Lecture 18

Summary

Kinetic and potential energy
Conservation of mechanical energy
Energy diagrams
Nonconservative work

Chapter 9

The center of mass

concept
calculation applet
force and c.m. applet
BU center of mass applet
This applet allows you to visualize the change of the location of the center of mass whenever any of three mass values are changed. The masses remain fixed at the vertices of an equilateral triangle.

I have not yet found an HTML5 equivalent to the force and c.m. applet. Sorry!

Example #1

Example #2

PoP5 qq8.05
A baseball bat is cut at the location of its center of mass as shown in the figure. The piece with the smaller mass is Serway PSE6 Fig 9.20

A. the piece on the right
B. the piece on the left
C. Neither; each piece has the same mass.
D. impossible to determine.
Answer

sb5 9.42
M_Earth = 5.98×10²⁴ kg and M_Moon = 7.36×10²² kg. The distance between their centers is 3.84×10⁸ m. What is r_CM measured from the Earth's center?
A. 384,000 km
B. 4670 km
C. 3190 km
D. 6370 km
Answer

answer

B. the piece on the left

The piece with the handle will have less mass than the piece made up of the end of the bat. To see why this is true, take the origin of coordinates as the center of mass before the bat was cut. Replace each cut piece by a small sphere located at the center of mass for each piece. The sphere representing the handle piece is farther from the origin, but therefore must have less mass than the end piece. In this way, the product of less mass and greater distance (for the handle) balances the product of greater mass and less distance (for the end piece). Serway PSE6 QQ 9.10 answer image

answer

B. 4670 km
Picture (797x241, 6.3Kb)