Textbook Question
Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall. What is the bearing's impact velocity?
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Ch 02: Kinematics in One Dimension
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 2, Problem 20a
Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?
Verified step by step guidance1
Identify the key variables in the problem: the time of free fall is given as 4.0 seconds, and we need to find the height of the tower. Assume the acceleration due to gravity, \( g \), is \( 9.8 \; \text{m/s}^2 \), and the initial velocity \( v_0 \) is 0 since the drop starts from rest.
Use the kinematic equation for vertical motion under constant acceleration: \( h = v_0 t + \frac{1}{2} g t^2 \). Since \( v_0 = 0 \), the equation simplifies to \( h = \frac{1}{2} g t^2 \).
Substitute the known values into the simplified equation: \( h = \frac{1}{2} (9.8) (4.0)^2 \).
Simplify the expression inside the parentheses: \( h = \frac{1}{2} (9.8) (16.0) \).
Multiply the terms to find the height \( h \). This will give the required height of the tower in meters.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Free Fall
Free fall refers to the motion of an object under the influence of gravity alone, without any air resistance. In this scenario, the molten metal drops from a height and accelerates downward due to gravitational force, which is approximately 9.81 m/s² on Earth. Understanding free fall is essential to calculate the height of the tower based on the time it takes for the metal to solidify.
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08:36
Vertical Motion & Free Fall
Kinematic Equations
Kinematic equations describe the motion of objects under constant acceleration. For free-falling objects, one key equation relates distance, initial velocity, time, and acceleration: d = v₀t + 0.5at². In this case, the initial velocity (v₀) is zero, allowing us to simplify the equation to d = 0.5gt², which is crucial for determining the height of the shot tower.
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Solidification Time
Solidification time is the duration required for a material to transition from a liquid to a solid state. In this context, the molten metal needs 4.0 seconds to solidify sufficiently before impacting the ground. This time frame directly influences the calculation of the height of the tower, as it determines how long the metal will be in free fall before reaching the bottom.
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Related Practice
Textbook Question
Write a short description of the motion of a real object for which FIGURE EX1.20 would be a realistic position-versus-time graph.
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Textbook Question
FIGURE EX1.18 shows the motion diagram of a drag racer. The camera took one frame every 2 s. Make a position-versus-time graph for the drag racer. Because you have data only at certain instants, your graph should consist of dots that are not connected together.
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Textbook Question
As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 35 m/s. How fast is the watermelon going when it passes Superman?
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Textbook Question
A rock is tossed straight up from ground level with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep. What is the rock's speed as it hits the bottom of the hole?
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Textbook Question
A Porsche challenges a Honda to a 400 m race. Because the Porsche's acceleration of 3.5 m/s2 is larger than the Honda's 3.0 m/s2, the Honda gets a 1.0 s head start. Who wins? By how many seconds?
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