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Centripetal force is the force that makes objects move in a circular path. An object can move in a circular because the object being rotated has an acceleration towards the center of the circle called centripetal acceleration. The centripetal acceleration is caused by force directed towards the center of the path or is called the centripetal force. To find out the centripetal force acting on an object moving in a circular direction, we can use Second Newton's Law equation below:

[tex]F_{s} = m . a_{s}[/tex]

[tex]F_{s} = \frac{m . v^{2} }{r}[/tex]

where Fs is centripetal force (N), m is the object's mass (kg), [tex]a_{s}[/tex] is centripetal acceleration, v is the object's speed (m/s), and r is the radius or length of string (m)

Based on the questions above, the data are given:

Mass of ball (m) = 0.25 kg

length of string (r) = 0.50 m

speed of the ball (v) = 2 m/s

Solution:

Step 1: find the force needed to keep the ball on track.

[tex]F_{s} = \frac{m . v^{2} }{r}[/tex]

[tex]F_{s} = \frac{(0.25) . (2)^{2} }{0.50}[/tex]

[tex]F_{s} = \frac{1}{0.50}[/tex]

[tex]F_{s} = 2 N[/tex]

Step 2: find the needed force if the length of the rope is changed to 0.25 m.

[tex]F_{s} = \frac{m . v^{2} }{r}[/tex]

[tex]F_{s} = \frac{(0.25) . (2)^{2} }{0.25}[/tex]

[tex]F_{s} = \frac{1}{0.25}[/tex]

[tex]F_{s} = 4 N[/tex]

So, the force needed to keep the ball moving on its path is 2 N, and if the length of the string is changed to half the size of the original string, then the force becomes 4 N.

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