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.
∑ F or ∑ Fr = mar
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.
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
f k = µk n
The coefficient of friction
µ (‘mu’) depends on the
surfaces in contact
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 = µs n
uur uur
f s = -F
ƒs, max = µs n
Usually, µs > µN
Block on a Ramp
Axes are rotated as
usual on an incline
The direction of
impending motion
would be down the
Friction acts up the
Opposes the motion
Draw free body
Yada Yada Yada
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
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° = 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
Work done is negative if
lowering the box
„ force is upward, but
displacement is
Kinetic Energy
Energy associated with the motion
of an object
KE = mv
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