A solid steel ball rolls without slipping at 2.0 ,m/s relative to the laboratory…
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A solid steel ball rolls without slipping at 2.0\,m/s relative to the laboratory floor along a horizontal track before entering a smooth parabolic bowl whose vertical cross-section is given by y=0.50x2 (with x in meters measured horizontally from the bowl’s lowest point and y in meters measured upward). The ball rolls partway up one side, momentarily comes to rest, and then rolls back down. Four students propose the following reference frames for analyzing the motion:
• Frame 1 – the laboratory (ground) frame.
• Frame 2 – the instantaneous rest frame of the ball at the lowest point of the bowl.
• Frame 3 – a frame that moves horizontally to the right at 2.0\,m/s.
• Frame 4 – a frame that accelerates vertically upward with acceleration g.
(a) For each frame, state whether it is inertial or non-inertial and justify your classification.
(b) Identify which frame(s), if any, allow the analyst to treat the ball’s initial horizontal velocity as zero. Explain how doing so would simplify subsequent kinematic calculations.
(c) Choose the inertial frame you judge to be most efficient for computing the maximum height reached by the ball. Outline the sequence of kinematic relationships you would use to obtain that height (a full numerical solution is not required).
(d) Discuss the limitations that arise when using a non-inertial frame in this scenario and describe the additional apparent forces that must be considered.