Accelerating Frames

Goal of the class To understand how to calculate forces and accelerations in accelerating frames Question of the day: why happens if I weigh myself in a lift (elevator)?

Weighing Scales What do bathroom scales measure? Draw a box on some scales and then add a force Mass and weight are incorrect. The normal force is right Fn = mg + Fapplied Scales show Fn/g for kgs

Apparent Weight in Lift Fnet = ma Fn-mg = ma Fn = ma + mg ; ma +mg = apparent weight Scale reading = Fn/g = m(1+a/g) For 60kg man his apparent weight is 66 if a = 1m/s2 m

Accelerating Trains! Case 1 when train not moving Mg = T Case 2 when a is present -> All objects move to the right with a -> By Newton’s 2nd Fnet = ma -> But mg and T act vertically so there must be a horizontal force when train is in motion Θ is angle from vertical T cos Θ = mg 1 T sin Θ = ma 2 ----------------------------- Tan Θ = a/g Case 3 – Mass on Spring When train stationary spring is in equilibrium position not strecthed or compressed Case 4 – a -> When accelerating Fnet = ma Kx = ma X = ma/k Case 5 – frictionless Coffee cup on table doesn’t move a=0 Case 6 - friction Max value of fs = mu_s Fn = mu_s mg Ma < mu_s mg

Apparent Weight in Lift Imagine a lift moving downward with a constant velocity of 2m/s. A mass of 5kg hangs from the ceiling attached to a spring of force constant k = 500 N/m. What is the extension of the spring? Suddenly the lift cable breaks, what is the equilibrium extension now? a) Kx = mg X = 0.1m b) X = 0 As person on scales mg – Fn = ma, but a =g so Fn = 0

Homework Set (x) Read Chapter 5 on accelerating frames Answer questions from page 144 on Answer 5 questions from general problems section with a difficulty rating of 2 or 3, but don’t hand these in.