chapter 3 nonlinear motion. 1.motion is relative example: motion of a boat with respect to the...
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Chapter 3
Nonlinear Motion
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1. MOTION IS RELATIVE
Example: Motion of a boat with respect to the ground and with respect to the river.
Velocity of river
Velocity of boat with respect to river
Velocity of boat with respect to ground
Add the velocity of the river
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Velocity of river
Velocity of boat with respect to river
Velocity of boat with respect to ground
Add the velocity of the river
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Velocity of river
Velocity of boat with respect to river
Velocity of boat with respect to ground
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2. VELOCITY - A VECTOR QUANTITY
Scalars are quantities that are specified by magnitude only.
Examples: distance, time, mass, density Vectors are quantities that are specified by
magnitude and direction. Examples: displacement, velocity,
acceleration, force, momentum, angular momentum
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4 miles east
3 miles north5 miles
370 north of east
The Displacement Vector
What is the displacementfor this trip?
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3. PROJECTILE MOTION
Projectile motion is a combination of
vertical free-fall motion and horizontal
motion at a constant speed.
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Parabola (approximately)
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Demo - Ball projector and dropperDemo - Ball projector and dropper
Demo - Monkey in treeDemo - Monkey in tree
Demo - Cart and ball launcherDemo - Cart and ball launcher
Demo - Wall parabolaDemo - Wall parabola
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The free-fall motion of a projectile near the surface of the earth is very nearly parabolic.
A parabola is one of the of a conic sections.
Circle Ellipse Parabola Hyperbola
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For a particular range less than the maximum
and for a particular launch velocity,
two different launch angles will give that range.
The two angles add to give 900.
450 gives the maximum range.
Simulation
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Free Fall Results
Horizontal motion is constant Vertical Motion is accelerated Rise time = Fall Time Final speed = Initial speed
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Actual path and ideal path (free fall) are different.
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4. FAST-MOVING PROJECTILES - SATELLITES
Lets throw stones horizontally with ever
increasing velocity.
The Earth’s curvature is 16 ft for every 5 miles
(4.9 m for 8 km).
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16 ft
16 ftCurvature of Earth
5 miles
Throw an object faster, faster.faster,
We draw in each trajectory for 1 second
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Ellipse
Ellipse
Ellipse - Circle
Ellipse
Ellipse
Parabola
Vcircle = 5 mi/s = 8 km/s Vescape = 7 mi/s = 11 km/s
Hyperbola
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4. CIRCULAR MOTION
Linear speed and rotational speed
Linear speed is a distance divided by time.
Rotational speed is an angle measurement
divided by time.
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A B
Which fly has thegreater linear speed?
B
Which fly has the greater rotational speed?
Same for both.
A
B
AB
AB
A
B
A
B
Two Flies on a Turntable
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Chapter 3 Review Questions
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A rock is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? (Neglect air resistance.)
(a) it decreases
(b) it increases
(c) it remains the same
(c) it remains the same
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In the game of baseball which path would a home run most closely approximate? (Neglect air resistance.)(a) hyperbolic
(b) parabolic
(c) eccentric
(b) parabolic
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A projectile is launched upward at an angle of 75o from the horizontal and strikes the ground a certain distance down range. What other angle of launch at the same launch speed would produce the same distance? (Neglect air resistance.)(a) 450
(b) 150
(c) 250
(b) 150
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A horizontally traveling car drives off of a cliff next to the ocean. At the same time that the car leaves the cliff a bystander drops his camera. Which hits the ocean first? (Neglect air resistance.)
(a) car
(b) camera
(c) they both hit at the same time
(c) they both hit at the same time
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Bug A is 3 inches from the center of a rotating 33.33 rpm record. Bug B is 5 inches from the center of the same record. Bug A has linear speed and rotational speed as bug B.(a) less, less
(b) less, same
(c) same, less
(d) same, same
(e) less, greater
(b) less, same