Physics Vector Resolution
Force Components
In what direction is the leash pulling on the dog?
Answer: Vertically and Horizontally
50N
What would happen to the upward and rightward forces if the force on the chain were smaller?
30N
What would happen to the upward and rightward forces if the force on the chain were smaller?
30N
35 degrees
What would happen to the upward and rightward forces if the angle on the chain were smaller?
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
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:
1) Find the resultant Magnitude:__________
of the two vectors Direction:___________
Vector #1 = 20.5 N West
Vector #2 = 14.3 N North
Vector Diagram
24.99 N
34.90º N of W
V2
V1
VR=?
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 (+)
Vr
V2
V1
Conventions:
+
+
-
-
1. Draw vector diagram. (Draw axis)
2. Resolve vectors into components using trig:
Vadj = V cos θ Vopp = V sin θ
3. Sum x and y components:
ΣVxi ΣVyi
4. Redraw!! Determine resultant vector using Pythagorean’s Theorem and trig:
Magnitude= √(Σ Vxi)² + (Σ Vyi)²
Direction Action: θ = tan-1(opp/adj)
Practice: Find FR = Fnet =?
200 N due South, 100 N at 40º N of W
Answer: Fnet = N @ ˚ W of S
Skip
Net Force – Summing Forces
Equilibrium
Balanced? or Unbalanced?
Are these Objects are in Equilibrium?
50 N
151 N
25 N
15 N10 N
102 N
5 kgCeiling
The First Condition of Equilibrium: The upward forces must balance the downward forces, and the leftward forces must balance the rightward forces.
Fx = 0 Fy = 0 at 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 F1, FP, T1, etc.) Remember…this is a free-body diag.
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.
Example Problem
300 N
Fy
Solve for Fx & Fy?
Fx
20º
Ans: Fx = 102.61 N Fy = 281.9N
Fnet=300N 70 degrees left
300N
Step 1 – Drawthe 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 deg300N*sin(70)=y
Step 4- Vector sum the x and y components
x2 + y2 = R2
102.612 + 281.92 = R2
Fnet=300N 70 degrees left
X=102.67 N
Y=281.9N
• The analysis of the forces acting upon an object in equilibrium is commonly used to analyze situations involving objects at 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
Fg = 50 N
example• A sign is shown with the given mass of 5 kg.
Determine the tension of each cable.
Fg = mg = 49 N
TT
-Tcos40o
40o 40o
Tcos40o
Tsin40o + Tsin40o
Tsin40o + Tsin40o = 49 N
2Tsin40o = 49 N
T = 38.1 N
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: T1= N, T2= N
Top Related