1. Physics Vector Resolution Force Components

3. In what direction is the leash pulling on the dog? Answer: Vertically and Horizontally 50N

4. What would happen to the upward and rightward forces if the force on the chain were smaller? 30N

5. What would happen to the upward and rightward forces if the force on the chain were smaller? 30N 35 degrees

6. What would happen to the upward and rightward forces if the angle on the chain were smaller?

7. Vector Resolution 30N 35 degrees Vector Addition - You are given two perpendicular, linear or angular vectors and asked to find the resultant. Vector Resolution – You are given the angle and the resultant and you are asked to find the x and y components

11. Adding Vectors by Components Adding vectors: 1. Draw a diagram; add the vectors graphically. 2. Choose x and y axes. 3. Resolve each vector into x and y components. 4. Calculate each component using sines and cosines. 5. Add the components in each direction. 6. To find the length and direction of the vector, use:

12. 1) Find the resultant Magnitude:__________ of the two vectorsDirection:___________ Vector #1 = 20.5 N West Vector #2 = 14.3 N North Vector Diagram 24.99 N 34.90º N of W V2V2 V1V1 V R =?

13. 2) Find the component of the resultant = 255m 27º South of East Vector # 1 _______ Direction__________ Vector # 2________ Direction__________ Vector Diagram: 115.8 m 227.2 m South (-) East (+) VrVr V2V2 V1V1 Conventions: + + - -

14. 1.Draw vector diagram. (Draw axis) 2.Resolve vectors into components using trig: V adj = V cos θV opp = V sin θ 3.Sum x and y components: ΣV xi ΣV yi 4.Redraw!! Determine resultant vector using Pythagorean’s Theorem and trig: Magnitude= √(Σ V xi )² + (Σ V yi )² Direction Action: θ = tan -1 (opp/adj) Practice: Find F R = F net =? 200 N due South, 100 N at 40º N of W Answer: F net = N @ ˚ W of S Skip

15. Net Force – Summing Forces

16. Equilibrium

17. Balanced? or Unbalanced?

18. Are these Objects are in Equilibrium? 50 N 151 N 25 N 15 N 10 N 102 N 5 kg Ceiling

19. The First Condition of Equilibrium: The upward forces must balance the downward forces, and the leftward forces must balance the rightward forces.  F x = 0  F y = 0at equilibrium Solution of Problems in Static's: 1)Isolate a body. What point or object are you going to talk about? 2)Draw the forces acting on the body you have isolated, and label them. (If their value is not know, give them a symbol such as F 1, F P, T 1, etc.) Remember…this is a free-body diag.

20. 3)Split each of the forces into its x and y components, and label the components in terms of the symbols given in rule 2 and the proper sines and cosines. 4) Write down your summation equations for the first condition of equilibrium. 5) Solve the equations for the unknowns. Cont.

21. Example Problem 300 N FyFy Solve for F x & F y ? FxFx 20º Ans: F x = 102.61 N F y = 281.9N Fnet= 300N 70 degrees left 300N Step 1 – Draw the situation. 70 deg Step 2 – Solve for the x component. Step 3- Solve for the y component. 300N*cos(70)=x 300N 70 deg 300N*cos(70)=x 300N 70 deg 300N*sin(70)=y Step 4- Vector sum the x and y components x 2 + y 2 = R 2 102.61 2 + 281.9 2 = R 2 Fnet=300N 70 degrees left X=102.67 N Y=281.9N

22. The analysis of the forces acting upon an object in equilibrium is commonly used to analyze situations involving objects at static equilibrium.static equilibrium Example: a frame is shown with the given tension. Determine the weight of the frame. (50N)cos30 = 43 N(50N)cos120 = -43 N (50N)sin30 + (50N)sin30 = 50 N F g = 50 N

23. example A sign is shown with the given mass of 5 kg. Determine the tension of each cable. F g = mg = 49 N TT -Tcos40 o 40 o Tcos40 o Tsin40 o + Tsin40 o Tsin40 o + Tsin40 o = 49 N 2Tsin40 o = 49 N T = 38.1 N

24. Tension Warm-up Find the tension in each rope if the weight (W) is 50 N. Be sure to pick an appropriate point to draw your free-body- diagram. Then sum your x forces and then your y-forces. W 37º 45º Answers: T 1 = N, T 2 =N