1. Basic Info: balanced Forces Objects are balanced only if their net force is zero in both the vertical and horizontal directions Objects are balanced only if their net force is zero in both the vertical and horizontal directions Meaning all the forces in the x direction add up to zero AND all the forces in the y direction add up to zero Meaning all the forces in the x direction add up to zero AND all the forces in the y direction add up to zero All forces that act in a angle needs to be broken into components using trig. All forces that act in a angle needs to be broken into components using trig. Meaning using a right triangle with x and y components. Meaning using a right triangle with x and y components.

2. Vector Components In order to find the components of a vector (like force) you will need to use those timeless Trigonometric Functions. In order to find the components of a vector (like force) you will need to use those timeless Trigonometric Functions.

3. Vector Components So we have a person pulling a sled 30 o with respect to the horizontal at a force of 50 N. So we have a person pulling a sled 30 o with respect to the horizontal at a force of 50 N. We need to think of it like the sled being pulled vertically and horizontally at the same time, giving it both components. We need to think of it like the sled being pulled vertically and horizontally at the same time, giving it both components. Θ =30 o F=50N FyFy FxFx

4. Vector Components In order to calculate the components, we need to shift F y to make a right triangle. In order to calculate the components, we need to shift F y to make a right triangle. Then we can use trig functions to solve for F y and F x like they are sides of a right triangle. Then we can use trig functions to solve for F y and F x like they are sides of a right triangle. To solve for F x, we will use cosine because it is adjacent and we have the hypotenuse. To solve for F x, we will use cosine because it is adjacent and we have the hypotenuse. Θ =30 o F=50N FyFy FxFx

5. Vector Components To solve for v x, we will use cosine because it is the adjacent side and we have the hypotenuse. To solve for v x, we will use cosine because it is the adjacent side and we have the hypotenuse. To solve for v y, use the same process but with sine. To solve for v y, use the same process but with sine. Θ =30 o F=50m/s FyFy FxFx

6. F y equals? A. 43.3 N B. 25 N C. 28.9 N D. 50 N Θ =30 o F=50m/s FyFy

7. FBD Example 1 A 50 kg mass is suspended from two wires, as in the diagram below. What is the tension in the wires?

8. FBD Example 2 A 25.0 N picture is hanging from two wires. The wires make a 30˚ angle with the top of the picture. Calculate the tensional force on each wire.