Chapter 6: Problem 58
Calculate A kayaker paddles with a power output of \(50.0 \mathrm{~W}\) to maintain a steady speed of \(1.50 \mathrm{~m} / \mathrm{s}\). Find the force exerted by the kayaker.
Short Answer
Expert verified
The force exerted by the kayaker is 33.3 N.
Step by step solution
01
Understand the Power Formula
The power output of the kayaker is given by the formula: \[ P = F \times v \]where \( P \) is the power, \( F \) is the force, and \( v \) is the velocity.
02
Rearrange the Formula to Solve for Force
We need to rearrange the formula to find the force \( F \). This can be done by dividing both sides by the velocity \( v \):\[ F = \frac{P}{v} \]
03
Substitute the Given Values
Substitute the given values into the rearranged formula. We have the power \( P = 50.0 \mathrm{~W} \) and the velocity \( v = 1.50 \mathrm{~m/s} \):\[ F = \frac{50.0 \mathrm{~W}}{1.50 \mathrm{~m/s}} \]
04
Calculate the Force
Perform the division to calculate the force:\[ F = \frac{50.0}{1.50} = 33.3 \mathrm{~N} \]
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 Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Power Formula
In physics, power is a measure of how much work is done by a force within a certain time frame. The Power Formula helps us to connect power, force, and velocity through a simple equation:
- Power ( P ) is equal to force ( F ) times velocity ( v ), represented as: \[ P = F \times v \]
Force Calculation
Force is a critical concept in physics, representing the interaction that changes the motion of an object. In our scenario, the kayaker's purpose is to understand what force is needed to maintain a steady speed.To calculate this, we use the rearranged Power Formula:
- \[ F = \frac{P}{v} \]
Velocity
Velocity refers to the speed of an object in a specified direction. It is a vector quantity, meaning it conveys both how fast something is moving and its direction. For the kayaker, velocity is the steady speed of 1.50 meters per second.
Velocity is an integral part of the Power Formula because it dictates how much power will be transformed into consistent movement (force). Understanding the concept of velocity in physics helps students grasp the dynamics involved in motion.
Essentially, if you know the force applied and the resulting velocity, you can determine the efficiency of the action performed, like the kayaker's paddling in our example.
Essentially, if you know the force applied and the resulting velocity, you can determine the efficiency of the action performed, like the kayaker's paddling in our example.
Kayak Physics
Kayak Physics revolves around understanding how physical principles like power, velocity, and force interact when paddling. A kayaker uses energy, expressed as power, to propel the kayak forward.
The case of the kayaking problem involves:
- Applying force through paddling;
- Maintaining a constant velocity, requiring enough force to counteract water resistance;
- Measuring how much power is necessary to achieve this motion.