Apparent Weight or The mystery of the Bathroom

Apparent Weight or The mystery of the Bathroom Scale Poopsie Moomfard Jr. III, a 100 kg lad, decided to investigate the mystery of the bathroom scale by taking it into the elevator. He rode the elevator up and down carefully noting the numbers on the scale. We will follow Poopsie on his journey helping him along to make sense out of his observations. Mr. Moomfard wants to know once and for all what the bathroom scale shows. Is it: weight, mass, or some other force? Poopsie knows, of course, that his weight doesn't change. So, lets calculate Poopsie’s weight to start our investigation… Weight = Fg = m · g = (100)(9. 8) = 980 N This is Poopsie’s TRUE WEIGHT!

Apparent Weight or The mystery of the Bathroom Scale Poopsie = = This magnificent elevator accelerates at 2. 0 m/s 2

Case 1 Fg = 980 N Motion: V=0 a=0 FBD: FN y ∑Fy = m · ay FN - Fg = (100) · (0) FN - 980 = 0 FN = 980 N FN is called the apparent weight. x FN is the reading of the bathroom scale. Fg FN = Fg Apparent Weight = True Weight

Case 2 Fg = 980 N Motion: FBD: FN y V a ∑Fy = m · ay FN - Fg = (100) · (2. 0) FN - 980 = (100) · (2. 0) FN = 1, 180 N x Fg FN > Fg Apparent Weight > True Weight

Case 3 Fg = 980 N Motion: FBD: y V=const. a=0 FN ∑Fy = m · ay FN - Fg = (100) · (0) FN - 980 = 0 FN = 980 N x Fg FN = Fg Apparent Weight = True Weight

Case 4 Fg = 980 N Motion: FBD: y V a FN ∑Fy = m · ay FN - Fg = (100) · (-2. 0) FN - 980 = (100) · (-2. 0) FN = 780 N x Fg FN < Fg Apparent Weight < True Weight

Case 5 Fg = 980 N Motion: FBD: y V a FN ∑Fy = m · ay FN - Fg = (100) · (-2. 0) FN - 980 = (100) · (-2. 0) FN = 780 N x Fg FN < Fg Apparent Weight < True Weight

Fg = 980 N Case 5 a What if the cable breaks and the elevator starts free falling? Motion y V a=? x

Fg = 980 N Case 5 a Cable breaks and the elevator starts free falling… Motion: FBD: F N? y V a= g ∑Fy = m · ay FN - Fg = (100) · (-9. 8) FN - 980 = (100) · (-9. 8) FN = 0 N x Fg FN = 0 N Apparent Weight = ZERO!!!

Case 6 Fg = 980 N Motion: FBD: FN y V a ∑Fy = m · ay FN - Fg = (100) · (2. 0) FN - 980 = (100) · (2. 0) FN = 1, 180 N x Fg FN > Fg Apparent Weight > True Weight

Apparent Weight or The mystery of the Bathroom Scale The bathroom scale shows…the normal force (force of the scale on person)! However, the number we read on the bathroom scale is shown as mass: FN/9. 80 = MASS [kg]…

Conversions: 1 kg = 2. 2 lb. talking about pound mass! 1 kg = 4. 45 lb. talking about pound-force (weight)! …confused yet? Long Live English System of Measurements! NOT!!!

Physics!