The force, F newtons, exerted by a magnet on a metal object is inversely proportional to the square of the distance d cm. When d = 2 cm, F = 50 N. (a) Express F in terms of d.

To express \( F \) in terms of \( d \), we start by using the information that the force \( F \) exerted by a magnet on a metal object is inversely proportional to the square of the distance \( d \). This relationship can be written mathematically as:

\[
F \propto \frac{1}{d^2}
\]

This implies:

\[
F = \frac{k}{d^2}
\]

where \( k \) is the constant of proportionality.

### Step 1: Find the constant of proportionality (\( k \))

We are given that when \( d = 2 \) cm, \( F = 50 \) N. Substituting these values into the equation:

\[
50 = \frac{k}{2^2}
\]

\[
50 = \frac{k}{4}
\]

\[
k = 50 \times 4 = 200
\]

### Step 2: Express \( F \) in terms of \( d \)

Now that we have found \( k \), we can express \( F \) in terms of \( d \):

\[
F = \frac{200}{d^2}
\]

So, the expression for \( F \) in terms of \( d \) is:

\[
F = \frac{200}{d^2} \text{ N}
\]

Would you like more details or have any questions?

---

Here are 5 related questions for practice:

1. What is the force when the distance \( d \) is 5 cm?
2. If the force is 100 N, what is the distance \( d \)?
3. How does the force change if the distance is doubled?
4. Can you determine the distance at which the force is 25 N?
5. What would the force be at a distance of 1 cm?

**Tip:** For inverse proportionality, as one quantity increases, the other decreases in a reciprocal relationship, which can help in predicting how changes in one variable affect the other.

Understand how to express magnet force in terms of distance using inverse proportionality. Explore a detailed solution where force (F) is inversely proportional to the square of the distance (d), with practical examples and calculations. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation