laws of motion

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Transcript laws of motion

Newton’s
Laws of Motion
I. Law of Inertia
II. F=ma
III. Action-Reaction
Newton’s Laws of Motion
• 1st Law – An object at rest will stay at
rest, and an object in motion will stay in
motion at constant velocity, unless acted
upon by an unbalanced force.
• 2nd Law – Force equals mass times
acceleration.
• 3rd Law – For every action there is an
equal and opposite reaction.
2nd Law
The net force of an object is equal to
the product of its mass and
acceleration.
Newton’s 2nd Law proves that different masses
accelerate to the earth at the same rate, but with
different forces.
• We know that objects
with different masses
accelerate to the
ground at the same
rate.
• However, because of
the 2nd Law we know
that they don’t hit the
ground with the same
force.
F = ma
98 N = 10 kg x 9.8 m/s/s
F = ma
9.8 N = 1 kg x 9.8 m/s/s
Motion on a Smooth
Inclined Plane
Consider the forces acting on an object moving on an inclined plane
of inclination q to the horizontal.
The simplest case is one in which the object is sliding on the inclined
plane under the action of the weight and normal reaction only.
)
n
o
ti
c
a
e
R
l
a
m
r
o
N
R(
s
q
W (Weight)
oth
o
m
horizontal
The weight mg is resolved into two components.
The component mg sin q is along the inclined plane.
The component mg cos q is perpendicular to the inclined plane.
mg
q
n
i
s
mg
q
m
mg
q
s
o
c
R
s
q
n
i
gs
q
q
mg
horizontal
th
o
mo
Motion takes place along the inclined plane.
The resultant force on the object is mg sin q acting down-slope.
By Newton’s Second Law of Motion, the acceleration a of the
object also points down-slope.
No matter the object is moving up-slope or down-slope, the
resultant force and hence the acceleration points down-slope.
R
ot h
o
sm
)
n
o
ati
r
e
l
e
c
c
q
a
(
n
i
s
a
g
m
q
mg
q
s
co
q
horizontal
F = ma
mg sin q = ma
a = g sin q
For object sliding on a smooth inclined plane
• The acceleration depends on the inclination of the plane
only. It does not depend on the mass. Objects of different
masses slide on the inclined plane with the same
acceleration.
• The acceleration always points down-slope, independent
of the direction of motion (velocity) of the object.
R
a =
q
n
i
s
g
m
ot h
o
sm
q
n
i
gs
q
mg
q
s
co
q
horizontal
There is NO motion in the direction perpendicular to the inclined plane.
By Newton’s First Law of Motion, the forces in this direction
should balance each other.
Hence the normal reaction R = mg cos q
The normal reaction depends on the weight of the object and also it
decreases with the inclination q. The steeper the slope, the smaller is
the normal reaction.
R
a =
q
n
i
s
g
m
ot h
o
sm
q
n
i
gs
q
mg
q
s
co
q
horizontal
Example: A trolley of mass 0.5 kg is released from a point O on a
smooth runway inclined at 30o to the horizontal.
Assume g = 10 m s-2
Find the time and the velocity of the trolley when it reaches a point
A 2 m from O.
ey
l
l
tro
oth
o
sm
0
=
u
y
O
t
i
c
o
l
e
v
l
a
i
t
ini
2m
A
o

horizontal
Solution:
The acceleration a is uniform and independent of the mass of
the trolley.
a = g sin 30o
= 10  0.5
= 5 m s-2
The trolley reaches A with velocity v at time t.
S = ut+0.5at2
v2 = u2 – 2aS
2 = 0t + 0.5 5 t2
v2 = 02 + 2 5 2
t = 0.894 s
v = 4.47m s-1