Announcements:
Assignments:
Chapter 8 - Potential Energy
Conservation of Energy: Ei = Ef = mechanical energy + Wnc
Gravitational potential energy: Eg = mgh
Elastic potential energy: Es = 0.5kx^2 ,
note: The stiffness of a spring (k) depends on the length of the spring (how
many coils).
Work done by non-conservative forces cannot be easily converted to mechanical
energy: friction, heat, sound, etc.
Book problems: 7.68, 7.69
Example problems: 14, 24; 20, 40, 84
Demo: Loop-the-loop: What initial height is required for a ball to just barely complete the loop? Why is this answer different than in the homework problem?
ConcepTest questions for Chapter 8
Chapter 9: Momentum and Collisions
Newton's Second Law (as Newton defined it): F = dp/dt
Momentum (linear) is defined as: p = mv
If no external forces act on a system, momentum is conserved (constant): pi
= pf
A 2-dimensional collision can be analyzed along x and y axes.
Impulse = F*t = change in momentum
In an inelastic collision, momentum is conserved, but kinetic energy
is not.
In an elastic collision, both momentum and kinetic energy are conserved.
Most collisions are partially elastic/inelastic.
Demos:
Example
Problem:
If you jump up in the air to a height, h, how much force does the ground exert
on you when you land? What do you need to know?
Solution: You need to know the
distance your body moves as you bend your knees: x ~ 0.5 m
From conservation of energy, your speed just before touching the ground
is: v = sqrt(2gh).
From here, you can take two different approaches to solve this problem:
Conservation
of energy:
work done by ground = change in kinetic energy
F*x = 0.5mv2
F = mv2/(2x)
Conservation of momentum: impulse = change in momentum
F*t = mv
x = 0.5at2 and v2
= 2ax, so t = 2x/v
so F = mv2/(2x) - same as above
for conserv. of energy
What
is the maximum height a person can fall without suffering severe injury?
(see also problem 50 in chapter 5).
Human acceleration
response data