# UTPA STEM/CBI Courses/Physics (Calculus Based)/Static Equilibrium and Elasticity

Course Title: Calculus Based Physics I

Lecture Topic: Static Equilibrium and Elasticity

Instructor: Dr. Zeng

Institution: University of Texas-Pan American

## Backwards Design

[edit | edit source]**Course Objectives**

**Primary Objectives**- By the next class period students will be able to:- Know the conditions for equilibrium (net force = 0, net torque = 0)
- Know what we mean by a system being in static equilibrium (v=0)
- Analyze forces in x and y directions for a 2-D system, free body diagram
- Review center of mass and how it relates to gravitational forces on objects like beams (uniform density)
- Analyze the net torque for a system
- Know how to analyze systems where there are forces and torques acting on the system
- Know how to analyze elastic properties of solids (Young’s modulus, shear modulus, bulk modulus)

**Sub Objectives**- The objectives will require that students be able to:- text
- text

**Difficulties**- Students may have difficulty:- Selecting the proper coordinate systems for a given problem, forces
- Identifying all the acting forces and the respective directions of the forces; forces should point away from object (tension along cord, direction of friction opposite to the direction of impending motion, and normal forces perpendicular to the surface)
- Selecting a proper pivot point and calculating net torque
- Identifying the proper signs for torque

**Real-World Contexts**- There are many ways that students can use this material in the real-world, such as:- Balances: Triple beam balance*
- Bridges: Golden Gate Bridge, Queen Isabel Bridge
- Different types of trusses (roofs, towers, bridges, cranes): Lattice Truss, Pratt Truss (http://en.wikipedia.org/wiki/Truss)*
- Building structure: House frame, building frame*
- Ballerinas, skaters, skateboarders, gymnasts, and other athletes : Must be aware of their center of mass to better balance their self
- Support cables on electric posts*
- Cantilever beams*
- Unicycle*
- Stilts*
- Human pyramids, building a house of cards*

**Model of Knowledge**

**Concept Map**- text
- text
- text

**Content Priorities****Enduring Understanding**- Static equilibrium refers to an object at rest and satisfies two necessary conditions: net force = 0, net torque = 0)
- Draw free body diagrams to analyze forces in the x and y directions in a 2-D system
- The balancing force for the weight in a 2-D system must go through the center of mass (review the calculation of center of mass)
- Analyze the net torque for a system
- Know how to analyze systems where there are forces and torques acting on the system: how to select a pivot point, how to determine the direction of forces, how to identify all the acting forces
- Know how to do basic calculations for Young’s modulus, shear modulus, and bulk modulus

**Important to Do and Know**- Know when a system is in equilibrium, v = 0 or v = constant
- Determination of the tensile stress and breaking point of a material using stress-strain curves for elastic solids (Figure 12.13 Serway 7th edition page 348)

**Worth Being Familiar with**- Comparison of properties of materials (Young’s modulus, shear modulus, and bulk modulus, yield point), Table 12.1 page 348 in Serway 7th edition
- Analysis of forces acting on free body diagrams in three dimensions

**Assessment of Learning**

**Formative Assessment**- In Class (groups)
- text
- text

- Homework (individual)
- Pay attention to the following new units: N/m2 (Young’s modulus, shear modulus, bulk modulus)
- Self-reading Chapter 12 in the textbook

- In Class (groups)

**Summative Assessment**- text
- text

## Legacy Cycle

[edit | edit source]**OBJECTIVE**

By the next class period, students will be able to:

- text
- text
- text

The objectives will require that students be able to:

- text
- text
- text

**THE CHALLENGE**

Observe the electric poles in the following pictures – they were all taken from areas in or surrounding UTPA. Use free body diagrams to analyze all the forces present acting on each of the poles in the pictures. Justify why the support cables (metal cable(s) going from the upper half of the pole to the ground) are necessary. Make sure to go outside and look at these electric poles or other similar electric poles.

- Challenge question for the students (10 points each, 10% for 12 modules):

Instructions: students can refer to any resource to answer this question. Each person needs to scan and save the report as a pdf file, and email the report to Mr. Manuel Lara, Teaching Assistant on WebCT which answers the question with supporting data linking back with the relevant physics content. The report is usually due a week from the date when the question is assigned and will be kept in a WebCT folder. Rubric for grades (on a 0-10 point scale): 1. Correct free body diagram and analysis of forces for picture a (5 points). 2. Correct free body diagram and analysis of forces for picture b (5 points). Format: 1. Put down your name. 2. State challenge question and its number. 3. Show all your work.

