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A ball of mass 0.3 kg is tied to one end of a string 0.8 m long and revolved 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 would be the tension at the lowest point in this situation ? |
| Answer» 2.8 m/s ; 17.64 NExplanation: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 jouleAt 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 = 11.76At the lowest point, tension = mg + mu²/r = (0.3)(9.8) + 11.76/0.8 = 17.64 N | |