Questions 1,2,3

Question

An athlete swings a 6.84 kg ball horizontally on the end of a rope. The ball moves in a circle of radius 1.16 m at an angular speed of 0.797 rev/s.

 

a) What is the tangential speed of the ball?

 

b) What is its centripetal acceleration?

 

c) If the maximum tension the rope can withstand before breaking is 97.2 N, what is the maximum tangential speed the ball can have?

 

Answer 1

Hi Ragine – happy to help you work through this.

We’re given: mass m = 6.84 kg, radius r = 1.16 m, angular speed ω = 0.797 rev/s, and max tension Tmax = 97.2 N. First, convert angular speed to radians per second:

ω ≈ 0.797 × 2π ≈ 5.01 rad/s

(a) Tangential speed:

v = ω × r ≈ 5.01 × 1.16 ≈ 5.81 m/s

(b) Centripetal acceleration:

a_c = v² / r ≈ (5.81²) / 1.16 ≈ 29.1 m/s²

(c) Max tangential speed with given tension:

Tmax = m × v_max² / r → v_max = √(Tmax × r / m)

v_max ≈ √(97.2 × 1.16 / 6.84) ≈ 4.02 m/s

Final answers:

(a) 5.81 m/s

(b) 29.1 m/s²

(c) 4.02 m/s