Chapter 8, Problem 57GP

*BIO While browsing books on neurophysiology, you come across a book published in 1967 by Soviet neurophysiologist Nikolai Aleksandrovich Bernstein, The Co-ordination and Regulation of Movements, in which he describes a technique to determine the mass of a part of the human body if the position of the center of mass of that body part is known. His technique for determining the mass of the forearm is described as follows: The person lies on a support board, as shown in Figure P8.57. Two readings of the scale are taken: first with the forearm held in position 1 ( $m_1$) and second with it in position 2 ( $m_2$). Knowing the distance from the elbow to the center of mass of the forearm ( $d_{\text{c}}$) and the distance between the knife edges supporting the board (D), the mass of the forearm and hand can be calculated from the following expression:

$m_{\text{fh}}=\frac{D(m_2-m_1)}{d_{\text{c}}}$

(a) First, without deriving the expression, evaluate it to see if it is reasonable. Are the units correct? Is the sign of the expression positive? Are qualitative dependences reasonable? (b) Now derive the expression. (c) Why do you think it is important to place the support board on knife edges instead of rigid blocks?