The Laws of Motion

1
Chapter 4 The Laws of Motion
2

• 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 dont 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

• Newtons First Law
• If the net force on the body is zero, the bodys
  acceleration is zero

6

• Newtons Second Law
• If the net force on the body is not zero, the
  bodys 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

• Newtons Second Law
• SI unit of force kgm/s2 N (Newton)
• Newtons Second Law can be applied to all the
  components separately
• To solve problems with Newtons 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 3 000 kg,
what acceleration does it have? Ignore friction.
9

• Newtons 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 6.6710 11 Nm2/kg2
  6.6710 11 m3/(kgs2) 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 Newtons 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
• 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 0.250.
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