/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 116 The \(200-\mathrm{kg}\) boat is ... [FREE SOLUTION] | 91影视

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Chapter 15: Problem 116

The \(200-\mathrm{kg}\) boat is powered by the fan which develops a slipstream having a diameter of \(0.75 \mathrm{~m}\). If the fan ejects air with a speed of \(14 \mathrm{~m} / \mathrm{s}\), measured relative to the boat, determine the initial acceleration of the boat if it is initially at rest. Assume that air has a constant density of \(\rho_{w}=1.22 \mathrm{~kg} / \mathrm{m}^{3}\) and that the entering air is essentially at rest. Neglect the drag resistance of the water.

Short Answer

Expert verified
The initial acceleration of the boat can be calculated by summing up the forces acting on it (which in this case would only be the force by the fan as the drag of the water has been neglected) and using Newton's second law.

Step by step solution

01

Calculate the volume of air expelled per second

The volume of air expelled per second (V) can be calculated using the equation, V= \( \pi D^2 / 4 * v\), where D is the diameter of the fan's slipstream (0.75 m) and v is the speed of the expelled air (14 m/s).
02

Calculate the mass of the expelled air

The mass of the air expelled per second (m) can be calculated using the equation, m = V* \( \rho_{w}\), where \( \rho_{w}\) is the density of the air (1.22 kg/m^3).
03

Calculate the force exerted by the fan

The force exerted by the fan (F) can be calculated using the equation, F= m * v.
04

Determine the acceleration of the boat

The acceleration of the boat (a) can be calculated using Newton's second law, a = F / m_boat, where m_boat is the mass of the boat (200 kg).

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Most popular questions from this chapter

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