Chapter 4, Problem 26P

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-51. Determine the ratio of the tension in the coupling (think of it as a cord) between the locomotive and the first car (F_T1), to that between the first car and the second car (F_T2), for any nonzero acceleration of the train.

Figure 4-51 Problem 27.

To determine

The ratio of the tension in the coupling between the locomotive and the first car, to that between the first car and the second car for any nonzero acceleration of the train.

Answer to Problem 26P

Solution:

Ratio of the tension in the coupling between the locomotive and the first car is equal to 2.

Explanation of Solution

Given:

A train locomotive is pulling two cars of the same mass.

Consider the mass of each car as m.

Formula used:

From Newton’s second law of motion:

  ${\displaystyle \sum F}=ma$

Where, m is mass and a is acceleration.

Calculation:

The two cars and train locomotive move with the same acceleration as they are connected.

For car 2:

  $F_{T2}=ma$

Where, m is the mass of the car and a is its acceleration.

For car 1:

  $F_{T1}-F_{T2}=ma$

  $F_{T1}-ma=ma$

  $F_{T1}=2ma$ .

Take the ratio

  $\frac{F_{T1}}{F_{T2}}=2$

Conclusion:

The ratio is 2.