Dynamics - Cedarville University
Download
Report
Transcript Dynamics - Cedarville University
Force and Motion
Mousetrap Education
•
•
•
•
Don’t be in the wrong place at the wrong time.
Time and chance happen to us all.
One thing leads to another.
Actions have consequences.
• Causality
– Law of cause and effect
– Sewing and reaping (Gal. 6:7-9)
Newton’s
st
1
Law
• An object at rest remains at rest and an
object in motion remains in uniform straight
line motion unless acted on by an
unbalanced force.
• Inertia - Property of matter that resists
changes in motion.
Is inertia good or bad?
Newton’s 2nd Law
• Newton’s 2nd Law - The rate of change in
momentum is equal to the net force acting on
the body.
Fnet
dv
ma
m
dt
• Ex. What force must be applied to a 40 kg
ball for its velocity to be v 5.0t 2 iˆ 6.0t ˆjm / s
Additional Info
• Will use summation notation
for net force.
N
Fnet Fi F1 F2 F3 ... FN
i 1
Which way will
the ring move?
• Units for force
200 N
– From dimensional analysis
– In metric will use a newton
(N)
kg m
1N 1 2
s
LM
F 2
T
350 N
300 N
450 N
Fundamental Forces
•
•
•
•
•
Gravitational - Masses attract
Electrical - Unlike charges attract
Magnetic - Unlike poles attract
Weak - Responsible for radioactive decay
Strong - Holds the nucleus of the atom together
Weight
• Weight - The force due
to gravity.
W mg
• What is the weight of
Alexeyev on the
moon? On Jupiter?
At 157 kg
and lifting
246 kg
nd
2
Newton’s
Law
and Weight
• Ex. You and your bike weigh 882 N. If
your brakes can exert a force of 200 N,
what stopping distance do you need if you
are traveling at 11 m/s?
w
Elevator Ride
• You stand on a scales while in an elevator. You
know you weigh 150 lbs, but the scales say you
weigh 180 lbs. What is happening in the elevator?
•It is stationary.
•It is moving upward at constant v.
•It is moving downward at constant v.
•It is moving upward at increasing v.
•It is moving downward at increasing v.
•It is accelerating upward.
•It is accelerating downward.
Elevator (Cont.)
• Ex. You stand on a scales while in an
elevator. You know you weigh 150 lbs., but
the scales say you weigh 180 lbs. What is
your acceleration?
Fs
W
Fs W ma
Newton’s
• For every action
there is an equal and
opposite reaction.
FAB FBA
FBA FAB
rd
3
Law
Newton’s 3rd Law
• Ex. A 110 kg skydiver
accelerates towards the
earth at 9.8 m/s². How does
the earth respond to him?
mearth = 5.97 × 1024 kg
Hooke’s Law
• Hooke’s Law - The force exerted by a
spring is proportional to the distance the
spring is compressed or stretched from its
rest state.
F kx
k - spring constant (N/m)
• This is a restoring force. It opposes the
displacement from its rest state.
Plan of Action
1.
2.
3.
4.
5.
6.
7.
8.
Identify objects of interest.
Draw free-body diagram
Write Newton’s 2nd Law
Choose coordinate system.
Write out forces in chosen coordinates.
Solve equations symbolically.
Check the sense of the problem.
Insert the values for numerical answers.
Behind the Scenes
• A 15 kg stage prop is
suspended from the ceiling by
two ropes which are each run
through a pulley and attached
to a 20 kg sandbag. What
angle does each rope make
with respect to the horizontal?
(Assume no friction in pulleys
and massless ropes.)
Down the Ramp
• A 1.1 kg block is at the top of a 8.00 m long
ramp that is at an angle of 11.8°. If it starts
at rest, how long does it take to get to the
bottom of the ramp?
(Assume the surface is frictionless.)
q
Col. 1:16,17
“All the towering materialism which dominates the modern
mind rests ultimately upon one assumption; a false
assumption. It is supposed that if a thing goes on repeating
itself it is probably dead; a piece of clockwork. People feel
that if the universe was personal it would vary; if the sun
were alive it would dance. This is a fallacy even in
relation to known fact. For the variation in human affairs
is generally brought into them, not by life, but by death; by
the dying down or breaking off of their strength or desire.
A man varies his movements because of some slight
element of failure or fatigue.”
G.K. Chesterton (Orthodoxy)