   Chapter 11, Problem 65AP

Chapter
Section
Textbook Problem

An automobile has a mass of 1 500 kg, and its aluminum brakes have an overall mass of 6.00 kg. (a) Assuming all the internal energy transformed by friction when the car stops is deposited in the brakes and neglecting energy transfer, how many times could the car be braked to rest starting from 25.0 m/s before the brakes would begin to melt? (Assume an initial temperature of 20.0°C.) (b) Identify some effects that are neglected in part (a) but are likely to be important in a more realistic assessment of the temperature increase of the brakes.

(a)

To determine
The number of times could the car be braked to rest before the brakes begin to melt.

Explanation

Section1:

To determine: To determine the energy required to raise the temperature to the melting point.

Answer: The energy required is 3.46×106J

Explanation:

Given Info: Mass is 6.00 kg.

Formula to calculate the energy required to increase the temperature to the melting point is,

Q=mc(TfTi)

• Q is energy required to raise the temperature,
• m is mass of the brakes,
• c is the specific heat of the aluminum,
• Ti is the initial temperature of the brakes,
• Tf is the final temperature of the brakes,

The melting point temperature of the aluminum is 660°C .

Substitute 6.00 kg for m, 900J/kg°C for c, 20.0°C for Ti , and 660°C for Tf to find Q.

Q=(6.00kg)(900J/kg°C)(660.0°C20.0°C)=3456000J3.46×106J

Thus, to find energy required to melt is 3.46×106J

Section 2:

To determine: The internal energy added to the brakes on every stop.

Answer: The internal energy added is 4.69×105J

Explanation:

Given Info: mass of the car is 1500 kg and speed of the car is 25

(b)

To determine
The effects that are neglected but are likely to be important in realistic case.

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