Physics 1D03 - Lecture 81 Newton’s Laws (III) Blocks on ramps, and other problems Serway and Jewett : 5.7, 5.8

Physics 1D03 - Lecture 82 Doing problems with “F=ma” Draw the free-body diagram carefully. You may need to know the direction of a from kinematics, before considering forces (for friction). Any axes will do, but some choices make the algebra simpler – set up equations for each direction. You need one (scalar) equation for each (scalar) unknown, in general (but, the mass will often cancel out).

Physics 1D03 - Lecture 83 Example: Show that the contact forces are equal FAFA

Physics 1D03 - Lecture 84 Accelerated motion Example: A block slides down a ramp, with friction m  Assume m, ,  k are known, and find the acceleration.

Physics 1D03 - Lecture 85 Accelerated motion Example: A block is pushed with a force F A at an angle to the horizontal, find the acceleration. Friction is given by μ k. m θ FAFA

Physics 1D03 - Lecture 86 Example Obtain an expression for the stopping distance for a skier moving down a slope with friction with an initial speed of v 1. Find the distance given that μ k =0.18, v=20m/s and θ=5.0º. θ d

Physics 1D03 - Lecture 87 Increasing  so that, the block slips, from which we get: f n mg This is an easy method of measuring Question : Can we calculate μ s ?

Physics 1D03 - Lecture 88 M m  Frictionless surfaces, ideal pulleys, etc. For what angle  is the system in equilibrium?

Physics 1D03 - Lecture 89 Summary Problems using Newton’s Second Law: Set up free-body diagram, then and solve. Practice Problems : Chapter 5 Problems: 43, 46 (ans: N), (5 th ed) Problems 49, 53