Question

24) To determine the location of her center of mass, a physics student lies on a lightweight plank supported by two scales 2.50 m apart. If the left scale reads 435 N, and the right scale reads 183 N, find (a) the student’s mass and (b) the distance from the student’s head to her center of mass.

Answer 1

ANSWER:

a) 63 kg

b) 0.74 m

STEP-BY-STEP EXPLANATION:

Given:

F1 = 435 N

F2 = 183 N

L = 2.5 m

a)

Here the two forces F1 and F2 are actingupwards and his weight acting downwards.

$\begin{gathered} \sum ^{}_{}F_y=F_1+F_2-W=0 \\ W=F_1+F_2 \\ m\cdot g=F_1+F_2 \\ m=\frac{F_1+F_2}{g} \\ \text{ replacing} \\ m=\frac{435+183}{9.81} \\ m=62.99\cong63\text{ kg} \end{gathered}$

By using the principles of torque we get:

$\sum ^{}_{}\tau=L\cdot F_2-x\cdot W=0$

here x is the centerof the mass, solving and replacing for x:

$\begin{gathered} L\cdot F_2-x\cdot W=0 \\ L\cdot F_2=x\cdot W \\ x=\frac{L\cdot F_2}{W} \\ x=\frac{L\cdot F_2}{m\cdot g} \\ x=\frac{2.5\cdot183}{63\cdot9.81} \\ x=0.74\text{ m} \end{gathered}$