/*! 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 149 The car has a mass \(m_{0}\) and... [FREE SOLUTION] | 91影视

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Chapter 15: Problem 149

The car has a mass \(m_{0}\) and is used to tow the smooth chain having a total length \(l\) and a mass per unit of length \(m^{\prime}\). If the chain is originally piled up, determine the tractive force \(F\) that must be supplied by the rear wheels of the car, necessary to maintain a constant speed \(v\) while the chain is being drawn out.

Short Answer

Expert verified
The tractive force that must be supplied by the rear wheels of the car, necessary to maintain a constant speed while the chain is being drawn out, is 0 in this theoretical model. But in reality, the tractive force will not be zero due to resistive forces like air resistance and rolling resistance.

Step by step solution

01

Write down the known quantities

The known quantities are: the mass of the car \(m_{0}\), the length of the chain \(l\), the mass per unit length of the chain \(m^{\prime}\), and the speed of the car \(v\).
02

Write down the Newton's second law

According to Newton's second law, the total force acting on an object is equal to its mass times its acceleration. Here, since the speed of the car is constant, its acceleration is 0. So the total force acting on the car is 0. Note that the tractive force \(F\) is positive, and the friction force is negative because they have opposite directions.
03

Calculate the work done

The work done by the tractive force is equal to the force times the distance. Here, the distance is the length of the chain \(l\). So the work is \(W = F \cdot l\). The work done also equals the change in kinetic energy. Since the speed of the car is constant, the change in kinetic energy is 0. So we have \(W = 0\). Set them equal to each other, we get \(F \cdot l = 0\). This gives \(F = 0\). This result means that no tractive force is needed to maintain the car's constant speed.
04

Explanation of the result

At first glance, it seems strange that no force is needed. But remember, this is a simplified theoretical model. In reality, there are other forces at play such as air resistance and rolling resistance. Those forces are not zero and need to be overcome by the tractive force in order to maintain a constant speed.

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Most popular questions from this chapter

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