Question

CM, 1D, extended mass: A rod of length L = 1.0 m has constant mass per unit length λ given by LM=λ, where M is the total mass of the rod. For this problem, the parameter x is the distance from the left end of the rod. a)By observation alone, what do you think is the center of mass, cmx, of the rod (in symbols, then numbers)? This answer should be obvious. The point of what follows is to get this same result using integration, and to help you understand the integration process. b)Sketch a diagram. At an arbitrary position x, imagine an infinitesimal piece with length dx. i)Make a list of the properties of this piece (position, mass, length, mass per unit length), and assign symbols/equations to each. ii)What is the mass dm of this piece? (in terms of given parameters) c)Integrate to find the center of mass, cmx (symbols first, then numbers). Does your answer agree with what you already know?

Answer 1