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Newton’s Laws (IV) • Blocks, ramps, pulleys and other problems Physics 1D03 - Lecture 8 1 To be handed in for marks on Friday !!! A block of mass m=5kg is pulled with a force FA = 10N at an angle θ=45o to the horizontal, find the acceleration. Friction is given by μk=0.1. FA θ m Include you NAME and Student # Physics 1D03 - Lecture 8 2 Two blocks connected by a rope are being pulled by a horizontal force FA. Given that F=60 N, m1=12kg and m2=18kg, and that μk=0.1, find the tension in the rope between them and the acceleration of the system. T m1 m2 FA Physics 1D03 - Lecture 8 3 Elevator go up, elevator go down • A person of mass 70kg is standing on a scale in an elevator at rest. What is her weight ? • What is her weight when the elevator is accelerating up at 5m/s2 ??? • What is her weight when the elevator is accelerating down at 5m/s2 ??? Physics 1D03 - Lecture 8 4 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 5 Example • Find the acceleration of a system of two masses m=5kg and M=10kg. The angle θ=30o. No friction! • Also, find the tension, T, in the string. M m q There are two ways of solving the problem ! Physics 1D03 - Lecture 8 6 Kinematics in Two Dimensions • Position, velocity, acceleration vectors • Constant acceleration in 2-D • Free fall in 2-D Physics 1D03 - Lecture 8 7 The Position vector r points from the origin to the particle. y yj path (x,y) r xi x The components of r are the coordinates (x,y) of the particle: r x i y j For a moving particle, r (t ), x(t), y(t) are functions of time. Physics 1D03 - Lecture 8 8 Components: Each vector relation implies 2 separate relations for the 2 Cartesian components. r xi y j (i, j are unit vectors) We get velocity components by differentiation: dr v dt dx dy i j dt dt vx i v y j the unit vectors are constants Physics 1D03 - Lecture 8 9 Constant Acceleration + Projectile Motion If a is constant (magnitude and direction), then: v (t ) vo a t 2 1 r (t ) vo t 2 a t Where vo is the initial value at t = 0. In 2-D, each vector equation is equivalent to a pair of component equations: x(t ) vox t 1 2 a x t 2 y (t ) voy t 1 2 a y t 2 2 Example: Free fall : a g 9.8 m/s [down] Physics 1D03 - Lecture 8 10 Shooting the Gorilla Tarzan has a new slingshot. George the gorilla hangs from a tree, and bets that Tarzan can’t hit him. Tarzan aims at George, and is sorry that he didn’t pay more attention in physics class. Where should he aim? Physics 1D03 - Lecture 8 11 Example Problem A stone is thrown upwards from the top of a 45.0 m high building with a 30º angle above the horizontal. If the initial velocity of the stone is 20.0 m/s, how long is the stone in the air, and how far from the base of the building does it land ? Physics 1D03 - Lecture 8 12