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Example, Study notes of Acting

University of Luxemburg (UL)Acting

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 ...

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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.
(the dimensions shown are in inches)
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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. (the dimensions shown are in inches)

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
  1. Determine the two unknown forces (F 1 and F 2 ) 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 F 1 F 2
  1. Reaction Force Practice Problem P 1 and P 2 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;

KEY

Answers are in RED

Centroids-

  1. 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.
  2. 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
  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) 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: 2/3base 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
  1. Find the x bar and the y bar distances from point A to the centroid of the given triangle. (the dimensions shown are in inches) 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 = 10 0 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

POE REACTION FORCE PRACTICE PROBLEMS ANSWER KEY

  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? 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; 5FA = 30 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.

  1. Reaction Force Practice Problem P 1 and P 2 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
      • (210) + (515) = (8RFB) – 20 + 75 = 0 8 RFB = - 55 RFB = - 6. RAy + P1y + P2y + By = 0 RAy + - 10 + 15 + - 6.875 = 0 RAy = 1.

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.