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# [Physics] Use Newton’s 2nd law to find the tension force in the rope as well as the period?

Tether Ball is a game where a 2.00 m long pole sticks upwards out of the ground, a 1.8m long rope is tied to the top of the pole, and the other end is tied to a 500.0g ball. You hit the ball such that it goes in a horizontal circle around the pole, with the rope making an angle of 30.0degrees with the pole. This means the rope is sweeping out a cone, while the ball moves around the circle defining the base of the cone.

Apply Newton’s 2nd law to find the tension force in the rope supporting the ball as well as the time that it takes the ball to go through one circle around the pole.

### 1 Answer

- NCSLv 72 months agoFavorite Answer
a) There is no acceleration vertically, so it must be that

F*cosΘ = m*g → → where F is the tension

so F = m*g/cosΘ = 0.5000kg * 9.81m/s² / cos30.0º = 5.66 N

b) Horizontally, the centripetal acceleration is

a = F*sinΘ / m = 5.66N * sin30º / 0.5000kg = 5.66 m/s²

and a = ω²r = (2π/T)²*L*sinΘ

T² = 2π*L*sinΘ / a = 2π * 1.8m*sin30.0º / 5.66m/s² = 0.998 s²

T = 0.999 s

Hope this helps!