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 = 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
plane
Friction acts up the
plane
„
„
„
Opposes the motion
Draw free body
diagram
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
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° = 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