Question

Question 20: A pirate has left his treasure chest sitting on a hillside (inclined plane), where the static friction prevents it from sliding down. The treasure chest has mass m, and the incline makes an angle theta with the horizontal. a) (3 points) Draw the free-body diagram for the treasure chest sitting on the hillside. Label all forces, and make sure that directions and magnitudes are correct, to reasonable accuracy. Draw the coordinate system that you want to use, too. b) (7 points) Another pirate has found the treasure chest and pushes it up the hill with force F_up (parallel to the incline) so that it moves with constant speed. Draw the free-body diagram for the chest in this situation. Find an expression for F_up in terms of the mass m, the angle theta, and the kinetic friction coefficient, and possibly other constants. c) (7 points) After a short struggle with the second pirate, the original owner has now reclaimed his treasure chest. He is pushing it down the hill with force F_down (parallel to the incline), so that it moves with constant speed. Draw the free-body diagram for the chest and find an expression for F_down in terms of the mass m, the angle theta and the kinetic friction coefficient, and possibly other constants. d) (3 points) Which force has the bigger magnitude, F_up or F_down? First, state your answer based on your results from parts (b) and (c). Then, explain your result qualitatively: In each case, what does the pushing force have to act against?

Answer 1

in the case of chest moving in upside, the up-force applied by pirates is against kinetic frictional force(fk) and X-component of weight(mg) of chest(mgsinα).

In the case of chest moving down, the down-force applied by pirate is against only kinetic frictional force.