Q3.3 Choosing the right system (T)

Graphic - No title - walkway

The two figures show (schematically, and not to scale!) alternative designs for a suspended walkway, of three layers.

In both designs each layer rests on nuts threaded on vertical rods. Design A uses rods that extend through all three layers. Design B uses three times more rods, each of which connects only adjacent layers. Which design would you consider to be safer?

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Hint

Think of the forces that have to be exerted by the nuts supporting the top layer.
 

Solution

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Solution

Let us examine the forces experienced by the nuts supporting the topmost layer.

Appealing to the 3rd Law these forces can be identified by considering the forces which these nuts exert on this layer. To determine these forces we must consider all the forces acting on the top layer, and appeal to the fact that, in the (much to be desired) static equilibrium, these forces must sum to zero.

In the case of design A the relevant forces are (see the accompanying schematic) simply the two nut forces (each of magnitude FA, say) upwards, and the weight of the top layer, Mg, downwards.
Graphic - No title - walkwayA

The 2nd Law tells us that 2FA-Mg=0 or

\[ F_A=\frac{Mg}{2} \]

In the case of design B, however, the relevant downward force (again see the accompanying schematic) is the weight of all three layers, and so in this case the same argument shows that each nut must now supply an upward force of
\[ F_B=\frac{3Mg}{2} \]
Graphic - No title - walkwayB

Design A is thus to be preferred.

See HRW p100 for the consequences of not ‘choosing the right system’.