Question

which of the following is a correct expression for the mass, m, of the bone? assume friction between the bone and the table is negligible. choose 1 answer: a ( m = (f_{\text{s}} - f_{\text{b}})a ) b ( m = \frac{f_{\text{s}} - f_{\text{b}}}{a} ) c ( m = (f_{\text{s}} + f_{\text{b}})a ) d ( m = \frac{f_{\text{s}} + f_{\text{b}}}{a} )

Explanation:

Step1: Recall Newton's Second Law

Newton's second law states that the net force \( F_{\text{net}} \) acting on an object is equal to the mass \( m \) of the object multiplied by its acceleration \( a \), i.e., \( F_{\text{net}} = ma \).

Step2: Determine the Net Force

Assuming \( F_{\text{S}} \) and \( F_{\text{B}} \) are forces acting on the bone, and if they are in opposite directions (since we are subtracting them in the options), the net force \( F_{\text{net}} = F_{\text{S}} - F_{\text{B}} \) (assuming \( F_{\text{S}} > F_{\text{B}} \) for the direction of acceleration).

Step3: Solve for Mass

From \( F_{\text{net}} = ma \), we can solve for \( m \) by dividing both sides by \( a \). So, \( m=\frac{F_{\text{net}}}{a} \). Substituting \( F_{\text{net}} = F_{\text{S}} - F_{\text{B}} \), we get \( m = \frac{F_{\text{S}} - F_{\text{B}}}{a} \).

Answer:

B. \( m = \frac{F_{\text{S}} - F_{\text{B}}}{a} \)