1. Forces and Newton’s Laws of Motion
AP Physics Chapter 6
Forces and Newton’s Laws of Motion

2. Kinematics: How objects move
Dynamics: Why objects move
First studied by Isaac Newton

3. Isaac Newton Sir Isaac Newton at 46 in Godfrey Kneller's 1689 portrait
Born 4 January [O.S. 25 December 1642] 1643 Woolsthorpe-by-Colsterworth, Lincolnshire, England
Died 31 March [O.S. 20 March] 1727 Kensington, London
Residence England
Nationality English
Field Mathematics, physics, astronomy, alchemy, and natural philosophy
Institution University of Cambridge
Alma Mater University of Cambridge
Doctoral Advisor Isaac Barrow
Known for Gravitation, optics, calculus, mechanics
Societies President of the Royal Society,
Master of the Royal Mint
Prizes Knighthood
Religion Prophetic Unitarianism, Church of England

4. Force a push or a pull Can be a field force: gravity, magnetism
Does not involve physical contact.
Or it can be a contact force like friction

5. 4 types of forces
1. Gravitational: attractive force that exists between all objects that have mass,
It is the weakest of all forces
But holds the universe together

6. 2. Electromagnetic: result of electric charge, gives materials their physical characteristics, strength, ability to bend, squeeze, stretch, shatter, malleability
Greater than gravity

7. 3. Strong Nuclear: holds particles of nucleus together
strongest force
but only over a very, very small distance

8. 4. Weak Force: involved in radioactive decay of some nuclei,
may be a form of electromagnetic force

9. Force diagram Sketch a free body diagram Isolate the object
And draw the forces acting on it

10. Normal Force
It is the force supplied by the surface supporting the object
It is a contact force
Usually due to weight of the object
The object pushes down
The surface pushes up

11. Newton’s Laws of Motion
Newton’s 1st Law of Motion: an object with no outside force acting on it will move at a constant velocity in a straight line or remain at rest
Newton wrote the law, but Galileo speculated about this concept in his writings

12. Demo Ballistic Car Inertia apparatus Called the Law of Inertia
What is inertia?

13. Inertia is the tendency of a body or object to resist a change in its motion
The more mass a body has, the more inertia it has

14. Newton’s 1st Law of Motion
Law of Equilibrium (law of inertia): net sum of the forces is equal to zero
Uniform Motion
Constant velocity
Or no motion

15. Equilibrant
The equilibrant is equal to the resultant in magnitude but opposite in direction.
When the vector sum is not zero, a force can be applied that will produce equilibrium. That is the equilibrant force.

16. Mass
Is a measurement of inertia, a body’s tendency to stay in equilibrium

17. Friction The force that opposes motion between two surfaces
It is parallel to the surface and opposite the direction of motion

19. Static and Kinetic Friction
Static Friction: the force that opposes the start of motion, it is the maximum frictional force.
Kinetic friction: the force that opposes motion between two surfaces in relative motion.

20. Coefficient of Static Friction
Depends on the normal force and types of surfaces in contact

21. Coefficient of Kinetic Friction
Less than static friction, object is in motion
Is also called sliding friction

22. Frictional Force
Is the product of the coefficient and the normal

23. Free body diagram All vectors are drawn at the center of mass
Draw a free body diagram of a box moving at constant velocity across the floor with friction
What does Net Force mean?

24. Newton’s Second Law of Motion
The acceleration of a body is directly proportional to the Net Force on it and inversely proportional to its mass.
Net Force causes acceleration
ΣF = ma
Unit: the newton = 1kg meter/s2

25. Net Force
ΣF=ma

26. Weight The magnitude of the force of gravity on an object.
When the mass and acceleration due to gravity are known, the weight of an object can be calculated
Weight = mg

27. Example 1
Find the weight of a 2.25 kg bag of sugar. What direction is the force?

28. Mass There are two kinds of mass:
Gravitational – found on a scale or balance
Inertial mass – calculated using Newton’s 2nd law of motion

29. Weight and Mass Is your weight the same everywhere in the universe?
What about your mass?

30. Example 2
Roberto and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book toward Roberto. If the net external force acting on the book is 2.6 N to the right, what is the book’s acceleration?

31. Newton’s Third Law
If two object’s interact, the magnitude of the force exerted on Object #1 by Object #2 is equal to the magnitude of the force simultaneously exerted on Object #2 by Object #1, and these two forces are equal in magnitude and opposite in direction.
Forces always exist in pairs.

33. Newton’s 3rd Law of Motion
F1,2 = F2,1
Action – Reaction pairs
For every action, there is an opposite and equal reaction

34. Terminal Velocity
Objects reach terminal velocity in free fall when the drag force of air resistance (friction) equals the force of gravity
ΣF = 0
No acceleration, therefore, constant velocity
Uniform Motion

35. Terminal Velocity

36. Example 3
A smooth wooden block is placed on a smooth table top. A 14.0 N force is exerted to keep the 40.0 N block moving at a constant velocity.
What is the coefficient of kinetic friction?

37. If a 20.0 N brick is placed on top of the block, what force will be required to keep the block and brick system moving at a constant velocity?

38. Example 4
What net force is required to accelerate a kg car at m/s2?

39. Example 5
An artillery shell has a mass of 55.0 kg. It is fired and leaves the barrel with a velocity of m/s. The barrel is 1.50 meters long.
What is the force of the shell inside the barrel?

40. Example 6
If a 10.0 kg object is on a frictionless surface and has a N force acting on it, find the resulting acceleration.

41. If the same object rests on a rough surface where friction will oppose motion and the frictional force in N. What is the acceleration now?

42. A Fish in the Elevator
A spring scale hangs from the ceiling of an elevator that is not moving.
It supports a fish that weighs 25.0 N.
What upward force does the scale exert?

43. What force must the scale exert when the elevator and fish accelerate upward at +1.50 m/s2

44. Example 8
A 24.0 kg crate initially at rest on a horizontal floor requires a 75.0 N horizontal force to set it in motion.
Find the coefficient of static friction between the crate and the floor.

45. Simple Harmonic Motion
Repetitive motion
If a spring is vibrating, it has a restoring force
A force that wants to bring it back to equilibrium

47. Hooke’s Law At equilibrium position, velocity is reaches a maximum
At maximum displacement, spring force and acceleration reach a maximum
In SHM, restoring force is proportional to displacement
A stretched or compressed spring has elastic potential energy

48. Formula for Hooke’s Law

50. Example #1
A mass of 0.55 kg is attached to a vertical spring. It stretches 2.0 cm from equilibrium position.
What is the spring constant?

51. The Pendulum For small angles, is repetitive motion
The restoring force of a pendulum is a component of the bob’s weight
The pendulum’s motion is SHM
Gravitational potential energy increases as the pendulum’s displacement increases

53. The Pendulum Amplitude = maximum displacement from equilibrium
Period = the time it takes to make one complete cycle of motion or wave
Frequency = the number of cycles in one unit of time (usually the second)
Period and frequency are inversely related

54. Period of a Pendulum
Depends on the length of the pendulum and gravity

55. Example #2
You need to know the height of a tower, but darkness obscures the ceiling.
You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 seconds.
How tall is the tower?

56. Period of a mass-spring system
Depends on the mass and the spring constant (k)

57. Example #3
You have a 1275kg car, you and your friend have a combined mass of 153 kg.
You drive over a pothole that makes your car vibrate with a period of seconds.
Find the spring constant of one of your springs (shocks).