Concept #1: Conservative Forces are Path Independent
Practice: A 3 kg block is initially moving on a flat surface when it reaches the bottom of an inclined plane with 20 m/s. If the plane is smooth and makes 53° with the horizontal, how far up the plane will the block slide?
Example #1: Energy Problems in Inclines
Example #2: Energy Problems in Inclines
Example #3: Energy Problems in Inclines
Practice: When a 4-kg block is released from rest from the top of an inclined plane, it reaches the bottom with 4 m/s. The incline is 5 m long and makes 37° with the horizontal. Calculate the magnitude of the frictional force acting on the block.
Practice: When a block of unknown mass is released from the top of an inclined plane of length L meters, it slides down. The incline makes an angle of Θ degrees with the horizontal, and the coefficient of kinetic friction between the block and the plane is µ. Derive an expression for the speed of the block at the bottom of the plane.
Practice: A block of unknown mass is released from a distance D1 from the bottom of an inclined plane, then slides on a horizontal surface, and up a second inclined plane, as shown. Both planes make an angle of Θ degrees with the horizontal. The horizontal surface is smooth, but the coefficient of friction between the block and the two inclines is µ. Derive an expression for the maximum distance D2 that the block will reach on the second incline.