Certainly! Let's analyze the given problem step by step to find the restoring force when a spring with a spring constant of 45 newtons per meter is pulled 0.30 meters in the downward direction.
1. Hooke's Law:
- Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, it is expressed as:
[tex]\[
F = k \cdot x
\][/tex]
Where:
- [tex]\( F \)[/tex] is the restoring force exerted by the spring (in newtons).
- [tex]\( k \)[/tex] is the spring constant (in newtons per meter).
- [tex]\( x \)[/tex] is the displacement from the equilibrium position (in meters).
2. Given Values:
- Spring constant, [tex]\( k = 45 \)[/tex] newtons per meter.
- Displacement, [tex]\( x = 0.30 \)[/tex] meters.
3. Restoring Force Calculation:
- To find the magnitude of the restoring force, substitute the given values into Hooke’s Law equation:
[tex]\[
F = k \cdot x = 45 \, \text{N/m} \times 0.30 \, \text{m}
\][/tex]
- Performing the multiplication:
[tex]\[
F = 13.5 \, \text{N}
\][/tex]
4. Direction of the Restoring Force:
- Since the spring is pulled downward, the restoring force will act in the opposite direction, which is upward.
Therefore, the restoring force is 13.5 newtons in the upward direction. The correct answer is not provided in the options A, B, C, D, or E directly, but the closest value to the correct calculation is 14 newtons upward.
Thus, the best answer to select would be:
A. 14 newtons upward
