Final answer:
The breaking weight for a wire of the same material with double the radius and six times the length compared to the original is approximately 26.67 kg. This calculation considers the direct proportion of breaking weight to the cross-sectional area and the inverse proportion to the length of the wire.
Step-by-step explanation:
The student’s question is related to the strength of materials and specifically pertains to the concept of tensile stress in physics. When considering the breaking weight required for a wire with double the radius and six times the length, we must first understand that the breaking weight is directly proportional to the cross-sectional area and inversely proportional to the length. Using the original wire as a reference (40 kg to break a 1 m length), since the area is proportional to the square of the radius, doubling the radius would increase the area by a factor of four. Therefore, if a 1 m wire with the original radius requires 40 kg to break, a 1 m wire with double the radius would require 4 times the weight (i.e., 160 kg) to break.
However, as the wire is six times longer, this would reduce the required weight by a factor of six (since strength is inversely proportional to length). Therefore, the final weight required to break the wire that is both longer and thicker would be 160 kg / 6, which is approximately 26.67 kg.