A straight laboratory bench of length 2.0m is used for position measurements along a single line.
(i) Define a frame of reference with respect to which the position of a particle can be specified.
(ii) Student A chooses the left end of the bench as origin OA and takes the rightward direction as positive x. Student B fixes his origin OB at the right end and takes the leftward direction as positive x′. A point P on the bench is located at xA=0.60m in A’s frame. Determine the coordinate x′ of P in B’s frame.
(iii) A second point Q is later found at xA=1.80m in A’s frame. Calculate the displacement of Q with respect to P in each frame and show explicitly that both students obtain the same physical displacement even though their coordinate values differ.
(iv) Explain concisely why physical predictions must remain unchanged when the origin or sign convention is altered.