Transcript Physics 1710 Chapter 5: Laws of Motion—I

Physics 1710 Chapter 5: Laws of Motion—I
Quiz:
What lateral acceleration does a pilot experience
who is flying a jet at 350 m/s in a 1.00 km banked
turn?
v
a
= v 2/R
a
= (350. m/s) 2 /1000. m
= 122. m/s/s = 12 g. Wow!
R
Physics 1710 Chapter 5: Laws of Motion—I
Isaac Newton
(1642 –1727)
• Published Principia
• 1687
• At age 45
Physics 1710 Chapter 5: Laws of Motion—I
1′ Lecture
• Newton’s Laws of Motion are:
 Acceleration (or deceleration) occurs if and
only if there is a net external force.
 a = F/m [Note this is a vector eqn.]
 The force exerted by a first object on a
second is always equal and opposite the
the force exerted by the second on the
first. F12 = - F21
Physics 1710 Chapter 5: Laws of Motion—I
1′ Lecture –continued (30″ more)
• Weight is the force of gravity equal to
the mass of the object.
g times
• g =9.80 N/kg
• The force of friction is opposed to the motion of a
body and proportional to the normal force.
• Free body diagrams are sketches of all the
forces acting on a body.
Physics 1710 Chapter 5: Laws of Motion—I
Aristotle
(384-322 BC)
• Wrote Physica
• Thought that force
causes motion.
• i.e. F → v
• Error: v ≠ 0, but F =0
Physics 1710 Chapter 5: Laws of Motion—I
Laws of Motion
1st Law:
An acceleration is caused by a net external
force.
Subtleties:
No net force ⇆ no acceleration.
Acceleration is the secret to understanding
motion. Cf. Aristotle.
Physics 1710 Chapter 5: Laws of Motion—I
First Law of Motion (implications)
• Equilibrium suggests ∑ F = 0.
• Force is a vector: [ F, not F]
• “Nature is conservative;”
inertia is the tendency to resist
a change in the status quo. [ Φ \ Ω \ Δ]
• An inertial frame of reference is one
that is not accelerating. [ a1 = a2 ]
Physics 1710 Chapter 5: Laws of Motion—I
Balloon Drop
Physics 1710
Chapter 5 The Laws of Motion
Terminal Velocity
Weight is the force due to gravity
• Fg = g‧m;
g =9.80 N/kg
Air resistance depends on the wind velocity
• Fv ≈ - γA v 2
•Total ∑ F = Fg+ Fv = 0
• ∑ F = gm – γAvT2 = 0
• vT = √[g‧m/ γA]
Implications?
Physics 1710 Chapter 5: Laws of Motion—I
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-0.5
Velocity (m/s)
-1
Terminal Velocity
-1.5
-2
-2.5
-3
-3.5
-4
Time (sec)
0.45
Physics 1710 Chapter 5: Laws of Motion—I
1.05
Position (m)
1
0.95
0.9
At Terminal Velocity
Free Fall
0.85
0.8
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
0.3
0.35
0.4
0.45
Physics 1710 Chapter 5: Laws of Motion—I
Balloon Drop
vT = √[g‧m/γA]
vT ∝ √m
Physics 1710 Chapter 5: Laws of Motion—I
Terminal Velocity
Weight is the force due to gravity
•vT = √[g‧m/kA]
• Heavy (i.e. massive) objects fall faster than
lighter ones. For example
g‧m > 100 kA →vT > 10 m/s, a hard fall.
• A parachute slows you down.
kA > g‧m/100 →vT < 10 m/s,
not too bad
Physics 1710 Chapter 5: Laws of Motion—I
Why does a projectile follow a
parabolic trajectory?
There is only a Force acting in the vertical
(downward) direction. Therefore, the is only
a downward acceleration.
Physics 1710 Chapter 5: Laws of Motion—I
Concept Test:
A spaceship in deep space is moving sidewise initially when it fires it’s impulse engine,
producing a constant thrust.
Sketch the trajectory of the spacecraft.
Physics 1710 Chapter 5: Laws of Motion—I
Concept Test:
A spaceship in deep space is moving sidewise initially when it fires it’s impulse engine,
producing a constant thrust.
Sketch the trajectory of the spacecraft.
It then turns off its engine; what happens
then?
Physics 1710
Chapter 5 The Laws of Motion
There are two kinds of mass ( assumed to be
equivalent):
gravitational mass: Fg = g m
inertial mass: a ∝ 1/m
a1 /a2 = m2 /m1
Mass is an inherent property of matter,
independent of the surroundings and the
method used to measure it.
Physics 1710
Chapter 5 The Laws of Motion
Summary
• Newton’s 1st Law of Motion is:
A body at rest will remain at rest and a body in motion
will remain in the same state of motion unless acted
upon by an external unbalanced force.
That is: force causes acceleration.