PHYS 1501Q Lecture 9: PHYS 1501-Lecture 9-Center of Mass

physic lab 145.1

prelab 10 pdf link if needed http://www.physics.qc.edu/files.php
You will be allowed three submissions for this question. Assume theruler is exactly 1 m long, and the mass hangers have negligibbemass.

a) Suppose the ruler in procedure 2 is asymetrical, and it isbalanced at the 41.3 cm mark (at the center of mass). Now, mass Mis hung on the ruler at the 100 cm mark. Where must you hang mass1.69M so the system remains in equilibrium?
At the _________________ cm mark

b) The method of procedure 2 can be used to accurately determinethe mass of a light coin (as in procedure 4). Suppose the ruler isperfectly symmetrical, and it balances at the center. The coin ofunknown mass is placed at the 0 cm mark, it is balanced by a mass m= 22.9 g placed at the 76.6 cm mark. Find the mass of thecoin.
__________________________ g

c)Suppose the ruler in procedure 3 is asymmetrical, balancing atthe 57.2 cm mark. The ruler is now supported at the 45.3 cm mark,and a mass of 455 g is placed at the 31.3 cm mark. Find the mass ofthe ruler. ______________________ g

A) A 1.0 kg ball is located at the origin and a 2.0 kg ball is at1.0 m away in the x-direction. Where is the center of mass of thesetwo balls.
(Answer in ihat + jhat+ khat form)


B) A 3.0 kg ball is located at (x,y,z)=(0,1.0,0)m and a 4.0 kg ballis located at (1.0,1.0,0) m. Where is the center of mass of thesetwo balls?
(Answer in ihat + jhat+ khat form)

C) Where is the center of mass of all four balls? Determine thistwo ways: (1) find the center of mass of all four balls treatedindividually and then (2) find the center of mass acting as if thesystem was made up of two bodies located at the two centers ofmasses you found above (e.g. a total mass of 1 kg + 2 kg at thelocation of the first center of mass you found above). The tworesults should agree.
(Answer in ihat + jhat+ khat form)

D) Now, let's say that three identical, uniform rods, each 1.00 mlong, are welded perpendicular to one another at a common end so asto represent the positive x-, y-, and z-axes of a Cartesiancoordinate system. Where is the CM of this object?
(Answer in jhat+ khat form)