Aim: How can we describe resultant force (net force)?

1. Aim: How can we describe resultant force (net force)? • Identify some forces. • Identify the unit for force. • Explain the difference between mass and weight. • A student has a mass of 75 kg. The student weighs 831 newtons. Determine the acceleration due to gravity.

2. Aim: How can we describe resultant force (net force)? • List all vectors and units.

3. How can we describe forces acting on an object? • Two or more forces that act on the same object at the same time are called • concurrent forces. • Ex:

4. Combining forces • Resultant force (net force) • Is the single force that is equivalent to the combined effect of these concurrent forces. • Example 1: F1=10N F2=5N R = 15N Feq= -15N

5. The force vector needed to produce equilibrium is the same length as the resultant vector but it is pointing in the opposite direction. (Feq)

6. Example: 3 • If forces act in opposite directions, the angle between them is 180 degrees, the resultant force is the smallest. F2 = 10N F1 = 3N F1 = 3N F2 = 10N

7. Combining forces • Head-to-tail method – combine the head of one vector to the tail of the other vector. • If two forces act in the same direction, the angle between them is 0 degrees and the resultant force is the sum of their magnitudes (R = F1+F2) • Ex2: F1=10N F2=3N F1=10N F2=3N R = 13N

8. Sketch the Resultant force and Equilibrium force

9. How can we sketch the equilibrium force? • The vector sum of the concurrent forces acting on an object is called the net force Fnet. (Resultant force) • If the net force acting on the object is zero, the object is in equilibrium. F2 F1 F1 R Feq F2

10. If two concurrent forces act at right angles to each other, the head-to-tail method produces a right triangle. R F2 F2 F1 F1

11. When is resultant force is greater? • When the two forces act in the same direction, 0 degree angle, they produce the largest resultant force. • When the two forces act in opposite directions, 180 degree angle, they produce the smallest resultant force.

12. How can we analyze force vectors? • Find the resultant force vector. • A 10 Newton force and a 4 Newton force act concurrently on a point. As the angle increases from 0° to 180° what happens to the resultant force? 3N 7N

13. Triangular method of adding concurrent forces. • Leave the first force in the same position. Take the second force and slide it to the head of the first force. (Head-to-tail method) • To find the resultant force: draw a line from the tail of the first force vector to the head of the last vector. • To find the equilibrium force: draw the same size line as the resultant force but 180° from the resultant force. F2 F1 F1 R F2

14. Examples • Draw the resultant force for the following vectors. F2 R F1 F1 F2 P P

15. F2 F1 • Examples F3 F1 F2 R F3

16. Equilibrium force • The vector sum of the concurrent forces acting on an object is called the net force Fnet. (Resultant force) • If the net force acting on the object is zero, the object is in equilibrium. • The force vector needed to produce equilibrium is the same length as the resultant vector but it is pointing in the opposite direction. (Feq) F2 F1 F1 R Feq F2

17. If two concurrent forces act at right angles to each other, the head-to-tail method produces a right triangle. R F2 F2 F1 F1

18. Let’s calculate the resultant force vector using Pythagorean theorem • c2 = a2 + b2 • Use physics terms: R F2 = 40N F1= 30N

19. Using the same example in the previous slide. What is the angleof the resultant force. (The angle is located next to the tail of the resultant force) • Using Soh Cah Toa, find angle theta. (hint: Toa) R = 50N F2 = 40N θ F1= 30N

20. Aim: How can we analyze force vectors and components? • Calculate the resultant force and the angle. Sketch and label the equilibrium force. 10N 5N

21. R = 11.1N R = ? F2 = 10N • Example: Find the resultant force and the angle. θ F1= 5N

22. Aim: How can we analyze force vectors? • Sketch the resultant force and equilibrium force. • Calculate the magnitude of the equilibrium force. 2N 7N

23. 1) Which pair of vectors produce the greatest resultant force? • 2) Which pair of vectors produce the least resultant force?

24. The diagram below represents a force vector A, and resultant vector, R. • Where should we draw vector B? • Recall: The resultant vector goes from start to end. B R A

25. The diagram below represents a force vector A, and resultant vector, R. • Where should we draw vector B? B R A

26. Force vector components • A person is pulling a sled with a 100-newton force at a 30° angle with the horizontal. • 1) Sketch a picture • 2) Calculate the horizontal force. • 3) Calculate the vertical force. • 4) As the angle decreases, describe the horizontal force and vertical force.