5. If a force of 132 Newtons stretched a coil by 0.007 meters, what force would be needed to stretch the coil by 0.1 meter? Round to the nearest tenth.
Answer: D
1885.7N
To stretch the coil by 0.1 meters, a force of 1885.7 Newtons is required. This is determined by using Hooke's law, which states that the force needed to stretch or compress a spring is directly proportional to the distance it is stretched or compressed.
A) 92.4N
This option is incorrect as it significantly underestimates the force needed. The relationship dictated by Hooke's law shows that the force required increases as the extension increases, and 92.4N is not sufficient to stretch the coil by 0.1 meters.
B) 136.0N
This option is also incorrect. While it is closer than Option A, it still does not account for the increased stretching distance. The required force to stretch the coil from 0.007 meters to 0.1 meters is much higher than 136.0N.
C) 188.6N
Option C is incorrect as well. Similar to the previous options, this force does not adequately reflect the proportional increase in the required force when stretching the coil to 0.1 meters. The calculation shows that a much greater force is necessary.
D) 1885.7N
This is the correct answer. Using the proportional relationship from Hooke's law, the force necessary to stretch the coil to 0.1 meters is calculated to be 1885.7 Newtons, which aligns with the expectations of the problem based on the initial stretching data.
Conclusion
The correct answer of 1885.7N is derived from applying Hooke's law correctly, demonstrating the proportionality between force and displacement. All other options fail to meet the necessary calculations for the increased stretch length, underselling the actual force required. Hence, D is the only option that accurately reflects the physics of the situation.