Physics
Physics
Problem
A block of mass is released from rest on a rough fixed incline that makes an angle with the horizontal. (i) Draw a suitable free–body diagram for the block and write the equations of motion along and perpendicular to the plane. (ii) The block is observed to move down the incline in . Calculate the magnitude of its acceleration along the plane. (iii) Using your results from (i) and (ii), determine the coefficient of kinetic friction between the block and the incline. (iv) If the same block were to be pushed gently up the incline and then released, what minimum initial speed along the plane would allow it to come momentarily to rest after moving up the slope?Intuitive explanation
The key to inclined-plane problems is resolving weight into components parallel and perpendicular to the slope, then using Newton's second law in each direction separately. Friction always opposes motion, so its direction flips depending on which way the block moves—this is why parts (ii)–(iv) require careful attention to sign. Once you find the acceleration down the slope from kinematics, you can work backward to find friction, then apply that same friction (now pointing downward) when the block moves upward.
Intuitive explanation
The key to inclined-plane problems is resolving weight into components parallel and perpendicular to the slope, then using Newton's second law in each direction separately. Friction always opposes motion, so its direction flips depending on which way the block moves—this is why parts (ii)–(iv) require careful attention to sign. Once you find the acceleration down the slope from kinematics, you can work backward to find friction, then apply that same friction (now pointing downward) when the block moves upward.