Final answer:
The IMA of the screwdriver used to turn a "1/4 20" screw is 5.6, computed using the formula involving the length of the screwdriver handle and the pitch of the screw threads.
Step-by-step explanation:
The IMA (Ideal Mechanical Advantage) of the screwdriver is 5.6.To calculate the IMA of a screw, we use the formula IMA = length of handle/pitch of screw thread. The pitch (P) of a "1/4 20" screw is 1/20 of an inch because it has 20 threads per inch (TPI). The diameter of the handle (De) of the screwdriver is 1.75 inches, thus the radius (r) is De/2, which is 0.875 inches. The IMA is calculated as IMA = 2πr/P. By substituting the given values, we get IMA = 2π(0.875 inches)/(1/20 inches) which simplifies to IMA = 2π(0.875 inches) * 20, resulting in IMA = 110π inches. After converting the constant π to its numerical value (approximately 3.14), the calculation yields IMA = 5.6 (rounded to one decimal place).
It's important to note that IMA provides only a theoretical value without accounting for real-world factors such as friction.The IMA (Ideal Mechanical Advantage) of a device can be calculated using the formula: IMA = De / (P x TPI), where De is the diameter of the handle, P is the pitch of the screw, and TPI is the threads per inch of the screw. In this case, the diameter of the handle is 1.75 inches (De), the pitch is 1/20 inch (P), and the threads per inch is 20 (TPI). Plugging these values into the formula, we get: IMA = 1.75 / (1/20 x 20) = 17.5.