Conservation of Mechanical Energy

1
Conservation of Mechanical Energy

• Important points to consider
•  
• In the absence of friction, no energy is lost.
  It is only converted from one form to another.
  For example, energy may be converted from
  potential to kinetic and vice versa.
• Pay attention to units. In the S.I. System,
  distance is in meter, and mass is in kilogram,
  while energy is in Joule.

2
The Problem A 180-gram baseball is launched
upward by a vertically-oriented spring, with
spring constant k 1.0 k N/m, that is compressed
by an amount ?y 21 cm. (a) How high does the
ball rise above the launcher? (b) On the way
down, at what speed does the ball strike a
players glove which is held at the same height
as the launcher?
3
Let the spring release the ball at y 0. Then, h
max is some value of y. Now, all of the
potential energy stored in the compressed spring,
Uspring, is converted to kinetic energy, K, just
as the ball loses contact with the spring at y
0. Here, at y 0, ETotal K U and U 0
because h 0. As the ball rises, h gt 0 so K
begins to shift to U until, at the top,
K at the top is 0 because vTop 0. On the way
down, this process reverses which means vBottom
on the way up equals vBottom on the way down. So,
the total energy in the system equals the work
expended to compress the spring. Stated
mathematically
4
We are not interested in the velocity at the
bottom, so (a)
5
(b) Now, let us find the velocity at the bottom.
Earlier, we determined
and now we are not interested in UTop, so