119


20.  Suppose  that  the  radii  of  the  wheels  a,  d,  and/  (Fig.  112)  are,
respectively,  20  inches,  16  inches,  and  24  inches,  and  the  radii  of  their
axles  are,  respectively,  2  inches,  4  inches,  and  6  inches;  how  great
advantage  may  be  gained  by  the  compound  machine?


Fig.  113.
Fig.  114.
21.  How  would  you  calculate  the  mechanical  advantage  gained  by
a  machine  like  that  of  Figure  113  ?    (On  the  axle  A  is  an  endless  screw,
by  means  of  which  motion  is  communicated  from  the  axle  to  the
wheel  W.)

22.  (a)  What  kind  of  a  machine  is  a  claw-hammer  (Fig.  114)  ?
(&)  What  mechanical  advantage  is  gained  by  it  ?

23.  In  its  technical  meaning,  a  "  perpetual  motion  machine  w  is  not
a  machine  that  will  run  indefinitely,  but  a  machine  which  can  do  work
without  the  expenditure  of  energy.     Is  such  a  machine  possible?

24.  A  plank  12  feet  long  and  weighing  24  pounds  is  supported  by
two  props,  one  3  feet  from  one  end,  and  the  other  1  foot  from  the
other  end.     What  is  the  pressure  on  each  prop?

%    25.  With  a  movable  pulley  what  force  will  support  a  weight  of
100  pounds  ?

26.  The  gradient  of  a  certain  road  on  a  hillside  is  one  foot  in  ten
feet.     What  force  must  a  horse  exert  on  a  carriage  which  weighs  to-
gether with  its  load  one  ton,  to  prevent  its  descent  ?

27.  What  must  be  the  diameter  of  a  wheel  in  order  that  a  force  of
20  pounds  applied  at  its  circumference  may  be  in  equilibrium  with  a
resistance  of  600  pounds  applied  to  its  axle,  which  is  3  inches  in  diam-
eter?


120


WORK    AND    ENERGY.
