Question

An old Chrysler with mass 2400 kg is moving along a straight stretch of road at 80 km/h. It is followed by a Ford with mass 1600 kgmoving at 60 km/h. How fast is the center of mass of the two cars moving?

Short answer

The speed of the center of mass of the two cars is 72 km/h .

Step-by-step solution

Understanding the given information

1. Mass of Chrysler, $m_c$is 2400 kg .
2. Speed of Chrysler, $v_c$is 80 km/hr .
3. Mass of ford, $m_f$is 1600 kg .
4. Speed of ford, $v_f$is 60 km/hr .

Concept and formula used in the given question

Using the formula of conservation of momentum, we can find the speed of the center of mass of the two cars.

Calculation of how fast is the center of mass of the two moving cars

For conservation of momentum, we can write the momentum equation as,

$\left(m_c+m_f\right)v_{com}=m_c{v}_c+m_f{v}_f$

Here $v_{com}$is the velocity of the center of mass.

Substitute the values in the above expression, and we get,

$$\begin{gathered} \left(2400\mathrm{kg}+1600\mathrm{kg}\right)v_{com}=\left(2400\mathrm{kg}\right)\left(80\frac{\mathrm{km}}{\mathrm{h}}\right)+\left(1600\mathrm{kg}\right)\left(60\frac{\mathrm{km}}{\mathrm{h}}\right) \\ \left(4000\mathrm{kg}\right)v_{com}=288000\mathrm{kg}·\frac{\mathrm{km}}{\mathrm{h}} \\ {v}_{com}=\frac{288000\mathrm{kg}·{\displaystyle \frac{\mathrm{km}}{\mathrm{h}}}}{4000\mathrm{kg}} \\ =72\frac{\mathrm{km}}{\mathrm{h}} \end{gathered}$$

Therefore, the speed of the center of mass of the two cars is 72 km/h .