Transcript Dynamicsx

Dynamics:
Newton’s Laws of Motion
© 2014 Pearson Education, Inc.
Dynamics Notions of Motion & its Causes…
Aristotle (
)
Galileo (
)
Isaac Newton (
)
Inertia-
Inertia α _________
Ex: What does inertia have to do with getting
ketchup to spout of ketchup bottle?
Ex: Which vehicle would be tougher to…
Ex:
M
Start in Motion ___________
2M
Bring to stop
What if the car traveled at 2v?
Ex: What do car headrests have to do with inertia?
___________
A marble travels through a tube laying flat on a table.
What path will path take when it leaves?
N1L: Newton’s 1st Law -
Ex:
Ex:
Forces Balanced (At rest)
Forces UnBalanced (Accelerates)
Ex:
Forces Balanced (Constant Vel)
Ex:
Forces UnBalanced (Decelerates)
Forces & Free Body Diagrams
Force -
Types of Forces
Contact
Field
Free Body Diagram (FBD):
Equilibrium:
A 25N wooden crate is pulled at a constant velocity by a force
of 10N. What is the force of friction?
Maximizing and Minimizing the Resultant
Two forces of 70N and 30N act concurrently
at 0 degrees to each other…
Two forces of 70N and 30N act concurrently
at 180 degrees to each other…
“As the angle between two force vectors of 70N and 30N goes from 0˚ to 180˚,
the resultant goes from _______________ to ________________”
Resultants vs Equilibrants
Resultant -
Equilibrant Two forces of 70N and 30N act concurrently
at 0 degrees to each other…
Resultant =
Equilibrant =
Two forces of 70N and 30N act concurrently
at 180 degrees to each other…
Resultant =
Equilibrant =
Equilibrium vs Non-Equilibrium
Equilibrium:
Non-Equilibrium:
Jimmy fell down a well. Jimmy’s friend throws down a
rope and pulls upward with a force of 300N. If Jimmy
weighs 700N…
A file cabinet weighing 200N is being pushed by an
applied force of 100N. A retarding force (friction) of
50N opposes the motion…
a)
Does Jimmy get pulled out of the well?
a)
What is the net force acting on the file cabinet?
b)
What must be the normal force?
b)
Describe the motion of the file cabinet.
c)
Draw FBD
c)
Draw FBD
BIG IDEAS:
Forces at Angles
A man pulls a 20kg block of ice at a constant velocity by a rope. The rope makes an angle
of 25 degree with the horizontal and has a tension of 80N.
a) Draw FBD
b) What must be the force of friction?
c) What must be the normal force?
Weight
Q: An object with greater mass has a greater weight. This means there is a greater force acting on it.
Does a greater force lead to a greater acceleration? Discuss and explain..
An 80kg person weighs 48.8N on another planet.
a) What is acceleration due to gravity on this planet?
b) What would this person weigh on Earth?
N2L: Newton’s 2nd Law-
Frictionless.. A 20kg box is pushed on a
frictionless surface with a force of 50N.
Friction.. A 20kg box is pushed on a frictionless
surface with a force of 50N. The force of friction
is 25N.
a) What is the weight of the box?
a) What is the net force on the box?
b) What is the acceleration of the box?
b) What is the acceleration of the box?
Mathematical Relationships using N2L
F = ma
#1: Effects of Force on Acceleration (Constant Mass)
Big Idea -
What would acceleration be if we
doubled and tripled the force?
Force (N)
What force is necessary to accelerate
a 50kg object on frictionless surface at
1m/s2?
Acceleration (m/s2)
Mathematical Relationships using N2L
a = F/m
#2: Effects of Force on Mass (Constant Acceleration)
Big Idea -
What force ‘F’ is necessary to keep the
same acceleration on mass of ‘2m’ and
‘4m’ ?
Force (N)
What is the acceleration of a
200N force on a 100kg object?
Mass (kg)
Mathematical Relationships using N2L
m = F/a
#3: Effects of Mass on Acceleration (Constant Force)
Big Idea -
If the force remained the same, what
acceleration would a 50kg and 100kg
object have?
Acceleration (m/s2)
What is the mass of an object if a
25N force accelerates it at 1m/s2?
Mass (kg)
Mathematical Relationships using N2L
F = ma
Check Understanding…
If force ‘F’ is exerted on mass ‘m’
accelerating it at ‘a’, what force
would be needed to give
acceleration ‘4a’ ?
Force ‘F’ is exerted on mass ‘m’ giving
acceleration ‘a’. What would acceleration
be if force ‘F’ was exerted on mass ‘3m’ ?
An object is accelerating at 10m/s2 when
the net force on it is cut in half. What is
the acceleration now?
Force ‘F’ is exerted on mass ’m1’ giving it
acceleration ‘a’. If force ‘4F’ gives ‘m2’
an acceleration of ‘2a’, what is the ratio of
m1 to m2?
