example - centroids

Example - Centroids

1. True or False. The centroid of a shape is not related to the material it is made out of,

only the shape?

2. True or False. The centroid is always the same as the center of gravity. Explain.

3. Find the x bar and the y bar distances from point C to the centroid of the given triangle.

(the dimensions shown are in inches)

4. Find the x bar and the y bar distances from point A to the centroid of the given triangle.


Example – Vector Forces

Given the following Vectors – Solve for the x and y component

vectors for vector A.

Draw the component y vector on the above sketch (See Sketch) Draw the component x vector on the above sketch (See Sketch) Determine the equation from SOHCAHTOA that you would use to solve for Fy and Fx. 1) Solve Fy (FyA = A * Sin (Theta) )=

2) Solve Fx = 958.4lbs

3) Can you do the same for Vector B?

Can you add the components together and solve for the resultant vector force and the angle it makes with the positive x axis? Try it.

4) Fy (combined) = FyA + FyB 5) Fx (combined) = 6) Resultant = ? 7) Angle = ?

Fy

Fx

2.1.5 MOMENTS PRACTICE PROBLEMS

1) Calculate how much 1 lb is in Newtons.

Show your work here:

2) Calculate the moment of the force acting on the bicycle crankset shown below.

3) Calculate the moment of the force acting on the bolt shown below.

4) Determine the unknown force (F) when the system is in static equilibrium.

50 lb

Pivot

100 N

F

40 cm

20 cm

Pedal

0.8 ft

10.0 cm

4.0 cm

100 N

5) Determine the two unknown forces (F1 and F2) at equilibrium. Hint: the pivot point can be at the left or right end of the horizontal shelf, choose one.

POE REACTION FORCE PRACTICE PROBLEMS 1. Reaction Force Practice Problem

See-saw: Parent weighs 175lbs and child weighs 50lbs, Calculate the reaction force at the fulcrum? If the

beam is 9 feet long, how far from the fulcrum does the child have to sit and how far away would the parent

have to sit to generate the balanced see-saw on the right in the image?

2. Reaction Force Practice Problem; assume static equilibrium and solve.

50 cm

3 ft 10 ft

35 lb

F2 F1

3. Reaction Force Practice Problem

P1 and P2 Forces in lbs. Find the

reaction force values at the pin, point

A and the roller, point B. note:

distances in inches, want feet.

POE PLTW 2.1.6 TRUSS PRACTICE PROBLEMS & ANSWER KEY 1. Is the following truss statically determinate? Why or why not?

2. To make the following truss statically determinate what changes would you make?

3. Solve the following Trusses for all External Forces acting on the truss and indicate if a member is in Compression

or Tension.

a) Solve for Rotary Moments find reaction force or normal forces (notice pin on right)

b) Solve for y direction reaction forces

c) Solve for x direction reaction forces

d) Determine if obvious, whether internal forces

are Compression or Tension.

Sin(60o) = 0.866 ; sin(50o) = 0.766;

4. Solve the following Trusses for all External Forces acting on the truss and indicate if a member is in Compression

or Tension.

a) Solve for Rotary Moments find reaction force or normal forces (notice pin on right)

b) Solve for y direction reaction forces

c) Solve for x direction reaction forces

d) Determine if obvious, whether internal forces are Compression or Tension.

KEY Answers are in RED

Centroids- 5. True or False. The centroid of a shape is not related to the material it is made out of,

only the shape?

True – It doesn’t matter what material the shape is made from.

6. True or False. The centroid is always the same as the center of gravity. Explain.

False – The center of gravity is determined by shape and material. If a shape is made

from the same material, the center of gravity is the same as the centroid. However, if

the shape uses different materials, then the centroid will not be same as the center of

gravity

7. Find the x bar and the y bar distances from point C to the centroid of the given triangle.


From the formula sheet, the x bar is = to 1/3 *base length. This is the distance from

point B to the centroid in the x direction. However, the question asks what is the

distance from point C to the centroid. Therefore I formula becomes:

2/3*base length = x bar = 2/3 * 85 inches = 56.67 inches

Since the distance from C to the centroid is the same as the distance from B to the

centroid in the y direction, we can use the formula from the formula sheet to calculate

the value for y:

1/3*height = y bar = 1/3 * 150 inches = 50 inches

8. Find the x bar and the y bar distances from point A to the centroid of the given triangle.


The equations are the same as in the example 3 above, 1/3 * base and 1/3 * height from

point B. However, the distance from A to the centroid in the x direction is now:

2/3 * base = x bar = 100 inches

The distance from A in the y direction is the same as from B so:

Y bar = 1/3 *height = 28.33 inches

Example – Vector Forces

Given the following Vectors – Solve for the x and y component vectors for vector A.

1) Fy = A * Sin (Theta) = 1200 lbs * Sin(37 deg)

Solve Fy = 722.2lbs

2) Fx = A * Cos (Theta) = 1200lbs * Cos(37 deg)

Solve Fx = 958.4lbs

3) FyB = - 224.8lbs FxB = 556.31lbs Can you add the components together and solve for the resultant vector force and the angle it makes with the positive x axis? Try it.

4) Fy (combined) = 497.4lbs Up 5) Fx (combined) = 1514.7lbs to the right 6) Resultant = 1594.3lbs Up and to the right 7) Angle = 18.2˚ccw from the positive x axis

2.1.5 MOMENTS PRACTICE PROBLEMS

POE REACTION FORCE PRACTICE PROBLEMS ANSWER KEY


See-saw: Parent weighs 175lbs and child weighs 50lbs, Calculate the reaction force at the fulcrum? If the

beam is 9 feet long, how far from the fulcrum does the child have to sit and how far away would the parent

have to sit to generate the balanced see-saw on the right in the image?

The parent plus the child add up to 225 lbs of Force Down. So, the Reaction Force at the fulcrum is 225 lbs Up.

The distances are based on Moments, but they need to be proportional to the weights, so 175/50 = 3.5 so

child must sit 3.5 times further from the fulcrum than the parent so child sits at 7 feet and parent at 2 feet.

2. Reaction Force Practice Problem; assume static equilibrium and solve.

MA=MC; 5*FA = 30*100

5* FA = 3,000; FA = 600N

FA is Down + FC is Down = 700N;

so reaction Force at B {fulcrum or pivot}

must be 700N Up.


P1 and P2 Forces in lbs. Find the

reaction force values at the pin, point

A and the roller, point B.

MA+MB+MP1+MP2 = 0 0 + MB

+ -(2*10) + (5*15) =0

(8*RFB) – 20 + 75 = 0

8* RFB = -55

RFB = -6.875

RAy + P1y + P2y + By = 0

RAy + - 10 + 15 + - 6.875 = 0

RAy = 1.875

POE PLTW 2.1.6 TRUSS PRACTICE PROBLEMS ANSWER KEY ANSWER KEY

#1. Has 7 joints, 10 members and only 2

reaction forces. Change one support to a

pin from a roller, eliminate 1 member, and

eliminate 1 joint. Now it is statically

determinate.

example - centroids

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