Answer to Question #177525 in Classical Mechanics for Gannoz

Question

The question talks about a ship called the Lady Washington and and its scale model.

The length of the real ship is 34 meters. The length of the model is 37 inches.

1) The "rigging" of a ship is all of the ropes used to hold sails, floats, and weights. The total rigging on the scale model amounts to an astonishing 327 feet of string. Assuming this number is an accurate scaling of the real rigging, what is the total rigging of the Lady Washington?

2) The real Lady Washington can safely carry 99,000 kilograms of cargo. Assuming that densities of materials are the same and the scaling is really accurate, how much cargo can be carried by the scale model?

For reference, here is a question on the same topic that I answered correctly.

The sails of the real Lady Washington have an area of 410 SI units. What is the area of the sails of the scale model?

Correct Answer: 0.313

Answer 1

$L_r = 34[m]$

$L_m = 37[inch]$

$L_r *k = L_m(1)$

$k = \frac{37}{34}[\frac{inch}{m}]$

$\text{where } L_r\text{ length of the real ship}$

$L_m \text{ length of the model}$

$1) l_m = 327[ ft] = 327*12= 3924[ inch]$

$\text{from formula (1):}$

$lr*k =l_m$

$l_r= \frac{l_m}{k}=3924[inch]*\frac{34}{37}[\frac{m}{inch}]=3605[m]$

$2) m_r = \rho*V_r =99000[kg]$

$m_m = \rho*V_m$

$Vm[m^3]= V_r*k^3[inch^3]$

$[inch^3 ]= 0.000016387064[m^3]$

$m_m = \rho*V_r*k^3*0.000016387064=1.29 [kg]$

Ahswer: 1)3924[inch] 2)1.29 kg