CLASSICAL DYNAMICS OF PARTICLES AND SYST
5th Edition
ISBN: 9780357670675
Author: Thornton
Publisher: CENGAGE L
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Chapter 12, Problem 12.10P
To determine
The proof that normal coordinates have resonance corresponding to characteristic frequencies
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1.62 On a training flight, a Figure P1.62
student pilot flies from Lincoln,
Nebraska, to Clarinda, Iowa, next
to St. Joseph, Missouri, and then to
Manhattan, Kansas (Fig. P1.62). The
directions are shown relative to north:
0° is north, 90° is east, 180° is south,
and 270° is west. Use the method of
components to find (a) the distance
she has to fly from Manhattan to get
back to Lincoln, and (b) the direction
(relative to north) she must fly to get
there. Illustrate your solutions with a
vector diagram.
IOWA
147 km
Lincoln 85°
Clarinda
106 km
167°
St. Joseph
NEBRASKA
Manhattan
166 km
235°
S KANSAS MISSOURI
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CLASSICAL DYNAMICS OF PARTICLES AND SYST
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- 3.19 • Win the Prize. In a carnival booth, you can win a stuffed gi- raffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal dis- tance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. (a) What is the height of the shelf above the point where the quarter leaves your hand? (b) What is the vertical component of the velocity of the quarter just before it lands in the dish? Figure E3.19 6.4 m/s 2.1arrow_forwardCan someone help me answer this thank you.arrow_forward1.21 A postal employee drives a delivery truck along the route shown in Fig. E1.21. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram. (See also Exercise 1.28 for a different approach.) Figure E1.21 START 2.6 km 4.0 km 3.1 km STOParrow_forward
- help because i am so lost and it should look something like the picturearrow_forward3.31 A Ferris wheel with radius Figure E3.31 14.0 m is turning about a horizontal axis through its center (Fig. E3.31). The linear speed of a passenger on the rim is constant and equal to 6.00 m/s. What are the magnitude and direction of the passenger's acceleration as she passes through (a) the lowest point in her circular motion and (b) the high- est point in her circular motion? (c) How much time does it take the Ferris wheel to make one revolution?arrow_forward1.56 ⚫. Three horizontal ropes pull on a large stone stuck in the ground, producing the vector forces A, B, and C shown in Fig. P1.56. Find the magnitude and direction of a fourth force on the stone that will make the vector sum of the four forces zero. Figure P1.56 B(80.0 N) 30.0 A (100.0 N) 53.0° C (40.0 N) 30.0°arrow_forward
- 1.39 Given two vectors A = -2.00 +3.00 +4.00 and B=3.00 +1.00 -3.00k. (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector difference A - B; and (c) find the magnitude of the vector difference A - B. Is this the same as the magnitude of B - Ä? Explain.arrow_forward5. The radius of a circle is 5.5 cm. (a) What is the circumference in meters? (b) What is its area in square meters? 6. Using the generic triangle below, solve the following: 0 = 55 and c = 32 m, solve for a and b. a = 250 m and b = 180 m, solve for the angle and c. b=104 cm and c = 65 cm, solve for a and the angle b a 7. Consider the figure below representing the Temperature (T in degrees Celsius) as a function of time t (in seconds) 4 12 20 (a) What is the area under the curve in the figure below? (b) The area under the graph can be calculated using integrals or derivatives? (c) During what interval is the derivative of temperature with respect to time equal to zero?arrow_forwardPart 3: Symbolic Algebra Often problems in science and engineering are done with variables only. Don't let the different letters confuse you. Manipulate them algebraically as though they were numbers. 1. Solve 3x-7= x + 3 for x 2x-1 2. Solve- for x 2+2 In questions 3-11 solve for the required symbol/letter 3. v2 +2a(s-80), a = = 4. B= Ho I 2π r 5. K = kz² 6.xm= MAL ,d= d 7.T, 2 = 8.F=Gm 9. mgh=mv² 10.qV = mu² 80 12. Suppose that the height in meters of a thrown ball after t seconds is given by h =6+4t-t². Complete the square to find the highest point and the time when this happens. 13. Solve by completing the square c₁t² + cat + 3 = 0. 14. Solve for the time t in the following expression = 0 + vot+at²arrow_forward
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