CONSERVATION OF
MECHANICAL ENERGY
What is Mechanical
Energy?
Mechanical Energy
The
sum of kinetic energy
and all forms of potential
energy within a system.
Mechanical Energy
 The
sum of kinetic energy
and all forms of potential
energy
 “ME”
 ME = KE + PE
Conservation of Mechanical Energy
 Conserved
 The
means stays constant
law is
MEi = MEf or
Initial mechanical energy =
Final mechanical energy
(in the absence of friction)
Conservation of Mechanical Energy
 Another
way to write the law is
MEi = MEf
Or
0.5 mvi2 + mghi = 0.5 mvf2 + mghf
Conservation of Mechanical Energy
Example 1
Starting from rest, a child zooms down a frictionless
slide with an initial height of 3.00m. What is her
speed at the bottom of the slide? Assume she has a
mass of 25.0 kg.
Here is the formula – you try it first:
0.5 mvi2 + mghi = 0.5 mvf2 + mghf

Conservation of Mechanical Energy
Example 1
Starting from rest, a child zooms down a frictionless
slide with an initial height of 3.00m. What is her
speed at the bottom of the slide? Assume she has a
mass of 25.0 kg.
Here is the formula – you try it first:
0.5 mvi2 + mghi = 0.5 mvf2 + mghf

0.5 (25kg)(0) + 25kg(9.8m/s2)(3m) = 0.5 (25kg)vf2 + 25kg(9.8m/s2)(0 m)
0 + 735J = 12.5 vf2 + 0
7.67m/s = vf
Conservation of Mechanical Energy

Example 2
A small 10.0 g ball is held to a slingshot that is
stretched 6.0 cm. The spring constant is 200 N/m.
a. What is the elastic PE of the slingshot before it is
released?
Conservation of Mechanical Energy

Example 2
A small 10.0 g ball is held to a slingshot that is
stretched 6.0 cm. The spring constant is 200 N/m.
a. What is the elastic PE of the slingshot before it is
released? PEi = 0.5 kx2 = 0.5 (200N/m)(.06m)2 = .36J
Conservation of Mechanical Energy

Example 2
A small 10.0 g ball is held to a slingshot that is
stretched 6.0 cm. The spring constant is 200 N/m.
a. What is the elastic PE of the slingshot before it is
released? PEi = 0.5 kx2 = ½ (200N/m)(.06m)2 = .36J
b. What is the KE of the ball just after the slingshot is
released?
Conservation of Mechanical Energy

Example 2
A small 10.0 g ball is held to a slingshot that is
stretched 6.0 cm. The spring constant is 200 N/m.
a. What is the elastic PE of the slingshot before it is
released? PEi = 0.5 kx2 = ½ (200N/m)(.06m)2 = .36J
b. What is the KE of the ball just after the slingshot is
released? KEf = same as PEi = .36J, all the initial PE
was converted to the final KE
Conservation of Mechanical Energy
Example 2 continued
c. What is the ball’s speed at the instant it is
released?

Conservation of Mechanical Energy
Example 2 continued
c. What is the ball’s speed at the instant it is
released? KEf = 0.5 mv2
.36J = 0.5 (10.0kg)v2
8.5m/s = v

Conservation of Mechanical Energy

Video Clip:
http://www.youtube.com/watch?v=JLyWacUfTYY