Cranes

By Fengfeng Zhou • Michelle Daniel

Grade Level	12th
Subject Area	Physics
Duration	3 hours
Rationale	Integrating calculus and design into physics to solve real world problems.
Background Knowledge	Free body diagram, moment equilibrium, derivatives, extreme value
Author	Fengfeng Zhou / Michelle Daniel

Summary
In the first activity, students will determine minimum tension force in the supporting cable of a crane’s jib both experimentally and mathematically, and then they need to figure out a better design for the crane based on results they obtained in the first step. In the second activity, students will determine the weight of counterweight in a tower crane both experimentally and mathematically.

Objectives
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. Students will learn how to improve the design of a given model hoist. 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. Students will understand the concept of critical state and small disturbance. Students will be able to find experimentally the gravity center of the model tower crane. Students will know the scientific way to evaluate their findings. Students will understand how the technology of designing, constructing, and erecting huge cranes is driven and developed by human needs.

Materials Required
Model hoist and model crane Pulley Spring scale Bolt and nut Some weights Protractor Ruler Pieces of string Several nails

Ohio Standards
Science Construct, interpret and apply physical and conceptual models that represent or explain systems, objects, events or concepts. Identify a problem or need, propose designs and choose among alternative solutions for the problem. 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. 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. Mathematics Use trigonometric relationships to verify and determine solutions in problem situation. Technology Students will develop abilities to apply the design process.