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Chapter 6: Problem 55

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鈥� 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 sled with mass 12.00 kg moves in a straight line on a frictionless, horizontal surface. At one point in its path, its speed is 4.00 m/s; after it has traveled 2.50 m beyond this point, its speed is 6.00 m/s. Use the work\(-\)energy theorem to find the force acting on the sled, assuming that this force is constant and that it acts in the direction of the sled's motion.

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do 80.0 J of work when you compress the springs 0.200 m from their uncompressed length. (a) What magnitude of force must you apply to hold the platform in this position? (b) How much \(additional\) work must you do to move the platform 0.200 m \(farther\), and what maximum force must you apply?

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?

To stretch a spring 3.00 cm from its unstretched length, 12.0 J of work must be done. (a) What is the force constant of this spring? (b) What magnitude force is needed to stretch the spring 3.00 cm from its unstretched length? (c) How much work must be done to compress this spring 4.00 cm from its unstretched length, and what force is needed to compress it this distance?

The spring of a spring gun has force constant \(k = 400\) N/m and negligible mass. The spring is compressed 6.00 cm, and a ball with mass 0.0300 kg is placed in the horizontal barrel against the compressed spring. The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 6.00 cm long, so the ball leaves the barrel at the same point that it loses contact with the spring. The gun is held so that the barrel is horizontal. (a) Calculate the speed with which the ball leaves the barrel if you can ignore friction. (b) Calculate the speed of the ball as it leaves the barrel if a constant resisting force of 6.00 N acts on the ball as it moves along the barrel. (c) For the situation in part (b), at what position along the barrel does the ball have the greatest speed, and what is that speed? (In this case, the maximum speed does not occur at the end of the barrel.)
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