Download L05_projectile

Find your group
• Take your seat
• Be friendly
Announcements
• Exam 1 Thursday (yes, already)
• Standards covered:
– DVA: Relate distance, velocity, and acceleration mathematically,
graphically, and conceptually.
– Vector ops: Carry out mathematical operations involving vectors:
addition, subtraction, multiplication by a scalar, dot product, and
cross product.
– N1: Relate zero net force to constant velocity.
– N2: Relate net force to acceleration.
– Forces: Calculate and describe the magnitude and direction of
the forces of gravity (weight), friction, support, and tension.
Announcements
• Quiz ½
– Questions 2, 3, 4 evaluated Standard 1 (DVA)
– Still need to fix if not all were correct
– Mechanism TBA
– I’m trying to figure how to post standards
strandings
Projectile Motion
Two independent dimensions
Objective
• Describe and explain the motion of 2-D
free fall.
What’s the point?
• How do things move when they are
thrown?
Free-Fall Trajectories
• Only force is gravity (straight down)
• Acceleration is straight down with
magnitude g
• No acceleration in horizontal direction
• Vertical and horizontal components of
velocity are independent
Handout Work
1. Determine the trajectory for a projectile
dropped from rest.
a.
b.
c.
d.
e.
Find the velocity at the end of each second.
Find the average velocity each second.
Find the displacement each second.
Plot the position at the end of each second.
Repeat until landing.
Handout Work
2. Determine the trajectory for a projectile
tossed at an angle.
a.
b.
c.
d.
e.
Find the velocity at the end of each second.
Find the average velocity each second.
Find the displacement each second.
Plot the position at the end of each second.
Repeat until landing.
Air Resistance (Drag)
• Very complicated
• Depends on airspeed: faster airspeed
gives greater drag
Poll Question
What happens to an object with zero
net force acting on it?
A.
B.
C.
D.
It is motionless.
If it is moving, it soon stops.
It has a constant velocity.
It constantly accelerates.
Hint: Remember Newton’s first law. Or
Newton’s second law.
Falling through Air
airspeed
gravity
drag
net force
accel.
Initial
Transition
Terminal
0
0 < v < vT
vT
mg
mg
mg
0
0 > drag > –mg
–mg
mg
mg–drag > 0
mg–drag = 0
g
g>a>0
0
v increasing
maximum a
v increasing
a decreasing
v constant
a=0
(Here, positive = downward, negative = upward)
Whiteboard Work
3. For an object falling from rest to its
terminal velocity:
a. Sketch an acceleration-time graph.
b. Sketch a velocity-time graph.
c. Sketch a position-time graph.
Force Diagrams
Forces on one object
Objective
• Construct an object’s force diagram from
its physical circumstances.
What’s the point?
• How can we inventory an object’s forces?
• How can we check that our model
considers the correct forces?
Force diagrams
• To find net force  acceleration
• Analyze individual and net forces on a
body
• Analyze one body free from all others
• Diagram covers only the body and the
forces acting on it
Force Diagrams
• Vector arrows directed outward from
object
• Indicate every force!
Think Question
How many forces act on the anvil?
zero
net
force
Think Question
How many forces act on the table?
zero
net
force
Combining Forces
• What are the forces on the anvil? Table?
• Free-body diagrams for them?
zero
net
force
Anvil
Support from table
Its weight
Net force ∑F = 0
Table
support from ground
its weight
anvil’s weight
Net force ∑F = 0
Whiteboard Work
4. Construct force diagrams for:
a)
b)
c)
d)
A rock falling to the surface of the moon
A crumpled wad of paper thrown horizontally
A passenger in a braking car
A box sliding down a ramp, slowing down
Reading for Next Time
• Momentum: the “quantity of motion”
• Big ideas:
– Momentum is a vector
– Momentum changes when a force acts for a
time