Solving 700N + 98N Weight Distribution Problem

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SUMMARY

The problem involves calculating the area of contact between each tire of a mountain bike and the ground, given a total weight of 798 N (700 N rider + 98 N bike) and a gauge pressure of 7.55 x 105 Pa in each tire. The formula used is P = F/A, where P is pressure, F is force, and A is area. The correct calculation for the area of contact for each tire is A = F/P, leading to an area of 1.06 x 10-3 m2 for the total weight. However, since the problem specifies "each tire," the force applied per tire is 399 N, resulting in an area of 5.28 x 10-4 m2 per tire.

PREREQUISITES
  • Understanding of basic physics concepts, specifically pressure and force.
  • Familiarity with the equation P = F/A.
  • Knowledge of unit conversions, particularly between Newtons and Pascals.
  • Ability to perform calculations involving scientific notation.
NEXT STEPS
  • Review the principles of pressure in fluid mechanics.
  • Learn about the implications of tire pressure on vehicle performance.
  • Explore the effects of weight distribution on tire contact area.
  • Investigate common errors in applying physics formulas in real-world scenarios.
USEFUL FOR

Students studying physics, engineers working on vehicle dynamics, and anyone interested in understanding weight distribution and pressure calculations in practical applications.

BoogieL80
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I'm working on the following problem:

<i> A person who weighs 700 N is riding a 98 N mountain bike. Suppose the entire weight of the rider and bike is supported equally by the two tires. If the gauge pressure in each tire is 7.55 105 Pa, what is the area of contact between each tire and the ground?<i>

The equation that I'm trying to incorporate is P = F/A where P equals pressure, F equals perpendicular force and A equals area. So I figured that since the tires are supporting the entire weight of the bike and man, the combined force that would be used in this problem would be 798N. So I rearranged the formula to equal A = F/P. So I said 798N / 7.55E5 N/m^2 would equal 1.06E-3m^2. Of course webassign says that my answer is incorrect. Any constructive help would be appreciated.
 
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"each tire and the ground" , not "both tires".
 

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