Question

calculating spring constant and displacement using hooke’s law

what is the spring constant for a supermarket scale that stretches 0.01 m when a force of 4 n is applied?
□ n/m

what is the displacement of a spring if it has a spring constant of 10 n/m, and a force of 2.5 n is applied?
□ m

Explanation:

First Question: Calculating Spring Constant

Step1: Recall Hooke's Law

Hooke's Law is given by \( F = kx \), where \( F \) is the force applied, \( k \) is the spring constant, and \( x \) is the displacement. We need to solve for \( k \), so rearrange the formula to \( k=\frac{F}{x} \).

Step2: Substitute the values

Given \( F = 4\space N \) and \( x = 0.01\space m \). Substitute these values into the formula: \( k=\frac{4}{0.01} \).

Step3: Calculate the result

\( \frac{4}{0.01}=400 \).

Second Question: Calculating Displacement

Step1: Recall Hooke's Law

Again, use Hooke's Law \( F = kx \). We need to solve for \( x \), so rearrange the formula to \( x=\frac{F}{k} \).

Step2: Substitute the values

Given \( F = 2.5\space N \) and \( k = 10\space N/m \). Substitute these values into the formula: \( x=\frac{2.5}{10} \).

Step3: Calculate the result

\( \frac{2.5}{10}=0.25 \).

Answer:

First question (spring constant): \( 400\space N/m \)
Second question (displacement): \( 0.25\space m \)