Ch 09: Work and Kinetic Energy

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 09: Work and Kinetic Energy

Problem 10b

Chapter 9, Problem 10b

You throw a 5.5 g coin straight down at 4.0 m/s from a 35-m-high bridge. What is the speed of the coin just as it hits the water?

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Identify the known values: The mass of the coin is 5.5 g (not needed for this calculation), the initial velocity $ v_0 $ is 4.0 m/s (downward), the height $ h $ is 35 m, and the acceleration due to gravity $ g $ is 9.8 m/s² (downward).

Use the kinematic equation to find the final velocity $ v $: $ v^2 = v_0^2 + 2gh $, where $ v_0 $ is the initial velocity, $ g $ is the acceleration due to gravity, and $ h $ is the height.

Substitute the known values into the equation: $ v^2 = (4.0)^2 + 2(9.8)(35) $.

Simplify the terms inside the equation: Calculate $ (4.0)^2 $, $ 2(9.8)(35) $, and add them together to find $ v^2 $.

Take the square root of $ v^2 $ to find the final velocity $ v $. Remember that the velocity will be positive since the coin is moving downward, and the direction is consistent with the initial velocity.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinematics

Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this problem, kinematic equations can be used to relate the initial velocity, final velocity, acceleration due to gravity, and distance fallen to find the speed of the coin just before it hits the water.

Acceleration due to Gravity

Acceleration due to gravity is the acceleration experienced by an object when it is in free fall near the Earth's surface, typically denoted as 'g' and approximately equal to 9.81 m/s². This constant acceleration affects the motion of the coin as it falls, increasing its speed as it descends. Understanding this concept is crucial for calculating the final speed of the coin when it impacts the water.

Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the potential energy of the coin at the height of the bridge is converted into kinetic energy as it falls. By applying this principle, one can calculate the final speed of the coin by equating the initial potential energy to the final kinetic energy just before it hits the water.

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