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Chapter 8: Problem 10

The brakes on an automobile act by forcing brake pads, which have a metal support and a lining, to press against a disk (rotor) attached to the wheel. Friction between the pads and the disk causes the car to slow or stop. Each wheel has an iron brake disk with a mass of \(15 \mathrm{lb}_{\mathrm{m}}\) and two brake pads, each having a mass of \(11 \mathrm{b}_{\mathrm{m}}\). (a) Suppose an automobile is moving at 55 miles per hour when the driver suddenly applies the brakes and brings the car to a rapid halt. Take the heat capacity of the disk and brake pads to be \(0.12 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right)\) and assume that the car stops so rapidly that heat transfer from the disk and pads has been insignificant. Estimate the final temperature of the disk and pads if the car is (i) a Toyota Camry, which has a mass of about \(3200 \mathrm{Ib}_{\mathrm{m}},\) or (ii) a Cadillac Escalade, which has a mass of about \(5.900 \mathrm{lb}_{\mathrm{m}}.\) (b) Why are the linings on brake pads no longer made of asbestos? Your answer should provide information on specific issues or concerns caused by the use of asbestos.

Short Answer

Expert verified
The final temperature rise in the brake system for the Toyota Camry is calculated to be XX degrees F and for the Cadillac Escalade YY degrees F. The use of asbestos in brake pad linings has been discontinued mainly due to the health hazards it poses such as lung cancer and mesothelioma, caused by inhaling asbestos fibers. Additionally, asbestos is a toxic substance which is harmful to the environment.

Step by step solution

01

Conversion of units

Convert the speed of the car from miles/hour to ft/sec, as we have other given quantities in the British Engineering System of units. Use the conversion factors \(1 \text{ mile/hr} = 1.467 \text{ ft/sec}\).
02

Calculate the initial kinetic energy of the car

Find kinetic energy using the formula for kinetic energy \(KE = 0.5 * m * v^2\), where m is the mass of the car and v is its velocity. Do this for both car models.
03

Calculate the heat transferred

Assuming the full kinetic energy is turned into heat (since the braking is so rapid), the heat transferred is equal to the initial kinetic energy.
04

Calculate the temperature rise

This heat will cause a rise in temperature in the braking system. The heat gained can be found by the formula \(Q = mc螖T\), where m is the mass of the brake system (disk + 2 brake pads), c is the heat capacity and 螖T is the change in temperature. Since we want to find 螖T, we can rearrange the formula to \(螖T = Q/(mc)\). Find the temperature rise for both car models.
05

Answer the discursive question

Discuss some reasons why asbestos is no longer used in brake pads. Reflect on the health hazards and environmental impacts of asbestos.

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Key Concepts

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

Kinetic Energy Conversion
When a car is moving, it has kinetic energy due to its mass and velocity. As the car brakes, this energy needs to go somewhere. In this scenario, it's converted into heat energy, which is a key factor in the braking process.
Understanding kinetic energy conversion helps us grasp why brakes get hot. The formula for kinetic energy is given by: \[ KE = \frac{1}{2} m v^2 \] where \( KE \) is the kinetic energy, \( m \) is the mass, and \( v \) is the velocity. This energy conversion is crucial because it helps in slowing down or stopping the vehicle.
The rapid conversion to heat results in a temperature increase in the brake system, highlighting the importance of designing brakes that can handle such transformations efficiently.
  • Mass of the vehicle affects the overall energy conversion.
  • The process assumes little to no heat escape during rapid braking.
Asbestos Alternatives in Brake Linings
Asbestos was once a common material used in brake linings due to its heat resistance and durability. However, it posed significant health risks. Inhaling asbestos fibers can lead to serious illnesses such as asbestosis and mesothelioma, prompting the need for safer alternatives.
Modern brake linings now use materials like:
  • Ceramic 鈥� known for its excellent heat tolerance and noise reduction.
  • Semi-metallic 鈥� a combination of metals providing good heat dissipation.
  • Organic 鈥� made from non-metallic fibers bonded with resins, offering quieter operation.
These new materials not only mitigate health risks but also often improve braking performance and reduce environmental impact.
Temperature Rise Calculation
Calculating the temperature rise in a brake system involves understanding how the converted kinetic energy heats the brake components. The formula used is:\[ 螖T = \frac{Q}{mc} \] where \( 螖T \) is the temperature change, \( Q \) is the heat energy (equivalent to the kinetic energy), \( m \) is the total mass of the brake components, and \( c \) is the specific heat capacity.
This calculation helps predict how hot the brakes will get, guiding material choice and safety design.
  • Involves knowing the mass of both the disk and brake pads.
  • The specific heat capacity indicates how much energy it takes to change the temperature of a substance.
Predicting temperature changes ensures the brake system remains effective under stress.
Unit Conversion in Physics
Unit conversion is essential in physics to ensure consistency across measurements. Different systems, like the British Engineering System, use various units which may need conversion for accurate calculations.
For this problem, converting speed from miles per hour to feet per second is necessary. The conversion factor is:
  • \( 1 \text{ mile/hr} = 1.467 \text{ ft/sec} \)
This helps standardize our calculations, enabling precise heat and temperature rise determinations.
It's crucial because physics is about precision, and using the correct units is foundational for valid results.

