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Chapter 7: Problem 66

\(\bullet\) 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.

Short Answer

Expert verified
Each rider needs 742.5 W of power.

Step by step solution

01

Understand the Concept of Power

Power is the rate at which work is done or energy is transferred. It is calculated using the formula: \( P = F \times v \), where \( P \) is power, \( F \) is the force applied, and \( v \) is the velocity at which the force is applied.
02

Plug Values into Power Formula

Given that the force \( F = 165 \, \mathrm{N} \) and velocity \( v = 9.00 \, \mathrm{m/s} \), we plug these values into the power formula: \[ P = F \times v = 165 \, \mathrm{N} \times 9.00 \, \mathrm{m/s} \].
03

Calculate the Total Power

Perform the multiplication to find the total power required: \[ P = 165 \, \mathrm{N} \times 9.00 \, \mathrm{m/s} = 1485 \, \mathrm{W} \].
04

Distribute Power Equally Between Two Riders

Since the power is to be shared equally between the two riders, divide the total power by 2 to find the power needed per rider: \[ P_{\text{per rider}} = \frac{1485 \, \mathrm{W}}{2} = 742.5 \, \mathrm{W} \].

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Key Concepts

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

Understanding Force
Force is a push or pull upon an object resulting from its interaction with another object. It is a vector quantity, which means it has both magnitude and direction.
In our exercise, the tandem bicycle team needs to overcome a force of 165 Newtons to maintain their speed. This force may arise due to air resistance, friction with the ground, or any other opposing force.
Key points about force:
  • Measured in Newtons (N).
  • Affects the motion of objects according to Newton's laws.
  • Critical in determining how much work or power is needed to move something.
In the context of our problem, understanding the force helps us determine how much effort the cyclists need to apply to maintain their velocity.
Velocity Explained
Velocity is a vector quantity that refers to the rate at which an object changes its position. It combines both the speed and the direction of an object's movement.
For the tandem bicycle, the velocity is given as 9.00 meters per second (m/s). This is the constant speed the bike travels to counteract the force opposing it.
Key ideas about velocity include:
  • Velocity tells us how fast something is moving and in which direction.
  • Measured in meters per second (m/s) in the SI system.
  • Essential for calculating other quantities like momentum and power.
In solving the problem, knowing the velocity is crucial as it directly impacts how much power the riders need to maintain their speed.
The Concept of Work
Work is done when a force causes an object to move. In physics, work is calculated as the product of the force applied to an object and the distance over which that force is applied, aligned with the direction of the force.
However, in the context of power calculation, work is considered in terms of how quickly it is done, which relates to power. Some aspects about work:
  • Measured in joules (J) in the SI system.
  • Work happens when the force causes movement.
  • Work takes into account the direction of force and movement.
Though not explicitly calculated in this problem, understanding work helps connect force, distance, and energy transfer, facilitating problem-solving in physics.
Energy Transfer and Power
Energy transfer occurs when energy moves from one place, object, or form to another. Power measures how fast this transfer happens.
For our tandem bicycle team, the work done by the cyclists through pedaling transfers energy to overcome resistive forces at a rate described by power.Power calculation in our problem involved:
  • Multiplying force by velocity, \( P = F \times v \).
  • Indicating the rate of energy transfer necessary to maintain motion.
  • Expressed in watts (W), with 1 watt equating to 1 joule per second.
Understanding energy transfer and power is fundamental for problems like ours, where determining how much energy is needed over time is crucial for maintaining motion.

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Most popular questions from this chapter

\(\bullet\) \(\bullet\) An elevator has mass \(600 \mathrm{kg},\) not including passengers. The elevator is designed to ascend, at constant speed, a vertical distance of 20.0 \(\mathrm{m}\) (five floors) in \(16.0 \mathrm{s},\) and it is driven by a motor that can provide up to 40 hp to the elevator. What is the maximum number of passengers that can ride in the elevator? Assume that an average passenger has mass 65.0 \(\mathrm{kg}\) .

\(\cdot\) It takes 4.186 \(\mathrm{J}\) of energy to raise the temperature of 1.0 \(\mathrm{g}\) of water by \(1.0^{\circ} \mathrm{C}\) (a) How fast would a 2.0 \(\mathrm{g}\) cricket have to jump to have that much kinetic energy? (b) How fast would a 4.0 \(\mathrm{g}\) cricket have to jump to have the same amount of kinetic energy?

\(\cdot\) A 0.145 kg baseball leaves a pitcher's hand at a speed of 32.0 \(\mathrm{m} / \mathrm{s} .\) If air drag is negligible, how much work has the pitcher done on the ball by throwing it?

\(\bullet\) \(\bullet\) A slingshot obeying Hooke's law is used to launch pebbles vertically into the air. You observe that if you pull a pebble back 20.0 \(\mathrm{cm}\) against the elastic band, the pebble goes 6.0 \(\mathrm{m}\) high. (a) Assuming that air drag is negligible, how high will the peb- ble go if you pull it back 40.0 \(\mathrm{cm}\) instead? (b) How far must you pull it back so it will reach 12.0 \(\mathrm{m}\) (c) If you pull a pebble that is twice as heavy back \(20.0 \mathrm{cm},\) how high will it go?

\(\bullet\) \(\bullet\) \(\bullet\) Automotive power. A truck engine transmits 28.0 \(\mathrm{kW}\) \((37.5 \mathrm{hp})\) to the driving wheels when the truck is traveling at a constant velocity of magnitude 60.0 \(\mathrm{km} / \mathrm{h}(37.7 \mathrm{mi} / \mathrm{h})\) on a level road. (a) What is the resisting force acting on the on a level road. (a) What is the resisting force acting on the truck? (b) Assume that 65\(\%\) of the resisting force is due to rolling friction and the remainder is due to air resistance. If the force of rolling friction is independent of speed, and the force of air resistance is proportional to the square of the speed, what power will drive the truck at 30.0 \(\mathrm{km} / \mathrm{h} ?\) At 120.0 \(\mathrm{km} / \mathrm{h} ?\) Give your answers in kilowatts and in horse- power.
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