Question

1) In softball, the pitcher throws underhand with the arm fully extended (straight at the elbow). In a fast pitch the ball, of mass m = 0.156 kg, leaves the hand at a speed of 139 km/h, when the arm is pointed vertically downward.

A) Find the rotational kinetic energy, in joules, of the pitcher’s arm-ball system, given that the arm's moment of inertia is 0.725 kg⋅m² and the ball leaves the hand at a distance of 0.625 m from the pivot.

B) What force, in newtons, do the muscles exert to cause the arm to rotate, assuming the force is constant and its effective perpendicular lever arm is 3.2 cm? Assume also that the pitcher's arm starts extended horizontally behind her at rest and the ball is released at the bottom of the swing, as described in part (a). Approximate the arm as a uniform rod.

2. Zorch, an archenemy of Superman, decides to slow Earth’s rotation to once per 29.5 h by exerting a force parallel to the equator, opposing the rotation. He uses an old Saturn V rocket, stolen from NASA, which was originally used to send astronauts to the Moon. This rocket can exert a thrust of F = 3.85 × 10⁷ N.

A)  If the original angular velocity of Earth is ω₀ and Zorch is trying to get the Earth to an angular velocity of ω, how much time will it take him? Use M and R for the mass and radius of the Earth.

B)How long, in seconds, will it take him to do this? (Notice that this period gives Superman time to devote to thwarting other villains.)

Answer 1