A ball of mass 0.40 kg is thrown from ground level with an initial speed of 12 m s at…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
A ball of mass 0.40 kg is thrown from ground level with an initial speed of 12 m s−1 at an angle of 60° above the horizontal. Air resistance exerts a force on the ball that is always opposite its motion and proportional to the ball’s speed; over the entire flight this resistive force does a total of −9.0 J of work on the ball. Neglect any other non-gravitational forces.
Assume the ball lands on level ground at a point horizontally displaced from the launch point.
(a) Determine the total work done on the ball by Earth’s gravitational force during the flight. Show all reasoning.
(b) Determine the change in the ball’s kinetic energy from launch to just before it lands. Express your answer numerically in joules.
(c) The ball is now thrown a second time with the same initial speed and angle, but a strong tailwind reduces the magnitude of the resistive force so that air resistance now does −3.0 J of work. Without performing a new detailed calculation, determine whether the range (horizontal distance traveled) on this second throw is less than, equal to, or greater than in the first throw. Explain your reasoning by considering energy and work.
(d) For each of the two throws, state whether the net work done by Earth’s gravitational force over the complete flight depends on the details of the ball’s trajectory. Provide justification that refers to the properties of conservative and non-conservative forces.