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

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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