Understanding Restoring Force and Force Constant

This question involves the concept of restoring force in physics, typically encountered when dealing with springs or elastic materials. The restoring force is the force that acts to bring a displaced object back to its equilibrium position.

Hooke's Law describes the relationship between the restoring force ($F$) exerted by a spring or elastic object and its displacement ($x$) from its equilibrium position. The law states that the force is directly proportional to the displacement, and the constant of proportionality is called the force constant, denoted by $k$.

Applying Hooke's Law

The formula for Hooke's Law is:

$F = kx$

Where:

• $F$ is the magnitude of the restoring force (in Newtons, N).
• $k$ is the force constant (in Newtons per meter, $\frac{N}{m}$).
• $x$ is the displacement from the equilibrium position (in meters, m).

Given Information

From the question, we are given:

• Magnitude of restoring force, $F = 50.0$ N
• Displacement, $x = 0.5$ m

Calculating the Force Constant (k)

We need to find the value of the force constant, $k$. To do this, we can rearrange Hooke's Law formula:

$k = \frac{F}{x}$

Now, we substitute the given values into the rearranged formula:

$k = \frac{50.0 \text{ N}}{0.5 \text{ m}}$

Performing the division:

$k = 100.0 \frac{\text{N}}{\text{m}}$

Final Answer Analysis

The calculated value for the force constant ($k$) is $100.0 \frac{N}{m}$. Comparing this result with the given options:

• Option 1: 25.0 $\frac{N}{m}$
• Option 2: 5.0 $\frac{N}{m}$
• Option 3: 100.0 $\frac{N}{m}$
• Option 4: 50.0 $\frac{N}{m}$

Our calculated value matches Option 3.