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To maintain a constant speed, the force provided by a car's engine must equal the drag force plus the force of friction of the road (the rolling resistance). (a) What are the magnitudes of drag forces at 70 km/h and 100 km/h for a Toyota Camry? (Drag area is $0.70 \textrm{ m}^2$) (b) What is the magnitude of drag force at 70 km/h and 100 km/h for a Hummer H2? (Drag area is $2.44 \textrm{ m}^2$) Assume all values are accurate to three significant digits.
Question by OpenStax is licensed under CC BY 4.0.

a) $44.8 \textrm{ N}$, $91.5 \textrm{ N}$

b) $357 \textrm{ N}$, $729 \textrm{ N}$

Solution Video

OpenStax College Physics Solution, Chapter 5, Problem 23 (Problems & Exercises) (1:47)

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Video Transcript

This is College Physics Answers with Shaun Dychko. The first thing we do is convert the speeds that are given into meters per second because those are the units we’ll need to plug into our formula for the drag force. So 70 kilometers per hour times one hour for every 3600 seconds and then times by 1000 meters for every kilometer gives us units of meters per second, and this works out to 19.444 meters per second. This is equivalent to dividing by 3.6, so in the next step I just go 100 divided by 3.6, gives us 27.778 meters per second. So drag force is one half times drag coefficient times the density of the fluid times the cross sectional area of the object multiplied by speed squared. For a Toyota Camry, we have a drag coefficient of 0.28 and multiplied by the density of air times the cross sectional area of 0.7 meters squared that the question gives us, multiplied by 19.444 meters per second and square that speed, this gives us 44.8 Newtons is the drag force for Toyota Camry going 70 kilometers an hour. Then going at 100 kilometers an hour, all the numbers are the same except the speed is now 27.778 meters per second, and this gives 91.5 Newtons drag force. For a Hummer, the drag coefficient is 0.64 and cross sectional area is 2.44 meters squared. Otherwise, the numbers are the same as the Toyota Camry but the results are dramatically different. We have 357 Newtons is the drag force at 70 kilometers an hour. Going 100 kilometers an hour or 27.778 meters per second, we have a drag force of 729 Newtons.

Comments

Submitted by C-Mak Breezy on Wed, 11/27/2019 - 04:35

Why are you using 1.21kg/m^3? Table 11.1 in the book says 1.29kg/m^3 for air density. Also, why wouldn't we add the "x10^-3? Thanks

Submitted by ShaunDychko on Wed, 11/27/2019 - 10:04

Hello, thanks for the question. The "x10-3" isn't needed since, if you look closely at the column heading of Table 11.1 is says the units are "x10^3 kg/m^3". "x10-3 x 10^3" ends up making "1". The table just standardized the units to something that makes sense to the most materials (liquids and solids), and chose not to change the units for gases since making that change might be its own source of confusion.
As for 1.21 kg/m^3 instead of 1.29 kg/m^3, on page 203, equation 5.20, the text gives an example where they assume an air density of 1.21 kg/m^3. That's probably where I got it from. In any case, air density varies significantly with temperature -- https://en.wikipedia.org/wiki/Density_of_air.
All the best,
Shaun

In reply to by C-Mak Breezy