Estimating Car Weight from Tire Pressure

[A_Munk3y]

Homework Statement

The gauge pressure in each of the four tires of an automobile is 240 kPa. If each tire has a "footprint" of 220 cm2, estimate the mass of the car.

Homework Equations

F= ma ?
W1 = P1A1 ?

The Attempt at a Solution

total weight = W1+W2+W3+W4 = P(A1+A2+A3+A4) <------- since all tires have same surface area and same pressure.

240pka(2.2m^3 x 4) = 2112 kg??

dont think i did that right

 

[kuruman]

You are confusing gauge pressure and absolute pressure. Look up the definition of gauge pressure.

 

[tiny-tim]

Welcome to PF!

Hi A_Munk3y! Welcome to PF!

(try using the X² tag just above the Reply box )

… If each tire has a "footprint" of 220 cm2, estimate the mass of the car.
…
240pka(2.2m^3 x 4) = 2112 kg??

dont think i did that right

erm … 220 cm² = 220 m²/?

 

[A_Munk3y]

You are confusing gauge pressure and absolute pressure. Look up the definition of gauge pressure.

P = F/A ---- is that it?

Hi A_Munk3y! Welcome to PF!

(try using the X² tag just above the Reply box )erm … 220 cm² = 220 m²/?

its 220 cm² = 0.022m² isn't it

ok let me try this again :P

 

[A_Munk3y]

attempt 2
Pressure = Force/Area = Mg/Area = Pa
kPa= = 1000 pa

240Kpa x 1000 pa/kpa = 240,000 pa240,000 pa x 4 tires = 9.8 x m/ 880cm²(1/100)²

960,000 = 9.8m/0.088m²

or does the pressure remain 240000 (you don't add it?)
so its 240,000 = 9.8m/.088m²
m= 2155.1 kg?

 

[tiny-tim]

Hi A_Munk3y!

(just got up :zzz: …)

240pka(2.2m^3 x 4) = 2112 kg??

hmm … you're really not good at units, are you?

how about kN instead of kg?
​

(that slipped past me last night! )

 

[A_Munk3y]

Hi A_Munk3y!

(just got up :zzz: …)hmm … you're really not good at units, are you?

how about kN instead of kg?
​

(that slipped past me last night! )

nope, i completely suck at units! >:(

so you mean 240,000 = 9.8m/.088m² is still not right ?

 

[tiny-tim]

ah, you did put the 9.8 in in post #5 …

yes, m = 240 x 88 / 9.8 = 2155 kg looks right (and I think 2000 kg is a fairly average car weight in the USA).

 

[A_Munk3y]

ok! w000t!
thank you so much :)