Question

a) The tires on a small truck contain enough air to provide a gauge pressure of 1.8 105 Pascals. Each tire has 0.026 m2 of surface area pressed against the ground. From this information, what is the mass of the truck?

b)A beach ball has a radius of 19 cm and its density is about 3.22 kg/m3. What force is required to hold it completely submerged under water? magnitude N

Answer 1

1.

We know that

Force = Pressure*Area

Pressure = 1.8*10^5 Pa

Total Area = 4*Surface area of each tire = 4*0.026 m^2

So,

F = 1.8*10^5*4*0.026 = 18720 N

F = m*g = 18720 N

m = 18720/9.8 = 1910.2 kg

B.

Suppose force 'F' is required to hold the ball completely submerged, than

Using force balance in vertical direction

Fnet = 0 = F + W - B

F = B - W

F = Mb*g - Mw*g

W = weight of water replaced

B = Buoyancy force

F = rho_b*V*g - rho_w*g*V

V = Volume of ball = 4*pi*r^3/3 = 4*pi*0.19^3/3 = 0.0287 m^3

rho_b = density of ball = 3.22 kg/m^3

rho_w = 1000 kg/m^3

So,

F = 9.81*0.0287*(3.22 - 1000)

F = -280.64 N (-ve sign means force will be downward)

|F| = 280.64 N

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