Chapter 6: Problem 87
A physics student spends part of her day walking between classes or for recreation, during which time she expends energy at an average rate of 280 W. The remainder of the day she is sitting in class, studying, or resting; during these activities, she expends energy at an average rate of 100 W. If she expends a total of 1.1 \(\times\) 10\(^7\) J of energy in a 24-hour day, how much of the day did she spend walking?
Short Answer
Step by step solution
Introduction to the Energy Equation
Define Variables and Equations
Convert Time to Seconds
Set Up Equations with Converted Variables
Solve the Equation for \( t_w \)
Convert \( t_w \) Back to Hours
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
energy equation
In essence, power is the rate at which energy is used or transferred. By multiplying it with time, we can find the total energy consumption. To apply this in real-life scenarios, we typically need to know the power in Watts (Joules per second) and time in seconds. This equation is versatile and applicable to diverse problems in physics, especially those involving activities over various durations, just like a student's day spent dividing time between walking and sitting. Understanding this equation allows us to interrelate these quantities and solve for unknowns.
power and energy
Energy, on the other hand, is the capacity to do work. It can exist in different forms such as kinetic, potential, thermal, and more. It's usually measured in Joules (J).
To understand their relationship, consider this: if you know how much power is being used (i.e., the rate of energy usage), you can calculate how much energy is consumed over time using the energy equation \( E = P \times t \). Thus, knowing the power and the duration of the activity, it becomes straightforward to find the total energy used, just as in our problem to find out how a student expended energy throughout the day.
time conversion
In our physics problem, the total daily time of 24 hours is converted to seconds: \( 24 \times 3600 = 86400 \) seconds. This conversion makes calculations consistent and enables us to use the power values in Watts accurately.
Similarly, after finding results in seconds, converting back to more familiar units such as hours can be essential for practical interpretations of the results, like determining how many hours the student spent walking. This back-and-forth conversion ensures clarity and accuracy in results.
physics problem solving
- Firstly, understand the problem, identifying key information and what's being asked.
- Next, translate all verbal information into mathematical expressions or equations, using known formulas like the energy equation.
- Convert all units to ensure consistency. In this problem, time was converted from hours to seconds.
- Then, solve these equations for the unknowns, often using algebraic manipulation.
- Finally, interpret your answer. Convert units back if needed and check the answer for reasonableness.