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Chapter 5: Problem 5

The numbers in Table \(5.1\) are reasonable but should not be thought of as right. \(^{40}\) You can make your own table by using \(m g h\) for lifting and \(\frac{1}{2} m v^{2}\) for kinetic energy. For this exercise, pick three familiar activities or situations that allow you to estimate an energy scale in Joules and compute/estimate the results.

Short Answer

Expert verified
Question: Estimate the energy scale in Joules for the following three familiar activities: lifting a 1kg book, running at 3 m/s, and jumping 1 m high. Answer: The energy scales for these three activities are approximately 9.81 Joules for lifting a 1kg book, 270 Joules for running at 3 m/s, and 588.6 Joules for jumping 1 m high.

Step by step solution

01

Activity 1: Lifting a 1kg book

To estimate the energy involved in lifting a 1kg book, we will use the gravitational potential energy formula: Potential energy (PE) = mgh where m is the mass, g is the gravitational acceleration, and h is the height lifted. In this case, m = 1kg, g = 9.81m/s^2, and let's suppose we lift the book by 1m (h = 1m). Then, PE = (1kg)(9.81m/s^2)(1m) PE = 9.81 J The energy involved in lifting the book is approximately 9.81 Joules.
02

Activity 2: Running at 3 m/s

To estimate the energy involved in running at a velocity of 3 m/s, we will use the kinetic energy formula: Kinetic energy (KE) = 1/2 mv^2 where m is the mass and v is the velocity. Let's assume a mass of 60kg (average human weight) and a velocity of 3 m/s. Then, KE = 1/2(60kg)(3m/s)^2 KE = 0.5(60kg)(9m^2/s^2) KE = 270 J The energy involved in running at 3 m/s is approximately 270 Joules.
03

Activity 3: Jumping 1 m high

To estimate the energy involved in jumping 1 m high, we will use the gravitational potential energy formula: Potential energy (PE) = mgh where m is the mass, g is the gravitational acceleration, and h is the height. In this case, let's assume a mass of 60kg (average human weight) and jump height of 1m (h = 1m). Then, PE = (60kg)(9.81m/s^2)(1m) PE = 588.6 J The energy involved in jumping 1 m high is approximately 588.6 Joules. In summary, the energy scales for these three familiar activities are: 1. Lifting a 1 kg book = 9.81 J 2. Running at 3 m/s = 270 J 3. Jumping 1 m high = 588.6 J

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Most popular questions from this chapter

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