1. Chapter 4
The Laws of Motion

2. Newtonian mechanics Describes motion and interaction of objects
Sir Isaac Newton
(1643 – 1727)
Newtonian mechanics
Describes motion and interaction of objects
Applicable for speeds much slower than the speed of light
Applicable on scales much greater than the atomic scale
Applicable for inertial reference frames – frames that don’t accelerate themselves

3. Force
What is a force?
Colloquial understanding of a force – a push or a pull
Forces can have different nature
Forces are vectors
Several forces can act on a single object at a time – they will add as vectors

4. Force superposition
Forces applied to the same object are adding as vectors – superposition
The net force – a vector sum of all the forces applied to the same object

5. Newton’s First Law
If the net force on the body is zero, the body’s acceleration is zero

6. Newton’s Second Law
If the net force on the body is not zero, the body’s acceleration is not zero
Acceleration of the body is directly proportional to the net force on the body
The coefficient of proportionality is equal to the mass (the amount of substance) of the object

7. Newton’s Second Law SI unit of force kg*m/s2 = N (Newton)
Newton’s Second Law can be applied to all the components separately
To solve problems with Newton’s Second Law we need to consider a free-body diagram
If the system consists of more than one body, only external forces acting on the system have to be considered
Forces acting between the bodies of the system are internal and are not considered

8. Chapter 4
Problem 12
Two forces are applied to a car in an effort to move it. (a) What is the resultant of these two forces? (b) If the car has a mass of kg, what acceleration does it have? Ignore friction.

9. Newton’s Third Law
When two bodies interact with each other, they exert forces on each other
The forces that interacting bodies exert on each other, are equal in magnitude and opposite in direction

10. Forces of different origins
Gravitational force
Normal force
Tension force
Frictional force (friction)
Drag force
Spring force

11. Gravity force (a bit of Ch. 7)
Any two (or more) massive bodies attract each other
Gravitational force (Newton's law of gravitation)
Gravitational constant G = 6.67*10 –11 N*m2/kg2 = 6.67*10 –11 m3/(kg*s2) – universal constant

12. Gravity force at the surface of the Earth
g = 9.8 m/s2

13. Gravity force at the surface of the Earth
The apple is attracted by the Earth
According to the Newton’s Third Law, the Earth should be attracted by the apple with the force of the same magnitude

14. Weight
Weight (W) of a body is a force that the body exerts on a support as a result of gravity pull from the Earth
Weight at the surface of the Earth: W = mg
While the mass of a body is a constant, the weight may change under different circumstances

15. Tension force
A weightless cord (string, rope, etc.) attached to the object can pull the object
The force of the pull is tension ( T )
The tension is pointing away from the body

16. Free-body diagrams

17. Normal force
When the body presses against the surface (support), the surface deforms and pushes on the body with a normal force (n) that is perpendicular to the surface
The nature of the normal force – reaction of the molecules and atoms to the deformation of material

18. Normal force
The normal force is not always equal to the gravitational force of the object

19. Free-body diagrams

20. Free-body diagrams

21. Chapter 4
Problem 30
An object with mass m1 = 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 = 10.0 kg, as shown in the Figure. Find the acceleration of each object and the tension in the cable.

22. Frictional force Friction ( f ) - resistance to the sliding attempt
Direction of friction – opposite to the direction of attempted sliding (along the surface)
The origin of friction – bonding between the sliding surfaces (microscopic cold-welding)

23. Static friction and kinetic friction
Moving an object: static friction vs. kinetic

24. Friction coefficient Coefficient of kinetic friction μk
Experiments show that friction is related to the magnitude of the normal force
Coefficient of static friction μs
Coefficient of kinetic friction μk
Values of the friction coefficients depend on the combination of surfaces in contact and their conditions (experimentally determined)

25. Free-body diagrams

26. Free-body diagrams

27. Chapter 4
Problem 49
Find the acceleration reached by each of the two objects shown in the figure if the coefficient of kinetic friction between the 7.00-kg object and the plane is

28. Answers to the even-numbered problems
Chapter 4
Problem 2
25 N

29. Answers to the even-numbered problems
Chapter 4
Problem 6
7.4 min

30. Answers to the even-numbered problems
Chapter 4
Problem 26
4.43 m/s2 up the incline, 53.7 N

31. Answers to the even-numbered problems
Chapter 4
Problem 40
55.2°;
(b) 167 N

32. Answers to the even-numbered problems
Chapter 4
Problem 50
18.5 N;
(b) 25.8 N