2.A lead ball of mass 0.25 kg is swung round on the end of a string so that the ball moves in a
horizontal circle of radius 1.5 m. The ball travels at a constant speed of 8.6 m s–1    Calculate the tension in the string.
You may assume that the string is horizontal

To calculate the tension in the string, we need to use the formula for centripetal force, which is the force acting towards the center of a circular path that keeps the object moving in a circle. The tension in the string provides this centripetal force.

The formula for centripetal force (\( F_c \)) is:

\[
F_c = \frac{m v^2}{r}
\]

Where:
- \( m \) is the mass of the ball (0.25 kg),
- \( v \) is the speed of the ball (8.6 m/s),
- \( r \) is the radius of the circle (1.5 m).

We will now substitute the given values into the formula to find the tension (which equals the centripetal force).

\[
F_c = \frac{0.25 \times (8.6)^2}{1.5}
\]

Let me calculate this for you.The tension in the string is approximately \( 12.33 \, \text{N} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How does the tension in the string change if the speed of the ball increases?
2. What happens to the tension if the radius of the circle is reduced?
3. How would the tension change if the ball’s mass is doubled?
4. How would you calculate the tension if the string were not perfectly horizontal?
5. What is the relationship between centripetal force and acceleration?

**Tip**: In circular motion, the tension in the string is always directed towards the center of the circle and balances the centripetal force required for the motion.

A lead ball of mass 0.25 kg is swung round on the end of a string so that the ball moves in a horizontal circle of radius 1.5 m. The ball travels at a constant speed of 8.6 m s–1. Calculate the tension in the string. You may assume that the string is horizontal.

Calculate the tension in a string for a lead ball of mass 0.25 kg moving in a horizontal circle of radius 1.5 m at 8.6 m/s. This problem covers key concepts in circular motion and centripetal force, applying Newton's Second Law of Motion. Suitable for students in Grades 9-12.

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