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

Short Answer

Expert verified
The power required per rider is 742.5 W or approximately 0.995 hp.

Step by step solution

01

Understand the Formula for Power

Power (P) is defined as the rate at which work is done, which can be calculated using the formula:\[P = F \cdot v\]where F is the force and v is the velocity. We know the team must overcome a force of 165 N and maintain a velocity of 9.00 m/s.
02

Calculate Total Power Required

Substitute the given values into the formula:\[P = 165 \, \text{N} \times 9.00 \, \text{m/s}\]Calculate:\[P = 1485 \, \text{W}\]
03

Calculate Power per Rider

Since each rider contributes equally, divide the total power by the number of riders:\[P_{\text{per rider}} = \frac{1485 \, \text{W}}{2} = 742.5 \, \text{W}\]
04

Convert Power to Horsepower

Use the conversion factor where 1 horsepower is approximately 746 watts:\[P_{\text{hp}} = \frac{742.5 \, \text{W}}{746 \, \text{W/hp}} \approx 0.995 \, \text{hp}\]

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Key Concepts

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

Power Calculation
Calculating power involves determining how quickly work is performed. In physics, power is expressed using the formula:
  • \( P = F \cdot v \)
    • This tells us that power (\(P\)) is the product of force (\(F\)) and velocity (\(v\)).
      Force is the push or pull exerted on an object, measured in newtons (\(N\)). Velocity is the speed of the object in a particular direction, measured in \(m/s\) (meters per second).
      By multiplying force and velocity, we determine the rate at which work is done. For our tandem bicycle team, a force of 165 \(N\) is needed to maintain a speed of 9.00 \(m/s\), which calculates power by substituting into the formula.
Force and Motion
To fully grasp how power is related to force and motion, it's important to understand what force does. Force causes an object to move or change its motion.
  • The greater the force exerted, the greater the potential acceleration of the object.
  • In the case of a tandem bicycle, the team must exert a force to counteract resistance from factors like air drag and gravity.
Motion, measured as velocity, is how fast and in which direction the object moves. When force is applied in the direction of motion, work is done, and we can calculate power. For our bicycle team, keeping a consistent velocity of 9.00 m/s requires constant force application to maintain movement and counter usability forces.
Unit Conversion
Unit conversion is vital in physics to move between different measurement systems. Often, results might need to be presented in various units for clarity or to meet specific requirements.
  • Watts (\(W\)) is the standard unit of power in the International System of Units.
  • Horsepower is another unit often used, especially in vehicular power contexts.
To convert power from watts to horsepower, you use the conversion factor where 1 horsepower equals approximately 746 watts. By dividing the power in watts by this figure, you translate the power output to horsepower, as seen in the exercise where the riders’ power was approximately 0.995 horsepower.
Two-Person Bicycle Team
A tandem bicycle consists of two riders working together. The output from each participant combines to propel the bicycle forward, requiring synchronized pedaling efforts.
  • Each rider contributes equally to the work output.
  • Power output is split evenly, meaning that the total calculated power must be divided by two.
The efficiency of a tandem team largely depends on their cooperative ability. In this context, each must work at a rate that allows them to overcome the resistance forces together, with each exerting half of the total power necessary to maintain the desired speed. Understanding how these forces and calculations integrate helps riders maximize efficiency and performance. This exercise highlights how working together effectively can help achieve the goal with less effort individually.

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Most popular questions from this chapter

A 12.0-kg package in a mail-sorting room slides 2.00 m down a chute that is inclined at 53.0\(^\circ\) below the horizontal. The coefficient of kinetic friction between the package and the chute's surface is 0.40. Calculate the work done on the package by (a) friction, (b) gravity, and (c) the normal force. (d) What is the net work done on the package?

A 1.50-kg book is sliding along a rough horizontal surface. At point A it is moving at 3.21 m/s, and at point \(B\) it has slowed to 1.25 m/s. (a) How much work was done on the book between \(A\) and \(B\)? (b) If \(-\)0.750 J of work is done on the book from \(B\) to \(C\), how fast is it moving at point \(C\)? (c) How fast would it be moving at \(C\) if \(+\)0.750 J of work was done on it from \(B\) to \(C\)?

A pump is required to lift 800 kg of water (about 210 gallons) per minute from a well 14.0 m deep and eject it with a speed of 18.0 m/s. (a) How much work is done per minute in lifting the water? (b) How much work is done in giving the water the kinetic energy it has when ejected? (c) What must be the power output of the pump?

A surgeon is using material from a donated heart to repair a patient's damaged aorta and needs to know the elastic characteristics of this aortal material. Tests performed on a 16.0-cm strip of the donated aorta reveal that it stretches 3.75 cm when a 1.50-N pull is exerted on it. (a) What is the force constant of this strip of aortal material? (b) If the maximum distance it will be able to stretch when it replaces the aorta in the damaged heart is 1.14 cm, what is the greatest force it will be able to exert there?

A little red wagon with mass 7.00 kg moves in a straight line on a frictionless horizontal surface. It has an initial speed of 4.00 m/s and then is pushed 3.0 m in the direction of the initial velocity by a force with a magnitude of 10.0 N. (a) Use the work\(-\)energy theorem to calculate the wagon's final speed. (b) Calculate the acceleration produced by the force. Use this acceleration in the kinematic relationships of Chapter 2 to calculate the wagon's final speed. Compare this result to that calculated in part (a).

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