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Force and Motion
Some History:
The Copernican Revolution with Copernicus, Galileo, Kepler ...
Newton’s Principia: laws of motion
physics and calculus
Phys 250 Ch4 p1
The First Law of Motion (The Law of Inertia)
An object at rest will remain at rest and an object in motion will remain in motion (at
constant velocity) unless acted upon by an external force.
An object has a constant velocity unless there is a net force acting on it.
Forces are the “causes” of changes in motion.
forces on an object arise from interactions with other objects.
forces are vectors
the net force on an object is the vector sum of the individual forces acting on that
object
The inertia of an object is its resistance to changes in its motion.
Mass is a measure of inertia.
Inertial Frame of Reference:
a frame of reference in which Newton’s Law of Inertia holds
constant velocity!
counter examples: not an accelerating aircraft or a rotating merry go round
Phys 250 Ch4 p2
The Second Law of Motion
The rate of change of momentum with time is proportional to the net applied force and
is in the same direction as the net force


(mv )
 F
t
momentum= mass x velocity = mv


F
  ma
Force causes acceleration!
Mass is the measure of inertia
Units: 1 Newton = 1N = 1 kg · m/s2
Phys 250 Ch4 p3
1N ~ 1/4 pound
Example: What force is necessary to give a 0.80 kg cart a horizontal acceleration of 1.5 m/s2?
What is the acceleration of the cart if only 1/3 of this force is applied to the cart?
Example: A fully loaded Lockheed L-1011 has a mass of 2.17E5 kg. When it accelerates at full
throttle down a runway, the engines provide a combined force of 753 kN. If the plane starts
from rest, how far will it go during the 33.5 s that it takes to liftoff?
Phys 250 Ch4 p4
Weight: the force exerted by earth (via gravity) on an object
In free fall, gravity is the only force acting on the object
F = ma = mg = w
Weight = (mass)(acceleration of gravity)
Example: what is the weight of a two liter soda bottle which has a mass of 2.0 kg?
Phys 250 Ch4 p5
Normal Force: the contact force exerted by the surface of a rigid object
Normal Force N
Normal Force N
weight w
weight w
Normal means “perpendicular”
Normal force prevents object from sinking into surface
Example: A large crate of mass m is placed on a frictionless ramp. The ramp makes an angle q
with respect to the horizontal. What is the acceleration of the crate? What is the normal force
of the ramp on the crate?
Phys 250 Ch4 p6
Newton’s Third Law
“For every action there is an equal and opposite reaction”
For every action (force) there is a reactive force and the action and reaction forces are
equal in magnitude and opposite in direction, and act upon different bodies.
If body A exerts a force FAB on body B, then B exerts a force FBA on A so that FAB = - FBA
Action/Reaction
reaction force of table on computer
Forces on an Object
reaction force of table on computer
force of computer
on table
weight of computer
Phys 250 Ch4 p7
Example: A 68 kg passenger rides in an elevator that is accelerating upward at 1.00 m/s2.
What is the normal force of the floor on the passenger? What is the force exerted by the
passenger on the floor of the elevator?
Phys 250 Ch4 p8
Problem Solving Strategies:
Draw a “free body” diagram
all forces on each object are shown
•Choose the object to be isolated. Draw it and any geometric aspects are important.
Keep it simple!
•Draw all forces on that object as vector arrows, approximately to scale and in the
correct direction. Label all forces clearly!
•Choose a coordinate system and indicate it on the diagram. Shown the positive
direction of displacement, velocity, acceleration, etc. Resolve vectors into
components as necessary.
repeat for each object in the problem.
Phys 250 Ch4 p9
T
(+)
T-wA=FA
(+)
w
A
mA = 15kg
B
mB = 30kg
Phys 250 Ch4 p10
wB-T=FB
T=FB
mB = 30kg
(+)
B
(+)
mA = 15kg
T
A
wA -T=FA
=mA g-T
w
Phys 250 Ch4 p11
Example: A block of mass M is on a frictionless inclined plane joined by a string over a pulley
to a suspended mass m. What is the magnitude of the acceleration if the incline is at an angle
of 20º from horizontal?
Example 4.11 a bit too elaborate...
Phys 250 Ch4 p12
Friction
opposes motion
due to surfaces sticking together
Kinetic Friction: surfaces are moving relative to each other
a.k.a. Sliding Friction
Static Friction: surfaces are not moving relative to each other.
Static Friction prevents stationary objects from moving until sufficient force has been
applied.
Friction
Applied Force
Coefficient of Friction
Frictional forces depend upon
how hard the surfaces are being pressed together
-> force perpendicular to the surface = normal force
the types of surfaces that are in contact
-> coefficient of friction
F f   s FN
F f   k FN
Phys 250 Ch4 p13
Static Friction
Kinetic Friction
Material
glass on glass
wood on wood
wood on wood
steel on steel
steel on steel
rubber on solids
steel on Teflon
conditions
clean
clean and dry
wet
clean
motor oil
dry
clean

0.9 – 1.0
0.25-0.5
0.2
0.58
0.2
1-4
0.04
but ... much variation in trial to trial...0
Generally, static is (sometimes little) greater than kinetic
Example: A horizontal force of 100 N is applied to a box of books of mass 20 kg resting
on a horizontal table. Does the box slide if the coefficient of friction on the table is
0.40? If the box moves, find its acceleration.
Phys 250 Ch4 p14
Equilibrium
Static Equilibrium: no acceleration with bodies at rest.
Dynamic Equilibrium: no acceleration with moving bodies
Equilibrium implies SFi = 0
so that SFxi = 0 and SFyi = 0
Stable, unstable and neutral equi.
Example: A child sits on a sled that rests on a snow-covered hill making an angle q to the
horizontal. If the coefficient of friction is 0.10, what is the maximum angle at which the sled
will remain at rest?
Phys 250 Ch4 p15
Example: A lantern of mass 1 kg is suspended by a string that is joined to two other strings as
shown. What is the tension in each string if the top strings make an angle of 35º to the ceiling?
35º
Phys 250 Ch4 p16
35º
Example: A child of mass 30 kg sits on a light swing suspended by a rope of negligible mass.
His sister pushes him forward with a horizontal force until the rope is at an angle of 20º from
the vertical. What is the tension in the rope and how much horizontal force is required to hold
the child in that position?
Phys 250 Ch4 p17