To determine the restoring force of the spring, we will apply Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position:
[tex]\[ F = -k \cdot x \][/tex]
Where:
- [tex]\( F \)[/tex] is the restoring force,
- [tex]\( k \)[/tex] is the spring constant,
- [tex]\( x \)[/tex] is the displacement of the spring from its equilibrium position,
- The negative sign indicates the direction of the restoring force, which is opposite to the direction of displacement.
Given:
- The spring constant [tex]\( k \)[/tex] is 45 newtons per meter.
- The displacement [tex]\( x \)[/tex] is 0.30 meters (downward).
First, we calculate the force without considering direction:
[tex]\[ F = 45 \, \text{N/m} \times 0.30 \, \text{m} \][/tex]
[tex]\[ F = 13.5 \, \text{N} \][/tex]
Since the displacement is downward, the restoring force will be upward, making the force positive in the upward direction.
Therefore, the correct answer is:
â—‹ A. 13.5 newtons upward
