MECHANICAL ADVANTAGE 43

that is 20 cwt. +12 cwt. =32 cwt , leaving 1 cwt for the weight of the
tackle.

D. The stress on the becket when hoisting is given as 9| cwt. It
is evidently half the load less half the weight of the tackle as the top
block is supported by the beam, and half the load is supported by the
other part of the fall, that is,

| load — £ weight of tackle

10 cwt — i cwt = 9 1 cwt. as the stress on the
becket, which agrees nearly with the tested stress.

Example. — The Luff Tackle.— See Fig. 1.
A. The pull on the hauling part is given as 9 cwt

S=S '7 cwt., which is nearly the same

B The stress on the upper hook is given as 30 J cwt. It is the load+
the pull on hauling part+the weight of the tackle, that is

20 + 8 7 = 28-7 cwt. leaving 1*6 cwt. as the weight of the tackle.

D. The stress on the becket at the lower block when hoisting is
given as 5J cwt. It is approximately one-third the load as there are
three parts of rope supporting the load, less half the weight of the tackle.
* -5- load — £ tackle = stress on becket.

6'7 cwt. — *8 cwt. =5*9 cwt. which is slightly over the
test stress.

The other tackles may be worked out in a similar way.

Example, — What resistance could be overcome with a three-fold
purchase by applying a pull of 2 tons to the hauling part (no lead blocks).
£=2 tons, P=6, n=6 sheaves. W is required

10
— w 6TF — 10F + 6PF __ 16IF
x "" +~IQio io"
120
IQW = 120 .-. W = — = 7£ tons
16
The actual weight would be 7£ tons, but the total resistance (weight
plus friction) would be greater, Add for friction one-tenth of the
6
weight for each sheave, viz., 7-5 tons X — =4*5 tons.
Total resistance is 7*5+4-5=12 tons