Question

a stone of mass 0.3kg is tied to one end of the string 0.8 metre long and rotated in a vertical circle at what speed of the ball will the tension in the string be zero at the highest point of the circle what could be the tension at the lowest point in there in this case

Answer 1

Answer:

2.4 m/s         ;   17.64 N

Explanation:

At the highest point,  

centripetal force = tension(string) + gravity

⇒ mv²/r = T + mg

 Since, tension at the stage is 0,

⇒ mv²/r = mg

⇒ v² = rg

⇒ v = √(0.8)( 9.8) = 2.8 m/s

When the velocity of the mass at the highest point is 2.8, total energy was kinetic energy + potential = 1/2 mv² + mgh  

At a distance 2r(=2*0.8) from ground, total energy = 1/2 mv² + mg(1.6)

 ∴ energy = 1/2 mv² + 1.8mg

                  = 5.88 joule

At the lowest point, potential energy is 0, and kinetic energy is 1/2 mu², where u is the velocity at the point.  

⇒ 1/2 mu² = 5.88  ⇒ mu² = 11.76

At the lowest point,

tension = mg + mu²/r

             = (0.3)( 9.8) + 11.76/0.8

             = 17.64 N

Answer 2

Answer:

The tension at the lowest point, in this case, will be 17.64 N.

Explanation:

At the highest point, centripetal force = tension(string) + gravity

⇒ mv²/r = T + mg

Since, tension at the stage will be 0.

⇒ mv²/r = mg

⇒ v² = rg

⇒ v = √(0.8)( 9.8) = 2.8 m/s

Total energy was kinetic energy + potential energy when the mass's velocity at its maximum point was 2.8

= $\frac{1}{2}$ mv² + mgh

At a distance 2r(=2 × 0.8) from ground, total energy = $\frac{1}{2}$ mv² + mg(1.6)

∴ energy = $\frac{1}{2}$ mv² + 1.8mg

= 5.88 joule

Potential energy is 0 at the lowest point, and kinetic energy is  $\frac{1}{2}$ mu², where u is the point's velocity.

⇒ $\frac{1}{2}$ mu² = 5.88

⇒ mu² = 11.76

At the lowest point, tension = mg + mu²/r

= (0.3)( 9.8) + 11.76/0.8

= 17.64 N

Thus, a force over the length of a medium, particularly a force conveyed by a flexible medium like a rope or cable, is known as tension. Tension is described as a pair of opposing forces operating at each end of the elements in question.