1. Newton’s Laws
The Study of Dynamics

2. Isaac Newton Arguably the greatest physical genius ever.
Came up with 3 Laws of Motion to explain the observations and analyses of Galileo and Johannes Kepler.
Invented Calculus.
Published his Laws in 1687 in the book Mathematical Principles of Natural Philosophy.

3. What is Force? A force is a push or pull on an object.
Forces cause an object to accelerate…
To speed up
To slow down
To change direction

4. Newton’s First Law The Law of Inertia.
A body in motion stays in motion at constant velocity and a body at rest stays at rest unless acted upon by an external force.
This law is commonly applied to the horizontal component of velocity, which is assumed not to change during the flight of a projectile.

5. The First Law is Counterintuitive
Aristotle firmly believed this.
But Physics B students know better!

6. A force diagram illustrating no net force

7. A force diagram illustrating no net force

8. A force diagram illustrating no net force

9. A force diagram illustrating no net force

10. Another example illustrating no net force

11. Newton’s Second Law
A body accelerates when acted upon by a net external force.
The acceleration is proportional to the net force and is in the direction which the net force acts.
This law is commonly applied to the vertical component of velocity.

12. Newton’s Second Law ∑F = ma
where ∑F is the net force measured in Newtons (N)
m is mass (kg)
a is acceleration (m/s2)

13. Units of force Newton (SI system)
1 N = 1 kg m /s2
1 N is the force required to accelerate a 1 kg mass at a rate of 1 m/s2
Pound (British system)
1 lb = 1 slug ft /s2

14. Newton’s Third Law
For every action there exists an equal and opposite reaction.
If A exerts a force F on B, then B exerts a force of -F on A.

15. Step 1: Draw the problem Working a Newton’s 2nd Law Problem
Larry pushes a 20 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N. What is acceleration?
20 kg FL FM

16. Step 2: Diagram Working a Newton’s 2nd Law Problem Force diagram N FMFL FM FG N
20 kg FL FM FG N
Force diagram
Free Body diagram

17. Step 3: Set up equations F = ma Fx = max Fy = may
Working a Newton’s 2nd Law Problem
Step 3: Set up equations
F = ma
Fx = max
Fy = may
Always resolve two-dimensional problems into two one-dimensional problems.

18. Step 4: Substitute Make a list of givens from the word problem.
Working a Newton’s 2nd Law Problem
Step 4: Substitute
Make a list of givens from the word problem.
Substitute in what you know.

19. Step 5: Solve Plug-n-chug. Calculate your unknowns.
Working a Newton’s 2nd Law Problem
Step 5: Solve
Plug-n-chug.
Calculate your unknowns.
Sometimes you’ll need to do kimematic calculations following the Newton’s 2nd law calculations.

20. Gravity as an accelerating force
A very commonly used accelerating force is gravity. Here is gravity in action. The acceleration is g.

21. Gravity as an accelerating force
In the absence of air resistance, gravity acts upon all objects by causing the same acceleration…g.

22. Gravity as an accelerating force
The pulley lets us use gravity as our accelerating force… but a lot slower than free fall. Acceleration here is a lot lower than g.

23. 2-Dimensional problem
Larry pushes a 20 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N.
a) What is the acceleration?
b) What is the normal force? FL FM FG N
20 kg

24. The problem of weight Are weight and mass the same thing?
No. Weight can be defined as the force due to gravitation attraction.
W = mg

25. Flat surfaces – 1 D
N = mg for objects resting on horizontal surfaces. N mg

26. Ramps – 2 D N mg N = mgcos  
The normal force is perpendicular to angled ramps as well. It’s always equal to the component of weight perpendicular to the surface.
N = mgcos N 
mgcos
mgsin mg 

27. Ramps – 2 D N mg N = mgcos  
How long will it take a 1.0 kg block to slide down a frictionless 20 m long ramp that is at a 15o angle with the horizontal?
N = mgcos N 
mgcos
mgsin mg 

28. Applied forces affect normal force.
friction
applied force
weight
normal
N = applied force

29. Elevator Ride – going up!mg N
Ground
floor
Normal feeling
V = 0
A = 0 mg N
Just
starting up
Heavy feeling
V > 0
A > 0 mg N
Between
floors
Normal feeling
V > 0
A = 0 mg N
Arriving at
top floor
Light feeling
V > 0
A < 0
Elevator Ride – going up!

30. Elevator Ride – going down!mg N
Top
floor
Normal feeling
V = 0
A = 0 mg N
Beginning
descent
Light feeling
V < 0
A < 0 mg N
Between
floors
Normal feeling
V < 0
A = 0 mg N
Arriving at
Ground floor
Heavy feeling
V < 0
A > 0
Elevator Ride – going down!

31. Friction The force that opposes a sliding motion.
Enables us to walk, drive a car, etc.
Due to microscopic irregularities in even the smoothest of surfaces.

32. There are two types of friction
Static friction
exists before sliding occurs
Kinetic friction
exists after sliding occurs
In general fk <= fs

33. Friction and the Normal Force
The frictional force which exists between two surfaces is directly proportional to the normal force.
That’s why friction on a sloping surface is less than friction on a flat surface.

34. Static Friction fs  sN fs : static frictional force (N)
s: coefficient of static friction
N: normal force (N)
Static friction increases as the force trying to push an object increases… up to a point!

35. A force diagram illustrating Static Friction
Normal Force
Frictional Force
Applied Force
Gravity

36. A force diagram illustrating Static Friction
Normal Force
Bigger Applied Force
Bigger Frictional Force
Gravity

37. A force diagram illustrating Static Friction
The forces on the book are now UNBALANCED!
Normal Force
Frictional Force
Even Bigger Applied Force
Gravity
Static friction cannot get any larger, and can no longer completely oppose the applied force.

38. Kinetic Friction fk = kN fk : kinetic frictional force (N)
k: coefficient of kinetic friction
N: normal force (N)
Kinetic friction (sliding friction) is generally less than static friction (motionless friction) for most surfaces.

39. Determination of the Coefficients of Friction
Coefficient of Static Friction
Set a block of one material on an incline plane made of the other material.
Slowly increase angle of plane until the block just begins to move. Record this angle.
Calculate s = tan.

40. Determination of the Coefficients of Friction
Coefficient of Kinetic Friction
Set a block of one material on an incline plane made of the other material.
Slowly increase angle of plane until the block just begins to move at constant speed after giving it a slight tap. Record this angle.
Calculate k = tan.

41. Magic Pulleys T mg N -x x m1 m2

42. Pulley problem
Mass 1 (10 kg) rests on a frictionless table connected by a string to Mass 2 (5 kg). Find (a) the acceleration of each block and, (b) the tension in the connecting string. m1 m2

43. Pulley problem
Mass 1 (10 kg) rests on a table connected by a string to Mass 2 (5 kg) as shown. What must the minimum coefficient of static friction be to keep Mass 1 from slipping? m1 m2

44. Pulley problem
Mass 1 (10 kg) rests on a table connected by a string to Mass 2 (5 kg). If ms = 0.3 and mk = 0.2, what is a) the acceleration and b) the tension in the string? m1 m2