Announcements
Momentum
1. HW5 due Feb 25.
2. Midterm 1 is being graded.
3. Hope to post grades and solutions by Monday
4. If you forgot to bring ID during exam, you must
see Prof. Chan with your ID or your exam will not
be graded.
r
∆p m(v f − v i ) r
=
= Fnet
∆t
∆t
alternative statement of
Newton’s second law
The time rate of change of momentum of an
object is equal to the net force acting on it
p
Impulse
„
When a single, constant force acts on
the objectrfor time ∆t, there is an
impulse I delivered to the object:
r r
I = F∆
rt
= ∆p
F
Average Force in Impulse
„
= area under F-t curve
r r
= m(v f − vi )
r
∆p m(vf − vi ) r
=
= Fnet
∆t
∆t
The average force
can be thought of as
the constant force
that would give the
same impulse to the
object in the time
interval as the actual
time-varying force
gives in the interval
r
r r
I = ∆p = Fav ∆t
t
Conservation of
Momentum
„
Momentum in an isolated system in
which a collision occurs is conserved
„
„
„
„
A collision may be the result of physical
contact between two objects
“Contact” may also arise from the
electrostatic interactions of the electrons in
the surface atoms of the bodies
An isolated system will have not external
forces
the total momentum before the collision will
equal the total momentum after the
collision
Conservation of
Momentum, cont.
„
Mathematically:
„
„
„
Momentum is conserved for the system of
objects
Assumes only internal forces are acting during
the collision
Can be generalized to any number of
objects
1
Notes About A System
„
„
Remember conservation of
momentum applies to the system
You must define the isolated
system
So its not the velocity which is conserved
but the momentum mv.
Types of Collisions
„
„
Momentum is conserved in any collision
Inelastic collisions
„
Kinetic energy is not conserved
„
„
Perfectly inelastic collisions occur when the
objects stick together
„
Types of Collisions
„
Elastic collision
„
„
both momentum and kinetic energy
are conserved
Actual collisions
„
Most collisions fall between elastic
and perfectly inelastic collisions
Some of the kinetic energy is converted into other
types of energy such as heat, sound, work to
permanently deform an object
Not all of the KE is necessarily lost
73. A tennis ball of mass 57.0 g is held just above a
basketball of mass 590 g. With their centers vertically
aligned, both balls are released from rest at the same time,
to fall through a distance of 1.20 m, as shown in Figure
P6.69. (a) Find the magnitude of the downward velocity
with which the basketball reaches the ground. (b) Assume
that an elastic collision with the ground instantaneously
reverses the velocity of the basketball while the tennis ball
is still moving down. Next, the two balls meet in an elastic
collision. (b) To what height does the tennis ball rebound?
2