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 means stays constantThe 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 mvf

2 + mghf

Conservation of Mechanical Energy

Example 1Starting 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 mvf

2 + mghf

Conservation of Mechanical Energy

Example 1Starting 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 mvf

2 + 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 2A 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 2A 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 2A 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 2A 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