Question

As an oil well is drilled, each new section of drill pipe supports its own weight and that of the pipe and drill bit beneath it. Calculate the stretch in a new 6.00 , {m} length of steel pipe that supports 3.00 , {km} of pipe having a mass of 20.0 , {kg/m} and a 100 , {kg} drill bit. The pipe is equivalent in stiffness to a solid cylinder 5.00 , {cm} in diameter.

A. 2.92 , {mm}
B. 3.86 , {mm}
C. 4.71 , {mm}
D. 5.74 , {mm}

Answer 1

The stretch in the new 6.00 m length of steel pipe that supports 3.00 km of pipe and a 100 kg drill bit is approximately 2.92 mm.

Step-by-step explanation:

To calculate the stretch in the new 6.00 m length of steel pipe, we need to consider the weight of the pipe and drill bit it supports. The total weight is the sum of the weight of the pipe and the weight of the drill bit. The weight of the pipe is calculated as the mass per unit length of the pipe multiplied by the length of the pipe it supports. Similarly, the weight of the drill bit is calculated as the mass of the drill bit. Using the given values, we can calculate the total weight:

Total weight = (mass per unit length of pipe) × (length of pipe) + (mass of drill bit)

Once we have the total weight, we can calculate the force exerted on the new 6.00 m length of steel pipe:

Force = Total weight × acceleration due to gravity

Finally, we can calculate the stretch in the pipe using the formula:

Stretch = (Force × Length of pipe) / (Cross-sectional area of pipe × Young's modulus)

Plugging in the values and calculations, the stretch in the new 6.00 m length of steel pipe is approximately 2.92 mm.