nnouncements Exam grades will be posted on Sakai soon. Probably riday. Exam 3 will be riday, ugust 3. Today is July 19. Only weeks to the next exam. How do the test grades work? Highest exam 0% Next exam 15% Other exam 15% ormula for exam scores (HE/0)*0 + (NE/0)*15 + (OE/0)*15 Suppose your scores are 1, 16, 15. (16/0)*0 + (15/0)*15 + (1/0)*15 36.5 out of a possible 50. 7.5 rounded to 73% To be excused from the final, you need a B+ average for the three exams. The cutoff for a B+ is 8%. 8% of 50 is 41. You need the formula for exam scores to be at least 41 to be excused from the final. If you score a perfect on the third exam, what scores do you need on the other exams to be excused from the final? (0/0)*0 + (NE/0)*15 + (OE/0)*15 41 15(NE + OE)/0) 1 NE + OE 8 You need a combined 8 points (70%) on the first two exams to have the possibility of skipping the final. We will study the physics of music in Chapter 11. If you play an instrument would you consider bringing it to class? Chapter Elasticity and Oscillations In this problem 3 m 4 m 960 N we assume that the beam is perfectly rigid. The weight hanging from the end will not effect it. This assumption is not true. In this chapter we study the physical properties of solids. We studied fluids in the last chapter.
Some Vocabulary deformation is a change in the size or shape of an object. The deformation may be too small to see if the object is strong and the deforming force is small. When the forces are removed from an elastic object, the object returns to its original shape and size. More General Hooke s aw Suppose a force is applied to both ends of a wire. How does the amount of elongation depend on the original length of the wire? If causes to increase by, the same force should cause to increase by. Since the amount elongation depends on the original length of the wire, we defined the strain as strain Does changing the cross-sectional area of the wire change the effect of? thicker cable could be considered to be made of several thinner cables placed side by side. The force would be spread over a bigger area and it would be less effective. We define the stress as stress Stress is measured in N/m or Pa. We rewrite Hooke s law in terms of stress and strain. In general In terms of the definitions stress strain Y The constant of proportionality is called the elastic modulus or Young s modulus. If has the same units as stress. Hooke s law holds up to a maximum stress called the proportional limit.
Beyond the Proportional imit If the stress exceeds the proportional limit, the strain is no longer proportional to the stress. The solid will return to its original shape when the stress is removed. Some more vocabulary Elastic limit When the stress is less than the elastic limit, removing the stress will return the solid to the original shape. If the elastic limit is surpassed, the solid remains permanently deformed. Ultimate strength If the ultimate strength is surpassed, the solid fractures. The ultimate strength can be different for tensile and compressive stresses. Ductile ductile material continues to stretch beyond its ultimate strength without breaking and the stress decreases from the ultimate strength. Brittle brittle material has the ultimate strength and the breaking point close together. Other Deformations There are other ways to deform a solid. Two additional ways are shear deformation and volume deformation. Shear Deformation The forces act parallel to the edge of the solid. Tensile and compressive forces act perpendicular to the edges. shear stress It looks like the previous definition but the picture below shows otherwise.
x shear strain Define the shear modulus S as The shear modulus is also measured in Pa. x S Volume Deformation s an example, consider a solid immersed in a fluid. The pressure exerted on all sides will change its volume. The volume stress is created by the pressure.
volume stress P The strain will be the change in volume caused by the pressure The bulk modulus is defined in V volume strain V V P B V ike the other moduli, B is measured in Pa. P refers to the additional pressure above an atmosphere. Why is there a minus sign? Unlike the previous stresses and strains, volume stress can be applied to a fluid. The Short ife and Tragic End of Gallopin Gertie http://en.wikipedia.org/wiki/tacoma_narrows_bridge_%81940%9 http://www.youtube.com/watch?vj-zczjxsxnw Best of all. ong but worth it: http://video.google.com/videoplay?docid69397836847493737 You might be interested in other episodes of the Mechanical Universe series made in the 1980s at CalTech. Problem certain man s biceps muscle has a maximum cross-sectional area of 1 cm 1. -3 m. What is the stress in the muscle if it exerts a force of 300 N? Solution rom the definition of tensile stress, we have Stress 300 N.5 3 1. m Problem wire 1.5 m long has a cross-sectional area of.4 mm. It is hung vertically and stretches 0.3 mm when a -kg block is attached to it. ind (a) the stress, (b) the strain, and (c) Young s modulus for the wire. Solution ll measurements must be in SI units. 5 Pa.4 mm 1 m 00 mm.4 6 m 1 m 0.3 mm 3. 00 mm m
(a) Use the definition of stress Stress mg ( kg)(9.8 m/s 6.4 m ) 4.08 7 Pa (b) The definition of strain Strain 3. m.13 1.5 m (c) Young s modulus Y Stress YStrain 7 Stress 4.08 N/m Y Strain.13 1.9 7 Pa