1. CONSERVATION OF MECHANICAL ENERGY
What is Mechanical Energy?

2. Mechanical Energy
The sum of kinetic energy and all forms of potential energy within a system.

3. The sum of kinetic energy and all forms of potential energy
Mechanical Energy
The sum of kinetic energy and all forms of potential energy
“ME”
ME = KE + PE

4. Conservation of Mechanical Energy
Conserved means stays constant
The law is
MEi = MEf or
Initial mechanical energy =
Final mechanical energy
(in the absence of friction)

5. Conservation of Mechanical Energy
Another way to write the law is
MEi = MEf Or
0.5 mvi2 + mghi = 0.5 mvf2 + mghf

6. 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

7. 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)
J = 12.5 vf2 + 0
7.67m/s = vf

8. 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?

9. 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

10. 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?

11. 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

12. Conservation of Mechanical Energy
Example 2 continued
c. What is the ball’s speed at the instant it is released?

13. 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

14. Conservation of Mechanical Energy
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