/*! 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 53 A tandem (two-person) bicycle te... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 53

A tandem (two-person) bicycle team must overcome a force of 165 \(\mathrm{N}\) to maintain a speed of 9.00 \(\mathrm{m} / \mathrm{s} .\) Find the power required per rider, assuming that each contributes equally. Express your answer in watts and in horsepower.

Short Answer

Expert verified
Each rider requires 742.5 watts or 0.996 horsepower.

Step by step solution

01

Understanding Power and Force

Power is calculated as the work done per unit of time. Since the bicycle is moving at a constant speed, the power can also be calculated using the formula: \[ P = F \times v \] where \( P \) is power, \( F \) is the force, and \( v \) is the velocity. In this problem, \( F = 165 \, \mathrm{N} \) and \( v = 9.00 \, \mathrm{m/s} \).
02

Calculating Total Power

We substitute the given values into the power formula:\[ P = 165 \, \mathrm{N} \times 9.00 \, \mathrm{m/s} = 1485 \, \mathrm{W} \] Thus, the total power required to maintain the speed is 1485 watts.
03

Determining Power per Rider

Since each rider contributes equally, the power required per rider is half of the total power calculated:\[ P_{\text{per rider}} = \frac{1485 \, \mathrm{W}}{2} = 742.5 \, \mathrm{W} \]
04

Converting Watts to Horsepower

To convert the power from watts to horsepower, we use the conversion factor: \( 1 \, \text{horsepower} = 745.7 \, \mathrm{W} \).So, \[ P_{\text{per rider in hp}} = \frac{742.5 \, \mathrm{W}}{745.7} = 0.996 \, \text{horsepower} \]

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.

Power Calculation
Power calculation is fundamental in physics when determining how much work is done over a period of time. When bicyclists pedal, they exert a force to overcome friction and air resistance. Power can thus be calculated by using the formula:
\[ P = F \times v \]
where \( P \) represents power, \( F \) is the force applied, and \( v \) is the velocity at which the object moves. This formula is particularly useful in scenarios like the tandem bicycle example provided.
The force is given as 165 N, and the velocity is 9.00 m/s, so when multiplying these two numbers, we find the total power needed to maintain the bicycle's speed. Always remember, using this formula requires understanding that the direction of force and motion are the same.
Force and Velocity
Force and velocity are two integral concepts in understanding motion. Force, measured in Newtons (N), is any interaction that changes the motion of an object.
For the tandem bicycle, maintaining a constant velocity of 9.00 \( \mathrm{m/s} \) requires overcoming a steady force of 165 \( \mathrm{N} \).
Velocity, on the other hand, is the speed of an object in a particular direction. It tells us not just how fast something is moving, but also where it is headed. The constant velocity means the bicycle's speed does not change, indicating that the power used is solely to counteract resistive forces, such as friction and air resistance.
In practical scenarios, analyzing both force and velocity helps in understanding the energy dynamics involved in movement.
Unit Conversion
Unit conversion is a crucial skill in solving physics problems, as it allows for the translation between different measures used in specific contexts.
In the tandem bicycle example, after determining the power required per rider to be 742.5 watts, it's insightful to convert this power into other units like horsepower for a clearer understanding, especially in regions where horsepower is a more familiar unit.
To convert watts to horsepower, the conversion factor used is:
  • 1 horsepower = 745.7 watts
Thus, converting 742.5 watts gives approximately 0.996 horsepower per rider.
Such conversions are helpful for making different numerical values intuitive to different audiences and for ensuring the compatibility of numbers across varied industrial and scientific standards.

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

A 30.0 -kg crate is initially moving with a velocity that has magnitude 3.90 \(\mathrm{m} / \mathrm{s}\) in a direction \(37.0^{\circ}\) west of north. How much work must be done on the crate to change its velocity to 5.62 \(\mathrm{m} / \mathrm{s}\) in a direction \(63.0^{\circ}\) south of east?

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 \(\mathrm{W}\) . 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 \(\mathrm{W}\) . If she expends a total of \(1.1 \times 10^{7} \mathrm{J}\) of energy in a 24 -hour day, how much of the day did she spend walking?

A 2.50 -kg textbook is forced against a horizontal spring of negligible mass and force constant \(250 \mathrm{N} / \mathrm{m},\) compressing the spring a distance of 0.250 \(\mathrm{m} .\) When released, the textbook slides on a horizontal tabletop with coefficient of kinetic friction \(\mu_{\mathrm{k}}=0.30 .\) Use the work-energy theorem to find how far the textbook moves from its initial position before coming to rest.

A 12 -pack of Omni-Cola (mass 4.30 \(\mathrm{kg}\) ) is initially at rest on a horizontal floor. It is then pushed in a straight line for 1.20 \(\mathrm{m}\) by a trained dog that exerts a horizontal force with magnitude 36.0 \(\mathrm{N}\) . Use the work-energy theorem to find the final speed of the 12-pack if (a) there is no friction between the 12 -pack and the floor, and (b) the coefficient of kinetic friction between the 12 -pack and the floor is \(0.30 .\)

A typical flying insect applies an average force equal to twice its weight during each downward stroke while hovering. Take the mass of the insect to be \(10 \mathrm{g},\) and assume the wings move an average downward distance of 1.0 \(\mathrm{cm}\) during each stroke. Assuming 100 downward strokes per second, estimate the average power output of the insect.
See all solutions

Recommended explanations on Physics Textbooks

Quantum Physics

Read Explanation

Work Energy and Power

Read Explanation

Electrostatics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Electricity

Read Explanation

Dynamics

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.