What Air Resistance Force Does a Car Face at 65mi/hr?

[afg_91320]

Homework Statement

The force felt on an auto due to its movement through still air varies approx. as the square of the car's speed. (the force is also known as air resistance) assume the force varies exactly as the square of the speed. around town at 30mi/hr a car experiences an air resistance force of 100lbs. what size force would you expect the car to face while traveling at 65mi/hr?

Homework Equations

car travels at 65mi/hr
at 30 mi/hr its air resistance force is 100 lbs.

The Attempt at a Solution

ive been looking at this problem for the last hour, and i don't know what good the weight will help me with. I've tried conversion but it gets me nowhere. i don't want the answer, i just want to know how should i approach the problem, and how do i start!

 

[tiny-tim]

Welcome to PF!

The force felt on an auto due to its movement through still air varies approx. as the square of the car's speed. (the force is also known as air resistance) assume the force varies exactly as the square of the speed. around town at 30mi/hr a car experiences an air resistance force of 100lbs. what size force would you expect the car to face while traveling at 65mi/hr?

Hi afg_91320! Welcome to PF!

This is a dimensions problem.

So write an equation with a "proportional" sign in the middle, instead of an equals sign …

Force ~ (a function of v) …

multiply v by 65/30, and what happens?

 

[afg_91320]

ok-here is what i got:

65/30 = 100/v <-- equal sign means propotional
65v=3000
v=3000/65
v=46.153
but the answer in the back is 4.7 x 10^2 lb.
what did i do wrong?? :(

 

[mgb_phys]

Remember they said the drag was proportional to v²

 

[afg_91320]

so that would make it:
65/30 = 100/v^2
65v^2=3000
v^2=46.153
v=6.8 <--that is incorrect.

 

[mgb_phys]

drag is prop to v²

so drag₁/drag₂ =v₁²/v₂²

 

[afg_91320]

^^how does that help me?

this is what i did:
v1^2/v2^2=65/30
(100)^2/v2^2=65/30
65v^2=300,000
v^2=4615.384
but its still wrong!

can anyone show me the correct steps on how to do it! i have 3 more prblms similar to this! help me with this one, and ill be able to the others correctly!

 

[mgb_phys]

First make an estimate of the answer - so you know if your calculator got it right.
65mph is a little more than twice 30mph, so since force goes up by 4 if speed goes up by 2 we expect a force of around 400-500 lb

Now d1/2 = v1^2/v2^2
d1/100 = 65^2/30^2
d1 = 100 * (65^2/30^2) = 100 * (4225/900) = 100 * 4.69 = 470 lbs

 

[afg_91320]

oohhh! i got it! i was just doing my math all wrong! thanks!