Chapter 7, Problem 48P

To determine

The location of centre of mass of system of car and people inside the car

Answer to Problem 48P

2.74 m.

Explanation of Solution

Given:

Mass of the empty car $=m=1050\text{kg}$

Mass of the each person $=m_p=70\text{kg}$

Distance of centre of mass of car relative to front of the car $=r_{car}=2.50\text{m}$

Mass of the two people sitting in front seat $=m_1=2m_p=2(70)=140\text{kg}$

Mass of the three people sitting in back seat $=m_2=3m_p=3(70)=210\text{kg}$

Distance of the centre of mass of two people sitting in the front seat relative to front of the car $=r_1=2.80\text{m}$

Distance of the centre of mass of three people sitting in the back seat relative to front of the car $=r_2=3.90\text{m}$

Location of centre of mass of the system relative to front of the car $=r_{cm}$

Formula Used:

Centre of mass of system of masses is given as

  $\begin{array}{l}{r}_{cm}=\frac{m_1{r}_1+m_2{r}_2+m_3{r}_3+\mathrm{..}}{m_1+m_2+m_3+\mathrm{..}}\\ \text{Where }{m}_1,m_2\text{,}{m}_3\text{ are the masses and }{r}_1,r_2\text{,}{r}_3\text{ are their respective centre of masses}\text{.}\end{array}$

Calculation:

Centre of mass of system is given as

  $r_{cm}=\frac{m{r}_{car}+m_1{r}_1+m_2{r}_2}{m+m_1+m_2}$

Substituting the values

  $\begin{array}{l}{r}_{cm}=\frac{(1050)(2.50)+(140)(2.80)+(210)(3.90)}{1050+140+210}\\ r_{cm}=2.74\text{m}\end{array}$

Conclusion:

Therefore, the distance of the centre of mass is 2.74 m.