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Chapter 9: Q94P (page 254)

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

Expert verified

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

Step by step solution

01

Understanding the given information

  1. Mass of Chrysler, mcis 2400 kg .
  2. Speed of Chrysler, vcis 80 km/hr .
  3. Mass of ford, mfis 1600 kg .
  4. Speed of ford, vfis 60 km/hr .
02

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.

03

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,

mc+mfvcom=mcvc+mfvf

Here vcomis the velocity of the center of mass.

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

2400kg+1600kgvcom=2400kg80kmh+1600kg60kmh4000kgvcom=288000kg·kmhvcom=288000kg·kmh4000kg=72kmh

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

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