Free Body Diagram - Physics - Solved Paper, Exams of Physics

Download Free Body Diagram - Physics - Solved Paper and more Exams Physics in PDF only on Docsity! Question 1. T θ r R A string is attached to the drum (radius r) of a spool (radius R) as shown in side and end views here. (A spool is device for storing string, thread etc.) A tension T is applied to the string at angle θ above the horizontal. The coefficients of kinetic and static friction between floor and spool are µk and µs respectively. We are interested in whether and when the spool will move left or right, and how this depends on the nature of the floor. a) Draw a free body diagram for the spool, showing the forces acting on it, for the case when it is in mechanical equilibrium. (The force vectors need not be to scale, but they should be in approximately the correct direction.) b) If it slides or skids, in which direction will it move, when pulled by the string? c) If it rolls, in which direction will it move, when pulled by the string? d) Showing all working, calculate the critical value of θ (call it θc) at which the condition goes from rolling to skidding. e) If θ > θc, and you pull sufficiently hard on the string, which way does the spool move? (No explanation is required.) Question 1. W r R T θ F N fr W T θ F Nfr b) If it slides (kinetic friction F_ k) it moves right. c) If it rolls (static friction F_ s) it moves left. d) In mechanical equilibrium, no acceleration, so N2 vertical: T sin θ + N = W (i) N2 horizontal: T cos θ = Ffr (ii) Also no rotational acceleration, so torques add to zero: Tr = FfrR (iii) At point of sliding, Ffr = µsN (iv) Substitute (iv) in (ii) and (iii) gives: T cos θc = µsN and Tr = µsNR dividing these gives: cos θc = r R so θc = cos-1 r R e) Either: it goes left or: very hard and it goes up (and a bit to the left then to the right)