Question

As an oil well is drilled, each new section of drill pipe supports its own weight and the weight of the pipe and the drill bit beneath it. Calculate the stretch in a new 6.00-m-long steel pipe that supports a 100-kg drill bit and a 3.00-km length of pipe with a linear mass density of 20.0 kg/m. Treat the pipe as a solid cylinder with a 5.00-cm diameter.

a) 1.21 mm
b) 2.42 mm
c) 3.64 mm
d) 4.85 mm

Answer 1

The stretch in the new 6.00-m-long steel pipe is approximately 1.21 mm.

Step-by-step explanation:

To calculate the stretch in the steel pipe, we need to consider the weight of the drill bit and the length of the pipe it supports. The weight of the 100-kg drill bit is given, and we can calculate the weight of the 3.00-km length of pipe by multiplying the linear mass density by the length. The total weight is the sum of the weight of the drill bit and the weight of the pipe. Using the formula for the stretch of a cylinder, we can calculate the stretch in the pipe as follows:

S = (F * L) / (A * E)

where:

• S is the stretch
• F is the force
• L is the length
• A is the cross-sectional area
• E is the Young's modulus

Plugging in the values, we get:

S = ((100 kg + (20 kg/m * 3000 m)) * 9.8 m/s^2 * 6.00 m) / ((π * (5.00 cm / 2)^2) * 2.0 × 10^11 N/m^2)

Simplifying the expression gives us:

S ≈ 0.00121 m = 1.21 mm