# Newtons Laws (III) Blocks on ramps, and other Newtons Laws (III) Blocks on ramps, and other problems Serway and Jewett : 5.7, 5.8 Physics 1D03 - Lecture 8 1 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 8 2 Example: Show that the contact forces are equal FA

Physics 1D03 - Lecture 8 3 Accelerated motion Example: A block slides down a ramp, with friction v Assume m, , k are known, and find the acceleration.

m Physics 1D03 - Lecture 8 4 Accelerated motion Example: A block is pushed with a force FA at an angle to the horizontal, find the acceleration. Friction is given by k. FA

m Physics 1D03 - Lecture 8 5 Example Obtain an expression for the stopping distance for a skier moving down a slope with friction with an initial speed of v1. d

Find the distance given that k=0.18, v=20m/s and =5.0. Physics 1D03 - Lecture 8 6 Question : Can we calculate s ? mg f n Increasing so that max , the block slips, from

which we get: s tan max This is an easy method of measuring s Physics 1D03 - Lecture 8 7 Frictionless surfaces, ideal pulleys, etc. M

For what angle is the system in equilibrium? m Physics 1D03 - Lecture 8 8 Summary Problems using Newtons Second Law:

Set up free-body diagram, then F ma, and solve. Practice Problems : Chapter 5 Problems: 43, 46 (ans: 31.7-48.6N), (5th ed) Problems 49, 53 Physics 1D03 - Lecture 8 9