Problem 18.60 Suppose you increase the gauge pressure in the tires of your car b

ID: 1421489 • Letter: P

Question

Problem 18.60

Suppose you increase the gauge pressure in the tires of your car by 10 % .

Part A

How does the area of the tires in contact with a level road change?

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Part B

If the gauge pressure in the tires is 2.0 atm before you increase it, by what percentage does the actual tire pressure change?

Problem 18.60

Suppose you increase the gauge pressure in the tires of your car by 10 % .

Part A

How does the area of the tires in contact with a level road change?

A2A1 =

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Part B

If the gauge pressure in the tires is 2.0 atm before you increase it, by what percentage does the actual tire pressure change?

= %

part a:

gauge pressure =pressure difference between inside the tire with pressure of atmosphere

=net force applied on the tire/area

so assuming force to remain constant,

gauge pressure*area=constant

if initial gauge pressure was P1 and area was A1

now gauge pressure=P1*(1+0.1)=1.1*P1

then new area=A2=P1*A1/(1.1*P1)=0.9091*A1

==>A2/A1=0.9091

part B:

initial gauge pressure=2 atm

then actual pressure inside tire=2 atm+1 atm=3 atm

new gauge pressure=2*1.1=2.2 atm

then actual pressure in tire=2.2+1=3.2 atm

so percentage change in actual pressure=(3.2-3)*100/3=6.67%