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1. Clicker Registration • Remember to register your clicker at: www.iclicker.com/registration Physics 1D03 - Lecture 8

2. Newton’s Laws (III) • Blocks, ramps, pulleys and other problems Physics 1D03 - Lecture 8

3. 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 Physics 1D03 - Lecture 8

4. m θ Block on a ramp Determine all the forces acting on this block. Given m, θ and μk, what would the acceleration be • without friction • with friction Physics 1D03 - Lecture 8

5. Example A block is in equilibrium on a frictionless ramp. What is the tension in the rope? T m f Physics 1D03 - Lecture 8

6. m 37o Quiz The block has weight mg and is in equilibrium on the ramp. If ms = 0.9, what is the frictional force? • 0.90 mg • 0.72 mg • 0.60 mg • 0.54 mg Physics 1D03 - Lecture 8

7. 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). Physics 1D03 - Lecture 8

8. d θ ExampleObtain an expression for the stopping distance for a skier moving down a slope with friction with an initial speed of v1. Find the distance given that μk=0.18, v=20m/s and θ=5.0º. Physics 1D03 - Lecture 8

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

10. mg f n This is an easy method of measuring Question : Can we calculate μs ? Increasing  so that , the block slips, from which we get: Physics 1D03 - Lecture 8

11. 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 Physics 1D03 - Lecture 8

12. m M q 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. There are two ways of solving the problem ! Physics 1D03 - Lecture 8

13. m M q Example: Frictionless surfaces, ideal pulleys, etc. For what angle q is the system in equilibrium? Physics 1D03 - Lecture 8