Homework 3 Problems with Solutions - Introductory Physics | ME 6, Assignments of Mechanical Engineering

Download Homework 3 Problems with Solutions - Introductory Physics | ME 6 and more Assignments Mechanical Engineering in PDF only on Docsity! All problems are from the 2nd edition of Walker. Numerical values are different for each student. 1. Chapter 26, Problem 1: A laser beam is reflected by a plane mirror. It is observed that the angle between the incident and reflected beams is 38°. If the mirror is now rotated so that the angle of incidence increases by 5.0°, what is the new angle between the incident and reflected beams? Solution: i r i r i2 38 2(5.0 ) 48 2. Chapter 26, Problem 10(a): How rapidly does the distance between you and your mirror image decrease if you walk directly toward a plane mirror with a speed of 2.4 m/s? Solution: The distance decreases at twice the walking rate, since |di|=do for a plane mirror. m s2 2.4 4.8 m/s Physics 6C Summer 2006 Homework 3 Solutions by Michael Gary 3. Chapter 26, Problem 27: A person 1.6 m tall stands 3.2 m from a reflecting globe in a garden. (a) If the diameter of the globe is 18 cm, where is the image of the person, relative to the surface of the globe? (b) How large is the person’s image? (c) Describe the image. Solution: (a) 1 1 1 1 i o o o 1 1 2 1 4 1 4 1 4.4 cm 0.18 m 3.2 m d f d R d D d The image is 4.4 cm behind the surface of the globe. (b) i i o o o 0.044 m (1.6 m) 2.2 cm 3.2 m d h mh h d (c) virtual, behind the globe, upright 9. Chapter 26, Problem 76: A friend tells you that when she takes off her eyeglasses and holds them 21 cm above a printed page the image of the print is erect but enlarged to 1.5 times its actual size. (a) What is the focal length of your friend’s glasses? (b) Is the image real or virtual? Are the lenses in the glasses concave or convex? Solution: (a) First find the image distance: i o i o (1.5)(21 cm) –32 cm dm d d md Use this to find the focal length: i o 1 1 i o 1 1 1 1 1 1 1 63 cm 1.5(21 cm) 21 cm f d d f d d (b) Since di < 0, the image appears on the same side of the lens as the object, which means it is a virtual image. Since f > 0, the lenses are convex. 10. Chapter 27, Problem 1: Your friend is 1.6 m tall. (a) When she stands 3.0 m from you, what is the height of her image formed on the retina of your eye? (Consider the eye to consist of a thin lens 1.7 cm from the retina.) (b) What is the height of her image when she is 4.0 m from you? Solution: (a) i oi o o (0.017 m)(1.6 m) 9.1 mm 3.0 m d hh mh d (b) i (0.017 m)(1.6 m) 6.8 mm 4.0 m h 11. Chapter 27, Problem 39: With unaided vision, a librarian can focus only on objects that lie at distances between 5.0 m and 0.50 m. (a) Which type of lens (converging or diverging) is needed to correct his nearsightedness? Explain. (b) Which type of lens will correct his farsightedness? Explain. (c) Find the refractive power needed for each part of the bifocal eyeglass lenses that will give the librarian normal visual acuity from 25 cm out to infinity. (Assume the lenses rest 2.0 cm from his eyes. The 25cm is measured from his eye. ) Solution: (a) A diverging lens will produce an image of a distant object within the librarian’s far point. (b)A converging lens will produce an image beyond the librarian’s near point of an object that is within the near point. (c) diverging (distant objects): o i i 1 1 1 1 1 refractive 0.20 diopters (5.0 m 0.020 m)f d d d converging (near objects): o i 1 1 1 1 1 refractive power 2.3 diopters 0.25 m 0.020 m (0.50 m 0.020 m)f d d | --di---- | - | | |2.0cm| | -----5.0m---- | | | -do--- | | | -----------di----------- | | | ----------0.5m---------------- | refractiv power 12. Chapter 27, Problem 46: A magnifying glass is a single convex lens with a focal length of f=+12.0cm (Assume the person using the magnifying glass has a near point of 25 cm and the magnifying glass is directly in front of the person's eyes.) (a) What is the angular magnification when this lens forms a (virtual) image at - ? How far from the object should the lens be held? (b) What is the angular magnification when this lens forms a (virtual) image at the person’s near point? How far from the object should the lens be held in this case? Solution: (a) 25 cm 2.1 12.0 cm N M f (b) 25 cm 1 1 3.1 12.0 cm N M f o 1 N N M f d 1 1 o 1 1 1 1 8.11 cm 25 cm 12.0 cm d N f 13. Chapter 27, Problem 56: A compound microscope has the objective and eyepiece mounted in a tube that is 18.0 cm long. The focal length of the eyepiece is 2.62 cm, and the near-point distance of the person using the microscope is 25.0 cm. If the person can view the image produced by the microscope with a completely relaxed eye, and the magnification is -4525, what is the focal length of the objective? Solution: i total obj e d N M f f i obj total e (2.62 cm 18.0 cm)(0.250 cm) 0.324 mm ( 4525)(2.62 cm) d N f M f