Q2 E - University Physics with Modern Physics

Question

The center of gravity of a $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{-}\mathit{k}\mathit{g}$ irregular object is shown in Fig. E11.2. You need to move the center of gravity $\mathbf{2}\mathbf{.}\mathbf{20}\mathbf{ }\mathit{c}\mathit{m}$to the left by gluing on a $\mathbf{1}\mathbf{.}\mathbf{50}\mathbf{-}\mathit{k}\mathit{g}$mass, which will then be considered as part of the object. Where should the center of gravity of this additional mass be located?

                                                     

Step-by-Step Solution

Answer

Thus, the center of gravity is left shifted by a length of 9.53 cm.

Center of Gravity

There is a point inside any object where the whole weight of that body is concentrated, balancing all other parts of that body. This point is considered to be the Center of Gravity.

Find the distance

Given that the irregular object has mass $m_1=5.00 kg$. When the mass $m_2=1.50 kg$is added, the center of gravity shifts to the left by $x_m=2.20 cm$ .

Let the whole set up illustrated as a free body diagram shown in the figure as:

Now, for the center of gravity, we have:

$$\begin{gathered} x_{cm}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2} \\ -2.20 =\frac{\left(5.00\right)\left(0\right)+\left(1.50\right)\left(x\right)}{5.00+1.50} \\ -2.20 =\frac{1.50}{6.50}x \\ x=-9.53 cm \end{gathered}$$

Thus, the center of gravity of the object, after adding extra mass, is shifted to the left by 9.53 cm.