/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 Solve each formula for the quant... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 11

Solve each formula for the quantity given. $$ P=\frac{W}{t} \text { for } W $$

Short Answer

Expert verified
The solution is \( W = t \cdot P \).

Step by step solution

01

Recognize the Given Formula

We are given the formula \( P = \frac{W}{t} \) and need to solve this equation for \( W \). This means we want \( W \) on one side of the equation by itself.
02

Multiply Both Sides by \( t \)

To isolate \( W \), multiply both sides of the equation by \( t \), which will cancel \( t \) on the right side. The equation becomes \( t \cdot P = W \).
03

Rearrange the Equation

The equation \( W = t \cdot P \) is already in the form we need, with \( W \) by itself on one side. This is the solution for \( W \) in terms of \( P \) and \( t \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Physics Formulas
Physics formulas often come in different forms to describe relationships between physical quantities. The formula we are working with, \( P = \frac{W}{t} \), is known as the power formula. Power measures how quickly work is done. In this formula, \( P \) stands for power, \( W \) for work or energy, and \( t \) for time.
  • Power (P): Power is defined as the rate at which energy is transferred or converted. It is measured in watts (W), where 1 watt equals 1 joule per second.
  • Work (W): Work is the energy transferred by force acting over a distance. It is measured in joules (J).
  • Time (t): Time refers to the duration over which the work is done and is usually measured in seconds (s).
Understanding this equation helps you to calculate the most efficient way to use energy within a given time frame.
Algebraic Manipulation
Algebraic manipulation is a crucial skill in mathematics and physics. It involves rearranging equations to isolate one variable on one side. In our exercise, this involves isolating \( W \) from the original formula \( P = \frac{W}{t} \).
  • Identify the Target Variable: First, recognize which variable you need to isolate. Here, it is \( W \).
  • Reverse the Operations: Look at the operations affecting the target variable. Since \( W \) is divided by \( t \), you reverse this by multiplying.
  • Apply Operations to Both Sides: To maintain equality, multiply both sides by the same quantity, in this case \( t \).
Hence, multiplying both sides by \( t \) gives \( t \cdot P = W \). This is the essence of algebraic manipulation: using operations to "change" the equation while maintaining its equality.
Power Equation
The power equation is an essential concept in physics, capturing the relationship between power, work, and time. By rearranging this equation, different insights can be extracted depending on which quantity is needed.
  • Original Power Equation: The fundamental formulation \( P = \frac{W}{t} \) tells us how power depends on the work performed and the time taken.
  • Solving for Work (W): By isolating \( W \), as shown earlier, the equation becomes \( W = t \cdot P \). This rearranged form can be used to calculate the energy used or work done given the power and the time.
  • Applications: Understanding this equation is pivotal in fields such as engineering, where it helps in designing machines and systems by optimizing energy use.
Thus, knowing how to manipulate and use the power equation allows for practical applications in various real-world scenarios.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each formula for the quantity given. $$ w=m g \text { for } m $$

A cylindrical silo has a circumference of \(29.5 \mathrm{~m}\). Find its diameter.

Solve each formula for the quantity given. $$ F t=m\left(V_{2}-V_{1}\right) \text { for } V_{1} $$

Find the cross-sectional area of a pipe with outer diameter \(3.50 \mathrm{~cm}\) and inner diameter \(3.20 \mathrm{~cm}\).

Solve each formula for the quantity given. $$ v_{2}=v_{1}+a t \text { for } t $$
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Energy Physics

Read Explanation

Quantum Physics

Read Explanation

Turning Points in Physics

Read Explanation

Work Energy and Power

Read Explanation

Physics of Motion

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.