Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 12, Problem 45P
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A weight W is suspended from a vertical spring whose modulus is “K” N/m. The weight is pulled down “S” m from its equilibrium and then released. Determine its velocity when it returns to its equilibrium position.
A wire of length L, Young’s modulus Y, and crosssectional area A is stretched elastically by an amount ΔL. By Hooke’s law, the restoring force is -k ΔL. (a) Show that k = YA/L. (b) Show that the work done in stretching the wire byan amount ΔL is W = 1/2 YA(ΔL)2/L .
Without fracture of the Femur, determine the maximum height, in cm, from which a
70-kg woman can jump onto just one of her heels, where bare foot and where
keeping her leg straight. Assume that all of her stored gravitational potential energy is
transferred to strain potential energy in one of her femurs. Take the following values:
her femur length, / = 60 cm, her femur area, A = 3.5 cm2, Young's modulus for her
bone, Y= 1.2 x1010 N/m2, and the rupture stress for her bone is omax = 7.0 x 10
N/m2.
12 cm
110cm
9.9cm
56 cm
6.2 cm
9.5 cm
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Chapter 12 Solutions
Physics for Scientists and Engineers
Ch. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4PCh. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - Prob. 10P
Ch. 12 - Prob. 11PCh. 12 - Prob. 12PCh. 12 - Prob. 13PCh. 12 - Prob. 14PCh. 12 - Prob. 15PCh. 12 - Prob. 16PCh. 12 - Prob. 17PCh. 12 - Prob. 18PCh. 12 - Prob. 19PCh. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - Prob. 24PCh. 12 - Prob. 25PCh. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - Prob. 28PCh. 12 - Prob. 29PCh. 12 - Prob. 30PCh. 12 - Prob. 31PCh. 12 - Prob. 32PCh. 12 - Prob. 33PCh. 12 - Prob. 34PCh. 12 - Prob. 35PCh. 12 - Prob. 36PCh. 12 - Prob. 37PCh. 12 - Prob. 38PCh. 12 - Prob. 39PCh. 12 - Prob. 40PCh. 12 - Prob. 41PCh. 12 - Prob. 42PCh. 12 - Prob. 43PCh. 12 - Prob. 44PCh. 12 - Prob. 45PCh. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 53PCh. 12 - Prob. 54PCh. 12 - Prob. 55PCh. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61PCh. 12 - Prob. 62PCh. 12 - Prob. 63PCh. 12 - Prob. 64PCh. 12 - Prob. 65PCh. 12 - Prob. 66PCh. 12 - Prob. 67PCh. 12 - Prob. 68PCh. 12 - Prob. 69PCh. 12 - Prob. 70PCh. 12 - Prob. 72PCh. 12 - Prob. 73PCh. 12 - Prob. 74PCh. 12 - Prob. 75PCh. 12 - Prob. 76P
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- Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.arrow_forwardWithout fracture of the femur, determine the maximum height, in cm, from which a 70-kg woman can jump onto just one of her heels, where bare foot and where keeping her leg straight. Assume that all of her stored gravitational potential energy is transfered to strain potential energy in her femur. Take the following values : her femur length, l = 60cm, her femur area, A = 3.5cm2, Youngs modulus for her bone, Y = 1.2x1010 N/m2, and the rupture stress for her bone is σmax = 7.0 x 107 N/m2arrow_forwardYour biceps muscle is attached to your elbow by the distal biceps tendon. An average adults tendon has a 6 mm by 3 mm rectangular cross-section and is 63 mm in length. A tendon has a Young’s modulus of 1.5x10^9 N/m^2. How much work must be done to stretch the length of the distal biceps tendon by 10%? Assume that the tendon is a linearly elastic material and that stretching does not alter it’s cross-section.arrow_forward
- Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as in the figure below. The helper spring engages when the main leaf spring is compressed by distance Yo' then helps to support any additional load. Consider a leaf spring constant of 5.35 × 105 N/m, helper spring constant of 3.60 × 105 N/m, and y₁ = 0.500 m. Truck body Yo Axle (a) What is the compression of the leaf spring for a load of 4.10 × 105 N? 0.69 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m (b) How much work is done compressing the springs? J andarrow_forwardA wire of length 3 m and diameter 0.3 mm is stretched by hanging a weight of 2 kg from it and the elongation produced is 2 mm. Calculate the Young's modulus and the strain potential energy of the wire.arrow_forwardProof that the energy stored in the compact bone is given by E = AL0 (Sb) ^ 2 / 2γ. When Sb is bone stress. *arrow_forward
- The wooden pile shown in the figure has a diameter of 105 mm and is subjected to a load of P - 90 kN. Along the length of the pile and around its perimeter, soil supplies a constant frictional resistance of w- 3.85 kN/m. The length of the pile is L - 5.1m and its elastic modulus is E - 13.0 GPa. Calculate (a) the force Fg needed at the base of the pile for equilibrium. (b) the magnitude of the downward displacement at A relative to B. Answers: (a) Fs- i kN (b) UA- mmarrow_forwardThe nuchal ligament in a horse supports the weight of the horse’s head. This ligament is much more elastic than a typical ligament, stretching from 15% to 45% longer than its resting length as a horse’s head moves up and down while it runs. This stretch of the ligament stores energy, making locomotion more efficient. Measurements on a segment of ligament show a linear stress-versusstrain relationship until the stress approaches 0.80. Smoothed data for the stretch are shown. The segment of ligament tested has a resting length of 40 mm. How long is the ligament at a strain of 0.60?A. 46 mmB. 52 mmC. 58 mmD. 64 mmarrow_forwardThe nuchal ligament in a horse supports the weight of the horse’s head. This ligament is much more elastic than a typical ligament, stretching from 15% to 45% longer than its resting length as a horse’s head moves up and down while it runs. This stretch of the ligament stores energy, making locomotion more efficient. Measurements on a segment of ligament show a linear stress-versusstrain relationship until the stress approaches 0.80. Smoothed data for the stretch are shown. What is the approximate Young’s modulus for the ligament?A. 4 x 105 N/m2B. 8 x 105 N/m2C. 3 x 106 N/m2D. 6 x 106 N/m2arrow_forward
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