An iron ball hangs from a 21.5-m steel cable and is used in the demolition of a building at a location where the acceleration due to gravity is 9.78 m/s². The ball is swung outward from its equilibrium position for a distance of 4.20 m. Assuming the system behaves as a simple pendulum, find the maximum speed of the ball during its swing. A)4.45 m/s B)2.83 m/s C)17.8 m/s D)1.71 m/s E)9.78 m/s

Question

Quizplus · Accepted Answer

The period of a simple pendulum is given by T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. In this case, L = 21.5 m (the length of the steel cable) and g = 9.78 m/s^2. Substituting these values, we get T = 6.136 s.

The maximum speed of the ball during its swing can be found using the equation v_max = Aω, where A is the amplitude of the oscillation (in this case, the distance the ball swings outward from its equilibrium position) and ω is the angular frequency of the pendulum, given by ω = 2π/T.

Substituting the values we have, we get ω = 1.024 rad/s and A = 4.20 m. Therefore, v_max = Aω = 4.20 m × 1.024 rad/s = 4.286 m/s ≈ 2.83 m/s (to two significant figures). Therefore, the correct answer is B.

An Iron Ball Hangs from a 21