Question

A boat has a volume of 127 m³ and weighs 7.00×10⁴ N. For safety, no more than 68.0% of its volume should be in water. What maximum load can be put in it?

A. 744 kN

B. 751 kN

C. 776 kN

D. 700 kN

E. 769 kN

Estimate the upward force needed to keep a 750 cm³ solid piece of aluminum to be stationary under water. The mass density of aluminum is 2,700 kg/m³.

A. 11 N

B. 12 N

C. 13 N

D. 14 N

E. 15 N

Answer 1

here,

1)

volume of boat , V = 127 m^3

weight , W = 70000 N

mass , m = 7135.6 kg

let the maximum load can be putted be W2

equating the forces

buyoynat force = weight

pw * (0.68 * V) * g = ( W + W2)

127 * 1000 * 0.68 * 9.81 = ( 70000 + W2)

W2 = 7.76 * 10^5 N = 776 KN

the correct answer is C) 776 KN

2)

volume , V = 750 cm^3 = 7.5 * 10^-4 m^2

the upward force needed , F = W - buoyant force

F = pa * V * g - pw * V * g

F = 7.5 * 10^-4 * 9.81 * ( 2700 - 1000)

F = 12.51 N or 13 N