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Clicker Registration • Remember to register your clicker at: www.iclicker.com/registration Physics 1D03 - Lecture 8 1 Newton’s Laws (III) • Blocks, ramps, pulleys and other problems Physics 1D03 - Lecture 8 2 Equilibrium • A special case : a 0 (object doesn’t move, or moves at constant velocity) • Newton’s second law gives F ma 0 The vector sum of forces acting on a body in equilibrium is zero • This is equivalent to three independent component equations: Fx 0, Fy 0, Fz 0 • We can solve for 3 unknowns (or 2, in 2-D problems) Physics 1D03 - Lecture 8 3 Block on a ramp Determine all the forces acting on this block. Given m, θ and μk, what would the acceleration be a) without friction b) with friction m θ Physics 1D03 - Lecture 8 4 Example A block is in equilibrium on a frictionless ramp. What is the tension in the rope? T m f Physics 1D03 - Lecture 8 5 Quiz The block has weight mg and is in equilibrium on the ramp. If ms = 0.9, what is the frictional force? A) B) C) D) 0.90 mg 0.72 mg 0.60 mg 0.54 mg 37o Physics 1D03 - Lecture 8 6 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 7 Example Obtain an expression for the stopping distance for a skier moving down a slope with friction with an initial speed of v1. d θ Find the distance given that μk=0.18, v=20m/s and θ=5.0º. Physics 1D03 - Lecture 8 8 Accelerated motion Example: A block is pushed with a force FA at an angle to the horizontal, find the acceleration. Friction is given by μk. FA θ m Physics 1D03 - Lecture 8 9 Question : Can we calculate μs ? mg f n Increasing so that max , the block slips, from which we get: m s tan max This is an easy method of measuring ms Physics 1D03 - Lecture 8 10 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 11 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 ! Physics 1D03 - Lecture 8 12 Example: m Frictionless surfaces, ideal pulleys, etc. For what angle is the system in equilibrium? M Physics 1D03 - Lecture 8 13