Your right rear tire has to support a weight of 3000 Newtons. Normally the contact area of your tire with the road is 200 square centimeters. If the pressure in your tire is suddenly reduced from 32 pounds per square inch to 16 pounds per square inch, what must be the new contact area to support the car?

p1 =32 psi = 220632 Pa,

p2 =16 psi = 110316 Pa

p =F/A ,
A1 =F/p1 =3000/220632=0.0136 m² =136 cm²
A2 =F/p2 =3000/110316 =0.0272 m² =272 cm²

To find the new contact area required to support the car, we need to apply Pascal's Law, which states that the pressure inside the tire is transmitted equally in all directions.

First, let's convert the pressure units to a common measurement. We'll convert pounds per square inch (psi) to pascals (Pa).

1 psi = 6894.76 Pa

32 psi = 32 x 6894.76 Pa = 220609.2 Pa
16 psi = 16 x 6894.76 Pa = 110304.8 Pa

Now, let's find the original force exerted by the tire on the road using the original pressure and contact area:

Original force = Original pressure x Original contact area

Original force = 220609.2 Pa x 200 cm²

Next, let's find the force exerted by the tire on the road after the pressure is reduced:

New force = New pressure x New contact area

New force = 110304.8 Pa x New contact area

Since the force exerted on the road must remain constant to support the car, we can equate the original force to the new force:

Original force = New force

220609.2 Pa x 200 cm² = 110304.8 Pa x New contact area

Now, solve for the new contact area:

New contact area = (220609.2 Pa x 200 cm²) / 110304.8 Pa

New contact area ≈ 400 cm²

Therefore, the new contact area required to support the car is approximately 400 square centimeters.