*111. ssm At an airport, luggage is unloaded from a plane into the three cars of a luggage carrier, as the drawing shows. The acceleration of the carrier is 0.12 m/s2, and friction is negligible. The coupling bars have negligible mass. By how much would the tension in each of the coupling bars A, B, and C change if 39 kg of luggage were removed from car 2 and placed in (a) car 1 and (b) car 3? If the tension changes, specify whether it increases or decreases.

Free body Diagrams for each car

To find the tensions we only need to consider the x or horizontal components of forces.

 

 

Assuming that there is no slack in the coupling bars, all three cars are rigidly connected, so the accelerations are the same for all three, that is why we used just a rather than a1, a2, or a3.  Now solving for each tension we get

 

 

 

 

 

So the three tensions are:

 

 

Now we are to move luggage from car 2 to car 1, so the masses change as follows

 

 

 

 

Now we determine which if any of the tensions changed as a result

 

The Tension in C does not change.

 

 

The Tension in B changes by decreasing 4.7 N.

 

The Tension in A remains unchanged.

 

Now we are to move luggage from car 2 to car 3, so the masses change as follows

 

 

 

 

Now we determine which if any of the tensions changed as a result

 

The Tension in C is increased by 4.7 N.

 

The Tension in B is unchanged.

 

The Tension in A remains the same.

 

When you move luggage from car 2 to car 1, The Tension in A and C does not change. The Tension in B changes by decreasing 4.7 N.

When you move luggage from car 2 to car 3, The Tension in A and B does not change. The Tension in C changes by increasing 4.7 N.

 

 

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This page last updated on January 11, 2020