Advanced Newton's Laws Problem #27 - Motion of a Heavy Block Sliding Down a Light Movable Wedge

A wedge with mass M rests on a frictionless, horizontal tabletop. A block with mass m is place on the wedge.There is no friction between the block and the wedge. The system is released from rest. a.) Calculate the acceleration of the wedge and the horizontal & vertical components of the acceleration of the block. b.) Do your answers in part a reduce to the correct results when M is very large? c.) As seen by a stationary observer, what is the shape of the trajectory of the block? Problem Description (0:00) Free-Body Diagram of the Wedge (0:32) Free-Body Diagram of the Block (1:53) Sum of Forces on the Wedge (3:21) Sum of Forces on the Block (4:31) Solving for the Wedge's Acceleration A, pt. 1 (5:23) Solving for the Wedge's Acceleration A, pt. 2 (6:21) Solving for the Block's Acceleration, pt. 1 (6:49) Solving for the Block's Acceleration, pt. 2 (7:28) Solving for the Block's Acceleration, pt. 3 (8:22) X-Component of the Block's Accleration, pt. 1 (8:48) X-Component of the Block's Accleration, pt. 2 (9:33) Y-Component of the Block's Acceleration (10:14) What Happens When M is Very Large? pt. 1 (10:35) What Happens When M is Very Large? pt. 2 (11:39) What Happens When M is Very Large? pt. 3 (12:32) What Happens When M is Very Large? pt. 4 (13:11) What Happens When M is Very Large? pt. 5 (13:43) What Happens When M is Very Large? pt. 6 (14:59) What Happens When M is Very Large? pt. 7 (15:40) How Does the Block's Trajectory Look to a Stationary Observer? (16:44) What's the Slope of the New Trajectory? pt. 1 (17:55) What's the Slope of the New Trajectory? pt. 2 (19:05) What's the Slope of the New Trajectory? pt. 3 (19:52) Plotting the Regular & New Trajectories of the Block, pt. 1 (20:22) Plotting the Regular & New Trajectories of the Block, pt. 2 (22:34) Checking the Graph Slope vs. the Predicted Slope (24:01) Solution Card (24:31)