Select the correct answer.
Which displacement value will produce the smallest restoring force if the same spring is used in each case?
A. $\frac{1}{2} cm$
B. 2 cm
C. $\frac{1}{3} cm$
D. 3 cm
Answer (1)
The restoring force is directly proportional to the displacement (Hooke's Law).
The smallest displacement will produce the smallest restoring force.
Comparing the given displacement values: 2 1 cm, 2 cm, 3 1 cm, and 3 cm.
The smallest displacement value is 3 1 c m .
Explanation
Understanding the Problem We need to determine which displacement value will produce the smallest restoring force, given that the same spring is used in each case.
Applying Hooke's Law Hooke's Law states that the restoring force ( F ) is proportional to the displacement ( x ) and is given by the formula:
F = − k x
where k is the spring constant. Since the same spring is used in each case, the spring constant k is the same for all options. Therefore, the restoring force is directly proportional to the displacement.
Comparing Displacement Values This means that the smallest displacement will result in the smallest restoring force. We need to compare the given displacement values to find the smallest one. The options are:
A. 2 1 cm = 0.5 cm B. 2 cm C. 3 1 cm ≈ 0.33 cm D. 3 cm
Identifying the Smallest Displacement Comparing the values, we see that 3 1 cm is the smallest displacement.
Conclusion Therefore, the displacement value that will produce the smallest restoring force is 3 1 cm.
Examples
Springs are used in many everyday applications, such as in car suspensions, mattresses, and even simple pens. Understanding Hooke's Law helps engineers design these systems to provide the desired level of support or resistance. For example, when designing a car suspension, engineers need to choose springs with appropriate spring constants and displacements to ensure a comfortable ride. The smaller the displacement, the smaller the restoring force, which can be crucial in applications where sensitivity is important.
