CONSERVATION OF MECHANICAL ENERGY What is Mechanical Energy?

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

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

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)

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