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Dynamics: Newton’s Laws of Motion © 2014 Pearson Education, Inc.
Dynamics:Newton’s Laws of Motion
© 2014 Pearson Education, Inc.
Dynamics -
Notions of Motion & its Causes…
Aristotle ( ) Galileo ( ) Isaac Newton ( )
Inertia-
Ex: What does inertia have to do with getting ketchup to spout of ketchup bottle?
Ex: What do car headrests have to do with inertia?
Ex: Which vehicle would be tougher to…
M Start in Motion ___________
2M Bring to stop ___________
Ex: A marble travels through a tube laying flat on a table. What path will path take when it leaves?
What if the car traveled at 2v?
Inertia α _________
N1L: Newton’s 1st Law -
Ex: Forces Balanced (At rest)
Ex: 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:
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) Does Jimmy get pulled out of the well?
b) What must be the normal force?
c) Draw FBD
Non-Equilibrium:
A file cabinet weighing 200N is being pushed by an applied force of 100N. A retarding force (friction) of 50N opposes the motion…
a) What is the net force acting on the file cabinet?
b) Describe the motion of the file cabinet.
c) Draw FBD
BIG IDEAS:
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?
Forces at Angles
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..
Weight
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.
a) What is the weight of the box?
b) What is the acceleration of the box?
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 net force on the box?
b) What is the acceleration of the box?
Mathematical Relationships using N2L
#1: Effects of Force on Acceleration (Constant Mass)
What force is necessary to accelerate What would acceleration be if we a 50kg object on frictionless surface at doubled and tripled the force?1m/s2?
Forc
e (N
)
Acceleration (m/s2)
Big Idea -
F = ma
Mathematical Relationships using N2L
#2: Effects of Force on Mass (Constant Acceleration)
What is the acceleration of a What force ‘F’ is necessary to keep the 200N force on a 100kg object? same acceleration on mass of ‘2m’ and
‘4m’ ?
Forc
e (N
)
Mass (kg)
Big Idea -
a = F/m
Mathematical Relationships using N2L
#3: Effects of Mass on Acceleration (Constant Force)
What is the mass of an object if a If the force remained the same, what 25N force accelerates it at 1m/s2? acceleration would a 50kg and 100kg
object have?
Mass (kg)
Big Idea - Ac
cele
ratio
n (m
/s2 )
m = F/a
Mathematical Relationships using N2L
Check Understanding…
If force ‘F’ is exerted on mass ‘m’ Force ‘F’ is exerted on mass ‘m’ giving accelerating it at ‘a’, what force acceleration ‘a’. What would accelerationwould be needed to give be if force ‘F’ was exerted on mass ‘3m’ ?acceleration ‘4a’ ?
An object is accelerating at 10m/s2 when Force ‘F’ is exerted on mass ’m1’ giving it the net force on it is cut in half. What is acceleration ‘a’. If force ‘4F’ gives ‘m2’ the acceleration now? an acceleration of ‘2a’, what is the ratio of
m1 to m2?
F = ma
Expanding N2L
F = ma a = Δv t
A net force of 50N is applied to a 10kg A retarding force of 75N is exerted on a block initially at rest on a frictionless 50kg object initially traveling at +10m/s…surface…
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?
c) sketch the v-t graph
v
t
Newton’s Third Law – N3L
What exerts the greater force, bug on windshield or windshield on bug?
Revolving lawn sprinklers…
Would it be smart to push off of a Small rowboat and jump onto a dock?
Gun Recoil…
Airplane Lift…
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?
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.
i) If the box weighed 87.3N on another planet, is the acceleration due to gravity on that planet?
Position 1
Fnet =
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 Accelerate Up Accelerate Down
Rocket Science… A 2kg model rocket accelerates upwards at 8m/s2. What thrust force does the rocket need to attain this acceleration?
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?
Forces at Angles
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.
vv
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?
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
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
θ
Ex: A 5kg wooden crate initially at rest sits on a frictionless incline set at 35°…
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’?
