Solving 700N + 98N Weight Distribution Problem

[BoogieL80]

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.

 

[lightgrav]

"each tire and the ground" , not "both tires".

 

[quicknote]

Your approach to solving this problem is correct. It is important to remember that the gauge pressure in each tire is equal to the total weight supported by the tire divided by the area of contact. In this case, the total weight supported by both tires is 798N, so dividing that by the given gauge pressure of 7.55E5 N/m^2 gives an area of 1.06E-3m^2 for each tire.

One possible reason for the incorrect answer could be a rounding error. Make sure you are using the exact values given in the problem and not rounded values. Another possible reason could be a unit conversion error. Double check that all units are consistent (i.e. using meters for length, Newtons for force, etc.).

Overall, your approach to solving this problem is correct and it is important to carefully check for any errors in calculation or unit conversions.