
swing book:
Principia I (1687)
Scientific achievements
– OPTICS
– discovered
measurable,
mathematical
patterns in the
phenomenon of
color, found
white light as
mixture of
infinitely varied
colored
rays,…book:
Opticks (1692).
•
MATHEMATICS
– discovered general
methods of resolving
problems of
curvature, embraced
in his "method of
fluxions" and
"inverse method of
fluxions",..books:
Principia I and II
(1687)
Definitions
• Dynamics= the connection between force
and motion
• Force= a push or pull upon an object,
capable of accelerating that object,
resulting from that object’s interaction with
another object. Forces only exist as a
result of interaction. Measured using the
Newton (kg*m/s2).
Overview of Types of Forces
• 1. Applied Force= force applied to an object by a person or another object.
Example: a person pushes a desk across the room, applied force acting
upon the desk.
• 2. Gravity=force by which the earth, moon, or any other planet/massive
object attracts another object toward itself. Downward pull towards the
center, on earth.
• 3. Normal Force= support force exerted upon an object that is in contact
with another stable object.
• Example: an object is resting on a surface, then the surface is exerting an
upward force upon the object in order to support its weight.
• 4. Friction Force= force exerted by a surface as an object moves across it.
The two types of friction are kinetic and static friction.
• 5. Air Resistance= acts upon objects as they travel through the air. Often
opposes the motion of an object, but is frequently neglected due to
negligible magnitude. Example: the force that slows a skydiver while he is
falling.
• 6. Tension=transmitted through a string, rope, cable or wire when pulled
tight by forces from opposite ends
• 7. Spring Force= force exerted by a compressed or stretched spring upon
any object that is attached to it. The object that is compressed or stretched is
also acted upon by a restoring force that restores it to rest or equilibrium
position (Hooke’s Law)
Definitions
• Mass= refers to the amount of matter
contained by the object; never altered by
location, the pull of gravity, speed, or any
other force. The unit of mass is the
kilogram (kg) in SI units.
• Weight= the force of gravity acting on an
object, depends on which planet is
exerting the pull. Weight is measured in
Newtons or Pounds usually.
Newton’s First Law of Motion (the law of inertia)= An object at rest
remains at rest, unless acted upon by some net force. An object in
motion remains in motion unless acted upon by some net force.
Sometimes called the law of inertia.
• Inertia=the tendency of an object to move at a
constant velocity
• Net force= sum of all forces acting on a body
• Example 1: an ice hockey puck will continue to
move with the same velocity until it hits the
boards.
• Example 2: A car comes to a sudden stop, a
package in the car continues to slide forward
because it continues in its state of motion,
maintaining its velocity as the car decreases its
velocity.
Newton’s Second Law of Motion= the acceleration of an object is
directly proportional to the net force acting on it, and is inversely
proportional to its mass. The direction of the acceleration is the
direction of the net force acting on it.
• Example (simple): A 1.5 kg ball has an
acceleration of 9.0 m/s2 to the
left. What is the net force acting on the
ball?
• Givens/Formula: m=1.5kg and
acceleration=9.0m/s2 - F=ma
• Answer: F=1.5kg*9.0m/s2= 13.5N or
14N (rounded)
Try it yourself
• Example (simple): A 5.0kg bucket of
water is raised from a well by a rope. If
the upward acceleration of the bucket
is 3.0m/s2, find the force on the bucket
by the rope.
• Givens:
• Answer:
Newton’s Second Law of Motion= the acceleration of an object is
directly proportional to the net force acting on it, and is inversely
proportional to its mass. The direction of the acceleration is the
direction of the net force acting on it.
• Example (more difficult): A parachute on a race car that weighs
8820N opens at the end of the quarter mile run when the car is
traveling 35m/s. What net retarding force must be supplied by
the parachute to stop the car in a distance of 1100m?
• Givens: m=8820N vi=35m/s vf=0 d=1100m
• Formulas: F=ma vf2=vi2+2(dy)(a) rearranged for
acceleration: a = vf2-vi2/2*dy
• Answer: Solve for the mass of the car. Solve for a and then
solve for retarding force.
• F=ma 8820N=m*9.8m/s2 so m=8820N/9.8m/s2 = 899.9kg or
900kg (rounded)
• a = vf2-vi2/2*dy
a=(02-352) / 2*1100 = 1225/2200 =
0.557m/s2
•
• F=900kg*(-0.557m/s2) = -501.3N or -5.0x102N (rounded)
Try it yourself
• - Example(simple) A 3.0kg block starts from
rest at the top of a 30.0 degree incline and
accelerates unifromly down the incline
moving 2.00m in 1.50s. Find the magnitude
of acceleration of the block. Find the force
needed to stop the block after it has slid a
distance of 2.00m.
• Givens:
• Answer:
Newton’s Third Law of Motion = to every action, there is an equal
and opposite reaction. Every push produces two forces. Example:
when you push a box forward, you also feel the box pushing at
your hand.
• Example: When a person walks, with each step, he
exerts force on the ground with his foot and the ground
exerts force back on the person’s foot.
Newton’s Third Law
Try it yourself
• A person on a scale rides in an elevator. If
the mass of the person is 60.0 kg and the
elevator accelerates downward with an
acceleration of 4.90 m/s2, what is the
reading on the scale?