Question:

A small ball of mass 0.2 kg is attached to a string and spun in a horizontal circle with a radius of 0.5 m. The tension in the string is measured to be 6 N. Determine the centripetal force acting on the ball and the speed at which the ball is moving.

Answer:

Given data:

• Mass of the ball, m = 0.2 kg
• Radius of the circle, r = 0.5 m
• Tension in the string, T = 6 N

The centripetal force, Fc, acting on the ball is equal to the tension in the string. Since the string is providing the centripetal force to keep the ball moving in a circle, we can equate these two values.

Step 1: Determine the centripetal force (Fc)

Considering the tension in the string is providing the centripetal force, we have:

Fc = T

Fc = 6 N

So, the centripetal force acting on the ball is 6 N.

Step 2: Determine the speed of the ball (v)

The centripetal force is given by the equation:

Fc = mv²/r

Here, m = 0.2 kg and r = 0.5 m.

Substituting these values, we get:

6 N = 0.2 kg * v² / 0.5 m

Rearranging the equation to solve for v², we get:

v² = (6 N * 0.5 m) / 0.2 kg

v² = 3 N*m / 0.2 kg

v² = 15 m²/s²

Taking the square root of both sides, we find:

v = √(15 m²/s²)

v ≈ 3.87 m/s

Therefore, the speed at which the ball is moving is approximately 3.87 m/s.