Chapter 5, Problem 5.6P

Interpretation Introduction

Interpretation: The tension in the rope is to be calculated by using the second law of motion.

Concept introduction The second law of motion states that the rate of change of momentum is directly proportional to the applied force and its value can be found by the following equation,

  ${\text{F = <mover accent="true"> <mo>m</mo> <mo>˙</mo></mover> (v}}_{\text{2}}{\text{-v}}_{\text{1}}\text{)}$ ...... (1)

The mass flow rate of water is $\text{<mover accent="true"> <mo>m</mo> <mo>˙</mo></mover>}$ and the initial and final velocity is v₁ and v₂ respectively.

F is the applied force on the body.

Tension in a particular direction is given as,

  $\text{T = }\frac{\text{F}}{\text{cosθ}}$ ...... (2)

  $\text{θ}$ is the angle between the given two bodies.

The volumetric flow rate Q is given as,

  $\text{Q = A×v}$ ...... (3)

Here, A is the area of body and v is the velocity.

The mass flow rate of water $\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover>}$ can also be related to Q as,

  $\text{<mover accent="true"><mo>m</mo><mo>˙</mo></mover> = ρ×Q}$ ...... (4)

  $\text{ ρ}$ is the density of water = 62.4 lbs/ft³