Tension HW: Change in Coupling Bars A, B, C with 39 kg Removed

[TikiPost10]

This is the question: At an airport, luggage is unloaded from a plane into the three cars of a luggage carrier. The acceleration of the carrier is .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, specifiy whether it increases or decreases.

In setting the problem up, do you calculate say, Tension A with the mg of Car 1, Tension B with the mg of Car 2, etc. and then add those totals OR do you add all the x-components of the tensions and then all the y-components?

 

[OlderDan]

This is the question: At an airport, luggage is unloaded from a plane into the three cars of a luggage carrier. The acceleration of the carrier is .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, specifiy whether it increases or decreases.

In setting the problem up, do you calculate say, Tension A with the mg of Car 1, Tension B with the mg of Car 2, etc. and then add those totals OR do you add all the x-components of the tensions and then all the y-components?

The best way to approach problems of this sort is to look at each accelerating object separately, recognizing that they have a common acceleration. You can write an F = ma equation for each car, where in two of the three cases F is the difference between two tensions. See if you can write the three equations and take it from there.

It does turn out that each tension equals the mass of all cars trailing each bar times the acceleration.

 

[thepatientmental]

To calculate the change in tension in each of the coupling bars A, B, and C, we need to consider the forces acting on the luggage carrier. In this scenario, the only external force acting on the carrier is the weight of the luggage, which is equal to the mass of the luggage (39 kg) multiplied by the acceleration due to gravity (9.8 m/s2).

When 39 kg of luggage is removed from car 2 and placed in car 1, the total weight of the luggage acting on the carrier decreases by 39 kg. This means that the tension in coupling bar A, which is connected to car 1, will decrease by the weight of 39 kg. Similarly, the tension in coupling bar B, which is connected to car 2, will decrease by the weight of 39 kg. On the other hand, the tension in coupling bar C, which is connected to car 3, will not change as there is no change in the weight acting on that car.

If the 39 kg of luggage is instead placed in car 3, the total weight acting on the carrier remains the same. However, the distribution of weight among the cars changes, resulting in a change in the tension in each of the coupling bars. In this case, the tension in coupling bar A will decrease by the weight of 39 kg, while the tension in coupling bar C will increase by the weight of 39 kg. The tension in coupling bar B will remain the same as there is no change in the weight acting on that car.

To summarize, the change in tension in each coupling bar will depend on the change in weight acting on the car connected to that bar. Therefore, we need to consider the weight of the luggage in each car separately and calculate the change in tension based on that weight. Adding the x-components and y-components of the tensions will not give an accurate representation of the change in tension in each coupling bar.