Question

Three boxes are pulled to the left by strings with negligible mass on a horizontal surface, as shown above. The masses of the boxes are m1, m2, and m3, where m3>m2>m1. Friction between the boxes and the surface is negligible. The figure below shows force diagrams for each box. A student is trying to determine the tensions in the strings connecting the boxes. If the acceleration of the system and the pulling force F are known, which of the following pairs of equations could be used to find the tensions?

m3a3=TB and m2a2=TA−TB

Answer 1

To find the tensions in the strings connecting the boxes, we need to analyze each box separately and apply Newton's second law. The pair of equations m₃a₃ = T₋ and m₂a₂ = T₊-T₋ can be used to find the tensions.

Step-by-step explanation:

In order to find the tensions in the strings connecting the boxes, we need to analyze each box separately and apply Newton's second law. For block 1, we have T + w + N = mợ, where T is the tension, w is the weight, N is the contact force, and mợ is the mass. For block 2, we have T + 2 = m₂a₂, where T is the tension, and m₂ and a₂ are the mass and acceleration, respectively. Therefore, the pair of equations that can be used to find the tensions is m₃a₃ = T₋ and m₂a₂ = T₊-T₋.