1. Physics 1D03 - Lecture 81 Clicker Registration Remember to register your clicker at: www.iclicker.com/registration

2. Physics 1D03 - Lecture 82 Newton’s Laws (III) Blocks, ramps, pulleys and other problems

3. Physics 1D03 - Lecture 83 Equilibrium A special case : (object doesn’t move, or moves at constant velocity) Newton’s second law gives This is equivalent to three independent component equations: We can solve for 3 unknowns (or 2, in 2-D problems) The vector sum of forces acting on a body in equilibrium is zero

4. Physics 1D03 - Lecture 84 Block on a ramp Determine all the forces acting on this block. Given m, θ and μ k, what would the acceleration be a)without friction b)with friction θ m

5. Physics 1D03 - Lecture 85 Example A block is in equilibrium on a frictionless ramp. What is the tension in the rope? m  T

6. Physics 1D03 - Lecture 86 Quiz The block has weight mg and is in equilibrium on the ramp. If  s = 0.9, what is the frictional force? m 37 o A)0.90 mg B)0.72 mg C)0.60 mg D)0.54 mg

7. Physics 1D03 - Lecture 87 Remember, when 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 (the mass will often cancel out).

8. Physics 1D03 - Lecture 88 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

9. Physics 1D03 - Lecture 89 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

10. Physics 1D03 - Lecture 810 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 ?

11. Physics 1D03 - Lecture 811 Pulleys To solve pulley problems, we assume that: 1) the pulley is frictionless 2) the pulley is massless Hence, the force of tension on both sides of the pulley is the same

12. Physics 1D03 - Lecture 812 Example Find the acceleration of a system of two masses m and M, where M is the greater mass. Also, find the tension, T, in the string. m M  There are two ways of solving the problem !

13. Physics 1D03 - Lecture 813 m M  Example: Frictionless surfaces, ideal pulleys, etc. For what angle  is the system in equilibrium?