All Solutions

Exercise 1

Step 1

1 of 2

The equilibrium requires that the force caused by gauge pressure is equal to the force you exert by pushing so the equation is

$$
p_{gauge}S = F.
$$

Since the contact area is circular we know that $S=(d/2)^2pi$ and substituting this in the former equation we get for diameter $d$

$$
d=2sqrt{frac{F}{pi p_{gauge}}} = 2.7text{ cm}.
$$

Result

2 of 2

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Exercise 2

Step 1

1 of 2

Gauge pressure is the difference between the atmospheric pressure and the pressure inside the ball by definition so we get

$$
p_{ball} = p_{gauge} + p_{atm} = 74text{ kPa} + 101text{ kPa} = 175text{ kPa}.
$$

Result

2 of 2

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Exercise 3

Step 1

1 of 2

Total force created by gauge pressure gas to balance your car’s weight so we have

$$
mg= 4p_{gauge}S
$$
which gives for the area
$$
S= frac{mg}{4p_{gauge}} =14.4times10^{-3}text{ m}^3.
$$

Result

2 of 2

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