A person who weighs 655 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 8.70 X 10^5 Pa, what is the area of contact between each tire and the ground?

P=F/A

A=F/P

A=655N/ 8.70 x 10^5

A= 0.000753

The system is saying this answer is incorrect. Was I suppose to multiply the answer by 2?

You have to add the weight of the bike (98 N) and the weight of the rider (655 N) and divide by two (the number of tires). That is the force that each tire supports.

Thanks!!!!

A= (655N + 98N)/(8.70 x 10^5)

A= 0.0015 m^2

You're welcome! I'm glad I could help. And yes, you are correct. Since the weight of the rider and the bike is supported equally by the two tires, you should multiply the force by 2. So the area of contact between each tire and the ground would be:

A = (655 N + 98 N) / (8.70 × 10^5 Pa)

A = 753 N / (8.70 × 10^5 Pa)

A ≈ 0.000866 m^2

Just remember to make sure that your units are consistent throughout the calculations.

Yes, you're correct! I apologize for the confusion in my initial response. To find the force that each tire supports, you need to add the weight of the bike and the weight of the rider, and then divide by 2.

So, the total weight supported by each tire is (98 N + 655 N) / 2 = 376.5 N.

Then, you can use the formula A = F/P to find the area of contact between each tire and the ground. Plugging in the values, we get:

A = 376.5 N / (8.70 x 10^5 Pa)

Calculating the area, we get:

A ≈ 0.0004327 m^2 (rounded to 4 significant figures)

Therefore, the area of contact between each tire and the ground is approximately 0.0004327 square meters.

You're on the right track! To find the area of contact between each tire and the ground, you need to calculate the force that each tire supports and then divide it by the gauge pressure in each tire.

Firstly, add the weight of the bike (98 N) and the weight of the rider (655 N):
Total weight supported by both tires = 98 N + 655 N = 753 N

Since the weight of the rider and bike is equally supported by the two tires, the force that each tire supports is half of the total weight:
Force per tire = 753 N / 2 = 376.5 N

Next, divide the force per tire by the gauge pressure in each tire to find the area of contact:
Area of contact per tire = Force per tire / Gauge pressure

Plug in the values:
Area of contact per tire = 376.5 N / (8.70 x 10^5 Pa)

Dividing these values gives you the area of contact per tire. Make sure to check the units of the gauge pressure and convert them if needed.

I hope this clears up the confusion. Let me know if you have any other questions!