Answered

Select the correct answer.

What will be the restoring force if a spring with a spring constant of 45 newtons per meter is pulled 0.30 meters in the downward direction?

A. 14 newtons upward
B. 45 newtons upward
C. 67 newtons upward
D. 130 newtons upward
E. 150 newtons upward



Answer :

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:

○ A. 13.5 newtons upward