Explanation Introduction: The impulse-momentum theorem for a body is written as, P i + J e x t e r n a l = P f Here, P i is the initial momentum, P f is the final momentum and J e x t e r n a l is the impulse on the ball due to an external agency. The expression for impulse due to an external agency is written as, J e x t e r n a l = F e x t e r n a l Δ t Here, F e x t e r n a l is the force exerted by the external agency and Δ t is the time interval for the application of force. Sign convention: Consider all quantities measured in the downward direction as positive and quantities measured in the upward direction as negative. Explanation: Understand that the only external interactions for the system (ball) are the reaction force from the ground on the ball and the impulse from the earth. Consider, the happy ball has a mass m and with initial and final velocities as v h i and v h f , respectively. Draw a schematic diagram depicting the motion of happy ball. Write the impulse-momentum equation for the happy ball as the system. P h i + J h , g r o u n d + J h , e a r t h = P h f Here, P h i is the initial momentum of the happy ball and P h f is the final momentum of the happy ball. J h , g r o u n d is the impulse force due to the normal reaction when the happy ball hits the ground and J h , e a r t h is the impulse force due to the force of gravity acting on the body. Since momentum is the product of mass and velocity, substitute m v h i for P h i and m v h f for P h f , m v h i + J h , g r o u n d + J h , e a r t h = m v h f …… (1) The expression for the impulse due to earth on happy ball can be written as, J h , e a r t h = F e a r t h Δ t Substitute mg for F e a r t h (positive sign is means that the weight acts in the downward direction), J h , e a r t h = ( m g ) Δ t Write the kinematic equation of motion for the happy ball when it reaches the ground after being dropped from a height, h . v h i 2 = u h 2 + 2 g h Since, the happy ball is dropped with no initial velocity, substitute 0 m/s for u h , v h i 2 = ( 0 m/s ) + 2 g h v h i = 2 g h Observe that after rebounding to the same height, the magnitude of velocity will remain the same but its direction would be reversed, that is, v h f is − 2 g h . For the happy ball, a new mathematical expression is developed using impulse-momentum equation. Substitute 2 g h for v h i , − 2 g h for v h f , ( m g ) Δ t for J h , e a r t h in equation (1), m ( 2 g h ) + J h , g r o u n d + ( m g ) Δ t = m ( − 2 g h ) J h , g r o u n d = − [ 2 m ( 2 g h ) + ( m g ) Δ t ] The negative sign implies that, the impulse from the ground acts in the upward direction

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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.

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Chapter 6, Problem 30P

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The impulse-momentum bar chart representation of a sad ball and a happy ball when both the balls of the same mass fall from a height h, the happy ball rebounds to the same height and the sad ball does not bounce at all, considering the ball as the system.

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Chapter 6, Problem 29P

Chapter 6, Problem 31P

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Chapter 6 Solutions

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Ch. 6 - Review Question 6.1 When you burn a log in a fire...Ch. 6 - Review Question 6.2 Ryan says, “Based on the...Ch. 6 - Review Question 6.3 An apple is falling from a...Ch. 6 - Review Question 6.4 If in solving the problem in...Ch. 6 - Review Question 6.5 As the bullet enters the block...Ch. 6 - Review Question 6.6 The following equation is a...Ch. 6 - Review Question 6.7 Object A, moving in the...Ch. 6 - The gravitational force that Earth exerts on an...Ch. 6 - A bullet fired at a door makes a hole in the door...Ch. 6 - How would you convince somebody that the momentum...

