Explanation Given: Mass of the particle, m = 500 g = 0.5 kg The initial velocity of a particle at x = 0 , v 0 = 2.0 m/s Formula used: 1. Area under the force-displacement curve gives work done by the particle. 2. Work-energy theorem is used in this question where work done is given by, d W = F × d x along the x -axisand the energy was calculated using E = 1 2 m v 2 as particle possesses no potential energy during its motion from x = 0 m to x = 3 m . Calculation: Till x = 1 m , the force is constant ( F x = 15 N ) but after that, it gradually decreases till x = 3 m . So, firstly calculate the work done by the particle at x = 0 m using the work-energy theorem; Work done by the system = total energy possessed by the particle. Therefore, we have work done, W 0 = 1 2 m v 2 = ( 0.5 ) × ( 0.5 k g ) × ( 2 m/s ) 2 = 1 J The area under the curve gives work done; therefore, the area under the curve till x = 1 m is given by the area of a rectangle, W 1 = base×height = 1 m × 15 N = 15 J Again using, the work-energy theorem we get;total work done till x = 1 m is given by W 0 + W 1 = 1 2 m v 2 16 J = ( 0

Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)

4th Edition

ISBN: 9780134110684

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Helmholtz Free Energy

The Helmholtz free energy is a thermodynamic potential used to calculate the measure of useful work from a closed system. This system is kept at constant temperature and volume. German physicist Hermann Helmholtz introduced this concept in 1882.

Question

Chapter 9, Problem 21EAP

To determine

The velocity of the particle at x=3 m .

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Chapter 9, Problem 20EAP

Chapter 9, Problem 22EAP

Chapter 9 Solutions

Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)

Ch. 9 - If a particle’s speed increases by a factor of 3,...Ch. 9 - Prob. 2CQ Ch. 9 - 3. An elevator held by a single cable is ascending...Ch. 9 - The rope in FIGURE Q9.4 pulls the box to the left...Ch. 9 - 5. A 0.2 kg plastic cart and a 20 kg lead cart...Ch. 9 - A particle moving to the left is slowed by a force...Ch. 9 - 7. A particle moves in a vertical plane along the...Ch. 9 - 8. You need to raise a heavy block by pulling it...Ch. 9 - 9. A ball on a string travels once around a circle...Ch. 9 - A sprinter accelerates from rest. Is the work done...

Ch. 9 - 11. A Spring has an unstretched length of 10cm. It...Ch. 9 - 12. The left end of a spring is attached to a...Ch. 9 - The driver of a car traveling at 60 mph slams on...Ch. 9 - Prob. 14CQ Ch. 9 - Which has the larger kinetic energy, a 10 g bullet...Ch. 9 - At what speed does a 1000 kg compact car have the...Ch. 9 - 3. A mother has four times the mass of her young...Ch. 9 - 4. A horizontal rope with 15 N tension drags a 25...Ch. 9 - 5. A 25 kg box sliding to the left across a...Ch. 9 - A 2.0 kg book is lying on a 0.75-m-high table. You...Ch. 9 - Prob. 7EAP Ch. 9 - Prob. 8EAP Ch. 9 - 9. You throw a 5.5 g coin straight down at 4.0 m/s...Ch. 9 - Prob. 10EAP Ch. 9 - 12. Evaluate the dot product if and . and . Ch. 9 - 12. Evaluate the dot product if and . and . Ch. 9 - 13. What is the angle ? between vectors and in...Ch. 9 - Prob. 14EAP Ch. 9 - Prob. 15EAP Ch. 9 - 16. A 25 kg air compressor is dragged up a rough...Ch. 9 - Prob. 17EAP Ch. 9 - The two ropes seen in FIGURE EX9.18 are used to...Ch. 9 - 19. The three ropes shown in the bird’s-eye view...Ch. 9 - Prob. 20EAP Ch. 9 - Prob. 21EAP Ch. 9 - Prob. 22EAP Ch. 9 - A particle moving on the x-axis experiences a...Ch. 9 - Prob. 24EAP Ch. 9 - A horizontal spring with spring constant 750 N/m...Ch. 9 - 26. A 35-cm-long vertical spring has one end fixed...Ch. 9 - A 10-cm-long spring is attached to the ceiling....Ch. 9 - A 60 kg student is standing atop a spring in an...Ch. 9 - 29. A 5.0 kg mass hanging from a spring scale is...Ch. 9 - A horizontal spring with spring constant 85 N/m...Ch. 9 - 31. One mole (6.02 × 1023 atoms) of helium atoms...Ch. 9 - 32. A 55 kg softball player slides into second...Ch. 9 - A baggage handler throws a 15 kg suitcase along...Ch. 9 - 34. An 8.0 kg crate is pulled 5.0 m up a 30°...Ch. 9 - Justin, with a mass of 30 kg, is going down an...Ch. 9 - Prob. 36EAP Ch. 9 - Prob. 37EAP Ch. 9 - 38. How much energy is consumed by (a) a 1.2 kW...Ch. 9 - 39. At midday, solar energy strikes the earth with...Ch. 9 - Prob. 40EAP Ch. 9 - Prob. 41EAP Ch. 9 - Prob. 42EAP Ch. 9 - 43. A 1000 kg elevator accelerates upward at 1.0...Ch. 9 - 44. a. Starting from rest, a crate of mass m is...Ch. 9 - Prob. 45EAP Ch. 9 - 46. A particle of mass m moving along the x-axis...Ch. 9 - 47. A ball shot straight up with kinetic energy...Ch. 9 - 48. A pile driver lifts a 250 kg weight and then...Ch. 9 - Prob. 49EAP Ch. 9 - 50. You’re fishing from a tall pier and have...Ch. 9 - Hook’s law describes an ideal spring. Many real...Ch. 9 - 52. The force acting on a particle is Fx =...Ch. 9 - 53. The gravitational attraction between two...Ch. 9 - 54. An electric dipole consists of two equal...Ch. 9 - Prob. 55EAP Ch. 9 - 56. When a 65 kg cheerleader stands on a...Ch. 9 - Prob. 57EAP Ch. 9 - Prob. 58EAP Ch. 9 - 59. A horizontal spring with spring constant 250...Ch. 9 - 60. A 90 kg firefighter needs to climb the stairs...Ch. 9 - Prob. 61EAP Ch. 9 - 62. When you ride a bicycle at constant speed,...Ch. 9 - 63. A farmer uses a tractor to pull a 150 kg...Ch. 9 - Prob. 64EAP Ch. 9 - Prob. 65EAP Ch. 9 - Prob. 66EAP Ch. 9 - In problems 67 through 69 you are given the...Ch. 9 - Prob. 68EAP Ch. 9 - Prob. 69EAP Ch. 9 - Prob. 70EAP Ch. 9 - Prob. 71EAP Ch. 9 - Prob. 72EAP

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