Textbook Question
A rubber ball bounces. We'd like to understand how the ball bounces. Draw a free-body diagram of the ball during its contact with the ground. Is there a net force acting on the ball? If so, in which direction?
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Ch 05: Force and Motion
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 5, Problem 56a
A rubber ball bounces. We'd like to understand how the ball bounces. A rubber ball has been dropped and is bouncing off the floor. Draw a motion diagram of the ball during the brief time interval that it is in contact with the floor. Show 4 or 5 frames as the ball compresses, then another 4 or 5 frames as it expands. What is the direction of a during each of these parts of the motion?
Verified step by step guidance1
Step 1: Understand the motion of the ball. When the ball is dropped, it accelerates downward due to gravity. Upon hitting the floor, the ball compresses as it decelerates to a stop momentarily. Then, it expands as it rebounds upward. The motion diagram will represent these phases: compression and expansion.
Step 2: During the compression phase (as the ball is in contact with the floor and compressing), the acceleration vector points upward. This is because the floor exerts an upward force on the ball, opposing its downward motion and decelerating it.
Step 3: During the expansion phase (as the ball is in contact with the floor and expanding), the acceleration vector still points upward. This is because the floor continues to exert an upward force, now propelling the ball upward.
Step 4: To draw the motion diagram, represent the ball's position at equal time intervals. For the compression phase, the spacing between the positions will decrease as the ball slows down. For the expansion phase, the spacing will increase as the ball speeds up. Use arrows to indicate the direction of acceleration (upward) during both phases.
Step 5: Label the diagram clearly to show the compression and expansion phases, and indicate the direction of acceleration (a) during each phase. This will help visualize how the ball's motion changes while in contact with the floor.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Elastic Potential Energy
When a rubber ball is compressed upon impact with the floor, it stores elastic potential energy. This energy is a result of the deformation of the ball's material, which allows it to return to its original shape. The amount of energy stored depends on the degree of compression and the material properties of the ball.
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Potential Energy Graphs
Newton's Third Law of Motion
Newton's Third Law states that for every action, there is an equal and opposite reaction. When the ball hits the floor, it exerts a force on the floor, and the floor exerts an equal force back on the ball. This reaction force is what causes the ball to bounce back up after it compresses.
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Acceleration During Bouncing
During the contact with the floor, the ball experiences acceleration due to the forces acting on it. When compressing, the acceleration is directed downward as gravity pulls it down, while during expansion, the acceleration is directed upward as the ball pushes off the floor. Understanding the direction and magnitude of these accelerations is crucial for analyzing the motion of the ball.
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Related Practice
Textbook Question
Problems 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, and 52 describe a situation. For each, draw a motion diagram, a force-identification diagram, and a free-body diagram. A model rocket is fired straight down from the top of a tower.
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Textbook Question
If a car stops suddenly, you feel 'thrown forward.' We'd like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there's nothing for you to hold onto. Draw your free-body diagram. Is there a net force on you? If so, in which direction?
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Textbook Question
Problems 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, and 52 describe a situation. For each, draw a motion diagram, a force-identification diagram, and a free-body diagram. A rocket is being launched straight up. Air resistance is not negligible.
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Textbook Question
Problems 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, and 52 describe a situation. For each, draw a motion diagram, a force-identification diagram, and a free-body diagram. A Styrofoam ball has just been shot straight up. Air resistance is not negligible.
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Textbook Question
If a car stops suddenly, you feel 'thrown forward.' We'd like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there's nothing for you to hold onto. Describe what happens to you as the car slows down.
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