- a) Southeast corner of the intersection of Van Week Street and Sugar Road.

- b) Northeast corner of the intersection of Sugar Road and University Drive.

**GENERATE IDEAS**

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**MULTIPLE PERSPECTIVES**

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**RESEARCH & REVISE**

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**TEST YOUR METTLE**

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**GO PUBLIC**

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## Pre-Lesson Quiz

[edit | edit source]- 1. (Static equilibrium sum of forces = 0, sum of torque = 0, cantilever: Serway 7th edition page 357 #37). A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of food hanging at the end of the beam (see figure). The beam is uniform, weighs 200 N, and is 6.00 m long; the basket weighs 80.0 N.
- a. Draw a free-body diagram for the beam.
- b. When the bear is at x = 1.00 m, find the tension in the wire and the components of the force exerted by the wall on the left end of the beam.
- c. If the wire can withstand a maximum tension of 900 N, what is the maximum distance the bear can walk before the wire breaks?

- 1. (Static equilibrium sum of forces = 0, sum of torque = 0, cantilever: Serway 7th edition page 357 #37). A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of food hanging at the end of the beam (see figure). The beam is uniform, weighs 200 N, and is 6.00 m long; the basket weighs 80.0 N.

- 2. (Static equilibrium sum of forces = 0, sum of torque = 0, fish on scale: Serway 7th edition page 358 #43). A 10 000-N shark is supported by a cable attached to a 4.00 m rod that can pivot at the base. Calculate the tension in the tie rope between the rod and the wall, assuming the tie rope is holding the system in the position shown in the figure. Find the horizontal and vertical forces exerted on the base of the rod. Ignore the weight of the rod.

- 3. (Static equilibrium sum of forces = 0, sum of torque = 0, hammer and nail: Serway 7th edition page 355 #10). The figure below shows a claw hammer being used to pull a nail out of a horizontal board. A force of 150 N is exerted horizontally as shown. Assume the force the hammer exerts on the nail is parallel to the nail.
- a. Find the force exerted by the hammer claws on the nail.
- b. Find the force exerted by the surface on the point of contact with the hammer head.

- 3. (Static equilibrium sum of forces = 0, sum of torque = 0, hammer and nail: Serway 7th edition page 355 #10). The figure below shows a claw hammer being used to pull a nail out of a horizontal board. A force of 150 N is exerted horizontally as shown. Assume the force the hammer exerts on the nail is parallel to the nail.

- 4. (Static equilibrium sum of forces = 0, sum of torque = 0, chain: Serway 7th edition page 355 #15). A flexible chain weighing 40.0 N hangs between two hooks located at the same height (see figure). At each hook, the tangent to the chain makes an angle θ = 42.0° with the horizontal.
- a. Find the magnitude of the force each hook exerts on the chain.
- b. Find the tension in the chain at its midpoint. Suggestion: make a free-body diagram for half of the chain.

- 4. (Static equilibrium sum of forces = 0, sum of torque = 0, chain: Serway 7th edition page 355 #15). A flexible chain weighing 40.0 N hangs between two hooks located at the same height (see figure). At each hook, the tangent to the chain makes an angle θ = 42.0° with the horizontal.

- 5. (Young’s modulus: Serway 7th edition page 356 #26). A steel wire of diameter 1 mm can support a tension of 0.2 kN. A cable to support a tension of 20 kN should have diameter of what order of magnitude?
- 6. (Shear modulus: Serway 7th edition page 356 #27). Assume that if the shear stress in steel exceeds about 4.00 x 108 N/m2, the steel ruptures.
- a. Determine the shearing force necessary to shear a steel bolt 1.00 cm in diameter.
- b. Determine the shearing force necessary to punch a 1.00-cm-diameter hole in a steel plate 0.500 cm thick.

- 7. (Bulk modulus: Serway 7th edition page 357 #29). When water freezes, it expands by about 9%. What pressure increase would occur inside your automobile engine block if the water in it froze? (The bulk modulus of ice is 2.00 x 109 N/m2).

## Test Your Mettle Quiz

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