Ch. 6 - 4. A wagon full of medicine balls is rolling along...Ch. 6 - 5. When can you apply the idea that momentum is...Ch. 6 - 6. Choose an example in which the momentum of a...Ch. 6 - Figure Q6.7 shows the velocity-versus-time graphs...Ch. 6 - Which is a safer car bumper in a collision: one...Ch. 6 - 9. Why does an inflated balloon shoot across a...Ch. 6 - In which situation does the momentum of a tennis...Ch. 6 - 11. A toy car with very low friction wheels and...Ch. 6 - You hold a clay ball above a scale and then drop...Ch. 6 - 13. You hold a rubber ball above a scale and then...Ch. 6 - 14 Two battery-powered fan carts are resting on a...Ch. 6 - 15. According to a report on traumatic brain...Ch. 6 - 16. Jim says that momentum is not a conserved...Ch. 6 - Say five important things about momentum (for...Ch. 6 - Three people are observing the same car. One...Ch. 6 - When would a ball hitting a wall have a greater...Ch. 6 - 20. In the previous question, in which case does...Ch. 6 - 21. Explain the difference between the concepts of...Ch. 6 - Why do you believe that momentum is a conserved...Ch. 6 - A heavy bar falls straight down onto the bed of a...Ch. 6 - Construct impulse-momentum bar charts to represent...Ch. 6 - A person moving on Rollerblades throws a medicine...Ch. 6 - A small ball of mass m rolls at a constant speed v...Ch. 6 - 1. You and a friend are playing tennis. (a) What...Ch. 6 - 2. You are hitting a tennis ball against a wall....Ch. 6 - A ball of mass m and speed v travels horizontally,...Ch. 6 - Figure P6.4 shows the velocity-versus-time graph...Ch. 6 - 5. A 1300-kg car is traveling at a speed of 10 m/s...Ch. 6 - * The rules of tennis specify that the 0.057-kg...Ch. 6 - * A cart of mass m moving right at speed v with...Ch. 6 - 8. * A cart of mass m moving right collides with...Ch. 6 - ESTEstimate your momentum when you are walking at...Ch. 6 - 10. A 100-g apple is falling from a tree. What is...Ch. 6 - * The same 100-g apple is falling from the tree....Ch. 6 - 12. Why does Earth exert the same impulse during...Ch. 6 - 13. * Van hits concrete support In a crash test, a...Ch. 6 - BIO Force exerted by heart on blood About 80 g of...Ch. 6 - 15. The train tracks on which a train travels...Ch. 6 - 16. ** EST Your friend is catching a falling...Ch. 6 - 17 BIO Traumatic brain injury According to a...Ch. 6 - * A 65-kg astronaut pushes against the inside back...Ch. 6 - 19. * You decide to use your garden hose to wash...Ch. 6 - 20. * An egg rolls off a kitchen counter and...Ch. 6 - 21. ** Proportional reasoning During a collision...Ch. 6 - (a) What force is required to stop a 1500-kg car...Ch. 6 - 23. ** EST You drop a 78-g ball vertically onto a...Ch. 6 - * Air bag force on head The graph in Figure P6.24...Ch. 6 - 25. * Equation Jeopardy 1 Invent a problem for...Ch. 6 - * Equation Jeopardy 2 Invent a problem for which...Ch. 6 - * Two carts (100 g and 150 g) on an air track are...Ch. 6 - * A tennis ball of mass m hits a wall at speed v...Ch. 6 - 29. * A tennis ball traveling at a speed of v...Ch. 6 - Prob. 30P Ch. 6 - Prob. 31P Ch. 6 - * You hold a beach ball above your head and then...Ch. 6 - 33. * A basketball player drops a 0.60-kg...Ch. 6 - * Bar chart Jeopardy Invent a problem for each of...Ch. 6 - * A baseball bat contacts a 0.145-kg baseball for...Ch. 6 - A cannon mounted on the back of a ship fires a...Ch. 6 - A 10-kg sled carrying a 30-kg child glides on a...Ch. 6 - 38. A 10,000-kg coal car on the Great Northern...Ch. 6 - * Avoiding chest injury A person in a car during a...Ch. 6 - * Bruising apples An apple bruises if a force...Ch. 6 - * Fast tennis serve The fastest server in womens...Ch. 6 - 42. * You are in an elevator whose cable has just...Ch. 6 - ** You jump from the window of a burning hotel and...Ch. 6 - * After a 70-kg person steps from a boat onto the...Ch. 6 - 45. * BIO Leg injuries during car collisions...Ch. 6 - 46. * BIO Bone fracture The zygomatic bone in the...Ch. 6 - 47. ** You are investigating a newly discovered...Ch. 6 - 48. * An impulse of stops your head during a car...Ch. 6 - A cart is moving on a horizontal track when a...Ch. 6 - 50. * A cart is moving on a horizontal track. A...Ch. 6 - 51. Your friend shoots an 80-g arrow through a...Ch. 6 - 52. * BIO EST Cuttlefish use jet propulsion to...Ch. 6 - * BIO Potassium decay in body tissue Certain...Ch. 6 - 54. Drifting space mechanic An astronaut with a...Ch. 6 - Prob. 55P Ch. 6 - 56. Rocket stages A 5000-kg rocket ejects a...Ch. 6 - 57. * A rocket has just ejected fuel. With the...Ch. 6 - 58. * Car collision A 1180-kg car traveling south...Ch. 6 - 59. * Ice skaters collide While ice skating, you...Ch. 6 - 1015-kg meteorite traveling at about 10 km/s...Ch. 6 - 61. * Three friends play beach volleyball. The...Ch. 6 - 62. ** Two forces exert impulses on a hockey puck,...Ch. 6 - 64. * A cart of mass m traveling in the negative...Ch. 6 - 65. ** Two cars of unequal mass moving at the same...Ch. 6 - 66. ** Restraining force during collision A...Ch. 6 - * EST A carpenter hammers a nail using a 0.80-kg...Ch. 6 - 68. ** A 0.020-kg bullet traveling at a speed of...Ch. 6 - 69. * Two identical lightweight arms are mounted...Ch. 6 - * In a first experiment, a 30-g clay ball is shot...Ch. 6 - 71. ** EST A record rainstorm produced 304.8 mm...Ch. 6 - 72. * While dangling a hairdryer by its cord, as...Ch. 6 - 73. ** While dangling a hairdryer by its cord, as...Ch. 6 - Prob. 74GP Ch. 6 - 75. * A 2045-kg sports utility vehicle hits the...Ch. 6 - 76. ** A car of mass m1 traveling north at a speed...Ch. 6 - ** You have two carts, a force probe connected to...Ch. 6 - BIO Heartbeat detector A prisoner tries to escape...Ch. 6 - BIO Heartbeat detector A prisoner tries to escape...Ch. 6 - BIO Heartbeat detector A prisoner tries to escape...Ch. 6 - BIO Heartbeat detector A prisoner tries to escape...Ch. 6 - BIO Heartbeat detector A prisoner tries to escape...Ch. 6 - Space Shuttle launch The mass of the Space Shuttle...Ch. 6 - Space Shuttle launch The mass of the Space Shuttle...Ch. 6 - Space Shuttle launch The mass of the Space Shuttle...Ch. 6 - Space Shuttle launch The mass of the Space Shuttle...Ch. 6 - Space Shuttle launch The mass of the Space Shuttle...Ch. 6 - Space Shuttle launch The mass of the Space Shuttle...Ch. 6 - Space Shuttle launch The mass of the Space Shuttle...

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The impulse-momentum bar chart representation of a sad ball and a happy ball when both the balls of the same mass fall from a height h , the happy ball rebounds to the same height and the sad ball does not bounce at all, considering the ball as the system.

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The impulse-momentum bar chart representation of a sad ball and a happy ball when both the balls of the same mass fall from a height h, the happy ball rebounds to the same height and the sad ball does not bounce at all, considering the ball as the system.

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Chapter 6 Solutions