1. Physics 1D03 - Lecture 81 Newton’s Laws (IV) Blocks, ramps, pulleys and other problems

2. Physics 1D03 - Lecture 82 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. m θ FAFA Include you NAME and Student #

3. Physics 1D03 - Lecture 83 Two blocks connected by a rope are being pulled by a horizontal force F A. Given that F=60 N, m 1 =12kg and m 2 =18kg, and that μ k =0.1, find the tension in the rope between them and the acceleration of the system. m1m1 m2m2 FAFA T

4. Physics 1D03 - Lecture 84 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/s 2 ??? What is her weight when the elevator is accelerating down at 5m/s 2 ???

5. Physics 1D03 - Lecture 85 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

6. Physics 1D03 - Lecture 86 Example Find the acceleration of a system of two masses m=5kg and M=10kg. The angle θ=30 o. No friction! Also, find the tension, T, in the string. M m  There are two ways of solving the problem !

7. Physics 1D03 - Lecture 87 Kinematics in Two Dimensions Position, velocity, acceleration vectors Constant acceleration in 2-D Free fall in 2-D

8. Physics 1D03 - Lecture 88 The Position vector points from the origin to the particle. The components of are the coordinates (x,y) of the particle: For a moving particle,, x(t), y(t) are functions of time. x y (x,y) path xixi yjyj

9. Physics 1D03 - Lecture 89 (i, j are unit vectors) the unit vectors are constants We get velocity components by differentiation: Components: Each vector relation implies 2 separate relations for the 2 Cartesian components.

10. Physics 1D03 - Lecture 810 Constant Acceleration + Projectile Motion If is constant (magnitude and direction), then: Where is the initial value at t = 0. In 2-D, each vector equation is equivalent to a pair of component equations: Example:

11. Physics 1D03 - Lecture 811 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?

12. Physics 1D03 - Lecture 812 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 ?