Question

Consider a block of wood given an initial velocity directed up an incline of angle θ. It reaches some maximum distance up the incline, turns around, and slides back down. There is friction present. Take the motion of the block to be after any push necessary to provide the initial velocity. (a) Draw and label separate free body diagrams (FBDs) for (i) the motion up the incline and (ii) the motion back down. Include coordinate axes and indicate acceleration. (b) Given the coefficient of kinetic friction µk and angle of the ramp θ, determine algebraically the acceleration up aup and the acceleration down adown the ramp in terms of µk, θ, and g. (c) Sketch the velocity versus time and the acceleration versus time for the entire trip up and down. Indicate the point where the block turns around on both of your graphs. Try to be semi-quantitative, though you do not have numeric values. (d) If the static coefficient of friction of the ramp is µs = 0.5, determine the minimum angle θmin of the ramp such that the block will slide back down after coming momentarily to rest at the top.

Answer 1