Storyline Chapter 12 Static Equilibrium and Elasticity Physics

Storyline Chapter 12: Static Equilibrium and Elasticity Physics for Scientists and Engineers, 10 e Raymond A. Serway John W. Jewett, Jr.

Analysis Model: Rigid Object in Equilibrium The net external force on the object must equal zero: The net external torque on the object about any axis must be zero:

Analysis Model: Rigid Object in Equilibrium

Quick Quiz 12. 1 Consider the object subject to the two forces of equal magnitude in the figure. Choose the correct statement with regard to this situation. (a) (b) (c) (d) The object is in force equilibrium but not torque equilibrium. The object is in torque equilibrium but not force equilibrium. The object is in both force equilibrium and torque equilibrium. The object is in neither force equilibrium nor torque equilibrium.

Quick Quiz 12. 1 Consider the object subject to the two forces of equal magnitude in the figure. Choose the correct statement with regard to this situation. (a) The object is in force equilibrium but not torque equilibrium. (b) The object is in torque equilibrium but not force equilibrium. (c) The object is in both force equilibrium and torque equilibrium. (d) The object is in neither force equilibrium nor torque equilibrium.

Quick Quiz 12. 2 Consider the object subject to the three forces in the figure. Choose the correct statement with regard to this situation. (a) (b) (c) (d) The object is in force equilibrium but not torque equilibrium. The object is in torque equilibrium but not force equilibrium. The object is in both force equilibrium and torque equilibrium. The object is in neither force equilibrium nor torque equilibrium.

Quick Quiz 12. 2 Consider the object subject to the three forces in the figure. Choose the correct statement with regard to this situation. (a) The object is in force equilibrium but not torque equilibrium. (b) The object is in torque equilibrium but not force equilibrium. (c) The object is in both force equilibrium and torque equilibrium. (d) The object is in neither force equilibrium nor torque equilibrium.

Analysis Model: Rigid Object in Equilibrium

More on the Center of Gravity

Center of Gravity

Quick Quiz 12. 3 A meterstick of uniform density is hung from a string tied at the 25 -cm mark. A 0. 50 -kg object is hung from the zero end of the meterstick, and the meterstick is balanced horizontally. What is the mass of the meterstick? (a) 0. 25 kg (b) 0. 50 kg (c) 0. 75 kg (d) 1. 0 kg (e) 2. 0 kg (f) impossible to determine

Examples of Rigid Objects in Static Equilibrium

Problem-Solving Strategy: Rigid Object in Equilibrium 1. Conceptualize 2. Categorize 3. Analyze 4. Finalize

Example 12. 1: The Seesaw Revisited A seesaw consisting of a uniform board of mass M and length , supports at rest a father and daughter with masses mf and md, respectively. The support (called the fulcrum) is under the center of gravity of the board, the father is a distance d from the center, and the daughter is a distance /2 from the center.

Example 12. 1: The Seesaw Revisited

Example 12. 1: The Seesaw Revisited (B) Determine where the father should sit to balance the system at rest.

Example 12. 1: The Seesaw Revisited Suppose we had chosen another point through which the rotation axis were to pass. For example, suppose the axis is perpendicular to the page and passes through the location of the father. Does that change the results to parts (A) and (B)? No change to either part.

Example 12. 1: The Seesaw Revisited

Example 12. 2: Standing on a Horizontal Beam A uniform horizontal beam with a length of = 8. 00 m and a weight of Wb = 200 N is attached to a wall by a pin connection. Its far end is supported by a cable makes that an angle of = 53. 0 with the beam. A person of weight Wp = 600 N stands a distance d = 2. 00 m from the wall. Find the tension in the cable as well as the magnitude and direction of the force exerted by the wall on the beam.

Example 12. 2: Standing on a Horizontal Beam

Example 12. 2: Standing on a Horizontal Beam What if the person walks farther out on the beam? Does T change? Does R change? Does change?

Example 12. 3: The Leaning Ladder A uniform ladder of length rests against a smooth, vertical wall. The mass of the ladder is m, and the coefficient of static friction between the ladder and the ground is s = 0. 40. Find the minimum angle min at which the ladder does not slip.

Example 12. 3: The Leaning Ladder

Example 12. 4: Negotiating a Curb (A) Estimate the magnitude of the force F a person must apply to a wheelchair’s main wheel to roll up over a sidewalk curb. This main wheel that comes in contact with the curb has a radius r, and the height of the curb is h.

