PHYSICS by Cutnell: ch 11 problem 14. A bike and person has a combined weight of
ID: 1575519 • Letter: P
Question
PHYSICS by Cutnell: ch 11 problem 14. A bike and person has a combined weight of 723 N. Suppose the entire weight of the bike and rider is supported equally by two tires. If the gauge pressure in each tire is 7.6X10^5 Pa, what is the area of contact between each tire and ground. My question: Why is the pressure on the ground the same as the tire pressure? Wouldn't you solve for the pressure that the tire exerts on the ground by the equation Gauge pressure equals Tire pressure minus atmospheric pressure?
Explanation / Answer
Since you are given GAUGE pressure you do not have to worry about subtracting atmospheric pressure.
The total weight of the person and the bike is
W = 723 N.
The force F on the two tires are equal since it is supportedlyequally.
Then the force on each of the tire is
F +F = W
2F = 723
F = 361.5 N
The force F = P*A
A = F/P
A = 361.5/7.6*105
A = 4.76*10-4 m2
so,the area of contact =4.76*10-4 m2.
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