ASTRONAUT PUSHES SPACECRAFT

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ASTRONAUT PUSHES SPACECRAFT
F 40 N ma 80 kg ms 15000 kg
as F/ms 40N/15000 kg 0.0027 m/s2
aa -F/ma -40N/80kg -0.5 m/s2
If tpush 0.5 s, then vs astpush .0014 m/s,
and va aatpush - 0.25 m/s.
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QUALITATIVE QUIZ
If we add a baffle to our propeller-driven cart,
the acceleration of the cart will a. Increase a
lot b. increase a little c. not change d.
decrease a little e. decrease a lot
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NEWTONS LAWS IN EVERYDAY LIFE
You are standing still, then begin to walk. What
was the external forced that caused you to
accelerate?
Hint It is very hard to start walking if you are
standing on ice.
What force causes a car to accelerate when a
traffic light turns green?
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NEWTON AND THE APPLE
Newton knew that at the surface of the
earth bodies (apples) fall 5 m in the first
second, and that this acceleration is due to
earths gravity.
He showed that the gravity force is the same
as if all earths mass were at its center, 4000
mi from the surface. (This required inventing
Calculus).
He wondered whether the same force attracts the
moon towards earth.
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ACCELERATION OF OBJECT MOVING IN A CIRCLE
Speed is rate of motion without regard
for direction. A car goes 60 mph.
But to tell where the car goes, direction must be
specified as well as speed.
The term velocity is used to describe both
speed and direction.
Acceleration in Newtons second law, is the rate
of change of velocity, not just speed.
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UNIFORM CIRCULAR MOTION

• Centripetal Acceleration
• Centripetal Force
• Example The moon

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Uniform Circular Motion is the motion of
an object traveling at constant speed in a
circular path.
Examples
spot on a phonograph record
washing machine during spin cycle
ball whirled around on a string
car turning a corner
moon in orbit around Earth
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CENTRIPETAL ACCELERATION
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ac v2/r
?r/r ?v/v
And, ?r v?t so
?v v(v?t)/r ?v/?t v2/r
Centripetal Acceleration ac ac v2/r
The centripetal acceleration points radially
inward toward the center of the circle.
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RELATIVE DIRECTIONS
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BALL ON STRING

• r 0.5 m, T 2 s. What is ac?
• v 2?r/T 3.14/2 1.6 m/s
• ac v2/r 2.5/0.5 5 m/s2
• What if we cut the period in half?
• ac quadruples to 20 m/s2

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Centripetal Force

• The name given to the net force needed to keep a
  mass m moving with speed v in a circle of radius
  r.
• Magnitude Fc mv2/r
• Toward the center of the circle

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EXAMPLE
How fast can a car turn a corner on a flat road?
What provides the centripetal force?
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DEFINITION OF NORMAL FORCE
A normal force FN is the component of the force
a surface exerts on an object that
is perpendicular to the surface.
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APPARENT WEIGHT
In a vertically accelerated reference frame, eg
an elevator, your apparent weight is just the
normal force exerted on you by the floor.
Applying Newtons second law FN - mg ma, or
FN mg ma
Apparent weight true weight ma where a
upward acceleration
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VERTICAL CIRCULAR MOTION
At the top Minimum v for FN 0 (apparent
weightlessness)
Fc mg
mv2/r mg
v (rg)1/2
At the bottom FN Fc mg
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Roller Coaster Numbers

• r 10 m for vertical loop
• For apparent weightlessness at top

v (rg)1/2 (109.8)1/2 10 m/s
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NEWTONS CANNON
v
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ACCELERATION OF MOON
Does a gravity force cause the moons
acceleration toward earth? If so, does it vary
inversely as the square of the distance?
ac moon v2/r (2pr/T)2/r r 3.85108 m, T
27.3 days ac moon 2.7910-3 m/s2
ac moon/g 2.7910-4
(rearth/rmoon)2 (4000mi/240000mi)2 2.7810-4