Calculate the values of x and y in the following table. $\begin{array} { | l | l | l | l | }
\hline F _ { 1 } & d _ { 1 } & F _ { 2 } & d _ { 2 } \
\hline 27 \mathrm { lb } & 6 \text { in. } & x \mathrm { lb } & 2 \mathrm { in. } \
\hline y \mathrm { lb } & 4.2 \mathrm { in } . & 512.6 \mathrm { lb } & 4.4 \mathrm { in } . \
\hline
\end{array}$
A) x = 240, y = 537.0
B) x = 8.1, y = 5,370.1
C) x = 81, y = 537.0
D) x = 80, y = 537.0
E) x = 240, y = 1,074.0

Question

Calculate the values of x and y in the following table.   $\begin{array} { | l | l | l | l | } 
\hline F _ { 1 } & d _ { 1 } & F _ { 2 } & d _ { 2 } \
\hline 27 \mathrm { lb } & 6 \text { in. } & x \mathrm { lb } & 2 \mathrm { in. } \
\hline y \mathrm { lb } & 4.2 \mathrm { in } . & 512.6 \mathrm { lb } & 4.4 \mathrm { in } . \
\hline
\end{array}$
A) x = 240, y = 537.0
B) x = 8.1, y = 5,370.1
C) x = 81, y = 537.0
D) x = 80, y = 537.0
E) x = 240, y = 1,074.0

Quizplus · Accepted Answer

The principle of moments (or the law of the lever) states that for a system in equilibrium, the sum of clockwise moments about a pivot is equal to the sum of anticlockwise moments about the same pivot. For the first row, using $F_1d_1 = F_2d_2$, we have $27 \times 6 = x \times 2$, solving for $x$ gives $x = 81$. For the second row, using the same principle, $y \times 4.2 = 512.6 \times 4.4$, solving for $y$ gives $y = 537.0$.

Calculate the Values of X and Y in the Following