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Newton’s Laws (IV)

Newton’s Laws (IV). Blocks, ramps, pulleys and other problems. F A. θ. m. To be handed in for marks on Friday !!!. A block of mass m=5kg is pulled with a force F A = 10N at an angle θ =45 o to the horizontal, find the acceleration. Friction is given by μ k =0.1.

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Newton’s Laws (IV)

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

  2. FA θ m To be handed in for marks on Friday !!! A block of mass m=5kg is pulled with a force FA= 10Nat an angle θ=45o to the horizontal, find the acceleration. Friction is given by μk=0.1. Include you NAME and Student # Physics 1D03 - Lecture 8

  3. 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 m2 FA m1 Physics 1D03 - Lecture 8

  4. 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

  5. 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

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

  7. Kinematics in Two Dimensions • Position, velocity, acceleration vectors • Constant acceleration in 2-D • Free fall in 2-D Physics 1D03 - Lecture 8

  8. The components of are the coordinates (x,y) of the particle: For a moving particle, , x(t), y(t) are functions of time. y The Position vectorpoints from the origin to the particle. path (x,y) yj xi x Physics 1D03 - Lecture 8

  9. Components: Each vector relation implies 2 separate relations for the 2 Cartesian components. (i, j are unit vectors) We get velocity components by differentiation: the unit vectors are constants Physics 1D03 - Lecture 8

  10. If is constant (magnitude and direction), then: Constant Acceleration + Projectile Motion Where is the initial value at t = 0. In 2-D, each vector equation is equivalent to a pair of component equations: Example: Physics 1D03 - Lecture 8

  11. 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

  12. 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

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