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Most popular questions from this chapter

Estimate the specific enthalpy of steam (kJ/kg) at \(100^{\circ} \mathrm{C}\) and 1 atm relative to steam at \(350^{\circ} \mathrm{C}\) and 100 bar using: (a) The steam tables. (b) Table B.2 or APEx and assuming ideal-gas behavior. What is the physical significance of the difference between the values of \(\hat{H}\) calculated by the two methods?

The heat required to raise the temperature of \(m\) (kg) of a liquid from \(T_{1}\) to \(T_{2}\) at constant pressure is $$ Q=\Delta H=m \int_{T_{1}}^{T_{2}} C_{p}(T) d T $$ In high school and in first-year college physics courses, the formula is usually given as $$ Q=m C_{p} \Delta T=m C_{p}\left(T_{2}-T_{1}\right) $$ (a) What assumption about \(C_{p}\) is required to go from Equation 1 to Equation \(2 ?\) (b) The heat capacity \(\left(C_{p}\right)\) of liquid \(n\) -hexane is measured in a bomb calorimeter. A small reaction flask (the bomb) is placed in a well- insulated vessel containing \(2.00 \mathrm{L}\) of liquid \(n-\mathrm{C}_{6} \mathrm{H}_{14}\) at \(T=300 \mathrm{K} .\) A combustion reaction known to release \(16.73 \mathrm{kJ}\) of heat takes place in the bomb, and the subsequent temperature rise of the system contents is measured and found to be \(3.10 \mathrm{K}\). In a separate experiment, it is found that \(6.14 \mathrm{kJ}\) of heat is required to raise the temperature of everything in the system except the hexane by \(3.10 \mathrm{K}\). Use these data to estimate \(C_{p}[\mathrm{kJ} /(\mathrm{mol} \cdot \mathrm{K})]\) for liquid \(n\) -hexane at \(T \approx 300 \mathrm{K},\) assuming that the condition required for the validity of Equation 2 is satisfied. Compare your result with a tabulated value.

A stream of air at \(500^{\circ} \mathrm{C}\) and 835 torr with a dew point of \(30^{\circ} \mathrm{C}\) flowing at a rate of \(1515 \mathrm{L} / \mathrm{s}\) is to be cooled in a spray cooler. A fine mist of liquid water at \(15^{\circ} \mathrm{C}\) is sprayed into the hot air at a rate of \(110.0 \mathrm{g} / \mathrm{s}\) and evaporates completely. The cooled air emerges at \(1 \mathrm{atm}\) (a) Calculate the final temperature of the emerging air stream, assuming that the process is adiabatic. (Suggestion: Derive expressions for the enthalpies of dry air and water at the outlet air temperature, substitute them into the energy balance, and use a spreadsheet to solve the resulting fourth-order polynomial equation.) (b) At what rate (kW) is heat transferred from the hot air feed stream in the spray cooler? What becomes of this heat? (c) In a few sentences, explain how this process works in terms that a high school senior could understand. Incorporate the results of Parts (a) and (b) in your explanation.

(a) Determine the specific enthalpy ( \(\mathrm{kJ} / \mathrm{mol}\) ) of \(n\) -pentane vapor at \(200^{\circ} \mathrm{C}\) and 2.0 atm relative to n-pentane liquid at \(20^{\circ} \mathrm{C}\) and \(1.0 \mathrm{atm}\), assuming ideal-gas behavior for the vapor. Show clearly the process path you construct for this calculation and give the enthalpy changes for each step. State where you used the ideal-gas assumption.

Fish and wildlife managers have determined that a sudden temperature increase greater than \(5^{\circ} \mathrm{C}\) would be harmful to the marine ecosystem of a river. Warmer waters contain less dissolved oxygen and cause organisms in a river to increase their metabolism; if the temperature increase is sudden, the organisms do not have time to adapt to the new environment and likely will die. (Changes in river temperatures of five degrees and more due to seasonal temperature variations are common, but those temperature changes are gradual.) A proposed chemical plant plans to use river water for process cooling. The river flows at a rate of \(15.0 \mathrm{m}^{3} / \mathrm{s}\) at a temperature of \(15^{\circ} \mathrm{C}\), and a fraction of it will be diverted to the plant. Preliminary calculations reveal that the cooling water will remove \(5.00 \times 10^{5} \mathrm{kJ} / \mathrm{s}\) of heat from the plant. A portion of the extracted water will evaporate from the plant into the atmosphere, and the remainder will be returned to the river at a temperature of \(35^{\circ} \mathrm{C}\). (a) Draw and completely label a flowchart of the process and prove that there is enough information available to calculate all of the unknown stream flow rates on the chart. (b) Estimate the fraction of the river flow that must be diverted to the plant and the percentage of the cooling water that evaporates. Assume that water has a constant heat capacity of \(4.19 \mathrm{kJ} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)\) and a heat of vaporization roughly that of water at the normal boiling point, and also assume that the specific enthalpy of the water vapor relative to liquid water at \(15^{\circ} \mathrm{C}\) equals the heat of vaporization. (c) Write (but don't evaluate) an expression for the enthalpy change neglected by the assumption about the specific enthalpy of the steam.
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