A 450-kg piano is being unloaded from a truck by rolling itdown a ramp inclined at 22. There is negligible friction andthe ramp is 11.5 m long. Two workers slow the rate at whichthe piano moves by pushing with a combined force of1420 N parallel to the ramp. If the piano starts from rest,how fast is it moving at the bottom?

Modern Physics Lecture 1: Foundations and Special Relativity Position, Time, and Rotation are all continuous symmetries (discrete symmetries such as reflection do not produce the same results as below): Invariance in position (changing where in space you perform your experiment) proves momentum conservation Invariance in rotation (eg. rotating your entire experiment by 90 degrees) proves conservation of angular momentum Invariance in time (changing when in time you perform your experiment, eg. today vs. tomorrow) proves energy conservation Newtonian Mechanics: Inertia F=ma The force of object 1 on object 2 is equal in magnitude to the force of object 2 on object 1 True in an inertial reference frame