Automobile Hydrostatic Pressure

[SAT2400]

Homework Statement

1) A typical automobile tire has a gauge pressure of around 30 Ib/in^2. How much is that in pascals? If a car weighs 8897N(=2000lb), how much area(SI units) on each tire is in contact with the road?

2) A swimming pool 5m wide by 10m long is filled to a depth of 3m. What's the total force exerted on the bottom due to the water?

3) GIven that most people cannot suck water up a straw any higher than about 1.1m, what's the lowest gauge pressure they can creat in the lungs?

Homework Equations

F=PA
F=P(4A)

PA=F

P= p(h2O)gh

The Attempt at a Solution

1) 2.1 x 10^5 Pa and .011m^2 are answers..I didn't get these answers though..
2) 1.5 x10^6 n is the answer
3) -1.1 x10^4 Pa is the answer..

Please help me to get these answers by giving me steps and equations.
Thank you!

 

[rl.bhat]

Show your attempts.

 

[kerimek]

1) To convert 30 lb/in^2 to pascals, we need to use the conversion factor 1 lb/in^2 = 6894.76 Pa. Therefore, 30 lb/in^2 is equal to 30 x 6894.76 = 206842.8 Pa.

To find the area of each tire in contact with the road, we can use the equation F=PA, where F is the weight of the car (8897N) and P is the pressure (206842.8 Pa). Rearranging the equation to solve for A, we get A = F/P = 8897N/206842.8 Pa = 0.043 m^2. Since each tire has this area in contact with the road, the total area for all four tires would be 4 x 0.043 m^2 = 0.172 m^2.

2) To find the total force exerted on the bottom of the pool, we can use the equation F=PA, where P is the pressure due to the water and A is the area of the pool's bottom (5m x 10m = 50 m^2). The pressure due to the water can be calculated using the equation P = p(h2O)gh, where p is the density of water (1000 kg/m^3), g is the acceleration due to gravity (9.8 m/s^2), and h is the depth of the water (3m). Plugging in these values, we get P = 1000 kg/m^3 x 9.8 m/s^2 x 3m = 29400 Pa. Therefore, the total force exerted on the bottom of the pool is F = 29400 Pa x 50 m^2 = 1.47 x 10^6 N.

3) The lowest gauge pressure that a person can create in their lungs is equal to the atmospheric pressure at sea level, which is approximately 101325 Pa. However, the question states that most people cannot suck water up a straw any higher than 1.1m, which means that the pressure in their lungs cannot be lower than the pressure at a depth of 1.1m in a pool. Using the equation P = p(h2O)gh, we can calculate the pressure at a depth of 1.1m in water, which is approximately 107