frictionless, horizontal, frozen lake. both iceboats start ... · two iceboats (one of mass m, one...
TRANSCRIPT
Two iceboats (one of mass m,
one of mass 2m) hold a race on a
frictionless, horizontal, frozen
lake. Both iceboats start at rest,
and the wind exerts the same
constant force on both iceboats.
A. The iceboat of mass m: it has twice as much KE as the other.
B. The iceboat of mass m: it has 4 times as much KE as the other.
C. The iceboat of mass 2m: it has twice as much KE as the other.
D. The iceboat of mass 2m: it has 4 times as much KE as the other.
E. They both cross the finish line with the same kinetic energy.
Which iceboat crosses the finish line with more kinetic
energy (KE)?
Review: Newton’s Laws
Newton’s First Law
The velocity of an object does not change
unless a force acts on the object
Newton’s Second Law: Fnet= m a
The acceleration of an object is
proportional to the net force on the object
Newton’s Third Law
For every force an object exerts on a
second object, there is an equal and
opposite force exerted on the first object
1F
2F 3F
4F
More force was
needed to stop the rock
These are equal and
opposite forces even if
you break the wall or
your fist keeps going!
ALWAYS!
A
B
C
D
E
A
B
C
D
E
Free-Body Diagrams (FBDs)
• A FBD labels all of the
forces acting on (not
by) an object.
• Only forces acting on
an object will affect its
motion (acceleration).
weightFG
If it doesn’t have units of
Newtons (kg m/s2), then it
doesn’t belong on a FBD!
(No velocity or acceleration)Fpull
n
fk
mg
Friction• Static Friction: Force that keeps object from
sliding against a surface when it is at rest
fstat msn
• Kinetic Friction: Force that slows you down
when moving
fk = mkn
Ffr=µsn
Once it starts moving,
kinetic friction takes
over.
Why it is easier to
move something after
it gets started moving.
Ffr=µsnFfr=µkn
Work Done by a Constant (or
Average) Force
• Force F acting on an object causes the
object to move a distance Δx does work W
xFW ||
x magnitude of displacement of object
F|| component of force parallel to displacement of object
Units: N m = Joule (J)
Or equivalently:
Only concerned with
movement in the
direction of the force
The Work-Energy Principle
2
212
21
onet mvmvW
The work done on an object by a net force is
Translational kinetic energy (energy of motion) of an object:
2
21 mvKE
The net work done on an object is equal to
the change in its kinetic energy
ofnet KEKEKEW
KE increases KE decreases
Gravitational Potential Energy
)( oG yymgymgW
ymgmgymgy o if PEPEPE
PEGW
Work done by gravity in going
between two points is equal to the
negative of the change in PE
Note:
1. Origin to measure y is arbitrary, thus so is PE (PE is not)
2. Gravity does work only in the vertical direction, so work done by
gravity in going from point 1 to point 2 only depends on y,
independently of path taken
oy
fy
Δy
mgygravPE
Mechanical Energy
Last Time: Work-energy principle KEWnet Separate net work done into work done by conservative and
nonconservative forces:
KE CNCnet WWW
But WC = -PE
KEPE NCW
If WNC = 0, 0)KEKE()PEPE(KEPE0 fif i
PEi + KEi = PEf + KEf
Mechanical energy (PE + KE) of an object remains the same (is
conserved) if only conservative forces act on the object
KEPE)( NCW
Last Time: Linear Momentum & Impulse
vmp
• Linear momentum of an object is mass times velocity
• Linear momentum is a vector. Direction of linear
momentum is the same as the velocity of the object
Units: kg m/s
tFpI
1. A force must act on an object for impulse to occur
2. In a collision, an impulse occurs in the direction of
the force acting on the object
t
pFnet
Conservation of Linear Momentum
in Isolated Systems.
systemisystemf pp ,,
ffii vmvmvmvm 22112211
A system is a set of objects interacting with each other
An isolated system has no unbalanced external forces, meaning no unbalanced forces outside the system (e.g., normal/gravity)
Elastic and Inelastic Collisions
• Inelastic collisions: mechanical energy (KE+PE)
is not conserved
• Special case: Perfectly inelastic, objects stick
• Elastic collisions: mechanical energy is conserved
For both elastic and inelastic collisions
linear momentum is conserved
Clicker answers
• E, A, A