Chapter 7 Forces In Two Dimensions

Equilibrant: Motion along an inclined plane x Θ y Θ

PSS for Inclined Planes 1. Sketch the problem 2. Choose a coordinate system with the x- axis along the incline 3. Identify and draw the right triangle. 4. Use trig to resolve the vectors into components. 5. Draw your force diagram with the components. 6. Solve as previously.

7.2 Projectile Motion A. Independence of motion in two dimensions. -A projectile launched horizontally has the same motion as an object that is dropped. 1. Motion in two dimensions can be solved be breaking the problem into two one-dimensional problems: A horizontal problem and a vertical problem. 2. The vertical motion of a projectile is exactly the same as an object thrown or dropped straight up or down.

3. The horizontal motion of a projectile is the same as solving a constant velocity problem. 4. Both motions are connected through time. Solving for time in one dimension automatically gives you the time in the other.

B. Projectile Launched horizontally. - Has no initial vertical velocity - Downward velocity increases due to gravity (it is accelerated at a rate of 9.80 m/s 2 ).

Example: A stone is thrown horizontally at 15.0 m/s from the top of a cliff 44 m high. A stone is thrown horizontally at 15.0 m/s from the top of a cliff 44 m high. a. How far from the base of the cliff does it hit? b. How fast is it moving just before it hits?

PSS - Projectile Motion 1. Sketch the problem 2. List the knowns and unknowns. 3. Use the equation for the y – position to get and solve an equation for time. 4. Use kinematic equations in the x – direction to solve for range. 5. For final velocity, put the components of v together using Pythagorean relationship. v = √(v x 2 + v y 2 )