Expanding N2L
F = ma
A net force of 50N is applied to a 10kg
block initially at rest on a frictionless
surface…
a = Δv
t
A retarding force of 75N is exerted on a
50kg object initially traveling at +10m/s…
a) How long until the object comes to rest?
a) FBD
b) How far did the object go during that time?
b) What will be the final velocity if the
force is applied for 5 seconds?
v
c) sketch the v-t graph
t
Newton’s Third Law – N3L
Would it be smart to push off of a
Small rowboat and jump onto a dock?
Airplane Lift…
What exerts the greater force, bug on
windshield or windshield on bug?
Revolving lawn sprinklers…
Gun Recoil…
What will be a2 compared to a1?
Collaborative Work
Determine the weight of the accelerating force…
Collaborative Work
Determine the force of friction between M and the table…
Example: A 7kg box initially at rest is accelerated to the right at a rate of .5m/s2.
A frictional force of 20N works against the motion of the box…
a) What must be the applied force?
b) What is the weight of the box?
c) Complete the FBD using a scale of 1cm = 10N
d) If the applied force is exerted for 20s, how far did the box
move?
e) How fast is the box moving at the end of the 20s?
Position 1
Fnet =
f)
Label Fnet is equal to at position 1. Indicate the net force with a vector on the box.
g)
Using a scale of 1cm = 10m, draw where the box is at the end of 20s and label it position 2.
h)
At the end of 20s, the applied force is removed. What is the only force left acting on the box? Label what
the net force acting on the box is at position 2 indicating the direction.
i)
Calculate how far the box will move as it slides to rest. Draw the box at the correct location using the scale
and label it position 3. Label what the net force acting on the box is now.
g)
If the box weighed 87.3N on another planet,
is the acceleration due to gravity on that planet?
BONUS: Derive a single expression to determine
the answer in question ‘i’ in terms of the variables
(vi,F, m)
Terminal Velocity
Physics & Elevators
Constant Velocity
Rocket Science…
Accelerate Up
Accelerate Down
A 2kg model rocket accelerates upwards at 8m/s2. What thrust
force does the rocket need to attain this acceleration?
Forces at Angles
A man pulls the same block of ice at the same angle with a force of 100N.
a) Draw FBD
b) What is the acceleration?
c) What must be the normal force?
Friction TWO TYPES
Static Friction-
Kinetic Friction-
Coefficient of Friction
An 800N skier skies on level ground. How
much force doe the skier need to exert to
move forward at a constant velocity?
How much force would the girl need to
exert to get a 25kg rubber tire to start in
motion on dry asphalt?
The rope makes an angle of ______ with the horizontal… Under the conditions
from the previous slide, determine…
a) The tension in the rope
b) The normal force on both the tire and the girl.
c) The force the ground exerts on the girl.
d) The force the tire exerts on the girl.
Example: A college student pushes a heavy box across the floor into her
dorm room. She notices it takes 50N of force to get the box to start to move…
a) What is the force of static friction?
b) What is the weight of the box if the coefficient of static friction is .5?
c) Once the girl starts the box in motion, she notices it is easier to keep moving. If the
coefficient of kinetic friction is .3, how much kinetic friction is present?
d)
If the girl pushes with the same 50N of force, what will be the acceleration of the box?
e) Complete the FBD of the box as it accelerates.
Activity: Given the materials provided at your table. Determine the coefficient of static and
kinetic friction between the table top and the wooden box.
Follow Up Question: Which situation would cause the greater amount of friction when being
pulled at a constant velocity? Both blocks have the same mass.
v
v
Anti-lock braking system (ABS) is an automobile safety system that allows the
wheels on a motor vehicle to maintain tractive contact with the road surface
according to driver inputs while braking preventing the wheels from locking up
(ceasing rotation) and avoiding uncontrolled skidding
Example: Sliding Friction vs. Rolling Friction
A tired driver notices that the car in front of him has suddenly stopped. The driver slams on the breaks in an
attempt to not crash into the other car. The 1000kg car was going 20m/s when the driver slammed on the breaks …
a)
If the car did not have anti-lock breaks and the rubber tires locked causing the car to skid on dry asphalt, what
friction would be present to stop the car?
b)
What would be the deceleration of the car under these conditions?
c)
If the stopped car was 27m in front of the drivers car at the moment of braking, does he crash into the other car?
d)
Would the driver crash if he had anti-lock brakes?
A 1500kg car traveling at 20m/s slams on the breaks and comes to
a stop in 3.85seconds. What surface are the rubber tires in contact
with as the car skids to a halt? PROVE IT!!!
Derive an expression for the coefficient of friction in terms of a and g…
Incline Plane – All of Newton’s Law apply.. We simply make use of geometry to adapt the situation
Ex: A 5kg wooden crate initially at rest sits on
a frictionless incline set at 35°…
θ
a)
What is the normal force acting on the crate?
b)
What is the net force acting on the crate?
c)
What will be the acceleration of the crate down
the incline?
d)
If friction is considered and the wooden crate
started from rest on a wooden incline, what
frictional force opposes the motion?
e)
What would be the acceleration under the
conditions in part ‘d’?