radius and 1 ton mass, resting on a rough plane inclined at 30*^ to the
horizontal, from rolling down the plane?

Machines

55. Two children of 60 and 90 lb. weight sit at opposite ends of a
board 1 ft. from the end. The board is 12 ft. long and weighs 40 lb.
Where should it be supported to be in equilibrimn?

56. A body weighs 10.2 g. when weighed in the left pan and 10.4 g.
when weighed in the right pan of a balance. Find (a) the ratio of
the balance arms, (b) the true weight of the body.
57. If a load of 1000 lb. were hung from an axle of 2 in. diameter
how large a force acting on a rope passing over a wheel of 10 in. diam-
eter would be in equiUbrium with it?



114 NOTES, PROBLEMS AND EXERCISES

68. If the lever of a jack screw is 3 ft. long and the screw threads
are two to the inch, what force must be applied to the handle to lift
1 ton, supposing friction negligible.