Example 12. 4: Negotiating a Curb

Example 12. 4: Negotiating a Curb Would it be easier to negotiate the curb if the person grabbed the wheel at point D in the figure and pulled upward? It would be slightly easier for these values.

Example 12. 4: Negotiating a Curb

Elastic Properties of Solids 1. Young’s modulus measures the resistance of a solid to a change in its length. 2. Shear modulus measures the resistance to motion of the planes within a solid parallel to each other. 3. Bulk modulus measures the resistance of solids or liquids to changes in their volume.

Young’s Modulus: Elasticity in Length

Elastic Limit

Shear Modulus: Elasticity of Shape

Bulk Modulus: Volume Elasticity

Elastic Moduli Values

Quick Quiz 12. 4 Part I Which elastic modulus describes the relationship between stress and strain for a block of iron sliding across a horizontal floor? The friction force between the sliding block and the floor causes the block to deform. (a) Young’s modulus (b) shear modulus (c) bulk modulus (d) none of those choices

Quick Quiz 12. 4 Part II Which elastic modulus describes the relationship between stress and strain for a trapeze artist swinging through a circular arc. At the bottom of the swing, the wires supporting the trapeze are longer than when the trapeze artist simply hangs from the trapeze due to the increased tension in them. (a) Young’s modulus (b) shear modulus (c) bulk modulus (d) none of those choices

Quick Quiz 12. 4 Part III Which elastic modulus describes the relationship between stress and strain for a spacecraft carrying a steel sphere to a planet on which atmospheric pressure is much higher than on the Earth. The higher pressure causes the radius of the sphere to decrease. (a) Young’s modulus (b) shear modulus (c) bulk modulus (d) none of those choices

Prestressed Concrete

Example 12. 5: Stage Design Recall an earlier example where we analyzed a cable used to support an actor as he swings onto the stage. Now suppose the tension in the cable is 940 N as the actor reaches the lowest point. What diameter should a 10 -m-long steel cable have if we do not want it to stretch more than 0. 50 cm under these conditions?

Example 12. 5: Stage Design

Example 12. 6: Squeezing a Brass Sphere A solid brass sphere is initially surrounded by air, and the air pressure exerted on it is 1. 0 105 N/m 2 (normal atmospheric pressure). The sphere is lowered into the ocean to a depth where the pressure is 2. 0 107 N/m 2. The volume of the sphere in air is 0. 50 m 3. By how much does this volume change once the sphere is submerged?

Example 12. 6: Squeezing a Brass Sphere

Assessing to Learn A uniform rod of length L, mass M, is suspended by two thin strings. Which of the following statements is true regarding the tensions in the strings? 1. 2. 3. 4. 5. 6. T 2 = T 1 T 2 = 2. 5 T 1 T 2 = 0. 6 T 1 T 2 = 0. 8 T 1 None of the above Not enough information to determine

Assessing to Learn A uniform rod is hinged to a wall and held at a 30° angle by a thin string that is attached to the ceiling and makes a 90° angle to rod. Which statement(s) must be true? (At least one of them is true and at least one is false. ) 1. The hinge force is purely vertical. 2. The hinge force is purely horizontal. 3. The string tension is equal to the hinge force. 4. The string tension is smaller than the rod's weight. 5. 1 and 3 are true. 6. 2 and 3 are true. 7. 1 and 4 are true. 8. 2 and 4 are true. 9. 3 and 4 are true. 10. Three of the statements are true.

Assessing to Learn A uniform rod of length 4 L, mass M, is suspended by two thin strings, lengths L and 2 L as shown. What is the tension in the string at the left end of the rod? 1. 2. 3. 4. 5. Mg Mg/2 Mg/3 Mg/4 None of the above

Assessing to Learn A uniform disk with mass M and radius R sits at rest on an incline 30° to the horizontal. A string is wound around the disk and attached to the top of the incline as shown. The string is parallel to incline. What is the tension in the string? 1. 2. 3. 4. 5. 6. Mg Mg/2 2 Mg/5 Mg/4 None of the above Cannot be determined

Assessing to Learn A uniform disk with mass M and radius R sits at rest on an incline 30° to the horizontal. A string is wound around the disk and attached to the top of the incline as shown. The string is parallel to incline. What is the tension in the string? 1. 2. 3. 4. 5. 6. Mg/2, down the incline Mg/2, up the incline Mg/4, up the incline Mg/0. 86, down the incline None of the above Cannot be determined