Question

A friend asks you how much pressure is in your car tires. You know that the tire manufacturer recommends 30 psi, but it's been a while since you've checked. You can't find a tire gauge in the car, but you do find the owner's manual and a ruler. Fortunately, you've just finished taking physics, so you tell your friend, "I don't know, but I can figure it out." From the owner's manual you find that the car's mass is 1550 kg. It seems reasonable to assume that each tire supports one-fourth of the weight. With the ruler you find that the tires are 16 cm wide and the flattened segment of the tire in contact with the road is 14 cm long. What answer will you give your friend?

Answer 1

Answer:

25 psi

Explanation:

The weight of the car is:

W = mg

W = 1550 kg * 9.8 m/s²

W = 15,190 N

Divided by 4 tires, each tire supports:

F = W/4

F = 15,190 N / 4

F = 3797.5 N

Pressure is force divided by area, so:

P = F / A

P = (3797.5 N) / (0.16 m × 0.14 m)

P ≈ 170,000 Pa

101,325 Pa is the same as 14.7 psi, so:

P ≈ 170,000 Pa × (14.7 psi / 101,325 Pa)

P ≈ 25 psi

Answer 2

The pressure in each tire is ≈ 25 psi which falls within the recommended manufacturer pressure

Given data ;

mass of car ( m ) = 1550 kg

width of tires ( w ) = 16 cm = 0.16 m

length of tires ( l ) = 14 cm = 0.14 m

First step : Determine the Total weight of car

W = m*g  ---- ( 1 )

   = 1550 * 9.8 = 15,190 N

∴ Weight supported by each tire = ( W / 4 )

= 15,190 / 4 = 3797.5 N

Final step : determine the Pressure in the tires

P = F / A  -------- ( 2 )

F ( force ) = 3797.5 N

A ( area ) =  0.14 * 0.16 = 0.0224

back to equation ( 2 )

P = 3797.5 / 0.0224  

   ≈ 170,000 Pa

∴ Pressure in each tire ≈ 25 psi

Hence we can conclude that the pressure in each tire is ≈ 25 psi.

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