Question

You are building additional storage space in your garage. You decide to suspend a 10.0-kg sheet of plywood of dimensions 0.600 m wide by 2.25 m long from the ceiling. The plywood will be held in a horizontal orientation by four light vertical chains attached to the plywood at its corners and mounted to the ceiling. After you complete the job of suspending the ply- wood from the ceiling, you choose three cubic boxes to place on the shelf. Each box is 0.750 m on a side. Box 1 has a mass of 50.0 kg, box 2 has a mass of 100 kg, and box 3 has a mass of 125 kg. The mass of each box is uniformly distributed within the box and each box is centered on the front-to-back width of the shelf. Unbeknownst to you, one of the chains on the right- hand end of your shelf is defective and will break if subjected to a force of more than 700 N. There are six possible arrange- ments of the three boxes on the shelf, for example, from left to right, Box 1, Box 2, Box 3, and Box 1, Box 3, Box, 2, and four more. Which arrangements are safe (that is, the defective chain will not break if the boxes are arranged in this way), and which arrangements are dangerous?

Please show a detailed solution. Thank you!

Answer 1