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Expert-verified Found in: Page 230 ### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922 ## (II) Calculate $${F_{\rm{A}}}$$ and $${F_{\rm{B}}}$$ for the uniform cantilever shown in Fig. 9–9 whose mass is 1200 kg. The forces on A and B are $${F_{\rm{A}}} = - 2928\;{\rm{N}}$$ and $${F_{\rm{B}}} = 14700\;{\rm{N}}$$ , respectively.

See the step by step solution

## Step 1: Given data

The force on point A is $${F_{\rm{A}}}$$.

The force on point B is $${F_{\rm{B}}}$$.

The mass of the cantilever is $$m = 1200\;{\rm{kg}}$$.

## Step 2: Understanding the torque exerted on the cantilever

In order to determine the forces at points A and B, first, find the torque about the left end of the beam and apply the conditions of equilibrium.

## Step 3: Free body diagram and calculation of the force on point B

The following is the free body diagram. The relation to calculate the net torque can be written as:

$$\begin{array}{c}\sum \tau = 0\\\left( {{F_{\rm{B}}} \times 20\;{\rm{m}}} \right) - \left( {mg \times 25\;{\rm{m}}} \right) = 0\end{array}$$

Here, $$g$$ is the gravitational acceleration and $${F_{\rm{B}}}$$ is the force on point B.

On plugging the values in the above relation, you get:

$$\begin{array}{c}\left( {{F_{\rm{B}}} \times 20\;{\rm{m}}} \right) - \left( {1200\;{\rm{kg}} \times 9.8\;{\rm{m/}}{{\rm{s}}^2} \times 25\;{\rm{m}}} \right) = 0\\{F_{\rm{B}}} = 14700\;{\rm{N}}\end{array}$$

## Step 4: Calculation of force on point A

The relation to calculate the force on the beam can be written as:

$$\begin{array}{c}\sum {F_{\rm{y}}} = 0\\{F_{\rm{A}}} + {F_{\rm{B}}} - mg = 0\end{array}$$

Here, $${F_{\rm{A}}}$$ is the force on point A.

On plugging the values in the above relation, you get:

$$\begin{array}{c}{F_{\rm{A}}} + \left( {14700\;{\rm{N}}} \right) - \left( {1200\;{\rm{kg}}} \right)\left( {9.8\;{\rm{m/}}{{\rm{s}}^2}} \right) = 0\\{F_{\rm{A}}} = - 2928\;{\rm{N}}\end{array}$$

Thus, the forces on points A and B are $${F_{\rm{A}}} = - 2928\;{\rm{N}}$$ and $${F_{\rm{B}}} = 14700\;{\rm{N}}$$, respectively. ### Want to see more solutions like these? 