2. 2
Apply Newton's Laws as basic principles for dynamics of
particle in linear motion and vertical motion.
State each of Newton's laws of motion
Describe the definitions and types of forces acting on a body in
different situation (pulley, inclined surface, tension of string)
Apply F = m.a in solving problems related to linear motion of a
body
Apply F = m.a in solving problems related to vertical motion of
a body
Analyze relation between force and its frictional force
Analyze the coefficient of frictional force (static and kinetic
friction) through inclined plane
After studying this topic, you are expected to be able
to:
10. 10
A body is pulled in two opposing
directions by two ropes as shown in
Figure beside. The resultant force acting
is the vector sum of the forces.
How to calculate forces?
Force is Vector, so….
Calculate forces : calculate vectors!
Example:
If a body is pulled by two perpendicular
ropes as in Figure 2.33, then the vector
addition is solved using vectors addition.
14. 14
Forces Balanced Equilibrium
Another example:
Separate the vectors into 2 components:
x & y
If the box is in equilibrium, then:
Total component in x = 0 forces left = forces right
Total component in y = 0 forces up = forces down
15. 15
Example:
Consider the situation below. If the forces on this box are
balanced:
a) write an equation for the components of the forces
parallel to the ramp
b) write equation for the forces perpendicular to the ramp
c) find the friction (F) & normal force (N)
16. 16
Example:
A ball of weight 10 N is suspended on a
string and pulled to one side by another
horizontal string as shown beside.
If the forces are balanced:
(a) write an equation for the horizontal
components of the forces acting on the
ball
(b) write an equation for the vertical
components of the forces acting on the
ball
(c) use the second equation to calculate
the tension in the upper string, T
(d) use your answer to (c) plus the first
equation to find the horizontal force F.
17. 17
Example:
A rock climber is hanging from a rope
attached to the cliff by two bolts as
shown in Figure beside. If the forces are
balanced
a) write an equation for the vertical
component of the forces on the knot
b) write an equation for the horizontal
forces exerted on the knot
c) calculate the tension T in the ropes
joined to the bolts. The result of this
calculation shows why ropes should
not be connected in this way.
18. 18
Newton’s Laws of Motion
Forces balanced object is at rest (?)
Forces not balanced object moves (?)
How do we explain that with strong
argument?
Newton’s Laws of Motion
1st
Law:
A body will remain at rest or moving with constant
velocity unless acted upon by an unbalanced force.
Net force = 0 no acceleration
29. 29
Note:
If the forces are
balanced, will the
object always be at rest
or moving with
constant velocity?
30. 30
2nd Law:
The acceleration of an object is
directly proportional to the net force acting on it and
inversely proportional to its mass.
Σ 𝐹 = 𝑚. 𝑎
37. 37
Single isolated force
can’t exist
Pair of forces on
two different objects
3rd Law:
If body A exerts a force on body B then body B will
exert an equal and opposite force on body A.
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41. Example:
A car of mass m is on an icy driveway inclined at an
angle 30.0o
, as in Figure 4.16a. Determine (a) the
acceleration of the car, assuming that the incline is
frictionless. (b) If the length of the driveway is 20.0 m
and the car starts from rest at the top, how long does it
take to travel to the bottom? (c) What is the car’s speed
at the bottom?
41
47. 47
Static Frictional Force:
fs ≤ s.N
Maximum static frictional force: in verge of
slipping
fs max = s.N
s= coefficient of static friction depend on the
nature of surfaces
N = Normal force
Kinetic Frictional Force:
fk = k.N
k= coefficient of kinetic friction
51. 51
Example:
1. The hockey puck in Figure 4.22, struck by a
hockey stick, is given an initial speed of 20.0 m/s on
a frozen pond. The puck remains on the ice and
slides 120 m, slowing down steadily until it comes
to rest. Determine the coefficient of kinetic friction
between the puck and the ice.
52. 52
Suppose a block with a mass of
2.00 kg is resting on a ramp. If
the coefficient of static friction
between the block and ramp is
0.30, what maximum angle can
the ramp make with the
horizontal before the block starts
to slip down?
53. 53
A loaded penguin sled weighing 40√2 N
rests on a plane inclined at angle = 45° to
the horizontal (Figure beside). Between the
sled and the plane, the coefficient of static
friction is 0.25, and the coefficient of
kinetic friction is 0.15. Determine:
a. Maximum static friction between sled and plane.
b. Magnitude of the force required in order to make the sled stay at
rest, not sliding down the plane. (remember, there are frictional
force and weight of object)
c. What is the minimum magnitude F that will start the sled moving
up the plane? (Hint: draw the force first)
d. What value of F is required to move the sled up the plane at
constant velocity?
54. 54
A block with mass m1 = 4.00 kg and
a ball with mass m2 = 7.00 kg are
connected by a light string that
passes over a frictionless pulley, as
shown in Figure 4.23a. The
coefficient of kinetic friction between
the block and the surface is 0.300.
Find the acceleration of the two
objects and the tension in the string.
