Final answer:
To calculate the stretch of a steel drill pipe supporting its own weight and additional weight, you need to find the total force due to the weight, the cross-sectional area, and use Hooke's Law with the modulus of elasticity for steel.
Step-by-step explanation:
To calculate the stretch in a new 6.00 m long steel drill pipe that supports a 3.00 km length of pipe and a 100-kg drill bit, we need to use Hooke's Law for elongation, which states that δ = (F · L) / (A · E), where δ is the elongation, F is the force applied, L is the original length of the pipe, A is the cross-sectional area, and E is the modulus of elasticity of steel. First, we calculate the total weight (W) supported by the pipe. The weight of the 3.00 km length of pipe (Wpipe) is 3.00 km × 20.0 kg/m × 9.81 m/s². The weight of the drill bit (Wbit) is 100 kg × 9.81 m/s². The total weight (F) is Wpipe + Wbit. Next, the cross-sectional area (A) of the pipe can be calculated using the diameter (d = 5.00 cm), through the formula A = π · (d/2)^2. Finally, using the modulus of elasticity for steel (which can be found in textbooks or engineering tables), we can substitute the values into the Hooke's Law formula to find the stretch of the drill pipe.