To solve the problem using the GRESA method (Given, Required, Equation, Solution, Answer), let's break it down:

Given:

• Mass of the child ($m$) = 5.0 kg
• Radius of the circular path ($r$) = 3.0 meters
• Speed of the child ($v$) = 4.0 m/s

Required:

• The centripetal force ($F_c$) acting on the child.

Equation:

The formula for centripetal force is:

$F_c = \frac{m \cdot v^2}{r}$

Where:

• $m$ is the mass,
• $v$ is the velocity, and
• $r$ is the radius of the circular path.

Solution:

Substitute the given values into the equation:

$F_c = \frac{5.0 \, \text{kg} \cdot (4.0 \, \text{m/s})^2}{3.0 \, \text{m}}$

$F_c = \frac{5.0 \, \text{kg} \cdot 16.0 \, \text{m}^2/\text{s}^2}{3.0 \, \text{m}}$

$F_c = \frac{80.0 \, \text{kg} \cdot \text{m}/\text{s}^2}{3.0}$

$F_c = 26.67 \, \text{N}$

Answer:

The centripetal force acting on the child is 26.67 N.

Would you like more details or have any other questions?

Here are 5 related questions:

1. What is the relationship between centripetal force and velocity?
2. How would the centripetal force change if the radius was doubled?
3. What role does mass play in the calculation of centripetal force?
4. Can you calculate the centripetal acceleration for this scenario?
5. What are some real-world examples of centripetal force besides a swing?

Tip: When calculating forces in circular motion, always remember that centripetal force is directed towards the center of the circle, ensuring the object follows a curved path.