Writing Force Equations

1. Writing Force Equations

2. Writing force equations • Draw a FBD to identify all forces and the directions they act • Write an equation to sum up the horizontal forces making sure all forces that affect the object horizontally are accounted for in the equation. • - algebraic signs are used to indicate directions • - Keep in mind when in equilibrium, F = 0 • Write an equation for the vertical forces making sure all forces that affect the object vertically are accounted for in the equation

3. Let’s try it… A book is pushed to the right across the desktop at a constant speed.

4. This one has a little twist… • Sally is pushing a shopping cart downward and to the right at an angle of 40 degrees to the ground. The cart is moving at a constant speed. *** Lets review some vector math before attempting this one

5. Resolving vectors into components. • Every vector can be visualized as the hypotenuse of a right triangle. See the red arrows below. • “Resolving a vector” means to find the sides of this right triangle…it’s like working backwards to find the parts that would add to form the original vector

6. Resolving vectors into components What are the horizontal and vertical components of the tension in the chain? 60 N 40°

7. This one has a little twist… • Sally is pushing a shopping cart downward and to the right at an angle of 40 degrees to the ground. The cart is moving at a constant speed.

8. ExampleProblem A 15 kg lawn mower is pushed at a constant speed by a force of 100.0N directed along the handle at 40.0° to the horizontal. Determine the frictional force acting on the mower Calculate the normal force acting on the mower

9. Draw a force diagram of the mower: Write equations: FN FAcos - f = 0 f FA FN - FAsin - Fg = 0 Fg Use equations to solve problem: b) FN - FAsin - Fg = 0 FN = FAsin + Fg FN= FAsin + mg FN= (100 N)sin 40.0 + (15 kg)(10 m/s2) FN= 214.3 N FAcos - f = 0 f = FAcos f = (100 N)cos 40.0 f = 76.6 N