The question
Name: ______________________ Date: ____________ A scale in an elevator (10 points)
Diagram
A scale in an elevator
A student of mass m stands on a bathroom scale in an elevator. The elevator starts at rest at the ground floor. From t = 0 to t = 2.0 s it speeds up upward with a constant acceleration of size a. From 2.0 s to 8.0 s it moves upward at a constant speed. From 8.0 s to 10.0 s it slows to a stop with an acceleration of the same size a. Air resistance is negligible.
(a) Sketch a graph of the elevator's velocity against time from t = 0 to t = 10.0 s, taking upward as positive. Label the times 2.0 s, 8.0 s and 10.0 s. [3 points]
(b) Derive an expression for the scale reading FN during the first 2.0 s, in terms of m, a and physical constants. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. [3 points]
(c) Calculate the scale readings during the first 2.0 s and during the last 2.0 s for m = 60 kg and a = 1.5 m/s². Use g = 9.8 m/s². [2 points]
(d) A classmate claims: "From 2.0 s to 8.0 s the elevator is moving up, so the scale must read more than mg." Do you agree or disagree? Justify your answer. [2 points]