A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving upward. The ball reaches a height 600 cm above the floor. What was the tension in the string an instant before it broke?

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Answer:

Explanation:

Given

mass of ball [tex]m=100 gm[/tex]

Length of string [tex]L=60 cm[/tex]

ball reaches to a height of [tex]h=600 cm[/tex]

let us take initial velocity of ball at the time of breaking be u and v be the final velocity at top

using [tex]v^2-u^2=2 as[/tex]

[tex]0-u^2=2(-9.8)\cdot (6-2)[/tex]

[tex]u=\sqrt{78.4}[/tex]

[tex]u=8.85 m/s[/tex]

If T is the Tension in the string, then T is given by

[tex]T=\frac{mv^2}{L}[/tex]

[tex]T=\frac{0.1\cdot 8.85^2}{0.6}[/tex]

[tex]T=13.06 N[/tex]              

Tension force is the force produced when a load is applied in a direction away from one or more ends of material, The tension in the string an instant before it broke will be 13.06 N.

What is tension force?

Tension force is the force produced when a load is applied in a direction away from one or more ends of a material, usually to the cross-section of the material.

Tension is frequently described as a "pulling" force. To constitute a tension force, the load supplied to the material must be exerted axially.

The given data in the problem is;

m is the mass of ball = 100 gm

L is the Length of string = 60 cm

h is the height of ball reaches= 600cm

From Newton's equation of motion;

[tex]\rm v^2-u^2= 2as \\\\ 0-u^2 = 2 (-9.81)(6-2)\\\\ \rm u = \sqrt{78.4} \\\\ u= 8.85 \ m/sec[/tex]

The tension force is found by;

[tex]\rm T = \frac{mV^2}{L} \\\\ \rm T =\frac{0.1(8.85)^2}{0.6} \\\\ \rm T = 13.06 N[/tex]

Hence the tension in the string an instant before it broke will be 13.06 N.

To learn more about the tension force refer to the link;

https://brainly.com/question/2287912