1. Newton’s Second Law of Motion – Force & Acceleration
Chin-Sung Lin

2. Newton & His Second Law

3. Review – Newton’s First Law
Usually called the law of inertia
Every object continues in a state of rest, or of motion in a straight line at constant speed, unless it is compelled to change that state by an unbalanced force exerted upon it
Implies the second law of motion

4. Unbalanced Force F What will the unbalanced force result in?
Unbalanced force means the net force ≠ 0
What will the unbalanced force result in? F

5. Newton’s Second Law
Newton’s second law – Force & Acceleration The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object

6. Net Force = 0
Zero net force means zero acceleration No acceleration is the evidence of zero net force Zero acceleration means state of rest or state of constant velocity

7. Force Causes Acceleration
Acceleration ~ Net force
(Direct Proportion)
a ~ Fnet F a

8. Mass Resists Acceleration
Acceleration ~ 1/mass
(Inverse Proportion)
a ~ 1/m m a

9. Force Causes Acceleration
Acceleration ~ Net force
a ~ Fnet
Acceleration ~ 1/mass
a ~ 1/m
a = Fnet /m or Fnet = m a

10. F = m a

11. Example: How much Force?

12. Example: What’s the Acceleration?

13. Example: What’s the mass?
a = 100 m/s2
F = N

14. Weight is Gravitational Force
Fnet = m a
Fg = m g or
W = m g

15. Weight, mass and Acceleration

16. Weight, mass and Acceleration

17. Weight on Earth & Moon?
Same Mass

18. Mass on Earth & Moon?
Same Weight

19. Friction Force
Friction acts on materials that are in contact with each other, and is always acts in direction to oppose motion

20. When There is No Friction

21. Coefficient of Friction (m)
Friction mainly due to the irregularities in the two surfaces The irregularities between surfaces of different materials are described by the coefficients of friction (m) Friction mainly determined by the surface and the weight of the object

22. Friction Force (Ff)
Friction force (Ff) can be categorized into two different types: Static and Kinetic Ff F
Maximum Static Friction
Kinetic Friction
Maximum Static Friction

23. Coefficient of Friction (m)

24. Static Friction Force
As long as an object does not move, the friction force (Ff) must be equal in size and opposite in direction to the applied force (F)
Ff = F
The static frictional force can have any value from zero up to a max. value (maximum static friction force) Ff F
Maximum Static Friction

25. Maximum Static Friction Force
Maximum static friction force is directly proportional to the normal force and the coefficient of static friction (s). Ff = FN  s Ff F
Maximum Static Friction

26. Example: Static Friction Force
If a block is not moving, what’s the friction force?
50 kg
20 N

27. Example: Static Friction Force
If the coefficient of static friction between a block and the ground is 0.2, (a) what’s the maximum static friction force? (b) Will the block move? (c) What’s the friction force?
50 kg
80 N

28. Example: Static Friction Force
If a wooden block is resting on a wooden floor, (a) How much force is required to make the block move? (b) Will the block move? (c) What’s the friction force while moving?
50 kg
100 N

29. Kinetic Friction Force
If the applied force exceeds the maximum static friction force, the object will slide in the direction of the applied force, and the friction force reduces to a constant value called kinetic friction force The value of the kinetic friction is independent of the speed of the object Ff F
Kinetic Friction

30. Kinetic Friction Force
Kinetic friction force is directly proportional to the normal force and the coefficient of static friction (s). Ff = FN  k Ff F
Kinetic Friction

31. Example: Kinetic Friction Force
If a block is moving at constant velocity, what’s the friction force?
50 kg
20 N

32. Example: Kinetic Friction Force
If a block is moving and coefficient of kinetic friction between the block and the ground is 0.1, (a) what’s the friction force? (b) What’s the acceleration of the block?
50 kg
80 N

33. Example: Kinetic Friction Force
If a wooden block is sliding on a wooden floor, (a) what’s the friction force? (b) What’s the acceleration of the block?
20 kg
100 N

34. Example: Kinetic Friction Force
If a 40-kg block is pushed by a force of 100 N and accelerates at 2 m/s2, (a) what’s the friction force? (b) What’s the coefficient of kinetic friction between the block and the ground?
40 kg
100 N

35. Example: Kinetic Friction Force
If a 40-kg block is sliding down an incline plane of 30o at constant speed, (a) what’s the friction force while sliding? (b) What’s the coefficient of kinetic friction between the block and the ground?
40 kg
30o

36. Application – Anti-Lock Brake

37. Air Resistance R Fg

38. Free Falling & Air Resistance
When there is air resistance (R), the acceleration of a free falling object reduced. The acceleration of a falling object is:
a = Fnet/m = (Fg – R)/m = (mg – R)/m = g – R/m

39. Air Resistance & Terminal Speed
When the air resistance on an object equals the weight of the object, the net force is zero and no further acceleration occurs. Acceleration terminates: the object has reached its terminal speed or terminal velocity.
a = 0 m/s2 = g – R/m g = R/m R = mg

40. Reduce the Terminal Speed

41. Force vs. Pressure

42. Pressure
Pressure (P): The amount of force per unit of area Pressure = Force / Area of application or P = F/A Unit: Newtons per square meter, or pascals (Pa).

43. Example: Pressure Which one has larger pressure? 200 kg 5 kg 200 kg
2m x 2m x 2m
.2m x .2m x .2m

44. Summary Newton’s second law - Fnet = m a
Force causes acceleration & mass resists acceleration
Weight is gravitational force - Fg = m g
Acceleration of different masses on Earth
Mass and weight on Earth and moon
Friction force and coefficient of friction (m)
Static friction force and kinetic friction force

45. Summary Friction force Ff = m FN Air resistance and terminal speed
Pressure vs. force