People A and B are taking a lift of mass 500 kg which has constant acceleration and the force from the rope that pulls it is 7500 N. The scales where the people stand show a reading of 720 N and 500 N.
Question 1 : Find the acceleration of the lift.Implementing Newton's Second Law we have : F net =Mα lift --->T-F A -F B -Mg =Mα lift ---> α lift =( T-F A -F B -Mg )/M (1)Substituting the relevant values of the forces given by the question we get that α lift = 2.75 m/s 2 ( where g= 9.81 m/s 2 )Question 2 : Find the masses of people A and B.Normally most students would equal the reading of the scale with the multiplication if the mass of the person with gravitational acceleration. This is not the case!! The person also has an upward acceleration equal to the lift's.Again by Newton's second Law we obtain : Person A F A - m A g = m A α lift ---> m A = F A /(g + α lift ) ----> m A = 57.3 kgPerson B F B - m B *g = m A *α lift ---> m B = F B /(g + α lift ) ----> m B =39.8 kgThis problem although not advanced or complicated can lead to misleading results if students have learned to work mechanically based on solved problems they have seen. As i stated in my description my goal is to avoid that and develop an analytical thinking of the students in order to spot tricky questions like this. Otherwise they would think their solution provided is correct.
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