Hoist and Tower Crane

Objectives:

  1. Students will be able to experimentally determine the minimum force in the string which holds the jib of a model hoist in place. They will also be able to solve the same problem mathematically.
  2. Students will learn how to improve the design of a given model hoist.
  3. Students will be able to solve a practical problem --- determine the weight and location of counterweight of a model tower crane. They will also be able to mathematically solve the same problem.
  4. Students will understand the concept of critical state and small disturbance.
  5. Students will be able to find experimentally the gravity center of the model tower crane.
  6. Students will know the scientific way to evaluate their findings.
  7. Students will understand how the technology of designing, constructing, and erecting huge cranes is driven and developed by human needs.

Materials:

Each group of students need:

A model hoist and a model tower crane as shown in the following figure, a pulley, a spring scale, a bolt and nut, some weights, a protractor, a ruler, pieces of string, and several nails.

Procedures:

Students will be put in groups with 2 or 3 students in a group. Note: the bar with a pulley at one end will not be given to students until Step 6 of Activity one.

Activity One:

  1. Show students pictures about hoist. Ask students to hold the jib of the given hoist in a position such that the angle θ between the jib and the pedestal is 60˚. The string attached to one end of the jib is the control to change this angle. Ask students to put a load of 100 grams at the free end of the jib.
  2. Ask students to attach the other end of the string to points at different positions either on the pedestal or the wall (such as those indicated in the figure). Ask them to record the force F in the string on their worksheet. The purpose of this step is to find the minimum value of F.
  3. Ask students to mathematically determine the minimum value of F. Ask them to record their solutions on the worksheet, compare the mathematical and experiment results, and calculate the relative error.
  4. Ask students to repeat Step 2 but vary angle θ to different values such as 30˚, 45˚, and 75˚. Ask them to record the value of F for each case. Ask them how the variation of θ affects F.
  5. Suppose angle θ is 60˚, ask students to figure out a way to improve the design of the given hoist without using the wall (There is not a wall in a real hoist.) so that the force in the string will still be the minimum. Ask students to draw their improved design, if any, on the worksheet.
  6. Give students the bar with a pulley on one end. Tell them they may use it to reduce the force in the string.
  7. With their improved hoist, ask students to repeat Step 4. Ask them to compare the magnitude of F with that they got in Step 4. They should get better results (smaller F). This step serves as a confirmation that the performance of their hoists is indeed improved.

Activity Two:

  1. Show students pictures about tower crane. Tell them the basic parts of a tower crane such as jib and mast. Emphasize that preventing a tower crane from toppling is an important issue to be considered when designing and erecting a tower crane.
  2. Guide students to experimentally determine the weight of the counterweight of the model tower crane and the exact location where the counterweight should be hung on the jib of the crane. Tell students that some specifications of a crane should be determined as the first step of designing the crane according to customer demand. These specifications include maximum reach (R) and maximum lifting power (P) of the crane.
  3. Ask students to hang 500 grams of weight at the end of the longer arm of the jib and balance the crane with minimum weight on the shorter arm of the jib. Ask them to move the counterweight as close to the mast as possible while keeping the crane in balance. Ask them to record on the worksheet the total weight they added on the shorter arm and the location where the weight hangs on. Origin of the coordinate system is at the conjunction of the centerlines of the mast and jib.
  4. Tell students the crane is in critical equilibrium (state). If more weight is added on the longer arm, the crane will topple. However, if a trivial weight is added on the longer arm, the crane may rotate a little and remain in equilibrium. The trivial load is a small disturbance. A physical, chemical, or ecological system in critical equilibrium may remain in equilibrium when it experiences a small disturbance. Give students several examples of critical equilibrium and small disturbance. Ask students to give examples, too and record their examples on the worksheet.
  5. Ask students to remove the load on the longer arm of the jib and adjust, if necessary, the weight and location of the counterweight to balance the crane. Tell them this is another critical state of the crane. Ask them to record on the worksheet the adjusted weight and location of the counterweight, if any.
  6. Ask students to determine the minimum weight and distance of the counterweight such that the crane can maintain equilibrium in both critical states. Ask them to record on their worksheet the final values of the weight and location of the counterweight.
  7. Ask students to try some middle states which lie between the two critical states. The crane should not topple in these middle states. Tell students a system will be in equilibrium in any other states as long as it can keep its equilibrium in any critical states.
  8. Tell students the self-weight of the crane. Ask them to find the gravity center of the crane themselves.
  9. Ask students to determine the weight and location of the counterweight mathematically, then compare the mathematical results with the experimental results and calculate the errors, if any. The errors should not exceed 5%. Ask them to write their solutions on the worksheet. Tell students that acceptable errors are problem-dependent. For some engineering problems, the error may be as large as 15% and still be considered as good due the complexity of the problem and related limitations.
  10. Tell students how a tower crane is fixed on the ground in reality. Instead of using a pedestal, a real tower crane is anchored on a heavy concrete pad by large bolts to maintain its stability. Tell students there may be one or two mobile counterweight in addition to fixed counterweight for large capacity tower crane.

Assessment:

Check students’ worksheet.

Ohio standards with which these activities align:

Science:

  1. Construct, interpret and apply physical and conceptual models that represent or explain systems, objects, events or concepts.
  2. Identify a problem or need, propose designs and choose among alternative solutions for the problem.
  3. Describe how a physical, chemical or ecological system in equilibrium may return to the same state of equilibrium if the disturbances it experiences are small. Large disturbances may cause it to escape that equilibrium and eventually settle into some other state of equilibrium.
  4. Research how scientific inquiry is driven by the desire to understand the natural world and how technological design is driven by the need to meet human needs and solve human problems.

Math:

Use trigonometric relationships to verify and determine solutions in problem situation.

Technology:

Students will develop abilities to apply the design process.