1. Force Vectors and Equilibrium
Dynamics Unit

2. Forces at an Angle
So far we have worked with forces acting vertically or horizontally but not at an angle
When forces act at an angle, we need to find x and y components of the forces

3. Example
The two people pull the boat onto the beach using two ropes. Person A pulls with 60N at 24° N of E and Person B pulls at 60N at 24° S of E. Determine the net force acting on the boat.

4. Free Body Diagram

5. Determine components for each force.

6. Find the sum of x components and the sum of y components.

7. Use the sum of the components to calculate an Fnet solution
Use the sum of the components to calculate an Fnet solution. Remember to determine direction.
110N [E]

8. Example 2:
Two people are pulling a box along the ground. Person A pulls with 300 N at 30.0 degrees above the horizontal and Person B pulls with 250 N at 25.0 degrees below the horizontal. If the force of friction between the ground and the box is 100 N at 0 degrees to the horizontal, use a FBD to determine the net force acting on the box.

9. 1. Free Body Diagram

10. 2. Determine components from each force.
Person A Components
Person B Components

11. 3. Sum the components. Don’t forget to include friction in the horizontal.
Sum of x Components (including Friction)
Sum of y components

12. Draw a new diagram
The net force is 388N at an angle of 6.55 degrees above the horizontal.

13. Equilibrium
when the net force on an object is zero, the object is in equilibrium (not accelerating)
The sum of all forces in the x direction must add to zero
The sum of all forces in the y direction must add to zero

14. Example:
A 20.0 kg object is suspended as shown. Determine the tension in rope 2.

15. Free Body Diagram

18. Example:
A 65 kg object is suspended as shown below. Calculate the two forces required in order to suspend the object.

19. Free Body Diagram

20. Solution

21. Assignment