# Newton’s Second Law ```Newton’s Second Law

The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional
r to its mass.
r
aα
∑ F or ∑ Fr = mar
m
Newton’s Third Law
• If object 1 and object 2 interact, the force exerted by object
1 on object 2 is equal in magnitude but opposite in direction
to the force exerted by object 2 on object 1.
r
r
F12 = −F21
Friction Forces
Contact between bodies with a relative velocity produces friction
Kinetic friction: the
direction of the frictional
force is opposite the
direction of motion.

Kinetic friction is
proportional to the normal
force

f k = &micro;k n
The coefficient of friction
&micro; (‘mu’) depends on the
surfaces in contact
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Static Friction ƒs

Static friction acts to keep the
object from moving

If F increases, so does ƒs
If F decreases, so does ƒs

ƒs ≤ ƒs, max with ƒs, max = &micro;s n

uur uur
f s = -F
ƒs, max = &micro;s n
Usually, &micro;s &gt; &micro;N
Block on a Ramp



Axes are rotated as
usual on an incline
The direction of
impending motion
would be down the
plane
Friction acts up the
plane
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

Opposes the motion
Draw free body
diagram
Chapter 5.1-5.2
Energy and Work
Mechanical Energy
•Kinetic (associated with motion)
•Potential (associated with position)
Chemical Energy
Electromagnetic Energy
Nuclear Energy
Energy can be transformed from one form to another

But not destroyed– “Energy is conserved”
Work/Energy can be used in place of Newton’s laws to solve
certain problems more simply
Work done by a force F on an object
W ≡ (F cos θ)∆x
F is the magnitude of the force
 ∆ x is the magnitude of the object’s displacement
 θ is the angle between the force and the
displacement

Work is a scalar quantity
Work by the force is zero when force
and displacement are perpendicular
e. g., carrying a bucket of water

Displacement is horizontal

Force is vertical

cos 90&deg; = 0
W ≡ (F cos θ)∆x
So no work done!
Work is scalar,
but it can Be Positive or Negative


Work done by the
person on the box is
positive when lifting the
box
Work done is negative if
lowering the box
 force is upward, but
displacement is
downward
Kinetic Energy




Energy associated with the motion
of an object
1
2
KE = mv
2
Scalar quantity with the same
units as work
Work is related to kinetic energy
Work-Kinetic Energy Theorem
Wnet = KEf − KEi = ∆KE

When work is done by a net force on an
object and the only change in the object
is its speed, the work done is equal to
the change in the object’s kinetic energy
•
Speed will increase if work is positive
•
Speed will decrease if work is negative
Units of Work

W ≡ (F cos θ)∆x
In SI system
 Newton • meter = Joule
N • m = J
2 / s2
 J = kg • m
Food calorie = 4184 J
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